CURVATURE
MARTIN SARMIENTO
2025-12-01
1 Configuración y Carga de Datos
##### UNIVERSIDAD CENTRAL DEL ECUADOR #####
#### AUTOR: MARTIN SARMIENTO ####
### CARRERA: INGENIERÍA EN PETRÓLEOS #####
#### VARIABLE CURVATURA ####
## DATASET ##
# Cargar dataset
Datos <- read.csv("DataSet_Mundial_Final.csv", sep = ";", dec = ",", fileEncoding = "latin1")
# Estructura de los datos
str(Datos)## 'data.frame': 58978 obs. of 29 variables:
## $ ï..OBJECTID : int 2 3 4 5 6 7 8 9 10 11 ...
## $ code : chr "00001-AFG-P" "00002-AFG-P" "00003-AFG-P" "00004-AFG-P" ...
## $ plant_name : chr "Badghis Solar Power Plant" "Balkh solar farm" "Behsood solar farm" "Dab Pal 4 solar farm" ...
## $ country : chr "Afghanistan" "Afghanistan" "Afghanistan" "Afghanistan" ...
## $ operational_status : chr "cancelled - inferred 4 y" "cancelled - inferred 4 y" "cancelled - inferred 4 y" "shelved - inferred 2 y" ...
## $ longitude : num 62.9 67.1 70.4 66.2 65.7 ...
## $ latitude : num 35.1 36.7 34.4 33.8 31.7 ...
## $ elevation : int 918 359 629 2288 1060 1060 1392 398 410 1012 ...
## $ area : num 6.74 10.72 487.73 111.8 1929.96 ...
## $ size : chr "Small" "Small" "Small" "Small" ...
## $ slope : num 7.38 0.49 1.1 6.16 1.23 ...
## $ slope_type : chr "Moderado" "Plano o casi plano" "Plano o casi plano" "Moderado" ...
## $ curvature : num -0.024 0 0 0.045 -0.005 -0.005 -0.015 0 0 -0.009 ...
## $ curvature_type : chr "Superficies cóncavas / Valles" "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies convexas / Crestas" ...
## $ aspect : num 96.8 358.5 36.2 305.8 248.4 ...
## $ aspect_type : chr "East" "North" "Northeast" "Northwest" ...
## $ dist_to_road : num 7037.1 92.7 112.1 1705.3 115.8 ...
## $ ambient_temperature : num 14.4 17.88 21.32 8.86 19.64 ...
## $ ghi : num 5.82 5.58 5.8 6.75 6.62 ...
## $ humidity : num 47.7 42.3 36.4 37.3 24.2 ...
## $ wind_speed : num 0.039 0.954 0.234 0.943 0.37 ...
## $ wind_direction : num 187.5 207.4 255.6 160.3 97.7 ...
## $ dt_wind : chr "South" "Southwest" "West" "South" ...
## $ solar_aptitude : num 0.72 0.635 0.685 0.659 0.819 0.819 0.818 0.642 0.63 0.374 ...
## $ solar_aptitude_rounded: int 7 6 7 7 8 8 8 6 6 4 ...
## $ solar_aptittude_class : chr "Alta" "Alta" "Alta" "Alta" ...
## $ capacity : num 32 40 60 3000 100 100 36 50 25 100 ...
## $ optimal_tilt : num 30 31 31.1 33 31 ...
## $ pv_potential : num 4.61 4.41 4.57 5.42 5.17 ...##
## Adjuntando el paquete: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union2 Cálculo de Intervalos y Frecuencias
# Extraer variable
Variable <- na.omit(Datos$curvature)
N <- length(Variable)
# CÁLCULO LÍMITES DECIMALES
min_dec <- min(Variable)
max_dec <- max(Variable)
k_dec <- floor(1 + 3.322 * log10(N))
rango_dec <- max(Variable) - min(Variable)
amplitud_dec <- rango_dec / k_dec
# Cortes exactos
cortes_dec <- seq(min(Variable), max(Variable), length.out = k_dec + 1)
cortes_dec[length(cortes_dec)] <- max(Variable) + 0.0001
# Frecuencias
inter_dec <- cut(Variable, breaks = cortes_dec, include.lowest = TRUE, right = FALSE)
ni_dec <- as.vector(table(inter_dec))
# CÁLCULOS MATEMÁTICOS
hi_dec <- (ni_dec / N) * 100
Ni_asc_dec <- cumsum(ni_dec)
Hi_asc_dec <- cumsum(hi_dec)
Ni_desc_dec <- rev(cumsum(rev(ni_dec)))
Hi_desc_dec <- rev(cumsum(rev(hi_dec)))
# Dataframe Decimal
TDF_Decimal <- data.frame(
Li = cortes_dec[1:k_dec],
Ls = cortes_dec[2:(k_dec+1)],
MC = (cortes_dec[1:k_dec] + cortes_dec[2:(k_dec+1)]) / 2,
ni = ni_dec,
hi = hi_dec,
Ni_asc = Ni_asc_dec,
Ni_desc = Ni_desc_dec,
Hi_asc = Hi_asc_dec,
Hi_desc = Hi_desc_dec)
# CÁLCULO LÍMITES ENTEROS
Amplitud_int <- 0.10
min_int <- floor(min(Variable) / Amplitud_int) * Amplitud_int
# Generamos la secuencia de cortes
cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = 2)
while(max(cortes_int) < max(Variable)) {
cortes_int <- seq(from = min_int, to = max(cortes_int) + Amplitud_int + 0.0001, by = Amplitud_int)
}
# Definimos los límites
K_real <- length(cortes_int) - 1
lim_inf_int <- cortes_int[1:K_real]
lim_sup_int <- cortes_int[2:(K_real+1)]
# Frecuencias
inter_int <- cut(Variable, breaks = cortes_int, include.lowest = TRUE, right = FALSE)
ni_int <- as.vector(table(inter_int))
# CÁLCULOS MATEMÁTICOS
hi_int <- (ni_int / N) * 100
Ni_asc_int <- cumsum(ni_int)
Hi_asc_int <- cumsum(hi_int)
Ni_desc_int <- rev(cumsum(rev(ni_int)))
Hi_desc_int <- rev(cumsum(rev(hi_int)))
# Dataframe Entero
TDF_Enteros <- data.frame(
Li = lim_inf_int,
Ls = lim_sup_int,
MC = (lim_inf_int + lim_sup_int) / 2,
ni = ni_int,
hi = hi_int,
Ni_asc = Ni_asc_int,
Ni_desc = Ni_desc_int,
Hi_asc = Hi_asc_int,
Hi_desc = Hi_desc_int)3 Tabla de Distribución de Frecuencias
3.1 Tabla con Límites Decimales
# Crear Dataframe
TDF_Dec_Final <- data.frame(
Li = as.character(round(TDF_Decimal$Li, 2)),
Ls = as.character(round(TDF_Decimal$Ls, 2)),
MC = as.character(round(TDF_Decimal$MC, 2)),
ni = as.character(TDF_Decimal$ni),
hi = as.character(round(TDF_Decimal$hi, 2)),
Ni_asc = as.character(TDF_Decimal$Ni_asc),
Ni_desc = as.character(TDF_Decimal$Ni_desc),
Hi_asc = as.character(round(TDF_Decimal$Hi_asc, 2)),
Hi_desc = as.character(round(TDF_Decimal$Hi_desc, 2))
)
# Calcular Totales
total_ni <- sum(TDF_Decimal$ni)
total_hi <- round(sum(TDF_Decimal$hi), 2)
fila_total_dec <- c("TOTAL", "-", "-", total_ni, total_hi, "-", "-", "-", "-")
TDF_Dec_Final <- rbind(TDF_Dec_Final, fila_total_dec)
# Generar GT
TDF_Dec_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°1 de Distribución de Frecuencias de Curvatura de las Plantas Solares**")) %>%
tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
cols_align(align = "center", columns = everything()) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°1 de Distribución de Frecuencias de Curvatura de las Plantas Solares | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| -0.17 | -0.15 | -0.16 | 3 | 0.01 | 3 | 58978 | 0.01 | 100 |
| -0.15 | -0.12 | -0.13 | 9 | 0.02 | 12 | 58975 | 0.02 | 99.99 |
| -0.12 | -0.09 | -0.1 | 47 | 0.08 | 59 | 58966 | 0.1 | 99.98 |
| -0.09 | -0.06 | -0.08 | 194 | 0.33 | 253 | 58919 | 0.43 | 99.9 |
| -0.06 | -0.03 | -0.05 | 914 | 1.55 | 1167 | 58725 | 1.98 | 99.57 |
| -0.03 | -0.01 | -0.02 | 7952 | 13.48 | 9119 | 57811 | 15.46 | 98.02 |
| -0.01 | 0.02 | 0.01 | 47601 | 80.71 | 56720 | 49859 | 96.17 | 84.54 |
| 0.02 | 0.05 | 0.03 | 1672 | 2.83 | 58392 | 2258 | 99.01 | 3.83 |
| 0.05 | 0.08 | 0.06 | 409 | 0.69 | 58801 | 586 | 99.7 | 0.99 |
| 0.08 | 0.1 | 0.09 | 123 | 0.21 | 58924 | 177 | 99.91 | 0.3 |
| 0.1 | 0.13 | 0.12 | 41 | 0.07 | 58965 | 54 | 99.98 | 0.09 |
| 0.13 | 0.16 | 0.15 | 11 | 0.02 | 58976 | 13 | 100 | 0.02 |
| 0.16 | 0.19 | 0.17 | 1 | 0 | 58977 | 2 | 100 | 0 |
| 0.19 | 0.21 | 0.2 | 0 | 0 | 58977 | 1 | 100 | 0 |
| 0.21 | 0.24 | 0.23 | 0 | 0 | 58977 | 1 | 100 | 0 |
| 0.24 | 0.27 | 0.26 | 1 | 0 | 58978 | 1 | 100 | 0 |
| TOTAL | - | - | 58978 | 100 | - | - | - | - |
| Autor: Martin Sarmiento | ||||||||
3.2 Tabla con Límites Enteros
# Crear Dataframe
TDF_Int_Final <- data.frame(
Li = as.character(round(TDF_Enteros$Li, 2)),
Ls = as.character(round(TDF_Enteros$Ls, 2)),
MC = as.character(round(TDF_Enteros$MC, 2)),
ni = as.character(TDF_Enteros$ni),
hi = as.character(round(TDF_Enteros$hi, 2)),
Ni_asc = as.character(TDF_Enteros$Ni_asc),
Ni_desc = as.character(TDF_Enteros$Ni_desc),
Hi_asc = as.character(round(TDF_Enteros$Hi_asc, 2)),
Hi_desc = as.character(round(TDF_Enteros$Hi_desc, 2))
)
# Calcular Totales
total_ni_int <- sum(TDF_Enteros$ni)
total_hi_int <- round(sum(TDF_Enteros$hi), 2)
fila_total_int <- c("TOTAL", "-", "-", total_ni_int, total_hi_int, "-", "-", "-", "-")
TDF_Int_Final <- rbind(TDF_Int_Final, fila_total_int)
# Generar GT
TDF_Int_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°2 de Distribución de Frecuencias de Curvatura (Intervalos 0.02)**")) %>%
tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
cols_align(align = "center", columns = everything()) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°2 de Distribución de Frecuencias de Curvatura (Intervalos 0.02) | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| -0.2 | -0.1 | -0.15 | 38 | 0.06 | 38 | 58978 | 0.06 | 100 |
| -0.1 | 0 | -0.05 | 26488 | 44.91 | 26526 | 58940 | 44.98 | 99.94 |
| 0 | 0.1 | 0.05 | 32394 | 54.93 | 58920 | 32452 | 99.9 | 55.02 |
| 0.1 | 0.2 | 0.15 | 57 | 0.1 | 58977 | 58 | 100 | 0.1 |
| 0.2 | 0.3 | 0.25 | 1 | 0 | 58978 | 1 | 100 | 0 |
| TOTAL | - | - | 58978 | 100 | - | - | - | - |
| Autor: Martin Sarmiento | ||||||||
4 Análisis Gráfico
4.1 Histogramas de Cantidad
par(mar = c(8, 7, 5, 2))
barplot(TDF_Enteros$ni,
names.arg = round(TDF_Enteros$MC, 2),
main = "",
xlab = "",
ylab = "",
col = "#778899",
ylim = c(0, max(TDF_Enteros$ni) * 1.2),
space = 0,
las = 2,
cex.names = 0.7)
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Curvatura", side = 1, line = 4)
mtext("Gráfica N°1: Distribución de Cantidad de Plantas Solares por Curvatura",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
par(mar = c(8, 7, 5, 2))
barplot(TDF_Enteros$ni,
main = "",
xlab = "",
ylab = "",
names.arg = round(TDF_Enteros$MC, 2),
col = "#778899",
space = 0,
cex.names = 0.7,
las = 2,
ylim = c(0, 58978))
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Curvatura", side = 1, line = 4)
mtext("Gráfica N°2: Distribución de Cantidad de Plantas Solares por Curvatura",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
4.2 Histogramas Porcentuales
par(mar = c(8, 5, 5, 2))
bp3 <- barplot(TDF_Enteros$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#778899",
space = 0,
names.arg = round(TDF_Enteros$MC, 2),
cex.names = 0.7,
las = 2,
ylim = c(0, max(TDF_Enteros$hi) * 1.2))
mtext("Curvatura", side = 1, line = 4)
mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Curvatura",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
text(x = bp3,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 2), "%"),
pos = 3, cex = 0.6, col = "black")
par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#778899",
space = 0,
names.arg = round(TDF_Enteros$MC, 2),
las = 2,
cex.names = 0.7,
ylim = c(0, 100))
mtext("Curvatura", side = 1, line = 4)
mtext("Gráfica N°4: Distribución Porcentual de las Plantas Solares por Curvatura",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
text(x = bp4,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 2), "%"),
pos = 3, cex = 0.6, col = "black")
4.3 Diagrama de Cajas (Boxplot)
par(mar = c(5, 5, 4, 2))
boxplot(Variable,
horizontal = TRUE,
col = "#778899",
xlab = "Curvatura",
cex.main = 0.9,
main = "Gráfica N°5: Distribución de la Curvatura en las Plantas Solares")
4.4 Ojivas
par(mar = c(5, 5, 7, 10), xpd = TRUE)
# Coordenadas
x_asc <- TDF_Enteros$Ls
x_desc <- TDF_Enteros$Li
y_asc <- TDF_Enteros$Ni_asc
y_desc <- TDF_Enteros$Ni_desc
# 1. Dibujar la Ascendente
plot(x_asc, y_asc,
type = "b",
main = "",
xlab = "Curvatura",
ylab = "Frecuencia acumulada",
col = "black",
pch = 19,
xlim = c(min(TDF_Enteros$Li), max(x_asc)),
ylim = c(0, sum(TDF_Enteros$ni)),
bty = "l"
)
# 2. Agregar la Descendente
lines(x_desc, y_desc, col = "#A8A8A8", type = "b", pch = 19)
grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Curvatura en las Plantas Solares",
side = 3,
line = 3,
adj = 0.5,
cex = 0.9,
font = 2)
legend("left",
legend = c("Ascendente", "Descendente"),
col = c("black", "#A8A8A8"),
lty = 1,
pch = 1,
cex = 0.6,
inset = c(0.05, 0.05),
bty = "n")
5 Indicadores Estadísticos
## INDICADORES DE TENDENCIA CENTRAL
# Media aritmética
media <- round(mean(Variable), 2)
# Mediana
mediana <- round(median(Variable), 2)
# Moda
max_frecuencia <- max(TDF_Enteros$ni)
moda_vals <- TDF_Enteros$MC[TDF_Enteros$ni == max_frecuencia]
moda_txt <- paste(round(moda_vals, 2), collapse = ", ")
## INDICADORES DE DISPERSIÓN
# Varianza
varianza <- var(Variable)
# Desviación Estándar
sd_val <- sd(Variable)
# Coeficiente de Variación
cv <- round((sd_val / abs(media)) * 100, 2)
## INDICADORES DE FORMA
# Coeficiente de Asimetría
asimetria <- skewness(Variable, type = 2)
# Curtosis
curtosis <- kurtosis(Variable)
# Outliers
Q1 <- quantile(Variable, 0.25)
Q3 <- quantile(Variable, 0.75)
IQR_val <- Q3 - Q1
lim_inf <- Q1 - 1.5 * IQR_val
lim_sup <- Q3 + 1.5 * IQR_val
outliers_data <- Variable[Variable < lim_inf | Variable > lim_sup]
num_outliers <- length(outliers_data)
if(num_outliers > 0){
rango_outliers <- paste0(num_outliers, " [", round(min(outliers_data), 2), "; ", round(max(outliers_data), 2), "]")
} else {
rango_outliers <- "0 [Sin Outliers]"
}
tabla_indicadores <- data.frame(
"Variable" = c("Curvatura"),
"Rango_MinMax" = paste0("[", round(min(Variable), 2), "; ", round(max(Variable), 2), "]"),
"X" = c(media),
"Me" = c(mediana),
"Mo" = c(moda_txt),
"V" = c(varianza),
"Sd" = c(sd_val),
"Cv" = c(cv),
"As" = c(asimetria),
"K" = c(curtosis),
"Outliers" = rango_outliers)
# Generar Tabla GT
tabla_conclusiones_gt <- tabla_indicadores %>%
gt() %>%
tab_header(title = md("**Tabla N°3 de Conclusiones de Curvatura de las Plantas Solares**")) %>%
tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
cols_label(
Variable = "Variable",
Rango_MinMax = "Rango",
X = "Media (X)",
Me = "Mediana (Me)",
Mo = "Moda (Mo)",
V = "Varianza (V)",
Sd = "Desv. Est. (Sd)",
Cv = "C.V. (%)",
As = "Asimetría (As)",
K = "Curtosis (K)",
Outliers = "Outliers [Intervalo]"
) %>%
tab_options(
heading.title.font.size = px(16),
column_labels.background.color = "#F0F0F0"
)
tabla_conclusiones_gt| Tabla N°3 de Conclusiones de Curvatura de las Plantas Solares | ||||||||||
| Variable | Rango | Media (X) | Mediana (Me) | Moda (Mo) | Varianza (V) | Desv. Est. (Sd) | C.V. (%) | Asimetría (As) | Curtosis (K) | Outliers [Intervalo] |
|---|---|---|---|---|---|---|---|---|---|---|
| Curvatura | [-0.17; 0.27] | 0 | 0 | 0.05 | 0.0001966899 | 0.01402462 | Inf | 0.5474426 | 21.23696 | 11174 [-0.17; 0.27] |
| Autor: Martin Sarmiento | ||||||||||
6 Conclusiones
La variable “Curvatura” fluctúa entre -0.17 y 0.27 y sus valores se encuentran alrededor de 0, con una desviación estándar de 0.01402462, siendo una variable muy heterogénea, cuyos valores se concentran en la parte media baja de la variable con la agregación de valores atípicos de 11174 outliers; por todo lo anterior, el comportamiento de la variable es muy perjudicial.