Transporte de petróleo mediante oleoductos en Ecuador
Variable: Pérdida estimada (%) (cuantitativa continua)
*
2026-11-14
1 Carga de librerias
library(readxl)
library(dplyr)
library(gt)
library(e1071)2 Carga de datos
setwd("C:/Users/HP/Desktop/tabla_petro")
archivo <- list.files(pattern = "^tabla_transporte_petroleo.*\\.xlsx$")[1]
if (is.na(archivo)) stop("No se encontró el archivo .xlsx dentro de la carpeta tabla_petro")
datos <- as.data.frame(read_excel(archivo, sheet = "Datos_10000"))
dim(datos)## [1] 10000 203 Selección de la variable
Variable <- as.numeric(na.omit(datos$Perdida_estimada_pct))
if (length(Variable) == 0) {
stop("ERROR: No hay datos válidos para la variable seleccionada.")
}4 Frecuencia
Se agrupan los datos en K clases con la regla de Sturges.
N <- length(Variable)
K <- floor(1 + 3.322 * log10(N))
breaks_table <- seq(min(Variable), max(Variable), length.out = K + 1)
ni <- as.vector(table(cut(Variable, breaks = breaks_table, include.lowest = TRUE, right = FALSE)))
hi <- (ni / sum(ni)) * 100
Ni_asc <- cumsum(ni)
Ni_desc <- rev(cumsum(rev(ni)))
Hi_asc <- cumsum(hi)
Hi_desc <- rev(cumsum(rev(hi)))5 Tabla de Distribución de Frecuencia
A continuación se presenta la tabla de distribución de frecuencias obtenida.
5.1 Tabla General
TDF_General <- data.frame(
Li = round(breaks_table[1:K], 4),
Ls = round(breaks_table[2:(K + 1)], 4),
MC = round((breaks_table[1:K] + breaks_table[2:(K + 1)]) / 2, 4),
ni = ni,
hi = hi,
Ni_asc = Ni_asc,
Ni_desc = Ni_desc,
Hi_asc = Hi_asc,
Hi_desc = Hi_desc
)
TDF_General %>%
gt(rowname_col = "Li") %>%
tab_header(
title = md("**DISTRIBUCIÓN DE FRECUENCIAS: Pérdida estimada (%)**"),
subtitle = md("Variable: **Pérdida estimada**")
) %>%
tab_source_note(source_note = "Autor: *") %>%
grand_summary_rows(
columns = c(ni, hi),
fns = list("TOTAL" = ~sum(., na.rm = TRUE))
) %>%
fmt_number(
columns = c(ni, Ni_asc, Ni_desc),
decimals = 0,
use_seps = TRUE
) %>%
fmt_number(
columns = c(hi, Hi_asc, Hi_desc),
decimals = 2
) %>%
cols_label(
Ls = "Lím. Sup", MC = "Marca Clase (Xi)",
ni = "ni", hi = "hi (%)",
Ni_asc = "Ni (Asc)", Ni_desc = "Ni (Desc)",
Hi_asc = "Hi (Asc)", Hi_desc = "Hi (Desc)"
) %>%
tab_stubhead(label = "Lím. Inf") %>%
cols_align(align = "center", columns = everything()) %>%
tab_style(
style = cell_text(align = "center"),
locations = cells_stub()
) %>%
tab_style(
style = list(cell_fill(color = "#235347"), cell_text(color = "white", weight = "bold")),
locations = list(cells_title(), cells_column_labels(), cells_stubhead())
) %>%
tab_options(
table.border.top.style = "none",
table.border.bottom.color = "#235347",
column_labels.border.bottom.color = "#235347",
data_row.padding = px(6)
)| DISTRIBUCIÓN DE FRECUENCIAS: Pérdida estimada (%) | ||||||||
| Variable: Pérdida estimada | ||||||||
| Lím. Inf | Lím. Sup | Marca Clase (Xi) | ni | hi (%) | Ni (Asc) | Ni (Desc) | Hi (Asc) | Hi (Desc) |
|---|---|---|---|---|---|---|---|---|
| 0.0050 | 0.0196 | 0.0123 | 421 | 4.21 | 421 | 10,000 | 4.21 | 100.00 |
| 0.0196 | 0.0342 | 0.0269 | 531 | 5.31 | 952 | 9,579 | 9.52 | 95.79 |
| 0.0342 | 0.0488 | 0.0415 | 917 | 9.17 | 1,869 | 9,048 | 18.69 | 90.48 |
| 0.0488 | 0.0634 | 0.0561 | 1,296 | 12.96 | 3,165 | 8,131 | 31.65 | 81.31 |
| 0.0634 | 0.0780 | 0.0707 | 1,614 | 16.14 | 4,779 | 6,835 | 47.79 | 68.35 |
| 0.0780 | 0.0926 | 0.0853 | 1,563 | 15.63 | 6,342 | 5,221 | 63.42 | 52.21 |
| 0.0926 | 0.1072 | 0.0999 | 1,423 | 14.23 | 7,765 | 3,658 | 77.65 | 36.58 |
| 0.1072 | 0.1219 | 0.1146 | 1,066 | 10.66 | 8,831 | 2,235 | 88.31 | 22.35 |
| 0.1219 | 0.1365 | 0.1292 | 611 | 6.11 | 9,442 | 1,169 | 94.42 | 11.69 |
| 0.1365 | 0.1511 | 0.1438 | 332 | 3.32 | 9,774 | 558 | 97.74 | 5.58 |
| 0.1511 | 0.1657 | 0.1584 | 149 | 1.49 | 9,923 | 226 | 99.23 | 2.26 |
| 0.1657 | 0.1803 | 0.1730 | 53 | 0.53 | 9,976 | 77 | 99.76 | 0.77 |
| 0.1803 | 0.1949 | 0.1876 | 19 | 0.19 | 9,995 | 24 | 99.95 | 0.24 |
| 0.1949 | 0.2095 | 0.2022 | 5 | 0.05 | 10,000 | 5 | 100.00 | 0.05 |
| TOTAL | — | — | 10000 | 100 | — | — | — | — |
| Autor: * | ||||||||
5.2 Tabla Simplificada
Se redefinen las clases con límites redondeados y una amplitud constante.
breaks_table <- pretty(Variable, n = K)
amplitud <- breaks_table[2] - breaks_table[1]
K <- length(breaks_table) - 1
ni <- as.vector(table(cut(Variable, breaks = breaks_table, include.lowest = TRUE, right = FALSE)))
hi <- (ni / sum(ni)) * 100
Ni_asc <- cumsum(ni)
Ni_desc <- rev(cumsum(rev(ni)))
Hi_asc <- cumsum(hi)
Hi_desc <- rev(cumsum(rev(hi)))
TDF_Simple <- data.frame(
Li = round(breaks_table[1:K], 4),
Ls = round(breaks_table[2:(K + 1)], 4),
MC = round((breaks_table[1:K] + breaks_table[2:(K + 1)]) / 2, 4),
ni = ni,
hi = hi,
Ni_asc = Ni_asc,
Ni_desc = Ni_desc,
Hi_asc = Hi_asc,
Hi_desc = Hi_desc
)
TDF_Simple %>%
gt(rowname_col = "Li") %>%
tab_header(
title = md("**DISTRIBUCIÓN DE FRECUENCIAS SIMPLIFICADA: Pérdida estimada (%)**"),
subtitle = md(paste0("Variable: **Pérdida estimada** (Amplitud = ", round(amplitud, 4), ")"))
) %>%
tab_source_note(source_note = "Autor: *") %>%
grand_summary_rows(
columns = c(ni, hi),
fns = list("TOTAL" = ~sum(., na.rm = TRUE))
) %>%
fmt_number(
columns = c(ni, Ni_asc, Ni_desc),
decimals = 0,
use_seps = TRUE
) %>%
fmt_number(
columns = c(hi, Hi_asc, Hi_desc),
decimals = 2
) %>%
cols_label(
Ls = "Lím. Sup", MC = "Marca Clase (Xi)",
ni = "ni", hi = "hi (%)",
Ni_asc = "Ni (Asc)", Ni_desc = "Ni (Desc)",
Hi_asc = "Hi (Asc)", Hi_desc = "Hi (Desc)"
) %>%
tab_stubhead(label = "Lím. Inf") %>%
cols_align(align = "center", columns = everything()) %>%
tab_style(
style = cell_text(align = "center"),
locations = cells_stub()
) %>%
tab_style(
style = list(cell_fill(color = "#235347"), cell_text(color = "white", weight = "bold")),
locations = list(cells_title(), cells_column_labels(), cells_stubhead())
) %>%
tab_options(
table.border.top.style = "none",
table.border.bottom.color = "#235347",
column_labels.border.bottom.color = "#235347",
data_row.padding = px(6)
)| DISTRIBUCIÓN DE FRECUENCIAS SIMPLIFICADA: Pérdida estimada (%) | ||||||||
| Variable: Pérdida estimada (Amplitud = 0.02) | ||||||||
| Lím. Inf | Lím. Sup | Marca Clase (Xi) | ni | hi (%) | Ni (Asc) | Ni (Desc) | Hi (Asc) | Hi (Desc) |
|---|---|---|---|---|---|---|---|---|
| 0.00 | 0.02 | 0.01 | 430 | 4.30 | 430 | 10,000 | 4.30 | 100.00 |
| 0.02 | 0.04 | 0.03 | 824 | 8.24 | 1,254 | 9,570 | 12.54 | 95.70 |
| 0.04 | 0.06 | 0.05 | 1,557 | 15.57 | 2,811 | 8,746 | 28.11 | 87.46 |
| 0.06 | 0.08 | 0.07 | 2,192 | 21.92 | 5,003 | 7,189 | 50.03 | 71.89 |
| 0.08 | 0.10 | 0.09 | 2,096 | 20.96 | 7,099 | 4,997 | 70.99 | 49.97 |
| 0.10 | 0.12 | 0.11 | 1,616 | 16.16 | 8,715 | 2,901 | 87.15 | 29.01 |
| 0.12 | 0.14 | 0.13 | 811 | 8.11 | 9,526 | 1,285 | 95.26 | 12.85 |
| 0.14 | 0.16 | 0.15 | 357 | 3.57 | 9,883 | 474 | 98.83 | 4.74 |
| 0.16 | 0.18 | 0.17 | 92 | 0.92 | 9,975 | 117 | 99.75 | 1.17 |
| 0.18 | 0.20 | 0.19 | 21 | 0.21 | 9,996 | 25 | 99.96 | 0.25 |
| 0.20 | 0.22 | 0.21 | 4 | 0.04 | 10,000 | 4 | 100.00 | 0.04 |
| TOTAL | — | — | 10000 | 100 | — | — | — | — |
| Autor: * | ||||||||
6 Gráficas De Distribución De Frecuencias
Esta sección presenta la visualización de la distribución de los datos.
6.1 Histogramas de Frecuencia
col_barras <- "#235347"
col_ejes <- "#163832"
col_claro <- "#8EB69B"
h_base <- hist(Variable, breaks = breaks_table, right = FALSE, include.lowest = TRUE, plot = FALSE)
limite_x <- range(breaks_table)
etiquetas_x <- format(breaks_table, scientific = FALSE, trim = TRUE)6.2 GRÁFICO 1: Histograma Absoluto (Local)
par(mar = c(8, 5, 4, 2))
plot(h_base,
main = "Gráfica N°1: Distribución de Pérdida estimada",
xlab = "Pérdida estimada (%)", ylab = "Frecuencia absoluta",
col = col_barras, border = "white", axes = FALSE,
ylim = c(0, max(h_base$counts) * 1.1),
xlim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
axis(2)
grid(nx = NA, ny = NULL, col = "#D7DBDD", lty = "dotted")
6.3 GRÁFICO 2: Histograma Absoluto (Global)
par(mar = c(8, 5, 4, 2))
plot(h_base,
main = "Gráfica N°2: Distribución de Pérdida estimada",
xlab = "Pérdida estimada (%)", ylab = "Total registros",
col = col_barras, border = "white", axes = FALSE,
ylim = c(0, sum(h_base$counts)),
xlim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
axis(2)
grid(nx = NA, ny = NULL, col = "#D7DBDD", lty = "dotted")
6.4 Gráficos Porcentuales
h_porc <- h_base
h_porc$counts <- (h_porc$counts / sum(h_porc$counts)) * 1006.5 GRÁFICO 3: Porcentajes (Local)
par(mar = c(8, 5, 4, 2))
plot(h_porc,
main = "Gráfica N°3: Distribución porcentual de Pérdida estimada",
xlab = "Pérdida estimada (%)", ylab = "Porcentaje (%)",
col = col_barras, border = "white", axes = FALSE, freq = TRUE,
ylim = c(0, max(h_porc$counts) * 1.2),
xlim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
axis(2)
text(x = h_base$mids, y = h_porc$counts,
labels = paste0(round(h_porc$counts, 1), "%"),
pos = 3, cex = 0.6, col = col_ejes)
6.6 GRÁFICO 4: Porcentajes (Global)
par(mar = c(8, 5, 4, 2))
plot(h_porc,
main = "Gráfica N°4: Distribución porcentual de Pérdida estimada",
xlab = "Pérdida estimada (%)", ylab = "% del total",
col = col_barras, border = "white", axes = FALSE, freq = TRUE,
ylim = c(0, 100),
xlim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
axis(2)
text(x = h_base$mids, y = h_porc$counts,
labels = paste0(round(h_porc$counts, 1), "%"),
pos = 3, cex = 0.6, col = col_ejes)
6.7 GRÁFICO 5: Boxplot
par(mar = c(8, 5, 4, 2))
boxplot(Variable, horizontal = TRUE, col = col_barras,
main = "Gráfica N°5: Diagrama de caja de Pérdida estimada",
xlab = "Pérdida estimada (%)", outline = TRUE, outpch = 19,
outcol = col_claro, axes = FALSE, xlim = c(0.7, 1.3),
ylim = limite_x, cex.main = 1)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.7)
box()
6.8 GRÁFICO 6: Ojivas
par(mar = c(8, 5, 4, 8), xpd = TRUE)
plot(breaks_table, c(0, Ni_asc), type = "o", col = col_barras,
lwd = 2, pch = 19, axes = FALSE,
main = "Gráfica N°6: Ojivas ascendente y descendente de Pérdida estimada",
xlab = "Pérdida estimada (%)", ylab = "Frecuencia acumulada", cex.main = 1)
lines(breaks_table, c(Ni_desc, 0), type = "o", col = col_claro,
lwd = 2, pch = 19)
axis(1, at = breaks_table, labels = etiquetas_x, las = 2, cex.axis = 0.6)
axis(2)
legend("right", legend = c("Ascendente", "Descendente"),
col = c(col_barras, col_claro),
lty = 1, pch = 19, cex = 0.7, lwd = 2,
inset = c(-0.2, 0), bty = "n")
par(xpd = FALSE)7 Indicadores Estadísticos
media_val <- mean(Variable)
mediana_val <- median(Variable)
sd_val <- sd(Variable)
cv_val <- (sd_val / abs(media_val)) * 100
asimetria_val <- skewness(Variable, type = 2)
curtosis_val <- kurtosis(Variable, type = 2)
atipicos <- boxplot.stats(Variable)$out
status_atipicos <- if (length(atipicos) > 0) {
paste0(length(atipicos), " [ ", round(min(atipicos), 4), " ; ", round(max(atipicos), 4), " ]")
} else {
"0 (Sin atípicos)"
}
df_resumen <- data.frame(
Variable = "Pérdida estimada",
Rango = paste0("[", round(min(Variable), 4), " ; ", round(max(Variable), 4), "]"),
X = media_val,
Me = mediana_val,
Mo = paste(round(TDF_Simple$MC[TDF_Simple$hi == max(TDF_Simple$hi)], 4), collapse = ", "),
Varianza = var(Variable),
sd = sd_val,
CV = cv_val,
As = asimetria_val,
K = curtosis_val,
Atipicos = status_atipicos
)
df_resumen %>%
gt() %>%
tab_header(title = md("**CONCLUSIONES Y ESTADÍSTICOS**"), subtitle = "Variable: Pérdida estimada") %>%
tab_source_note(source_note = "Autor: *") %>%
cols_label(
X = "X",
Me = "Me",
Mo = "Mo",
sd = "sd",
CV = "CV",
As = "As",
K = "K",
Atipicos = "Valores atípicos"
) %>%
fmt_number(columns = c(X, Me, sd), decimals = 4) %>%
fmt_number(columns = Varianza, decimals = 6) %>%
fmt_number(columns = c(CV, K), decimals = 2) %>%
fmt_number(columns = As, decimals = 4) %>%
cols_width(
Variable ~ px(140),
Rango ~ px(150),
Mo ~ px(100),
Atipicos ~ px(220),
everything() ~ px(85)
) %>%
tab_options(
column_labels.background.color = "#235347",
table.border.top.style = "solid",
table.border.bottom.style = "solid",
heading.border.bottom.style = "solid",
column_labels.border.top.style = "solid",
column_labels.border.bottom.style = "solid",
data_row.padding = px(8)
) %>%
tab_style(
style = list(
cell_text(weight = "bold", color = "white"),
cell_borders(sides = c("left", "right"), color = "#D3D3D3", weight = px(1))
),
locations = cells_column_labels()
) %>%
tab_style(
style = cell_borders(sides = c("left", "right"), color = "#D3D3D3", weight = px(1)),
locations = cells_body()
)| CONCLUSIONES Y ESTADÍSTICOS | ||||||||||
| Variable: Pérdida estimada | ||||||||||
| Variable | Rango | X | Me | Mo | Varianza | sd | CV | As | K | Valores atípicos |
|---|---|---|---|---|---|---|---|---|---|---|
| Pérdida estimada | [0.005 ; 0.2095] | 0.0805 | 0.0799 | 0.07 | 0.001209 | 0.0348 | 43.20 | 0.1005 | −0.21 | 36 [ 0.1765 ; 0.2095 ] |
| Autor: * | ||||||||||
txt_cv <- if (cv_val < 15) "homogéneo" else if (cv_val <= 30) "moderadamente heterogéneo" else "heterogéneo"
txt_ubic <- if (asimetria_val > 0.5) "se agrupan en la parte baja de la variable" else if (asimetria_val < -0.5) "se agrupan en la parte alta de la variable" else "se reparten de forma equilibrada alrededor de la media"
txt_asim <- if (abs(asimetria_val) < 0.5) "aproximadamente simétrica" else if (asimetria_val > 0) "asimétrica positiva (sesgo a la derecha)" else "asimétrica negativa (sesgo a la izquierda)"
txt_curt <- if (abs(curtosis_val) < 0.5) "mesocúrtica (similar a la normal)" else if (curtosis_val > 0) "leptocúrtica (más concentrada y con colas más pesadas)" else "platicúrtica (más aplanada)"
txt_atip <- if (length(atipicos) > 0) {
paste0("Se identificaron ", length(atipicos), " valores atípicos, en el rango de ", round(min(atipicos), 4), " a ", round(max(atipicos), 4), ".")
} else {
"No se identificaron valores atípicos."
}8 Conclusiones
Los valores de Pérdida estimada fluctúan entre 0.005 y 0.2095 y giran en torno a la media de 0.0805 (mediana de 0.0799), con una desviación estándar de 0.0348. Con un coeficiente de variación de 43.2 %, el conjunto de datos es heterogéneo y sus valores se reparten de forma equilibrada alrededor de la media. La distribución es aproximadamente simétrica (As = 0.1005) y mesocúrtica (similar a la normal) (K = -0.21). Se identificaron 36 valores atípicos, en el rango de 0.1765 a 0.2095.