CLIMA VOLCAN ANTISANA
UNIVERSIDAD CENTRAL DEL ECUADOR
ESTUDIO ESTADÍSTICO DEL CLIMA EN EL VOLCAN ANTISANA
FECHA: 24/01/2026
#INTEGRANTES: JUAN ARTEAGA, RONALD CARRERA, ANDRE LABANDA, ALEXANDER SAILEMA
#INTRODUCCIÓN
#Planteamiento del problema:
#Las variaciones de las condiciones meteorológicas constituyen un fenómeno ambiental de gran importancia,
#ya que influyen directamente en los ecosistemas, los recursos hídricos y diversas actividades humanas.
#Con el paso del tiempo, factores como la temperatura, la precipitación, el viento y la radiación solar pueden presentar cambios significativos que afectan el equilibrio ambiental y climático.
#En este contexto, el uso de herramientas estadísticas permite analizar los datos meteorológicos registrados en la estación Antisana,
#identificando patrones y tendencias que contribuyen a comprender el comportamiento del clima y su impacto en el entorno natural durante el período de estudio.
#Mapa de Ubicación
library(magick)
library(cowplot)
img <- image_read("C:/Users/JOSUE/Downloads/ESTADISTICA/img/Mapa Antisana.jpeg")
ggdraw() + draw_image(img)
#Objetivo General
#Aplicar la estadística para el estudio de las variables meteorológicas registradas en la estación Antisana durante todo el año 2012, mediante el uso de herramientas para la medición, análisis e interpretación de datos climáticos.
#Objetivos Especificos
#Conocer el comportamiento de las variables meteorológicas registradas en la estación Antisana, identificando sus principales características mediante el uso de medidas estadísticas descriptivas.
#Emplear modelos de probabilidad para establecer conclusiones sobre la variabilidad de las condiciones meteorológicas a partir de los resultados obtenidos en la muestra analizada.
#Deducir relaciones entre las variables meteorológicas con el fin de realizar estimaciones y análisis que contribuyan a la interpretación del comportamiento climático en el período de estudio.
#Para esta base de datos las primeras variables no se ocupan ya que tienen valores constantes y se van a ocupar para hacer el mapa de ubicación
#así que se va a trabajar con las demás Variables para realizar el análisis estadístico.
#ESTADÍSTICA DESCRIPTIVA
#Poblacion
#Todos los días del año en la estación meteorológica Antisana.
#P={x∣x ∈ dias de registro meteorologico ∧ Estacion(x)="Antisana"}
#Individuo
#Cada día de registro meteorológico en la estación Antisana.
#Individuo: xi,i=1,2,3,…,n
#Muestra
#Los datos disponibles corresponden a una muestra de días registrados en la estación meteorológica Antisana durante el período observado.
#M={x∣x∈dıas de registro meteorologico ∧ Estacioˊn(x)="Antisana" ∧ Año(x)=2012}
#Tabla de variables
Tabla_de_variables<-read.csv("tabla_variables_Antisana.csv",header = TRUE,dec = ".",
sep = ";")
Tabla_de_variablesdatos<-read.csv("weatherdataANTISANA.csv",header = TRUE,dec = ".",
sep = ",")
#Variables Cuantitativas continuas
# Temperatura Máxima
#Extracción Variable Cuantitativa Continua
Temp_max<- datos$Max.Temperature
min <-min(Temp_max)
max <-max(Temp_max)
R <-max-min
K <- floor(1+3.33*log10(length(Temp_max)))
A <-R/K
Li <-round(seq(from=min,to=max-A,by=A),2)
Ls <-round(seq(from=min+A,to=max,by=A),2)
Mc <-(Li+Ls)/2
ni<-c()
for (i in 1:K) {
if (i < K) {
ni[i] <- length(subset(Temp_max, Temp_max >= Li[i] & Temp_max < Ls[i]))
} else {
ni[i] <- length(subset(Temp_max, Temp_max >= Li[i] & Temp_max <= Ls[i]))
}
}
sum(ni)## [1] 366hi <-ni/sum(ni)*100
Ni_asc<-cumsum(ni)
Hi_asc<-cumsum(hi)
Ni_desc<-rev(cumsum(rev(ni)))
Hi_desc<-rev(cumsum(rev(hi)))
TDF_Temp_max <- data.frame(
Li, Ls, Mc, ni, round(hi, 2), Ni_asc, Ni_desc, round(Hi_asc, 2), round(Hi_desc, 2)
)
colnames(TDF_Temp_max) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(ni),
hi=sum(hi),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Temp_max_final <-rbind(TDF_Temp_max,totales)
library(dplyr)
library(gt)
TDF_Temp_max_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("*Tabla de distribución de la Temperatura Máxima (°C)*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 1 | ||||||||
| Tabla de distribución de la Temperatura Máxima (°C) | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 10.32 | 11.82 | 11.07 | 26 | 7.1 | 26 | 366 | 7.1 | 100 |
| 11.82 | 13.31 | 12.565 | 60 | 16.39 | 86 | 340 | 23.5 | 92.9 |
| 13.31 | 14.81 | 14.06 | 71 | 19.4 | 157 | 280 | 42.9 | 76.5 |
| 14.81 | 16.31 | 15.56 | 60 | 16.39 | 217 | 209 | 59.29 | 57.1 |
| 16.31 | 17.8 | 17.055 | 62 | 16.94 | 279 | 149 | 76.23 | 40.71 |
| 17.8 | 19.3 | 18.55 | 44 | 12.02 | 323 | 87 | 88.25 | 23.77 |
| 19.3 | 20.8 | 20.05 | 23 | 6.28 | 346 | 43 | 94.54 | 11.75 |
| 20.8 | 22.29 | 21.545 | 14 | 3.83 | 360 | 20 | 98.36 | 5.46 |
| 22.29 | 23.79 | 23.04 | 6 | 1.64 | 366 | 6 | 100 | 1.64 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoT <- hist(
Temp_max,
main = "Gráfica Nº1: Distribución de la Temperatura Máxima",
xlab = "Temperatura Máxima(°C)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Temp_Max<-hist(Temp_max,breaks = 8,plot = F)
k<-length(Hist_Temp_Max$breaks)
Li<-Hist_Temp_Max$breaks[1:(length(Hist_Temp_Max$breaks)-1)]
Ls<-Hist_Temp_Max$breaks[2:length(Hist_Temp_Max$breaks)]
ni<-Hist_Temp_Max$counts
sum(ni)## [1] 366Mc<-Hist_Temp_Max$mids
hi<-(ni/sum(ni))
sum(hi)## [1] 1Ni_asc<-cumsum(ni)
Hi_asc<-cumsum(hi)
Ni_desc<-rev(cumsum(rev(ni)))
Hi_desc<-rev(cumsum(rev(hi)))
TDF_Temp_Maxima<-data.frame(Li=round(Li,2),
Ls=round(Ls,2),
Mc=round(Mc,2),
ni=ni,
hi=round(hi*100,2),
Ni_asc=Ni_asc,
Ni_desc=Ni_desc,
Hi_asc=round(Hi_asc*100,2),
Hi_desc=round(Hi_desc*100,2))
colnames(TDF_Temp_Maxima)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Temp_Maxima$ni)),
hi = sum(as.numeric(TDF_Temp_Maxima$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Temp_Maxima_final<-rbind(TDF_Temp_Maxima,totales)
library(dplyr)
library(gt)
TDF_Temp_Maxima_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 2"),
subtitle = md("*Tabla Simplificada de distribución de la Temperatura Máxima en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 2 | ||||||||
| Tabla Simplificada de distribución de la Temperatura Máxima en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 10 | 12 | 11 | 30 | 8.2 | 30 | 366 | 8.2 | 100 |
| 12 | 14 | 13 | 94 | 25.68 | 124 | 336 | 33.88 | 91.8 |
| 14 | 16 | 15 | 78 | 21.31 | 202 | 242 | 55.19 | 66.12 |
| 16 | 18 | 17 | 82 | 22.4 | 284 | 164 | 77.6 | 44.81 |
| 18 | 20 | 19 | 50 | 13.66 | 334 | 82 | 91.26 | 22.4 |
| 20 | 22 | 21 | 25 | 6.83 | 359 | 32 | 98.09 | 8.74 |
| 22 | 24 | 23 | 7 | 1.91 | 366 | 7 | 100 | 1.91 |
| TOTAL | - | - | 366 | 99.99 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Temp_max, breaks = 10,
main = "Gráfica N°3 Distribución para la Temperatura Máxima en el Volcan Antisana ",
xlab = "Temperatura Máxima (°C)",
ylab = "Cantidad",
ylim = c(0,max(ni)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Temp_Max$breaks,
labels = Hist_Temp_Max$breaks, las = 1,
cex.axis = 0.9)
hist(Temp_max, breaks = 10,
main = "Gráfica N°4: Distribución de la Temperatura Máxima en el volcan Antisana ",
xlab = "Temperatura Máxima (°C)",
ylab = "Cantidad",
ylim = c(0, length(Temp_max)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Temp_Max$breaks,
labels = Hist_Temp_Max$breaks, las = 1,
cex.axis = 0.9)
TDF_Temp_Maxima_final$hi <- as.numeric(TDF_Temp_Maxima_final$hi)
datos_grafico <- subset(TDF_Temp_Maxima_final, !(MC %in% c("-", "TOTAL")))
barplot(datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual de la Temperatura Máxima en el Volcan Antisana",
xlab = "Temperatura Máxima (°C)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$MC,
ylim = c(0, 30))
barplot(datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Temperatura Máxima en el Volcan Antisana",
xlab = "Temperatura °C",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$MC,
ylim = c(0, 100))
# Boxplot
boxplot(
Temp_max,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución de la Temperatura Máxima",
xlab = "Temperatura Máxima (°C)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
Li, Ni_desc,
main = "Gráfica Nº8: Distribución Ascendente y Descendente de la Temperatura Máxima",
xlab = "Temperatura Máxima(°C)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
Ls, Ni_asc,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
Li, Hi_desc,
main = "Gráfica Nº9: Distribución Ascendente y Descendente de la Temperatura Máxima",
xlab = "Temperatura Máxima (°C)",
ylab = "Porcentaje (%)",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 2
)
lines(
Ls, Hi_asc,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
media <- round(mean(Temp_max), 0)
media## [1] 16# Moda
# Moda
max_frecuencia <- max(TDF_Temp_Maxima_final$ni)
moda <- TDF_Temp_Maxima_final$MC[TDF_Temp_Maxima_final$ni == max_frecuencia]
moda## [1] "13"# Mediana
mediana <- median(Temp_max)
mediana## [1] 15.51# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianza <- var(Temp_max)
varianza## [1] 8.222732sd <- sd(Temp_max)
sd## [1] 2.867531# Coeficiente de Variación
cv <- round((sd / media) * 100, 2)
cv## [1] 17.92# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetria <- skewness(Temp_max, type = 2)
asimetria## [1] 0.3905542#Curtosis
curtosis <- kurtosis(Temp_max)
curtosis## [1] -0.5581832# TABLA RESUMEN FINAL
tabla_indicadores <- data.frame(
"Variable" = c("Temperatura Máxima"),
"Rango" = c(paste0("[", min(Temp_max), " ; ", max(Temp_max), "]")),
"X" = c(round(media, 0)),
"Me" = c(round(mediana, 0)),
"Mo" = c(paste(moda, collapse = ", ")),
"V" = c(round(varianza,2)),
"Sd" = c(round(sd, 0)),
"Cv" = c(cv),
"As" = c(round(asimetria, 2)),
"K" = c(round(curtosis, 2)),
"Valores Atípicos" = "-"
)
library(gt)
tabla_indicadores_gt <- tabla_indicadores %>%
gt() %>%
tab_header(
title = md("Tabla N°2.1"),
subtitle = md("*Indicadores estadísticos de la variable Temperatura Máxima*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Temperatura Máxiima"
)
)
tabla_indicadores_gt| Tabla N°2.1 | ||||||||||
| Indicadores estadísticos de la variable Temperatura Máxima | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Temperatura Máxima | [10.32 ; 23.79] | 16 | 16 | 13 | 8.22 | 3 | 17.92 | 0.39 | -0.56 | - |
| Autor: Grupo 3 | ||||||||||
#Temperatura Mínima
Temp_min<- datos$Min.Temperature
min2 <-min(Temp_min)
max2 <-max(Temp_min)
R2 <-max2-min2
K2 <- floor(1+3.33*log10(length(Temp_min)))
A2 <-R2/K2
Li2 <-round(seq(from=min2,to=max2-A2,by=A2),2)
Ls2 <-round(seq(from=min2+A2,to=max2,by=A2),2)
Mc2 <-(Li2+Ls2)/2
ni2<-c()
for (i in 1:K2) {
if (i < K2) {
ni2[i] <- length(subset(Temp_min, Temp_min >= Li2[i] & Temp_min < Ls2[i]))
} else {
ni2[i] <- length(subset(Temp_min, Temp_min >= Li2[i] & Temp_min <= Ls2[i]))
}
}
sum(ni2)## [1] 366hi2 <-ni2/sum(ni2)*100
Ni_asc2<-cumsum(ni2)
Hi_asc2<-cumsum(hi2)
Ni_desc2<-rev(cumsum(rev(ni2)))
Hi_desc2<-rev(cumsum(rev(hi2)))
TDF_Temp_min <- data.frame(
Li2, Ls2, Mc2, ni2, round(hi2, 2), Ni_asc2, Ni_desc2, round(Hi_asc2, 2), round(Hi_desc2, 2)
)
colnames(TDF_Temp_min) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(ni2),
hi=sum(hi2),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Temp_min_final <-rbind(TDF_Temp_min,totales)
library(dplyr)
library(gt)
TDF_Temp_min_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 3"),
subtitle = md("*Tabla de distribución de la Temperatura Mínima en el Volcan Antisana (°C)*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 3 | ||||||||
| Tabla de distribución de la Temperatura Mínima en el Volcan Antisana (°C) | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 2.65 | 3.56 | 3.105 | 1 | 0.27 | 1 | 366 | 0.27 | 100 |
| 3.56 | 4.47 | 4.015 | 4 | 1.09 | 5 | 365 | 1.37 | 99.73 |
| 4.47 | 5.38 | 4.925 | 6 | 1.64 | 11 | 361 | 3.01 | 98.63 |
| 5.38 | 6.29 | 5.835 | 21 | 5.74 | 32 | 355 | 8.74 | 96.99 |
| 6.29 | 7.21 | 6.75 | 55 | 15.03 | 87 | 334 | 23.77 | 91.26 |
| 7.21 | 8.12 | 7.665 | 108 | 29.51 | 195 | 279 | 53.28 | 76.23 |
| 8.12 | 9.03 | 8.575 | 80 | 21.86 | 275 | 171 | 75.14 | 46.72 |
| 9.03 | 9.94 | 9.485 | 60 | 16.39 | 335 | 91 | 91.53 | 24.86 |
| 9.94 | 10.85 | 10.395 | 31 | 8.47 | 366 | 31 | 100 | 8.47 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoT <- hist(
Temp_min,
main = "Gráfica Nº10: Distribución de la Temperatura Mínima",
xlab = "Temperatura Mínima(°C)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Temp_Min<-hist(Temp_min,breaks = 8,plot = F)
k2<-length(Hist_Temp_Min$breaks)
Li2<-Hist_Temp_Min$breaks[1:(length(Hist_Temp_Min$breaks)-1)]
Ls2<-Hist_Temp_Min$breaks[2:length(Hist_Temp_Min$breaks)]
ni2<-Hist_Temp_Min$counts
sum(ni2)## [1] 366Mc2<-Hist_Temp_Min$mids
hi2<-(ni2/sum(ni2))
sum(hi2)## [1] 1Ni_asc2<-cumsum(ni2)
Hi_asc2<-cumsum(hi2)
Ni_desc2<-rev(cumsum(rev(ni2)))
Hi_desc2<-rev(cumsum(rev(hi2)))
TDF_Temp_Mínima<-data.frame(Li=round(Li2,2),
Ls=round(Ls2,2),
Mc=round(Mc2,2),
ni=ni2,
hi=round(hi2*100,2),
Ni_asc=Ni_asc2,
Ni_desc=Ni_desc2,
Hi_asc=round(Hi_asc2*100,2),
Hi_desc=round(Hi_desc2*100,2))
colnames(TDF_Temp_Mínima)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<- c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Temp_Mínima$ni)),
hi = sum(as.numeric(TDF_Temp_Mínima$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-"
)
TDF_Temp_Mínima_final<-rbind(TDF_Temp_Mínima,totales)
library(dplyr)
library(gt)
TDF_Temp_Mínima_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 4"),
subtitle = md("*Tabla Simplificada de distribución de la Temperatura Mínima en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 4 | ||||||||
| Tabla Simplificada de distribución de la Temperatura Mínima en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 2.5 | 1 | 0.27 | 1 | 366 | 0.27 | 100 |
| 3 | 4 | 3.5 | 2 | 0.55 | 3 | 365 | 0.82 | 99.73 |
| 4 | 5 | 4.5 | 7 | 1.91 | 10 | 363 | 2.73 | 99.18 |
| 5 | 6 | 5.5 | 16 | 4.37 | 26 | 356 | 7.1 | 97.27 |
| 6 | 7 | 6.5 | 48 | 13.11 | 74 | 340 | 20.22 | 92.9 |
| 7 | 8 | 7.5 | 109 | 29.78 | 183 | 292 | 50 | 79.78 |
| 8 | 9 | 8.5 | 90 | 24.59 | 273 | 183 | 74.59 | 50 |
| 9 | 10 | 9.5 | 66 | 18.03 | 339 | 93 | 92.62 | 25.41 |
| 10 | 11 | 10.5 | 27 | 7.38 | 366 | 27 | 100 | 7.38 |
| TOTAL | - | - | 366 | 99.99 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Temp_min, breaks = 10,
main = "Gráfica N°11 Distribución para la Temperatura Mínima en el Volcan Antisana ",
xlab = "Temperatura Mínima (°C)",
ylab = "Cantidad",
ylim = c(0,max(ni2)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Temp_Min$breaks,
labels = Hist_Temp_Min$breaks, las = 1,
cex.axis = 0.9)
hist(Temp_min, breaks = 10,
main = "Gráfica N°12: Distribución de la Temperatura Mínima en el volcan Antisana ",
xlab = "Temperatura Mínima (°C)",
ylab = "Cantidad",
ylim = c(0, length(Temp_min)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Temp_Min$breaks,
labels = Hist_Temp_Min$breaks, las = 1,
cex.axis = 0.9)
df <- TDF_Temp_min_final
df$hi <- as.numeric(df$hi)
datos_grafico <- df[1:(nrow(df)-1), ]
barplot(
datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°13: Distribución porcentual de la Temperatura Mínima en el Volcán Antisana",
xlab = "Temperatura Mínima (°C)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$Mc, # si tu columna se llama MC, cámbialo por datos_grafico$MC
ylim = c(0, max(datos_grafico$hi, na.rm = TRUE) + 5)
)
datos_grafico$hi <- as.numeric(datos_grafico$hi)
sum(datos_grafico$hi)## [1] 100barplot(
datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°14: Distribución porcentual de la Temperatura Mínima en el Volcán Antisana",
xlab = "Temperatura Mínima (°C)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$MC,
ylim = c(0, 100)
)
# Boxplot
boxplot(
Temp_min,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº15: Distribución de la Temperatura Mínima",
xlab = "Temperatura Mínima (°C)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
Li2, Ni_desc2,
main = "Gráfica Nº16: Distribución Ascendente y Descendente de la Temperatura Mínima",
xlab = "Temperatura Mínima(°C)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
Ls2, Ni_asc2,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
Li2, Hi_desc2,
main = "Gráfica Nº17: Distribución Ascendente y Descendente de la Temperatura Mínima",
xlab = "Temperatura Mínima (°C)",
ylab = "Porcentaje (%)",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 2
)
lines(
Ls2, Hi_asc2,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
media2 <- round(mean(Temp_min), 0)
media2## [1] 8# Moda
# Moda
max_frecuencia2 <- max(TDF_Temp_Mínima_final$ni)
moda2 <- TDF_Temp_Mínima_final$Mc[TDF_Temp_Mínima_final$ni == max_frecuencia2]
moda2## NULL# Mediana
mediana2 <- median(Temp_min)
mediana2## [1] 8.005# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianza2 <- var(Temp_min)
varianza2## [1] 1.888054sd2 <- sd(Temp_min)
sd2## [1] 1.374065# Coeficiente de Variación
cv2 <- round((sd2 / media2) * 100, 2)
cv2## [1] 17.18# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetria2 <- skewness(Temp_min, type = 2)
asimetria2## [1] -0.4376627#Curtosis
curtosis2 <- kurtosis(Temp_min)
curtosis2## [1] 0.5662281# TABLA RESUMEN FINAL
tabla_indicadores2 <- data.frame(
"Variable" = c("Temperatura Mínima"),
"Rango" = c(paste0("[", min(Temp_min), " ; ", max(Temp_min), "]")),
"X" = c(round(media2, 0)),
"Me" = c(round(mediana2, 0)),
"Mo" = c(paste(moda2, collapse = ", ")),
"V" = c(round(varianza2,2)),
"Sd" = c(round(sd2, 0)),
"Cv" = c(cv2),
"As" = c(round(asimetria2, 2)),
"K" = c(round(curtosis2, 2)),
"Valores Atípicos" = "7"
)
library(gt)
tabla_indicadores_gt2 <- tabla_indicadores2 %>%
gt() %>%
tab_header(
title = md("Tabla N°3.1"),
subtitle = md("*Indicadores estadísticos de la variable Temperatura Mínima*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Temperatura Mínima"
)
)
tabla_indicadores_gt2| Tabla N°3.1 | ||||||||||
| Indicadores estadísticos de la variable Temperatura Mínima | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Temperatura Mínima | [2.65 ; 10.85] | 8 | 8 | 1.89 | 1 | 17.18 | -0.44 | 0.57 | 7 | |
| Autor: Grupo 3 | ||||||||||
#Precipitación
#Extracción Variable Cuantitativa Continua
Precipitacion<- datos$Precipitation
minp <-min(Precipitacion)
maxp <-max(Precipitacion)
Rp <-maxp-minp
Kp <- floor(1+3.33*log10(length(Precipitacion)))
Ap<-Rp/Kp
Lip <-round(seq(from=minp,to=maxp-Ap,by=Ap),2)
Lsp <-round(seq(from=minp+Ap,to=maxp,by=Ap),2)
Mcp <-(Lip+Lsp)/2
nip<-c()
for (i in 1:Kp) {
if (i < Kp) {
nip[i] <- length(subset(Precipitacion, Precipitacion >= Lip[i] & Precipitacion < Lsp[i]))
} else {
nip[i] <- length(subset(Precipitacion, Precipitacion >= Lip[i] & Precipitacion <= Lsp[i]))
}
}
sum(nip)## [1] 366hip <-nip/sum(nip)*100
Ni_ascp<-cumsum(nip)
Hi_ascp<-cumsum(hip)
Ni_descp<-rev(cumsum(rev(nip)))
Hi_descp<-rev(cumsum(rev(hip)))
TDF_Precipitacion <- data.frame(
Lip, Lsp, Mcp, nip, round(hip, 2), Ni_ascp, Ni_descp, round(Hi_ascp, 2), round(Hi_descp, 2)
)
colnames(TDF_Precipitacion) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(nip),
hi=sum(hip),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Precipitacion_final <-rbind(TDF_Precipitacion,totales)
library(dplyr)
library(gt)
TDF_Precipitacion_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 5"),
subtitle = md("*Tabla de distribución de la Precipitación en el Volcan Antisana (mm)*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 5 | ||||||||
| Tabla de distribución de la Precipitación en el Volcan Antisana (mm) | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.01 | 10.53 | 5.27 | 158 | 43.17 | 158 | 366 | 43.17 | 100 |
| 10.53 | 21.06 | 15.795 | 89 | 24.32 | 247 | 208 | 67.49 | 56.83 |
| 21.06 | 31.58 | 26.32 | 56 | 15.3 | 303 | 119 | 82.79 | 32.51 |
| 31.58 | 42.1 | 36.84 | 33 | 9.02 | 336 | 63 | 91.8 | 17.21 |
| 42.1 | 52.63 | 47.365 | 16 | 4.37 | 352 | 30 | 96.17 | 8.2 |
| 52.63 | 63.15 | 57.89 | 9 | 2.46 | 361 | 14 | 98.63 | 3.83 |
| 63.15 | 73.67 | 68.41 | 3 | 0.82 | 364 | 5 | 99.45 | 1.37 |
| 73.67 | 84.2 | 78.935 | 0 | 0 | 364 | 2 | 99.45 | 0.55 |
| 84.2 | 94.72 | 89.46 | 2 | 0.55 | 366 | 2 | 100 | 0.55 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoP <- hist(
Precipitacion,
main = "Gráfica Nº1: Distribución de la Precipitación en el Volcan Antisana",
xlab = "Precitación(°C)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Precipitacion<-hist(Precipitacion,breaks = 8,plot = F)
kp<-length(Hist_Precipitacion$breaks)
Lip<-Hist_Precipitacion$breaks[1:(length(Hist_Precipitacion$breaks)-1)]
Lsp<-Hist_Precipitacion$breaks[2:length(Hist_Precipitacion$breaks)]
nip<-Hist_Precipitacion$counts
sum(nip)## [1] 366Mcp<-Hist_Precipitacion$mids
hip<-(nip/sum(nip))
sum(hip)## [1] 1Ni_ascp<-cumsum(nip)
Hi_ascp<-cumsum(hip)
Ni_descp<-rev(cumsum(rev(nip)))
Hi_descp<-rev(cumsum(rev(hip)))
TDF_Precipitacion_F<-data.frame(Li=round(Lip,2),
Ls=round(Lsp,2),
Mc=round(Mcp,2),
ni=nip,
hi=round(hip*100,2),
Ni_asc=Ni_ascp,
Ni_desc=Ni_descp,
Hi_asc=round(Hi_ascp*100,2),
Hi_desc=round(Hi_descp*100,2))
colnames(TDF_Precipitacion_F)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Precipitacion_F$ni)),
hi = sum(as.numeric(TDF_Precipitacion_F$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Precipitacion_F<-rbind(TDF_Precipitacion_F,totales)
library(dplyr)
library(gt)
TDF_Precipitacion_F %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 6"),
subtitle = md("*Tabla Simplificada de distribución de la Precipitación en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 6 | ||||||||
| Tabla Simplificada de distribución de la Precipitación en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 5 | 150 | 40.98 | 150 | 366 | 40.98 | 100 |
| 10 | 20 | 15 | 92 | 25.14 | 242 | 216 | 66.12 | 59.02 |
| 20 | 30 | 25 | 58 | 15.85 | 300 | 124 | 81.97 | 33.88 |
| 30 | 40 | 35 | 27 | 7.38 | 327 | 66 | 89.34 | 18.03 |
| 40 | 50 | 45 | 23 | 6.28 | 350 | 39 | 95.63 | 10.66 |
| 50 | 60 | 55 | 10 | 2.73 | 360 | 16 | 98.36 | 4.37 |
| 60 | 70 | 65 | 4 | 1.09 | 364 | 6 | 99.45 | 1.64 |
| 70 | 80 | 75 | 0 | 0 | 364 | 2 | 99.45 | 0.55 |
| 80 | 90 | 85 | 1 | 0.27 | 365 | 2 | 99.73 | 0.55 |
| 90 | 100 | 95 | 1 | 0.27 | 366 | 1 | 100 | 0.27 |
| TOTAL | - | - | 366 | 99.99 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Precipitacion, breaks = 10,
main = "Gráfica N°3 Distribución para la Precipitación en el Volcan Antisana ",
xlab = "Precipitación (mm)",
ylab = "Cantidad",
ylim = c(0,max(nip)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Precipitacion$breaks,
labels = Hist_Precipitacion$breaks, las = 1,
cex.axis = 0.9)
hist(Precipitacion, breaks = 10,
main = "Gráfica N°4: Distribución de la Precipitacion en el volcan Antisana ",
xlab = "Precipitación (mm)",
ylab = "Cantidad",
ylim = c(0, length(Precipitacion)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Precipitacion$breaks,
labels = Hist_Precipitacion$breaks, las = 1,
cex.axis = 0.9)
TDF_Precipitacion_F$hi <- as.numeric(TDF_Precipitacion_F$hi)
datos_grafico <- TDF_Precipitacion_F[1:(nrow(TDF_Precipitacion_F) - 1), ]
barplot(
datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual de la Precipitación en el Volcán Antisana",
xlab = "Precipitación (mm)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$Mcp,
ylim = c(0, max(datos_grafico$hi) + 5)
)
datos_grafico$hi <- as.numeric(datos_grafico$hi)
barplot(
datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Precipitación en el Volcán Antisana",
xlab = "Precipitación (mm)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$Mcp,
ylim = c(0, 100)
)
# Boxplot
boxplot(
Precipitacion,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución de la Precipitación",
xlab = "Precipitación (mm)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
Lip, Ni_descp,
main = "Gráfica Nº8: Distribución Ascendente y Descendente de la Precipitación",
xlab = "Precipitación(mm)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
Lsp, Ni_ascp,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
Lip, Hi_descp,
main = "Gráfica Nº9: Distribución Ascendente y Descendente de la Precipitación",
xlab = "Precipitación(mm)",
ylab = "Porcentaje (%)",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 2
)
lines(
Lsp, Hi_ascp,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
mediap <- round(mean(Precipitacion), 0)
mediap## [1] 17# Moda
max_frecuenciap <- max(TDF_Precipitacion_F$ni)
modap <- TDF_Precipitacion_F$MC[TDF_Precipitacion_F$ni == max_frecuenciap]
modap## [1] "15"# Mediana
medianap <- median(Precipitacion)
medianap## [1] 12.94# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianzap <- var(Precipitacion)
varianzap## [1] 259.6987sdp <- sd(Precipitacion)
sdp## [1] 16.11517# Coeficiente de Variación
cvp <- round((sdp / mediap) * 100, 2)
cvp## [1] 94.8# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetriap <- skewness(Precipitacion, type = 2)
asimetriap## [1] 1.305768#Curtosis
curtosisp <- kurtosis(Precipitacion)
curtosisp## [1] 1.951113# TABLA RESUMEN FINAL
tabla_indicadoresp <- data.frame(
"Variable" = c("Precipitación"),
"Rango" = c(paste0("[", min(Precipitacion), " ; ", max(Precipitacion), "]")),
"X" = c(round(mediap, 0)),
"Me" = c(round(medianap, 0)),
"Mo" = c(paste(modap, collapse = ", ")),
"V" = c(round(varianzap,2)),
"Sd" = c(round(sdp, 0)),
"Cv" = c(cvp),
"As" = c(round(asimetriap, 2)),
"K" = c(round(curtosisp, 2)),
"Valores Atípicos" = "8"
)
library(gt)
tabla_indicadores_gtp <- tabla_indicadoresp %>%
gt() %>%
tab_header(
title = md("Tabla N°4.1"),
subtitle = md("*Indicadores estadísticos de la variable Precipitación*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Precipitación"
)
)
tabla_indicadores_gtp| Tabla N°4.1 | ||||||||||
| Indicadores estadísticos de la variable Precipitación | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Precipitación | [0.01 ; 94.72] | 17 | 13 | 15 | 259.7 | 16 | 94.8 | 1.31 | 1.95 | 8 |
| Autor: Grupo 3 | ||||||||||
#Viento
Viento<- datos$Wind
minV <-min(Viento)
maxV <-max(Viento)
RV <-maxV-minV
KV <- floor(1+3.33*log10(length(Viento)))
AV<-RV/KV
LiV <-round(seq(from=minV,to=maxV-AV,by=AV),2)
LsV <-round(seq(from=minV+AV,to=maxV,by=AV),2)
McV <-(LiV+LsV)/2
niV<-c()
for (i in 1:KV) {
if (i < KV) {
niV[i] <- length(subset(Viento, Viento >= LiV[i] & Viento < LsV[i]))
} else {
niV[i] <- length(subset(Viento, Viento >= LiV[i] & Viento <= LsV[i]))
}
}
sum(niV)## [1] 366hiV <-niV/sum(niV)*100
Ni_ascV<-cumsum(niV)
Hi_ascV<-cumsum(hiV)
Ni_descV<-rev(cumsum(rev(niV)))
Hi_descV<-rev(cumsum(rev(hiV)))
TDF_Viento <- data.frame(
LiV, LsV, McV, niV, round(hiV, 2), Ni_ascV, Ni_descV, round(Hi_ascV, 2), round(Hi_descV, 2)
)
colnames(TDF_Viento) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(niV),
hi=sum(hiV),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Viento_final <-rbind(TDF_Viento,totales)
library(dplyr)
library(gt)
TDF_Viento_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 7"),
subtitle = md("*Tabla de distribución del Viento en el Volcan Antisana *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 7 | ||||||||
| *Tabla de distribución del Viento en el Volcan Antisana * | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.59 | 0.86 | 0.725 | 2 | 0.55 | 2 | 366 | 0.55 | 100 |
| 0.86 | 1.12 | 0.99 | 23 | 6.28 | 25 | 364 | 6.83 | 99.45 |
| 1.12 | 1.39 | 1.255 | 56 | 15.3 | 81 | 341 | 22.13 | 93.17 |
| 1.39 | 1.66 | 1.525 | 78 | 21.31 | 159 | 285 | 43.44 | 77.87 |
| 1.66 | 1.92 | 1.79 | 71 | 19.4 | 230 | 207 | 62.84 | 56.56 |
| 1.92 | 2.19 | 2.055 | 62 | 16.94 | 292 | 136 | 79.78 | 37.16 |
| 2.19 | 2.46 | 2.325 | 48 | 13.11 | 340 | 74 | 92.9 | 20.22 |
| 2.46 | 2.72 | 2.59 | 23 | 6.28 | 363 | 26 | 99.18 | 7.1 |
| 2.72 | 2.99 | 2.855 | 3 | 0.82 | 366 | 3 | 100 | 0.82 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoV <- hist(
Viento,
main = "Gráfica Nº1: Distribución del Viento en el Volcan Antisana",
xlab = "Viento(m/s)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Viento<-hist(Viento,breaks = 8,plot = F)
kV<-length(Hist_Viento$breaks)
LiV<-Hist_Viento$breaks[1:(length(Hist_Viento$breaks)-1)]
LsV<-Hist_Viento$breaks[2:length(Hist_Viento$breaks)]
niV<-Hist_Viento$counts
sum(niV)## [1] 366McV<-Hist_Viento$mids
hiV<-(niV/sum(niV))
sum(hiV)## [1] 1Ni_ascV<-cumsum(niV)
Hi_ascV<-cumsum(hiV)
Ni_descV<-rev(cumsum(rev(niV)))
Hi_descV<-rev(cumsum(rev(hiV)))
TDF_Viento_F<-data.frame(Li=round(LiV,2),
Ls=round(LsV,2),
Mc=round(McV,2),
ni=niV,
hi=round(hiV*100,2),
Ni_asc=Ni_ascV,
Ni_desc=Ni_descV,
Hi_asc=round(Hi_ascV*100,2),
Hi_desc=round(Hi_descV*100,2))
colnames(TDF_Viento_F)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Viento_F$ni)),
hi = sum(as.numeric(TDF_Viento_F$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Viento_F<-rbind(TDF_Viento_F,totales)
library(dplyr)
library(gt)
TDF_Viento_F %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 8"),
subtitle = md("*Tabla Simplificada de distribución del Viento en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 8 | ||||||||
| Tabla Simplificada de distribución del Viento en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.5 | 1 | 0.75 | 12 | 3.28 | 12 | 366 | 3.28 | 100 |
| 1 | 1.5 | 1.25 | 107 | 29.23 | 119 | 354 | 32.51 | 96.72 |
| 1.5 | 2 | 1.75 | 130 | 35.52 | 249 | 247 | 68.03 | 67.49 |
| 2 | 2.5 | 2.25 | 96 | 26.23 | 345 | 117 | 94.26 | 31.97 |
| 2.5 | 3 | 2.75 | 21 | 5.74 | 366 | 21 | 100 | 5.74 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Viento, breaks = 10,
main = "Gráfica N°3 Distribución para el Viento en el Volcan Antisana ",
xlab = "Viento (m/S)",
ylab = "Cantidad",
ylim = c(0,max(niV)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Viento$breaks,
labels = Hist_Viento$breaks, las = 1,
cex.axis = 0.9)
hist(Viento, breaks = 10,
main = "Gráfica N°4: Distribución del Viento en el volcan Antisana ",
xlab = "Viento (m/s)",
ylab = "Cantidad",
ylim = c(0, length(Viento)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Viento$breaks,
labels = Hist_Viento$breaks, las = 1,
cex.axis = 0.9)
TDF_Viento_F$`hi(%)` <- as.numeric(TDF_Viento_F$`hi(%)`)
datos_grafico_Viento <- TDF_Viento_F[1:(nrow(TDF_Viento_F)-1), ]
post <- barplot(datos_grafico_Viento$`hi(%)`,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual del viento en el volcán Antisana",
xlab = "Viento (m/s)",
ylab = "Porcentaje (%)",
ylim = c(0, max(datos_grafico_Viento$`hi(%)`) + 5))
axis(1, at = post, labels = datos_grafico_Viento$MC, las = 1, cex.axis = 0.8)
datos_grafico_Viento$hi <- as.numeric(datos_grafico_Viento$hi)
barplot(
datos_grafico_Viento$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Precipitación en el Volcán Antisana",
xlab = "Viento (m/S)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico_Viento$McV,
ylim = c(0, 100)
)
# Boxplot
boxplot(
Viento,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución del Viento",
xlab = "Viento (m/S)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
LiV, Ni_descV,
main = "Gráfica Nº8: Distribución Ascendente y Descendente del Viento",
xlab = " Viento (m/S)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
LsV, Ni_ascV,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
LiV, Hi_descV,
main = "Gráfica Nº9: Distribución Ascendente y Descendente del Viento",
xlab = " Viento",
ylab = "Porcentaje (%)",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 2
)
lines(
LsV, Hi_ascV,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
mediav <- round(mean(Viento), 0)
mediav## [1] 2# Moda
max_frecuenciav <- max(TDF_Viento_F$ni)
modaV <- TDF_Viento_F$MC[TDF_Viento_F$ni == max_frecuenciav]
modaV## [1] "2.25"# Mediana
medianaV <- median(Viento)
medianaV## [1] 1.75# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianzaV <- var(Viento)
varianzaV## [1] 0.2077148sdV <- sd(Viento)
sdV## [1] 0.4557574# Coeficiente de Variación
cvV <- round((sdV / mediav) * 100, 2)
cvV## [1] 22.79# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetriaV <- skewness(Viento, type = 2)
asimetriaV## [1] 0.1112888#Curtosis
curtosisV <- kurtosis(Viento)
curtosisV## [1] -0.719341# TABLA RESUMEN FINAL
tabla_indicadoresV <- data.frame(
"Variable" = c("Viento"),
"Rango" = c(paste0("[", min(Viento), " ; ", max(Viento), "]")),
"X" = c(round(mediav, 0)),
"Me" = c(round(medianaV, 0)),
"Mo" = c(paste(modaV, collapse = ", ")),
"V" = c(round(varianzaV,2)),
"Sd" = c(round(sdV, 0)),
"Cv" = c(cvV),
"As" = c(round(asimetriaV, 2)),
"K" = c(round(curtosisV, 2)),
"Valores Atípicos" = "-"
)
library(gt)
tabla_indicadores_gtV <- tabla_indicadoresV %>%
gt() %>%
tab_header(
title = md("Tabla N°8.1"),
subtitle = md("*Indicadores estadísticos de la variable Viento*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Precipitación"
)
)
tabla_indicadores_gtV| Tabla N°8.1 | ||||||||||
| Indicadores estadísticos de la variable Viento | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Viento | [0.59 ; 2.99] | 2 | 2 | 2.25 | 0.21 | 0 | 22.79 | 0.11 | -0.72 | - |
| Autor: Grupo 3 | ||||||||||
# Humead Relativa
Humedad<- datos$Relative.Humidity
minH <-min(Humedad)
maxH <-max(Humedad)
RH <-maxH-minH
KH <- floor(1+3.33*log10(length(Humedad)))
AH<-RH/KH
LiH <-round(seq(from=minH,to=maxH-AH,by=AH),2)
LsH <-round(seq(from=minH+AH,to=maxH,by=AH),2)
McH <-(LiH+LsH)/2
niH<-c()
for (i in 1:KH) {
if (i < KH) {
niH[i] <- length(subset(Humedad, Humedad >= LiH[i] & Humedad< LsH[i]))
} else {
niH[i] <- length(subset(Humedad, Humedad >= LiH[i] & Humedad <= LsH[i]))
}
}
sum(niH)## [1] 366hiH <-niH/sum(niH)*100
Ni_ascH<-cumsum(niH)
Hi_ascH<-cumsum(hiH)
Ni_descH<-rev(cumsum(rev(niH)))
Hi_descH<-rev(cumsum(rev(hiH)))
TDF_Humedad <- data.frame(
LiH, LsH, McH, niH, round(hiH, 2), Ni_ascH, Ni_descH, round(Hi_ascH, 2), round(Hi_descH, 2)
)
colnames(TDF_Humedad) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(niH),
hi=sum(hiH),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Humedad_final <-rbind(TDF_Humedad,totales)
library(dplyr)
library(gt)
TDF_Humedad_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 9"),
subtitle = md("*Tabla de distribución de la Humedad Relativa en el Volcan Antisana *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 9 | ||||||||
| *Tabla de distribución de la Humedad Relativa en el Volcan Antisana * | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.56 | 0.61 | 0.585 | 2 | 0.55 | 2 | 366 | 0.55 | 100 |
| 0.61 | 0.66 | 0.635 | 15 | 4.1 | 17 | 364 | 4.64 | 99.45 |
| 0.66 | 0.7 | 0.68 | 16 | 4.37 | 33 | 349 | 9.02 | 95.36 |
| 0.7 | 0.75 | 0.725 | 20 | 5.46 | 53 | 333 | 14.48 | 90.98 |
| 0.75 | 0.8 | 0.775 | 19 | 5.19 | 72 | 313 | 19.67 | 85.52 |
| 0.8 | 0.85 | 0.825 | 20 | 5.46 | 92 | 294 | 25.14 | 80.33 |
| 0.85 | 0.89 | 0.87 | 28 | 7.65 | 120 | 274 | 32.79 | 74.86 |
| 0.89 | 0.94 | 0.915 | 53 | 14.48 | 173 | 246 | 47.27 | 67.21 |
| 0.94 | 0.99 | 0.965 | 193 | 52.73 | 366 | 193 | 100 | 52.73 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoH <- hist(
Humedad,
main = "Gráfica Nº1: Distribución de la Humedad Relativa en el Volcan Antisana",
xlab = "Humedad(%)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Humedad<-hist(Humedad,breaks = 8,plot = F)
kH<-length(Hist_Viento$breaks)
LiH<-Hist_Humedad$breaks[1:(length(Hist_Humedad$breaks)-1)]
LsH<-Hist_Humedad$breaks[2:length(Hist_Humedad$breaks)]
niH<-Hist_Humedad$counts
sum(niH)## [1] 366McH<-Hist_Humedad$mids
hiH<-(niH/sum(niH))
sum(hiH)## [1] 1Ni_ascH<-cumsum(niH)
Hi_ascH<-cumsum(hiH)
Ni_descH<-rev(cumsum(rev(niH)))
Hi_descH<-rev(cumsum(rev(hiH)))
TDF_Humedad_F<-data.frame(Li=round(LiH,2),
Ls=round(LsH,2),
Mc=round(McH,2),
ni=niH,
hi=round(hiH*100,2),
Ni_asc=Ni_ascH,
Ni_desc=Ni_descH,
Hi_asc=round(Hi_ascH*100,2),
Hi_desc=round(Hi_descH*100,2))
colnames(TDF_Humedad_F)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Humedad_F$ni)),
hi = sum(as.numeric(TDF_Humedad_F$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Humedad_F<-rbind(TDF_Humedad_F,totales)
library(dplyr)
library(gt)
TDF_Humedad_F %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 10"),
subtitle = md("*Tabla Simplificada de distribución de la Humedad Relativa en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 10 | ||||||||
| Tabla Simplificada de distribución de la Humedad Relativa en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0.55 | 0.6 | 0.58 | 2 | 0.55 | 2 | 366 | 0.55 | 100 |
| 0.6 | 0.65 | 0.62 | 15 | 4.1 | 17 | 364 | 4.64 | 99.45 |
| 0.65 | 0.7 | 0.68 | 18 | 4.92 | 35 | 349 | 9.56 | 95.36 |
| 0.7 | 0.75 | 0.73 | 21 | 5.74 | 56 | 331 | 15.3 | 90.44 |
| 0.75 | 0.8 | 0.78 | 18 | 4.92 | 74 | 310 | 20.22 | 84.7 |
| 0.8 | 0.85 | 0.83 | 25 | 6.83 | 99 | 292 | 27.05 | 79.78 |
| 0.85 | 0.9 | 0.88 | 41 | 11.2 | 140 | 267 | 38.25 | 72.95 |
| 0.9 | 0.95 | 0.92 | 59 | 16.12 | 199 | 226 | 54.37 | 61.75 |
| 0.95 | 1 | 0.98 | 167 | 45.63 | 366 | 167 | 100 | 45.63 |
| TOTAL | - | - | 366 | 100.01 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Humedad, breaks = 10,
main = "Gráfica N°3 Distribución para la Humedad Relativa en el Volcan Antisana ",
xlab = "Humedad Relativa (%)",
ylab = "Cantidad",
ylim = c(0,max(niH)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Humedad$breaks,
labels = Hist_Humedad$breaks, las = 1,
cex.axis = 0.9)
hist(Humedad, breaks = 10,
main = "Gráfica N°4: Distribución de la Humedad Relativa en el volcan Antisana ",
xlab = "Humedad Relativa (%)",
ylab = "Cantidad",
ylim = c(0, length(Humedad)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Humedad$breaks,
labels = Hist_Humedad$breaks, las = 1,
cex.axis = 0.9)
TDF_Humedad_F$hi <- as.numeric(TDF_Humedad_F$hi)
datos_grafico <- subset(TDF_Humedad_F, !(McH %in% c("-", "TOTAL")))
barplot(datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual de la Humedad Relativa en el Volcan Antisana",
xlab = "Humedad (%)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$McH,
ylim = c(0, 100))
barplot(datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de de la Humedad Relativa en el Volcan Antisana",
xlab = "Humedad (%)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$McH,
ylim = c(0, 100))
# Boxplot
boxplot(
Humedad,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución de la Humedad Relativa",
xlab = "Humedad Relativa (%)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
LiH, Ni_descH,
main = "Gráfica Nº8: Distribución Ascendente y Descendente de la Humedad Relativa",
xlab = " Humedad Relativa (%)",
ylab = "Cantidad",
xlim = c(0, 10),
col = "red",
type = "o",
lwd = 3
)
lines(
LsH, Ni_ascH,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
LiH, Hi_descH,
main = "Gráfica Nº9: Distribución Ascendente y Descendente de la Humedad Relativa",
xlab = " Humedad (%)",
ylab = "Porcentaje (%)",
xlim = c(0, 10),
col = "red",
type = "o",
lwd = 2
)
lines(
LsH, Hi_ascH,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
mediaH <- round(mean(Humedad), 0)
mediaH## [1] 1# Moda
max_frecuenciaH <- max(TDF_Humedad_F$ni)
modaH <- TDF_Humedad_F$MC[TDF_Humedad_F$ni == max_frecuenciaH]
modaH## [1] "0.92"# Mediana
medianaH <- median(Humedad)
medianaH## [1] 0.94# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianzaH <- var(Humedad)
varianzaH## [1] 0.0118026sdH <- sd(Humedad)
sdH## [1] 0.1086398# Coeficiente de Variación
cvH <- round((sdH / mediaH) * 100, 2)
cvH## [1] 10.86# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetriaH <- skewness(Humedad, type = 2)
asimetriaH## [1] -1.186766#Curtosis
curtosisH <- kurtosis(Humedad)
curtosisH## [1] 0.2001903# TABLA RESUMEN FINAL
tabla_indicadoresH <- data.frame(
"Variable" = c("Viento"),
"Rango" = c(paste0("[", min(Humedad), " ; ", max(Humedad), "]")),
"X" = c(round(mediaH, 0)),
"Me" = c(round(medianaH, 0)),
"Mo" = c(paste(modaH, collapse = ", ")),
"V" = c(round(varianzaH,2)),
"Sd" = c(round(sdH, 0)),
"Cv" = c(cvH),
"As" = c(round(asimetriaH, 2)),
"K" = c(round(curtosisH, 2)),
"Valores Atípicos" = "3"
)
library(gt)
tabla_indicadores_gtH <- tabla_indicadoresH %>%
gt() %>%
tab_header(
title = md("Tabla N°10.1"),
subtitle = md("*Indicadores estadísticos de la variable Humedad*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Precipitación"
)
)
tabla_indicadores_gtH| Tabla N°10.1 | ||||||||||
| Indicadores estadísticos de la variable Humedad | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Viento | [0.56 ; 0.99] | 1 | 1 | 0.92 | 0.01 | 0 | 10.86 | -1.19 | 0.2 | 3 |
| Autor: Grupo 3 | ||||||||||
#Radiación Solar
Radiacion<- datos$Solar
minS <-min(Radiacion)
maxS <-max(Radiacion)
RS <-maxS-minS
KS <- floor(1+3.33*log10(length(Radiacion)))
AS<-RS/KS
LiS <-round(seq(from=minS,to=maxS-AS,by=AS),2)
LsS <-round(seq(from=minS+AS,to=maxS,by=AS),2)
McS <-(LiS+LsS)/2
niS<-c()
for (i in 1:KS) {
if (i < KS) {
niS[i] <- length(subset(Radiacion, Radiacion >= LiS[i] & Radiacion< LsS[i]))
} else {
niS[i] <- length(subset(Radiacion, Radiacion >= LiS[i] & Radiacion <= LsS[i]))
}
}
sum(niS)## [1] 366hiS <-niS/sum(niS)*100
Ni_ascS<-cumsum(niS)
Hi_ascS<-cumsum(hiS)
Ni_descS<-rev(cumsum(rev(niS)))
Hi_descS<-rev(cumsum(rev(hiS)))
TDF_Radiacion <- data.frame(
LiS, LsS, McS, niS, round(hiS, 2), Ni_ascS, Ni_descS, round(Hi_ascS, 2), round(Hi_descS, 2)
)
colnames(TDF_Radiacion) <- c("Li","Ls","Mc","ni","hi","Ni_asc","Ni_desc","Hi_asc(%)","Hi_desc(%)")
#Crear fila de totales
totales<-c(
Li="TOTAL",
Ls="-",
Mc="-",
ni=sum(niS),
hi=sum(hiS),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Radiacion_final <-rbind(TDF_Radiacion,totales)
library(dplyr)
library(gt)
TDF_Radiacion_final %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 11"),
subtitle = md("*Tabla de distribución de la Radiación Solar en el Volcan Antisana *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 11 | ||||||||
| *Tabla de distribución de la Radiación Solar en el Volcan Antisana * | ||||||||
| Li | Ls | Mc | ni | hi | Ni_asc | Ni_desc | Hi_asc(%) | Hi_desc(%) |
|---|---|---|---|---|---|---|---|---|
| 1.26 | 4.48 | 2.87 | 40 | 10.93 | 40 | 366 | 10.93 | 100 |
| 4.48 | 7.71 | 6.095 | 57 | 15.57 | 97 | 326 | 26.5 | 89.07 |
| 7.71 | 10.93 | 9.32 | 55 | 15.03 | 152 | 269 | 41.53 | 73.5 |
| 10.93 | 14.15 | 12.54 | 55 | 15.03 | 207 | 214 | 56.56 | 58.47 |
| 14.15 | 17.38 | 15.765 | 30 | 8.2 | 237 | 159 | 64.75 | 43.44 |
| 17.38 | 20.6 | 18.99 | 17 | 4.64 | 254 | 129 | 69.4 | 35.25 |
| 20.6 | 23.82 | 22.21 | 35 | 9.56 | 289 | 112 | 78.96 | 30.6 |
| 23.82 | 27.05 | 25.435 | 48 | 13.11 | 337 | 77 | 92.08 | 21.04 |
| 27.05 | 30.27 | 28.66 | 29 | 7.92 | 366 | 29 | 100 | 7.92 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
# Histograma
histoS<- hist(
Radiacion,
main = "Gráfica Nº1: Distribución de la Radiacion Solar en el Volcan Antisana",
xlab = "Radiación (J/m2)",
ylab = "Cantidad",
col = "blue"
)
#Simplificación con el histograma
Hist_Radiacion<-hist(Radiacion,breaks = 8,plot = F)
kS<-length(Hist_Radiacion$breaks)
LiS<-Hist_Radiacion$breaks[1:(length(Hist_Radiacion$breaks)-1)]
LsS<-Hist_Radiacion$breaks[2:length(Hist_Radiacion$breaks)]
niS<-Hist_Radiacion$counts
sum(niS)## [1] 366McS<-Hist_Radiacion$mids
hiS<-(niS/sum(niS))
sum(hiS)## [1] 1Ni_ascS<-cumsum(niS)
Hi_ascS<-cumsum(hiS)
Ni_descS<-rev(cumsum(rev(niS)))
Hi_descS<-rev(cumsum(rev(hiS)))
TDF_Radiacion_F<-data.frame(Li=round(LiS,2),
Ls=round(LsS,2),
Mc=round(McS,2),
ni=niS,
hi=round(hiS*100,2),
Ni_asc=Ni_ascS,
Ni_desc=Ni_descS,
Hi_asc=round(Hi_ascS*100,2),
Hi_desc=round(Hi_descS*100,2))
colnames(TDF_Radiacion_F)<-c("Lim inf","Lim sup","MC","ni","hi(%)","Ni asc","Ni desc","Hi asc(%)","Hi desc(%)")
#Crear fila de totales
totales<-c(Li="TOTAL",
Ls="-",
Mc="-",
ni = sum(as.numeric(TDF_Radiacion_F$ni)),
hi = sum(as.numeric(TDF_Radiacion_F$hi)),
Ni_asc="-",
Ni_desc="-",
Hi_asc="-",
Hi_desc="-")
TDF_Radiacion_F<-rbind(TDF_Radiacion_F,totales)
library(dplyr)
library(gt)
TDF_Radiacion_F %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 11"),
subtitle = md("*Tabla Simplificada de distribución de la Radiacion Solar en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 11 | ||||||||
| Tabla Simplificada de distribución de la Radiacion Solar en el volcan Antisana | ||||||||
| Lim inf | Lim sup | MC | ni | hi(%) | Ni asc | Ni desc | Hi asc(%) | Hi desc(%) |
|---|---|---|---|---|---|---|---|---|
| 0 | 5 | 2.5 | 51 | 13.93 | 51 | 366 | 13.93 | 100 |
| 5 | 10 | 7.5 | 86 | 23.5 | 137 | 315 | 37.43 | 86.07 |
| 10 | 15 | 12.5 | 79 | 21.58 | 216 | 229 | 59.02 | 62.57 |
| 15 | 20 | 17.5 | 33 | 9.02 | 249 | 150 | 68.03 | 40.98 |
| 20 | 25 | 22.5 | 57 | 15.57 | 306 | 117 | 83.61 | 31.97 |
| 25 | 30 | 27.5 | 58 | 15.85 | 364 | 60 | 99.45 | 16.39 |
| 30 | 35 | 32.5 | 2 | 0.55 | 366 | 2 | 100 | 0.55 |
| TOTAL | - | - | 366 | 100 | - | - | - | - |
| Autor: Grupo 3 | ||||||||
#Gráficas
hist(Radiacion, breaks = 10,
main = "Gráfica N°3 Distribución para la Radiacion Solar Relativa en el Volcan Antisana ",
xlab = "Radiación Solar (J/m2)",
ylab = "Cantidad",
ylim = c(0,max(niS)),
col = "yellow",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Radiacion$breaks,
labels = Hist_Radiacion$breaks, las = 1,
cex.axis = 0.9)
hist(Radiacion, breaks = 10,
main = "Gráfica N°4: Distribución de la Radiación Solar en el volcan Antisana ",
xlab = "Radiación Solar (J/m2)",
ylab = "Cantidad",
ylim = c(0, length(Radiacion)),
col = "green",
cex.main = 0.9,
cex.lab = 1,
cex.axis = 0.9,
xaxt = "n")
axis(1, at = Hist_Radiacion$breaks,
labels = Hist_Radiacion$breaks, las = 1,
cex.axis = 0.9)
TDF_Radiacion_F$hi <- as.numeric(TDF_Radiacion_F$hi)
datos_grafico <- TDF_Radiacion_F[1:(nrow(TDF_Radiacion_F) - 1), ]
barplot(
datos_grafico$hi,
space = 0,
col = "blue",
main = "Gráfica N°5: Distribución porcentual de la Radiación Solar en el Volcán Antisana",
xlab = "Radiación Solar (J/m²)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$McS,
ylim = c(0, max(datos_grafico$hi) + 5)
)
datos_grafico$hi <- as.numeric(datos_grafico$hi)
hi_100 <- datos_grafico$hi / max(datos_grafico$hi) * 100
barplot(
hi_100,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Radiación Solar en el Volcán Antisana",
xlab = "Radiación Solar (J/m²)",
ylab = "Porcentaje relativo (%)",
names.arg = datos_grafico$McS,
ylim = c(0, 100)
)
# Boxplot
boxplot(
Radiacion,
horizontal = TRUE,
col = "pink",
main = "Gráfica Nº7: Distribución de la Radiación Solar",
xlab = "Radiación Solar (J/m2)",
outline = TRUE,
pch = 19
)
# Ojivas
plot(
LiS, Ni_descS,
main = "Gráfica Nº8: Distribución Ascendente y Descendente de la Radiación Solar",
xlab = " Radiación Solar (J/m2)",
ylab = "Cantidad",
xlim = c(0, 100),
col = "red",
type = "o",
lwd = 3
)
lines(
LsS, Ni_ascS,
col = "green",
type = "o",
lwd = 3
)
# Ojiva Porcentual
plot(
LiS, Hi_descS,
main = "Gráfica Nº9: Distribución Ascendente y Descendente de la Radiación Solar",
xlab = " Radiación Solar (J/m2)",
ylab = "Porcentaje (%)",
xlim = c(0,100),
col = "red",
type = "o",
lwd = 2
)
lines(
LsS, Hi_ascS,
col = "blue",
type = "o",
lwd = 3
)
# INDICADORES ESTADISTICOS
# Indicadores de Tendencia Central
# Media aritmética
mediaS <- round(mean(Radiacion), 0)
mediaS## [1] 14# Moda
max_frecuenciaS <- max(TDF_Radiacion_F$ni)
modaS <- TDF_Radiacion_F$McS[TDF_Radiacion_F$ni == max_frecuenciaS]
modaS## NULL# Mediana
medianaS <- median(Radiacion)
medianaS## [1] 12.655# INDICADORES DE DISPERSIÓN #
# Desviación Estándar
# Varianza
varianzaS <- var(Radiacion)
varianzaS## [1] 69.3595sdS <- sd(Radiacion)
sdS## [1] 8.328235# Coeficiente de Variación
cvS <- round((sdS / mediaS) * 100, 2)
cvS## [1] 59.49# INDICADORES DE FORMA #
# Coeficiente deAsimetría
library("e1071")
asimetriaS <- skewness(Radiacion, type = 2)
asimetriaS## [1] 0.2996237#Curtosis
curtosiss <- kurtosis(Radiacion)
curtosiss## [1] -1.244028# TABLA RESUMEN FINAL
tabla_indicadoresS <- data.frame(
"Variable" = c("Viento"),
"Rango" = c(paste0("[", min(Radiacion), " ; ", max(Radiacion), "]")),
"X" = c(round(mediaS, 0)),
"Me" = c(round(medianaS, 0)),
"Mo" = c(paste(modaS, collapse = ", ")),
"V" = c(round(varianzaS,2)),
"Sd" = c(round(sdS, 0)),
"Cv" = c(cvS),
"As" = c(round(asimetriaS, 2)),
"K" = c(round(curtosiss, 2)),
"Valores Atípicos" = "-"
)
library(gt)
tabla_indicadores_gtS <- tabla_indicadoresS %>%
gt() %>%
tab_header(
title = md("Tabla N°12.1"),
subtitle = md("*Indicadores estadísticos de la variable Radiación Solar*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black",
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_body(
rows = Variable == "Precipitación"
)
)
tabla_indicadores_gtS| Tabla N°12.1 | ||||||||||
| Indicadores estadísticos de la variable Radiación Solar | ||||||||||
| Variable | Rango | X | Me | Mo | V | Sd | Cv | As | K | Valores.Atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Viento | [1.26 ; 30.27] | 14 | 13 | 69.36 | 8 | 59.49 | 0.3 | -1.24 | - | |
| Autor: Grupo 3 | ||||||||||
#MODELO DE DISTRIBUCUIÓN NORMAL
#PASO 1: ESCOGER LA VARIABLE Y JUSTIFICAR POR QUE ES CONTINUA
#La variable velocidad del viento es una variable continua ya que puede tomar cualquier valor real, incluido decimales dentro
#de un intervalo determinado ya que su dominio es : D={x|x ∈ R+,0}, excepto valores negativos ya que esta variable no puede
#ser negativa
#PASO 2: TABLA DE DISTRIBUCIÓN DE FRECUENCIA
Viento <- datos$Wind
Hist_Viento <- hist(Viento, breaks = 8, plot = FALSE)
LiV <- Hist_Viento$breaks[-length(Hist_Viento$breaks)]
LsV <- Hist_Viento$breaks[-1]
niV <- Hist_Viento$counts
hiV <- (niV / sum(niV)) * 100
TDF_Viento_simple <- data.frame(
Lim_inf = round(LiV, 2),
Lim_sup = round(LsV, 2),
ni = niV,
hi_pct = round(hiV, 2)
)
TDF_Viento_simple <- rbind(
TDF_Viento_simple,
data.frame(Lim_inf = "Totales", Lim_sup = "", ni = sum(niV), hi_pct = 100)
)
library(gt)
TDF_Viento_simple %>%
gt() %>%
cols_label(
Lim_inf = "Lim inf",
Lim_sup = "Lim sup",
ni = "ni",
hi_pct = "hi (%)"
) %>%
fmt_number(columns = c(ni), decimals = 0) %>%
fmt_number(columns = c(hi_pct), decimals = 2) %>%
tab_header(
title = md("Tabla Nro. 8"),
subtitle = md("*Tabla simplificada de distribución del viento en el volcán Antisana*")
) %>%
tab_source_note(source_note = md("Autor: Grupo 3")) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 8 | |||
| Tabla simplificada de distribución del viento en el volcán Antisana | |||
| Lim inf | Lim sup | ni | hi (%) |
|---|---|---|---|
| 0.5 | 1 | 12 | 3.28 |
| 1 | 1.5 | 107 | 29.23 |
| 1.5 | 2 | 130 | 35.52 |
| 2 | 2.5 | 96 | 26.23 |
| 2.5 | 3 | 21 | 5.74 |
| Totales | 366 | 100.00 | |
| Autor: Grupo 3 | |||
#PASO 3: HISTOGRAMA
datos_grafico_Viento$hi <- as.numeric(datos_grafico_Viento$hi)
barplot(
datos_grafico_Viento$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°6: Distribución porcentual de la Precipitación en el Volcán Antisana",
xlab = "Viento (m/S)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico_Viento$McV,
ylim = c(0, 100)
)
#PASO 4: CONJETURA
#Gracias a la grafica de barras podemos asumir que las barras se comportan como un modelo de distribución normal
#PASO 5: CÁLCULO DE PARAMETROS
U <- mean(Viento)
U## [1] 1.767787Sigma <- sd(Viento)
Sigma## [1] 0.4557574#PASO 6 : GRÁFICA DE REALIDAD COMPARADA CON EL MODELO
breaks <- hist(Viento, breaks = 8, plot = FALSE)$breaks
hist(Viento,
breaks = breaks,
freq = FALSE,
main = "Gráfica N°2: Comparación modelo normal con la realidad de la velocidad del viento Estudio en el volcán Antisana)",
xlab = "Viento (m/s)",
ylab = "Densidad de probabilidad",
col = "lightblue",
xlim = range(breaks)
)
axis(1, at = breaks)
x <- seq(min(Viento, na.rm = TRUE), max(Viento, na.rm = TRUE), by = 0.01)
lines(x, dnorm(x, mean = U, sd = Sigma), lwd = 3, col = "black")
#PASO 7: TESTS DE BONDAD
#PASO 7.1: TEST DE PEARSON
#Frecuencia observada
FoV<-as.numeric(table(cut(Viento, breaks = breaks, include.lowest = TRUE)))
FoV## [1] 12 107 130 96 21nV <- length(Viento)
pV <- diff(pnorm(breaks, mean = U, sd = Sigma))
# Fe = Probabilidad * n
FeV <- pV * nV
FeV## [1] 15.85712 85.05226 152.39889 91.91160 18.53558CorrelaciónV<-cor(FoV,FeV)*100
CorrelaciónV## [1] 96.0468#PASO 7.2: TEST DE CHI CUADRADO
breaks_chi <- quantile(Viento, probs = seq(0, 1, length.out = 6))
chi2 <- sum((FoV - FeV)^2 / FeV)
chi2## [1] 10.40343k <- length(FoV)
gl <- kV - 1 - 2
gl## [1] 3umbrall_aceptacion <- qchisq(0.999, df = gl)
umbrall_aceptacion## [1] 16.26624chi2 < umbrall_aceptacion## [1] TRUE#PASO 8: CÁLCULO DE PROBABILIDADES
#¿Cuál es la probabilidad de que en 2027 la velocidad del viento en el volcán Antisana esté entre 1.8 y 2.2 m/s?
pnorm(2.2, U, Sigma) - pnorm(1.8, U, Sigma)## [1] 0.3003479#¿Cuál es la probabilidad de que en 2030 la velocidad del viento en el volcán Antisana sea mayor o igual a 2.5 m/s?
1 - pnorm(2.5, U, Sigma)## [1] 0.05407269# 9. INTERVALO DE CONFIANZA
media <-mean(Viento)
sigma<-sd(Viento)
n<-length(Viento)
error<- 2*(sigma/sqrt(n))
#Límites intevalo de cofianza
lim_infer<- round(media-error,2)
lim_super<- round(media+error,2)
tabla_intervalo <- data.frame(Intervalo = "P [1.72< µ < 1.82] = 95%")
tabla_intervalo %>%
gt() %>%
tab_header(
title = md("*Tabla Nro. 2*"),
subtitle = md("**Intervalo de confianza del viento en el estudio del clima en el volcán Antisana en 2012 **")
) %>%
tab_source_note(
source_note = md("Autor: GRUPO 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black")| Tabla Nro. 2 |
| **Intervalo de confianza del viento en el estudio del clima en el volcán Antisana en 2012 ** |
| Intervalo |
|---|
| P [1.72< µ < 1.82] = 95% |
| Autor: GRUPO 3 |
# PASO 10: CONCLUSIÓN
# La variable Velocidad del Viento en (m/s) se explica con un modelo normal con parametro µ= 1,76 y σ= 0.45 y
#podemos afirmar con el 95% de confianza que la media aritmética de está variable se encuentra entre 1.71 y 1.82 (m/s)
#con una desviación estándar de 0.455 (m/s).
#MODELO EXPONENCIAL
#PASO 1: DEFINIR LA VARIABLE DE INTERÉS
#La variable precipitación (mm) es continua porque su dominio corresponde al conjunto de los números reales no negativos incluido el cero.
#Esto se debe a que la cantidad de lluvia puede tomar infinitos valores posibles dentro de un intervalo.
precipitación<-datos$Precipitation
#PASO 2: TABLA DE DISTRIBUCIÓN DE FRECUENCIAS
Histograma_precipitación<-hist(precipitación,plot=FALSE)
breaks <- Histograma_precipitación$breaks
Li <- breaks[1:(length(breaks)-1)]
Ls <- breaks[2:length(breaks)]
ni<-Histograma_precipitación$counts
n<-length(precipitación)
hi <- (ni / n) * 100
TDF_precipitacion <- data.frame(
Intervalo = paste0("[", round(Li,2), " - ", round(Ls,2), ")"),
ni = ni,
hi= round(hi, 2)
)
colnames(TDF_precipitacion) <- c(
"Intervalo",
"ni",
"hi(%)"
)
totaless <- data.frame(
Intervalo = "Totales",
ni = sum(ni),
hi = sum(hi)
)
colnames(totaless) <- c(
"Intervalo",
"ni",
"hi(%)"
)
TDF_precipitacion <- rbind(TDF_precipitacion, totaless)
TDF_precipitacion %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("*Distribucion de frecuencia simplificado de la precipitación, estudio del clima volcán Antisana en 2012 *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 1 | ||
| *Distribucion de frecuencia simplificado de la precipitación, estudio del clima volcán Antisana en 2012 * | ||
| Intervalo | ni | hi(%) |
|---|---|---|
| [0 - 10) | 150 | 40.98 |
| [10 - 20) | 92 | 25.14 |
| [20 - 30) | 58 | 15.85 |
| [30 - 40) | 27 | 7.38 |
| [40 - 50) | 23 | 6.28 |
| [50 - 60) | 10 | 2.73 |
| [60 - 70) | 4 | 1.09 |
| [70 - 80) | 0 | 0.00 |
| [80 - 90) | 1 | 0.27 |
| [90 - 100) | 1 | 0.27 |
| Totales | 366 | 100.00 |
| Autor: Grupo 3 | ||
#PASO 3: HISTOGRAMA
TDF_precipitacion$hi <- as.numeric(TDF_precipitacion$`hi(%)`)
TDF_precipitacion_graf <- TDF_precipitacion[TDF_precipitacion$Intervalo != "Totales", ]
par(mar = c(9, 5, 4, 2))
post <- barplot(
TDF_precipitacion_graf$hi,
space = 0,
col = "blue",
ylim = c(0, 100),
xaxt = "n",
ylab = "Porcentaje",
main = "Gráfica N°1:Distribución de la precipitación en el estudio
del clima en el volcán Antisana en 2012"
)
axis(
side = 1,
at = post,
labels = TDF_precipitacion_graf$Intervalo,
las = 2,
cex.axis = 0.8
)
mtext(
"Precipitación (mm)",
side = 1,
line = 7
)
#PASO 4: CONJETURA DE MODELO
#MI VARIABLE Y SUS BARRAS SE COMPORTAN COMO UN MODELO DE DISTRIBUCIÓN EXPONENCIAL
# 5. CÁLCULO DE PARÁMETROS DISTRIBUCIÓN EXPONELCIAL
media_exp <- mean(precipitación)
media_exp## [1] 17.10478lambda<-1/media_exp
lambda## [1] 0.05846318Histograma_precipitación <- hist(precipitación,
breaks = breaks,
freq = FALSE,
main = "Gráfica Nº2: Comparación modelo exponelcial realidad de la precipitación\n en el estudio del clima en el volcán Antisana",
xlab = " Precipitación (mm)",
ylab = "Densidad probabilidad ",
col = "lightblue", ylim = c(0,0.06),xaxt = "n"
)
axis(1, at = breaks)
# Curva exponencial
curve(dexp(x,rate = lambda),
from = 0, to = 100,
col = "orange", lwd = 2, add = TRUE)
#PASO 6: APLICACIÓN DE TESTS
#PASO 6.1: Test de Pearson
fo <- hist(precipitación, breaks=breaks, plot=FALSE)$counts
fo## [1] 150 92 58 27 23 10 4 0 1 1n <- length(precipitación)
p <- diff(pexp(breaks, rate=lambda))
fe <- p * n
fe## [1] 162.0241746 90.2978545 50.3239874 28.0461117 15.6304065 8.7109974
## [7] 4.8547347 2.7055970 1.5078590 0.8403464Correlación<-cor(fo,fe)*100
Correlación## [1] 99.55797#PASO 6.2 Test Chi-cuadrado
x2 <- sum((fo - fe)^2 / fe)
x2## [1] 8.857184k <- length(fo)
grados_libertad <- k - 2
grados_libertad## [1] 8umbral_aceptacion <- qchisq(0.95, df = grados_libertad)
umbral_aceptacion## [1] 15.50731x2<umbral_aceptacion## [1] TRUE#PASO 7: CÁLCULO DE PROBABILIDADES
#¿Cuál es la probabilidad de que la precipitación esté entre 20 y 50 mm en un día cualquiera?
probabilidad_20_50 <- pexp(50, rate = lambda) - pexp(20, rate = lambda)
probabilidad_20_50 * 100## [1] 25.6832#PASO 8: INTERVALO DE CONFIANZĀ
media <-mean(precipitación)
sigma<-sd(precipitación)
n<-length(precipitación)
error<- 2*(sigma/sqrt(n))
#Límites intevalo de cofianza
limite_inferior<- round(media-error,2)
limite_superior<- round(media+error,2)
tabla_intervalo <- data.frame(Intervalo = "P [15.42< µ < 18.79] = 95%")
tabla_intervalo %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 2"),
subtitle = md("*Intervalo de confianza de las precipitaciones en el estudio del clima en el volcán Antisana en 2012 *")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 2 |
| *Intervalo de confianza de las precipitaciones en el estudio del clima en el volcán Antisana en 2012 * |
| Intervalo |
|---|
| P [15.42< µ < 18.79] = 95% |
| Autor: Grupo 3 |
# PASO 9: CONCLUSIÓN
# La variable precipitación (mm) sigue o se explica con un modelo exponencial con parametro λ= 0.058 y
#podemos afirmar con 95% de confianza que la media aritmetica de está variable se encuentra entre 15.42 y 18.79 (mm)
#con una desviación estándar de 16.115 (mm).
#MODELO LOG NORMAL
#PASO 1: ESCOGER LA VARIABLE Y JUSTIFICAR POR QUE ES CONTINUA
#La temperatura mínima es una variable cuantitativa continua porque puede tomar cualquier valor real, incluidos decimales
#ya sean positivos o negativos ya que su dominio es D={x|x ∈ R}.
#PASO 2: TABLA DE DISTRIBUCIÓN DE FRECUENCIA
Temp_min<- datos$Min.Temperature
Hist_Temp_Min<-hist(Temp_min,breaks = 8,plot = F)
k2<-length(Hist_Temp_Min$breaks)
Li2<-Hist_Temp_Min$breaks[1:(length(Hist_Temp_Min$breaks)-1)]
Ls2<-Hist_Temp_Min$breaks[2:length(Hist_Temp_Min$breaks)]
ni2<-Hist_Temp_Min$counts
sum(ni2)## [1] 366hi2<-(ni2/sum(ni2))
sum(hi2)## [1] 1TDF_Temp_Mínima_Simple<-data.frame(Li=round(Li2,2),
Ls=round(Ls2,2),
ni=ni2,
hi=round(hi2*100,2))
colnames(TDF_Temp_Mínima_Simple)<-c("Lim inf","Lim sup","ni","hi(%)")
#Crear fila de totales
totales<- c(Li="TOTAL",
Ls="-",
ni = sum(as.numeric(TDF_Temp_Mínima_Simple$ni)),
hi = sum(as.numeric(TDF_Temp_Mínima_Simple$hi))
)
TDF_Temp_Mínima_Simple<-rbind(TDF_Temp_Mínima_Simple,totales)
library(dplyr)
library(gt)
TDF_Temp_Mínima_Simple %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("*Tabla Simplificada de distribución de la Temperatura Mínima en el volcan Antisana*")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 1 | |||
| Tabla Simplificada de distribución de la Temperatura Mínima en el volcan Antisana | |||
| Lim inf | Lim sup | ni | hi(%) |
|---|---|---|---|
| 2 | 3 | 1 | 0.27 |
| 3 | 4 | 2 | 0.55 |
| 4 | 5 | 7 | 1.91 |
| 5 | 6 | 16 | 4.37 |
| 6 | 7 | 48 | 13.11 |
| 7 | 8 | 109 | 29.78 |
| 8 | 9 | 90 | 24.59 |
| 9 | 10 | 66 | 18.03 |
| 10 | 11 | 27 | 7.38 |
| TOTAL | - | 366 | 99.99 |
| Autor: Grupo 3 | |||
#PASO 3: HISTOGRAMA
df <- TDF_Temp_min_final
df$hi <- as.numeric(df$hi)
datos_grafico <- df[1:(nrow(df)-1), ]
datos_grafico$hi <- as.numeric(datos_grafico$hi)
sum(datos_grafico$hi)## [1] 100barplot(
datos_grafico$hi,
space = 0,
col = "skyblue",
main = "Gráfica N°14: Distribución porcentual de la Temperatura Mínima en el Volcán Antisana",
xlab = "Temperatura Mínima (°C)",
ylab = "Porcentaje (%)",
names.arg = datos_grafico$MC,
ylim = c(0, 100)
)
#PASO 4: CONJETURA
# La variable temperatura mínima y sus barras se comportan como un modelo log normal, los valores más altos se encuentran
#en la parte media con una desviación a la derecha y los valores bajos se extienden hacia la parte izquierda, y concluimos
#que se comporta como un modelo log normal con sesgo hacia la izquierda.
#PASO 5: CÁLCULO DE PARÁMETROS
temp <- Temp_min
temp <- temp[is.finite(temp)] # por si hay NA/Inf
temp_pos <- temp[temp > 0]
log_temp <- log(temp_pos)
ulog <- mean(log_temp, na.rm = TRUE)
sigmalog <- sd(log_temp, na.rm = TRUE)
breaks <- hist(temp_pos, breaks = 8, plot = FALSE)$breaks
xlim <- range(breaks)
#PASO 6: GRÁFICA REALIDAD EN COMPARACIÓN CON EL MODELO LOG NORMAL
hist(
temp_pos,
breaks = breaks,
freq = FALSE,
col = "skyblue",
main = "Gráfica N°2: Comparación de la Realidad y el Modelo Log-normal de la temperatura mínima en el volcán Antisana",
xlab = "Temperatura mínima (°C)",
ylab = "Densidad de probabilidad",
cex.main = 0.9,
xlim = xlim,
xaxt = "n"
)
axis(1, at = breaks)
x <- seq(xlim[1], xlim[2], by = 0.001)
lines(x, dlnorm(x, meanlog = ulog, sdlog = sigmalog), col = "darkblue", lwd = 3)
#PASO 7: TEST DE BONDAD
#PASO 7.1: TEST DE PEARSON
fo_Temp_min <- hist(Temp_min, breaks=breaks, plot=FALSE)$counts
fo_Temp_min## [1] 1 2 7 16 48 109 90 66 27n_Temp_min <- length(Temp_min)
fe_Temp_min <- numeric(length(fo_Temp_min))
for(i in 1:length(fo_Temp_min)){
fe_Temp_min[i] <- n_Temp_min * (plnorm(breaks[i+1], meanlog = ulog, sdlog = sigmalog) -
plnorm(breaks[i], meanlog = ulog, sdlog = sigmalog))
}
fe_Temp_min## [1] 4.914119e-05 5.410726e-02 2.666588e+00 2.324386e+01 6.823973e+01
## [6] 9.706234e+01 8.401222e+01 5.137289e+01 2.453682e+01Correlación<-cor(fo_Temp_min,fe_Temp_min)*100
Correlación## [1] 96.62853#PASO 7.2: TEST DE CHI CUADRADO
fe_frac_TMIN <- fe_Temp_min / n_Temp_min
fe_frac_TMIN## [1] 1.342655e-07 1.478340e-04 7.285759e-03 6.350780e-02 1.864473e-01
## [6] 2.651976e-01 2.295416e-01 1.403631e-01 6.704049e-02fo_frac_TMIN <- fo_Temp_min / n_Temp_min
fo_frac_TMIN## [1] 0.002732240 0.005464481 0.019125683 0.043715847 0.131147541 0.297814208
## [7] 0.245901639 0.180327869 0.073770492x2_TMIN <- sum((fo_frac_TMIN - fe_frac_TMIN)^2 / fe_frac_TMIN)
x2_TMIN## [1] 55.84459k_TMIN <- length(fo_frac_TMIN)
gl_TMIN <- k - 1 -2
gl_TMIN## [1] 7umbral_aceptacionTMIN <- qchisq(0.9999999999, df = gl_TMIN)
umbral_aceptacionTMIN## [1] 60.8952x2_TMIN<umbral_aceptacionTMIN## [1] TRUE#PASO 9: CÁLCULO DE PROBABILIDADES
#Cuál es la probabilidad de que la temperatura mínima sea menor a 6 °C o mayor a 9.5 °C?
plnorm(6, ulog, sigmalog) + (1 - plnorm(9.5, ulog, sigmalog))## [1] 0.2374891#¿Cuál es la probabilidad de que la temperatura mínima sea mayor o igual a 9 °C?
1 - plnorm(9, ulog, sigmalog)## [1] 0.2478719#PASO 10: INTERVALO DE CONFIANZA
Media <-mean(Temp_min)
S<-sd(Temp_min)
n<-length(Temp_min)
error<- 2*(S/sqrt(n))
#Límites intevalo de cofianza
limite_inferior<- round(Media-error,2)
limite_superior<- round(Media+error,2)
tabla_intervaloTMIN <- data.frame(Intervalo = "P [7.9< µ <8.19] = 95%")
tabla_intervaloTMIN %>%
gt() %>%
tab_header(
title = md("*Tabla Nro. 2*"),
subtitle = md("**Intervalo de confianza de la temperatura mínima en el volcán Antisana **")
) %>%
tab_source_note(
source_note = md("Autor: Grupo 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 2 |
| **Intervalo de confianza de la temperatura mínima en el volcán Antisana ** |
| Intervalo |
|---|
| P [7.9< µ <8.19] = 95% |
| Autor: Grupo 3 |
#PASO 11: CONCLUSIÓN
# La variable temperatura mínima (°C) se explica con un modelo log-normal con sesgo a la izquierda con parametros µ = 2.068 y σ = 0.188
#y podemos afirmar con 95% de confianza que la media aritmética de está variable se encuentra entre 7.9 y 8.19 (°C)
#con una desviasión estándar de 1.37 (°C).
#ESTADÍSTICA MULTIVRIABLE
#Paso 1 Seleccionamos las dos variables
#Causa y efecto: Entre más radiación solar hay mayores temperaturas, mostrando una relacion proporcional.
Radiacion <- datos$Solar
Temp_max <- datos$Max.Temperature
x <- Radiacion
y <- Temp_max
#Paso 2 Tabla de pares de valores
TVP <- data.frame(x,y)
#Formato de la tabla
library(gt)
library(dplyr)
TVP %>%
gt() %>%
tab_header(
title = md("Tabla Nro. 1"),
subtitle = md("Pares de valores de temperatura máxima y radiación solar del clima volcán Antisana en 2012")
) %>%
tab_source_note(
source_note = md("Autor: GRUPO 3")
) %>%
tab_options(
table.border.top.color = "black",
table.border.bottom.color = "black",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
column_labels.border.top.color = "black",
column_labels.border.bottom.color = "black",
column_labels.border.bottom.width = px(2),
row.striping.include_table_body = TRUE,
heading.border.bottom.color = "black",
heading.border.bottom.width = px(2),
table_body.hlines.color = "gray",
table_body.border.bottom.color = "black"
)| Tabla Nro. 1 | |
| Pares de valores de temperatura máxima y radiación solar del clima volcán Antisana en 2012 | |
| x | y |
|---|---|
| 15.98 | 16.10 |
| 12.25 | 15.50 |
| 4.58 | 11.55 |
| 4.32 | 12.02 |
| 3.86 | 11.73 |
| 9.57 | 12.11 |
| 10.93 | 13.06 |
| 2.40 | 11.53 |
| 5.32 | 12.95 |
| 7.19 | 13.38 |
| 6.71 | 12.99 |
| 10.77 | 17.40 |
| 9.66 | 15.88 |
| 5.37 | 13.65 |
| 4.02 | 13.07 |
| 9.64 | 13.81 |
| 8.11 | 13.02 |
| 3.19 | 12.31 |
| 3.64 | 12.73 |
| 5.60 | 12.17 |
| 8.75 | 12.54 |
| 4.57 | 11.78 |
| 1.52 | 10.51 |
| 1.93 | 10.32 |
| 10.43 | 12.81 |
| 3.60 | 11.91 |
| 6.45 | 13.18 |
| 1.35 | 11.57 |
| 5.55 | 11.94 |
| 6.50 | 12.39 |
| 6.87 | 13.27 |
| 8.17 | 13.38 |
| 1.58 | 11.58 |
| 5.28 | 12.85 |
| 10.11 | 14.18 |
| 8.24 | 14.65 |
| 1.90 | 12.42 |
| 6.07 | 13.84 |
| 7.16 | 13.48 |
| 7.87 | 14.34 |
| 11.57 | 14.38 |
| 2.15 | 11.13 |
| 8.31 | 12.91 |
| 6.11 | 11.59 |
| 8.86 | 12.47 |
| 5.92 | 11.55 |
| 5.95 | 12.14 |
| 5.10 | 10.73 |
| 4.00 | 11.42 |
| 8.01 | 12.26 |
| 4.08 | 11.38 |
| 3.59 | 12.04 |
| 2.83 | 10.83 |
| 2.90 | 10.99 |
| 3.07 | 11.43 |
| 1.82 | 11.41 |
| 1.54 | 11.05 |
| 4.28 | 11.56 |
| 6.99 | 12.24 |
| 6.89 | 12.80 |
| 9.89 | 14.44 |
| 11.45 | 17.04 |
| 8.35 | 16.21 |
| 5.44 | 14.15 |
| 4.63 | 12.85 |
| 9.72 | 14.69 |
| 11.63 | 17.98 |
| 16.16 | 17.10 |
| 20.53 | 18.81 |
| 13.70 | 15.57 |
| 17.42 | 17.53 |
| 16.27 | 17.50 |
| 18.80 | 19.00 |
| 14.41 | 16.85 |
| 14.52 | 17.11 |
| 13.32 | 17.07 |
| 8.32 | 14.42 |
| 3.98 | 13.91 |
| 4.49 | 11.73 |
| 2.39 | 11.71 |
| 7.02 | 12.45 |
| 4.29 | 12.23 |
| 7.79 | 13.20 |
| 4.83 | 12.81 |
| 5.59 | 12.19 |
| 8.29 | 12.93 |
| 4.73 | 12.92 |
| 4.83 | 14.30 |
| 11.93 | 15.56 |
| 14.83 | 18.25 |
| 12.42 | 15.47 |
| 13.34 | 16.30 |
| 13.22 | 16.92 |
| 11.89 | 15.52 |
| 4.44 | 12.28 |
| 3.45 | 11.86 |
| 5.38 | 13.75 |
| 7.20 | 13.52 |
| 4.74 | 10.97 |
| 8.03 | 13.76 |
| 10.47 | 12.32 |
| 16.45 | 14.53 |
| 10.60 | 13.10 |
| 11.69 | 13.70 |
| 10.17 | 14.20 |
| 11.57 | 13.42 |
| 4.33 | 11.81 |
| 5.45 | 12.39 |
| 3.56 | 12.24 |
| 7.98 | 14.56 |
| 9.87 | 13.90 |
| 10.95 | 14.77 |
| 7.18 | 13.07 |
| 11.98 | 15.19 |
| 8.21 | 14.36 |
| 16.90 | 17.63 |
| 3.87 | 14.35 |
| 9.73 | 14.36 |
| 5.13 | 13.42 |
| 3.54 | 12.37 |
| 7.40 | 13.71 |
| 7.61 | 14.26 |
| 13.65 | 15.88 |
| 21.70 | 17.35 |
| 16.46 | 16.22 |
| 14.53 | 14.77 |
| 11.31 | 15.35 |
| 12.95 | 15.15 |
| 13.57 | 16.49 |
| 12.13 | 15.26 |
| 15.54 | 16.23 |
| 11.48 | 14.93 |
| 6.16 | 14.18 |
| 5.63 | 13.50 |
| 14.65 | 17.12 |
| 10.78 | 15.33 |
| 13.21 | 18.85 |
| 16.16 | 17.26 |
| 11.76 | 14.43 |
| 4.89 | 12.55 |
| 4.61 | 15.70 |
| 7.98 | 14.04 |
| 13.62 | 16.14 |
| 18.58 | 16.67 |
| 25.28 | 17.34 |
| 24.96 | 19.19 |
| 25.11 | 18.76 |
| 26.70 | 20.24 |
| 21.17 | 20.09 |
| 21.44 | 18.54 |
| 24.41 | 18.68 |
| 26.23 | 19.89 |
| 23.67 | 18.43 |
| 16.36 | 18.98 |
| 15.49 | 16.35 |
| 21.36 | 17.08 |
| 19.28 | 17.26 |
| 25.20 | 17.44 |
| 25.88 | 19.12 |
| 22.03 | 17.09 |
| 24.51 | 17.64 |
| 25.95 | 19.02 |
| 24.77 | 19.65 |
| 22.40 | 16.46 |
| 24.38 | 16.26 |
| 14.84 | 16.16 |
| 21.01 | 16.79 |
| 16.21 | 15.58 |
| 21.77 | 16.27 |
| 20.93 | 16.00 |
| 17.68 | 15.21 |
| 20.32 | 19.65 |
| 19.89 | 16.57 |
| 26.28 | 19.16 |
| 20.91 | 18.09 |
| 15.23 | 18.03 |
| 23.15 | 15.83 |
| 23.24 | 17.46 |
| 25.32 | 17.67 |
| 24.51 | 16.63 |
| 12.93 | 15.50 |
| 23.49 | 16.79 |
| 20.54 | 19.42 |
| 26.46 | 20.59 |
| 23.87 | 18.13 |
| 22.65 | 16.34 |
| 14.82 | 16.26 |
| 22.19 | 16.80 |
| 21.11 | 17.32 |
| 26.14 | 20.88 |
| 25.97 | 18.58 |
| 23.48 | 18.67 |
| 23.31 | 17.66 |
| 24.58 | 16.55 |
| 24.72 | 17.46 |
| 22.81 | 16.51 |
| 24.74 | 17.63 |
| 26.30 | 19.27 |
| 26.68 | 19.19 |
| 25.67 | 21.32 |
| 27.03 | 21.00 |
| 21.33 | 17.72 |
| 21.60 | 18.12 |
| 27.15 | 21.21 |
| 27.00 | 20.38 |
| 26.87 | 19.82 |
| 27.49 | 21.56 |
| 27.57 | 21.51 |
| 25.71 | 19.87 |
| 26.45 | 22.60 |
| 21.47 | 18.15 |
| 26.02 | 21.06 |
| 23.87 | 19.74 |
| 25.68 | 20.39 |
| 25.50 | 18.06 |
| 21.02 | 17.88 |
| 24.63 | 19.26 |
| 27.04 | 20.71 |
| 27.21 | 18.95 |
| 27.82 | 17.64 |
| 28.31 | 19.24 |
| 28.43 | 21.20 |
| 23.69 | 18.99 |
| 23.32 | 18.60 |
| 13.49 | 16.81 |
| 20.40 | 16.94 |
| 14.08 | 17.44 |
| 18.42 | 17.27 |
| 21.71 | 17.40 |
| 12.10 | 16.37 |
| 22.30 | 17.60 |
| 28.54 | 19.69 |
| 28.45 | 19.10 |
| 28.67 | 20.61 |
| 28.30 | 18.10 |
| 28.57 | 17.79 |
| 28.66 | 18.00 |
| 28.51 | 20.83 |
| 26.72 | 22.34 |
| 24.67 | 21.30 |
| 28.99 | 23.47 |
| 20.94 | 19.11 |
| 27.35 | 22.96 |
| 26.15 | 20.48 |
| 29.49 | 21.47 |
| 23.54 | 20.39 |
| 24.22 | 18.32 |
| 27.74 | 18.56 |
| 23.88 | 20.02 |
| 29.54 | 20.89 |
| 25.65 | 18.82 |
| 26.40 | 20.48 |
| 29.99 | 23.42 |
| 29.10 | 19.31 |
| 30.05 | 22.04 |
| 27.33 | 19.40 |
| 30.27 | 23.79 |
| 27.88 | 21.01 |
| 29.26 | 19.79 |
| 26.31 | 17.86 |
| 25.28 | 17.67 |
| 16.94 | 16.78 |
| 25.09 | 17.85 |
| 18.76 | 17.49 |
| 17.01 | 16.46 |
| 24.15 | 18.33 |
| 19.89 | 17.39 |
| 12.87 | 15.34 |
| 20.83 | 16.45 |
| 27.79 | 19.00 |
| 13.61 | 17.11 |
| 16.59 | 16.80 |
| 28.21 | 18.20 |
| 29.04 | 20.20 |
| 20.77 | 17.60 |
| 22.85 | 16.89 |
| 24.65 | 16.29 |
| 16.29 | 16.26 |
| 1.26 | 10.99 |
| 7.55 | 12.66 |
| 12.11 | 15.47 |
| 5.30 | 13.82 |
| 9.01 | 15.20 |
| 12.84 | 14.06 |
| 13.35 | 13.94 |
| 9.25 | 14.15 |
| 6.27 | 13.32 |
| 11.19 | 14.75 |
| 13.04 | 15.17 |
| 3.62 | 12.79 |
| 3.59 | 11.35 |
| 8.39 | 12.74 |
| 10.04 | 12.82 |
| 15.18 | 16.27 |
| 10.40 | 14.66 |
| 17.05 | 15.87 |
| 19.09 | 15.81 |
| 11.32 | 13.80 |
| 7.11 | 15.02 |
| 13.48 | 16.01 |
| 14.67 | 17.23 |
| 20.45 | 16.83 |
| 13.20 | 15.29 |
| 10.21 | 13.90 |
| 5.55 | 13.43 |
| 11.93 | 14.55 |
| 13.24 | 15.19 |
| 13.15 | 15.61 |
| 5.84 | 12.55 |
| 9.66 | 14.36 |
| 3.99 | 13.20 |
| 5.15 | 12.71 |
| 13.12 | 15.60 |
| 7.19 | 13.93 |
| 2.79 | 12.49 |
| 8.17 | 13.75 |
| 7.26 | 13.09 |
| 9.12 | 14.87 |
| 10.44 | 13.98 |
| 11.50 | 14.85 |
| 23.43 | 15.32 |
| 16.92 | 15.52 |
| 15.19 | 15.95 |
| 4.54 | 13.00 |
| 3.13 | 13.62 |
| 2.94 | 13.57 |
| 8.98 | 13.81 |
| 9.89 | 14.39 |
| 3.45 | 13.06 |
| 9.99 | 15.19 |
| 4.31 | 13.69 |
| 9.00 | 15.04 |
| 10.37 | 13.39 |
| 10.61 | 14.27 |
| 5.39 | 11.88 |
| 11.20 | 14.25 |
| 8.83 | 13.24 |
| 23.37 | 14.99 |
| 11.88 | 13.88 |
| 8.28 | 12.86 |
| 14.59 | 15.73 |
| 11.84 | 15.78 |
| 11.56 | 15.75 |
| 13.27 | 18.26 |
| 19.30 | 18.82 |
| 9.04 | 14.77 |
| 7.86 | 13.58 |
| 12.35 | 13.96 |
| 17.65 | 15.20 |
| 15.82 | 15.10 |
| 9.98 | 14.00 |
| 10.62 | 13.25 |
| 11.39 | 13.85 |
| 6.37 | 13.19 |
| 9.36 | 14.44 |
| 6.03 | 13.40 |
| 5.20 | 13.45 |
| 12.47 | 17.23 |
| 7.48 | 14.27 |
| 11.81 | 15.65 |
| 7.68 | 13.97 |
| 10.47 | 15.41 |
| 9.85 | 16.39 |
| 14.04 | 16.21 |
| 11.64 | 16.63 |
| 5.71 | 13.17 |
| Autor: GRUPO 3 | |
# Paso 3 Gráfica de nube de puntos
plot(x, y,
main = "Gráfica de nube de puntos entre la Temperatura máxima y la Radiación Solar del
Volcán Antisana 2012",
xlab = "Radiación Solar (J/m²)",
ylab = "Temperatura máxima (°C)",
col = "orange",
pch = 13,
xlim = c(0,max(x)),
ylim = c(0,max(y)),
)
#Paso 4 Conjetura
#Debido a la distribución de los puntos se sugiere que el mejor modelo para la gráfica de nube de puntos
#es un modelo lineal, ya que se ve una proporcionalidad, mientras la radiación solar aumenta
#la temperatura máxima tambien aumenta.
#Cálculo de parámetros modelo lineal
regresionlineal <- lm(y~x)
regresionlineal##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 11.2237 0.3129#Sustraemos pendiente e interceptor
I <- regresionlineal$coefficients[1]
I## (Intercept)
## 11.22374m <- regresionlineal$coefficients[2]
m## x
## 0.312879#Paso 6 Sobreponer : El modelo con la realidad
plot(x, y,
main = "Gráfica de nube de puntos entre la Temperatura máxima y la Radiación Solar del
Volcán Antisana 2012",
xlab = "Radiación Solar (J/m²)",
ylab = "Temperatura máxima (°C)",
col = "orange",
pch = 13,
xlim = c(0,max(x)),
ylim = c(0,max(y)),
)
abline(regresionlineal,col= "green",lwd = 2)
#Paso 7 :Test
#Test de Person
r <- cor(x,y)*100
r## [1] 90.87017#Paso 8: Coeficiente de determinación muestral
r2 <- r*r/100
r2## [1] 82.57388#Paso 9 :Restricciones
#Dominio [x]: D= {R+^0}
#Dominio [y]: D= {R}
# ¿Existe algún valor en dominio de x que sustituido en el modelo
#matemático genere un valor en y fuera de su dominio?
#Ningún valor de la radiación solar genera resultados fuera del rango de la
#temperatura máxima, ya que la radiación solar toma valores mayores o iguales a cero y,
#al aplicarse en el modelo lineal, siempre produce valores válidos de temperatura.
#Por lo tanto, el modelo es coherente con los valores que pueden tomar ambas variables.
#Paso 10: Aplicaciones del modelo
#¿Cuál sera la temperatura máxima esperada cuando se tenga una radiación solar de 16(J/m²)?
TemperaturaMax_Esperada <- m*16+I
TemperaturaMax_Esperada## x
## 16.22981# PASO 11: Conclusión
# Entre temperatura máxima (°C) y radiación solar (J/m2) existe la relación tipo lineal
#cuya ecuación es y=11.223+0.312x siendo y= máxima temperatura (°C),
#x= radiación solar (J/m2), donde la temperaatura máxima depende en un 82.57%
#de la radiación solar y el 18.43% se debe a otros factores.