1. CARGA DE DATOS Y LIBRERÍAS

# ==========================================
# Carga de librerías
# ==========================================

library(dplyr)
library(readxl)
library(gt)


# ==========================================
# Carga de la base de datos
# ==========================================

datos <- read_excel(
  
  "datos_deslizamientos.xlsx"

)


# ==========================================
# Visualización inicial de la base de datos
# ==========================================

str(datos)

## tibble [11,033 × 31] (S3: tbl_df/tbl/data.frame)
##  $ source_name              : chr [1:11033] "AGU" "Oregonian" "CBS News" "Reuters" ...
##  $ source_link              : chr [1:11033] "https://blogs.agu.org/landslideblog/2008/10/14/the-lifan-landslide-from-natural-disaster-to-cover-up/" "http://www.oregonlive.com/news/index.ssf/2009/01/landslide_plows_through_lake_o.html" "https://www.cbsnews.com/news/dozens-missing-after-peru-landslides/" "https://in.reuters.com/article/idINIndia-41450420090731" ...
##  $ event_id                 : num [1:11033] 684 956 973 1067 2603 ...
##  $ event_date               : POSIXct[1:11033], format: "2008-08-01" "2008-08-02" ...
##  $ HORA                     : chr [1:11033] "00:00:00" "02:00:00" "00:00:00" "00:00:00" ...
##  $ event_title              : chr [1:11033] "Sigou Village, Loufan County, Shanxi Province" "Lake Oswego, Oregon" "San Ramon district, 195 miles northeast of the capital, Lima," "Dailekh district" ...
##  $ event_description        : chr [1:11033] "occurred early in morning, 11 villagers buried in 7 houses" "Hours of heavy rain are to blame for an overnight mudslide in Lake Oswego." "(CBS/AP) At least 10 people died and as many as 80 were still missing Wednesday in central Peru after torrentia"| __truncated__ "One person was killed in Dailekh district, police said." ...
##  $ location_description     : chr [1:11033] "Sigou Village, Loufan County, Shanxi Province" "Lake Oswego, Oregon" "San Ramon district, 195 miles northeast of the capital, Lima," "Dailekh district" ...
##  $ location_accuracy        : chr [1:11033] "unknown" "5km" "10km" "unknown" ...
##  $ landslide_category       : chr [1:11033] "landslide" "mudslide" "landslide" "landslide" ...
##  $ landslide_trigger        : chr [1:11033] "rain" "downpour" "downpour" "monsoon" ...
##  $ landslide_size           : chr [1:11033] "large" "small" "large" "medium" ...
##  $ landslide_setting        : chr [1:11033] "mine" "unknown" "unknown" "unknown" ...
##  $ fatality_count           : num [1:11033] 11 0 10 1 0 0 0 3 NA 2 ...
##  $ injury_count             : num [1:11033] NA NA NA NA NA NA NA NA NA NA ...
##  $ storm_name               : chr [1:11033] NA NA NA NA ...
##  $ photo_link               : chr [1:11033] NA NA NA NA ...
##  $ notes                    : chr [1:11033] NA NA NA NA ...
##  $ event_import_source      : chr [1:11033] "glc" "glc" "glc" "glc" ...
##  $ event_import_id          : num [1:11033] 684 956 973 1067 2603 ...
##  $ country_name             : chr [1:11033] "China" "United States" "Peru" "Nepal" ...
##  $ country_code             : chr [1:11033] "CN" "US" "PE" "NP" ...
##  $ admin_division_name      : chr [1:11033] "Shaanxi" "Oregon" "Junín" "Mid Western" ...
##  $ admin_division_population: num [1:11033] 0 36619 14708 20908 798634 ...
##  $ gazeteer_closest_point   : chr [1:11033] "Jingyang" "Lake Oswego" "San Ramón" "Dailekh" ...
##  $ gazeteer_distance        : num [1:11033] 41.021 0.603 0.855 0.754 2.022 ...
##  $ submitted_date           : POSIXct[1:11033], format: "2014-04-01 00:00:00" "2014-04-01 00:00:00" ...
##  $ created_date             : POSIXct[1:11033], format: "2017-11-20 15:17:00" "2017-11-20 15:17:00" ...
##  $ last_edited_date         : POSIXct[1:11033], format: "2018-02-15 15:51:00" "2018-02-15 15:51:00" ...
##  $ longitude                : num [1:11033] 107.5 -122.7 -75.4 81.7 123.9 ...
##  $ latitude                 : num [1:11033] 32.6 45.4 -11.1 28.8 10.3 ...

# ==========================================
# Visualización de las primeras filas
# ==========================================

head(datos)

## # A tibble: 6 × 31
##   source_name         source_link event_id event_date          HORA  event_title
##   <chr>               <chr>          <dbl> <dttm>              <chr> <chr>      
## 1 AGU                 https://bl…      684 2008-08-01 00:00:00 00:0… Sigou Vill…
## 2 Oregonian           http://www…      956 2008-08-02 00:00:00 02:0… Lake Osweg…
## 3 CBS News            https://ww…      973 2008-08-03 00:00:00 00:0… San Ramon …
## 4 Reuters             https://in…     1067 2008-08-04 00:00:00 00:0… Dailekh di…
## 5 The Freeman         http://www…     2603 2008-08-05 00:00:00 12:0… sitio Baki…
## 6 BusinessWorld Onli… http://www…     4203 2008-08-06 00:00:00 00:0… Paguite, A…
## # ℹ 25 more variables: event_description <chr>, location_description <chr>,
## #   location_accuracy <chr>, landslide_category <chr>, landslide_trigger <chr>,
## #   landslide_size <chr>, landslide_setting <chr>, fatality_count <dbl>,
## #   injury_count <dbl>, storm_name <chr>, photo_link <chr>, notes <chr>,
## #   event_import_source <chr>, event_import_id <dbl>, country_name <chr>,
## #   country_code <chr>, admin_division_name <chr>,
## #   admin_division_population <dbl>, gazeteer_closest_point <chr>, …

2. PREPARACIÓN DE LA VARIABLE

2.1 Definición del orden de las categorías

# ==========================================
# Definición del orden ordinal
# ==========================================

orden_size <- c(

  "small",

  "medium",

  "large",

  "very_large"

)


orden_size

## [1] "small"      "medium"     "large"      "very_large"

2.2 Conversión de la variable a factor ordenado

# ==========================================
# Conversión a factor ordinal
# ==========================================

datos <- datos %>%

  mutate(

    landslide_size = factor(

      landslide_size,

      levels = orden_size,

      ordered = TRUE

    )

  )


# Verificación de la estructura ordinal

str(datos$landslide_size)

##  Ord.factor w/ 4 levels "small"<"medium"<..: 3 1 3 2 2 2 1 2 2 2 ...

2.3 Extracción de la variable de análisis

# ==========================================
# Selección de la variable ordinal
# ==========================================

variable_ordinal <- datos$landslide_size


head(variable_ordinal)

## [1] large  small  large  medium medium medium
## Levels: small < medium < large < very_large

2.4 Eliminación de valores faltantes

# ==========================================
# Identificación de valores faltantes
# ==========================================

NA_antes <- sum(is.na(variable_ordinal))


NA_antes

## [1] 863

# ==========================================
# Eliminación de valores NA
# ==========================================

variable_ordinal <- variable_ordinal[
  
  !is.na(variable_ordinal)

]


# ==========================================
# Verificación posterior
# ==========================================

NA_despues <- sum(is.na(variable_ordinal))


NA_despues

## [1] 0

2.5 Tamaño de la muestra

# ==========================================
# Número total de observaciones válidas
# ==========================================

n <- length(variable_ordinal)


n

## [1] 10170

3. DISTRIBUCIÓN DE PROBABILIDAD

3.1 Frecuencia absoluta

# ==========================================
# Frecuencia absoluta de cada categoría
# ==========================================

frecuencia_absoluta <- table(

  variable_ordinal

)


frecuencia_absoluta

## variable_ordinal
##      small     medium      large very_large 
##       2767       6551        750        102

3.2 Probabilidad simple

# ==========================================
# Probabilidad simple
# ==========================================

probabilidad_simple <- prop.table(

  frecuencia_absoluta

)


probabilidad_simple

## variable_ordinal
##      small     medium      large very_large 
## 0.27207473 0.64414946 0.07374631 0.01002950

# ==========================================
# Probabilidad porcentual
# ==========================================

probabilidad_porcentaje <- probabilidad_simple * 100


probabilidad_porcentaje

## variable_ordinal
##      small     medium      large very_large 
##  27.207473  64.414946   7.374631   1.002950

3.3 Construcción de la distribución de probabilidad

# ==========================================
# Tabla de distribución de probabilidad
# ==========================================

tabla_distribucion <- data.frame(

  Categoria = names(frecuencia_absoluta),

  ni = as.numeric(frecuencia_absoluta),

  hi = as.numeric(probabilidad_simple),

  P = as.numeric(probabilidad_porcentaje)

)


tabla_distribucion

##    Categoria   ni         hi         P
## 1      small 2767 0.27207473 27.207473
## 2     medium 6551 0.64414946 64.414946
## 3      large  750 0.07374631  7.374631
## 4 very_large  102 0.01002950  1.002950

3.4 Probabilidad acumulada

# ==========================================
# Frecuencia acumulada
# ==========================================

tabla_distribucion$Ni <- cumsum(

  tabla_distribucion$ni

)


# ==========================================
# Probabilidad acumulada
# ==========================================

tabla_distribucion$Hi <- cumsum(

  tabla_distribucion$hi

)


# ==========================================
# Probabilidad acumulada porcentual
# ==========================================

tabla_distribucion$P_acumulada <- tabla_distribucion$Hi * 100



tabla_distribucion

##    Categoria   ni         hi         P    Ni        Hi P_acumulada
## 1      small 2767 0.27207473 27.207473  2767 0.2720747    27.20747
## 2     medium 6551 0.64414946 64.414946  9318 0.9162242    91.62242
## 3      large  750 0.07374631  7.374631 10068 0.9899705    98.99705
## 4 very_large  102 0.01002950  1.002950 10170 1.0000000   100.00000

4. TABLA DE DISTRIBUCIÓN DE PROBABILIDAD

4.1 Tabla simple de distribución

# ==========================================
# Creación de la fila total
# ==========================================

fila_total <- data.frame(

  Categoria = "TOTAL",

  ni = sum(tabla_distribucion$ni),

  hi = sum(tabla_distribucion$hi),

  P = sum(tabla_distribucion$P),

  Ni = NA,

  Hi = NA,

  P_acumulada = NA

)



# ==========================================
# Tabla completa con total incluido
# ==========================================

tabla_distribucion_total <- rbind(

  tabla_distribucion,

  fila_total

)



tabla_distribucion_total

##    Categoria    ni         hi          P    Ni        Hi P_acumulada
## 1      small  2767 0.27207473  27.207473  2767 0.2720747    27.20747
## 2     medium  6551 0.64414946  64.414946  9318 0.9162242    91.62242
## 3      large   750 0.07374631   7.374631 10068 0.9899705    98.99705
## 4 very_large   102 0.01002950   1.002950 10170 1.0000000   100.00000
## 5      TOTAL 10170 1.00000000 100.000000    NA        NA          NA

4.2 Tabla de presentación

# ==========================================
# Diseño de la tabla final
# ==========================================

tabla_presentacion <- tabla_distribucion_total %>%

  gt() %>%

  tab_header(

    title = md("**Tabla N° 1**"),

    subtitle = md(
      "Distribución de probabilidad del tamaño de los deslizamientos a nivel mundial"
    )

  ) %>%

  cols_label(

    Categoria = "Tamaño del deslizamiento",

    ni = "Frecuencia absoluta (ni)",

    hi = "Probabilidad (hi)",

    P = "Probabilidad (%)",

    Ni = "Frecuencia acumulada (Ni)",

    Hi = "Probabilidad acumulada (Hi)",

    P_acumulada = "Probabilidad acumulada (%)"

  ) %>%

  fmt_number(

    columns = c(hi, Hi),

    decimals = 4

  ) %>%

  fmt_number(

    columns = c(P, P_acumulada),

    decimals = 2

  ) %>%

  tab_style(

    style = list(

      cell_fill(color = "#6D213C"),

      cell_text(

        color = "white",

        weight = "bold"

      )

    ),

    locations = cells_column_labels()

  ) %>%

  tab_style(

    style = cell_text(

      weight = "bold"

    ),

    locations = cells_body(

      rows = Categoria == "TOTAL"

    )

  ) %>%

  tab_source_note(

    source_note = md(
      "Autor: Grupo 1 – Carrera de Geología"
    )

  )


tabla_presentacion

Tamaño del deslizamiento	Frecuencia absoluta (ni)	Probabilidad (hi)	Probabilidad (%)	Frecuencia acumulada (Ni)	Probabilidad acumulada (Hi)	Probabilidad acumulada (%)
Tabla N° 1
Distribución de probabilidad del tamaño de los deslizamientos a nivel mundial
small	2767	0.2721	27.21	2767	0.2721	27.21
medium	6551	0.6441	64.41	9318	0.9162	91.62
large	750	0.0737	7.37	10068	0.9900	99.00
very_large	102	0.0100	1.00	10170	1.0000	100.00
TOTAL	10170	1.0000	100.00	NA	NA	NA
Autor: Grupo 1 – Carrera de Geología

5. GRÁFICAS DE LA DISTRIBUCIÓN DE PROBABILIDAD

5.1 Distribución de probabilidad

# ==========================================
# Preparación del gráfico
# ==========================================

par(

  mar = c(8,5,4,2)

)



pos_x <- barplot(

  tabla_distribucion$P,

  names.arg = tabla_distribucion$Categoria,

  col = "steelblue",

  border = "black",

  space = 0.20,

  ylim = c(0,100),

  las = 1,

  yaxt = "n",

  main = "Gráfica N° 1. Distribución de probabilidad\n del tamaño de los deslizamientos",

  xlab = "Tamaño del deslizamiento",

  ylab = "Probabilidad (%)"

)



# ==========================================
# Escala del eje Y
# ==========================================

ticks_y <- seq(

  0,

  100,

  20

)



axis(

  side = 2,

  at = ticks_y,

  labels = ticks_y,

  las = 1

)



# ==========================================
# Etiquetas de porcentaje
# ==========================================

text(

  x = pos_x,

  y = tabla_distribucion$P,

  labels = round(

    tabla_distribucion$P,

    2

  ),

  pos = 3,

  cex = 0.80,

  font = 2

)

5.2 Distribución acumulada

# ==========================================
# Preparación del gráfico acumulado
# ==========================================

par(

  mar = c(8,5,4,2)

)



pos_x <- barplot(

  tabla_distribucion$P_acumulada,

  names.arg = tabla_distribucion$Categoria,

  col = "skyblue",

  border = "black",

  space = 0.20,

  ylim = c(0,100),

  las = 1,

  yaxt = "n",

  main = "Gráfica N° 2. Distribución acumulada\n del tamaño de los deslizamientos",

  xlab = "Tamaño del deslizamiento",

  ylab = "Probabilidad acumulada (%)"

)



# ==========================================
# Escala del eje Y
# ==========================================

ticks_y <- seq(

  0,

  100,

  20

)



axis(

  side = 2,

  at = ticks_y,

  labels = ticks_y,

  las = 1

)



# ==========================================
# Línea de referencia del 100 %
# ==========================================

abline(

  h = 100,

  col = "red",

  lty = 2,

  lwd = 2

)



# ==========================================
# Etiquetas de porcentaje acumulado
# ==========================================

text(

  x = pos_x,

  y = tabla_distribucion$P_acumulada,

  labels = round(

    tabla_distribucion$P_acumulada,

    2

  ),

  pos = 3,

  cex = 0.80,

  font = 2

)

6. ESTADÍSTICA INFERENCIAL

6.1 Estimación puntual de la proporción

# ==========================================
# Estimación puntual de las proporciones
# ==========================================

proporcion_muestral <- tabla_distribucion$hi


proporcion_muestral

## [1] 0.27207473 0.64414946 0.07374631 0.01002950

# ==========================================
# Construcción de la tabla
# ==========================================

tabla_inferencia <- data.frame(

  Categoria = tabla_distribucion$Categoria,

  Proporcion = proporcion_muestral

)


tabla_inferencia

##    Categoria Proporcion
## 1      small 0.27207473
## 2     medium 0.64414946
## 3      large 0.07374631
## 4 very_large 0.01002950

6.2 Error estándar de la proporción

# ==========================================
# Error estándar de cada proporción
# ==========================================

error_estandar <- sqrt(

  proporcion_muestral *

  (1 - proporcion_muestral) / n

)


error_estandar

## [1] 0.0044129299 0.0047475185 0.0025916399 0.0009880758

# ==========================================
# Incorporación a la tabla
# ==========================================

tabla_inferencia$Error_estandar <- error_estandar


tabla_inferencia

##    Categoria Proporcion Error_estandar
## 1      small 0.27207473   0.0044129299
## 2     medium 0.64414946   0.0047475185
## 3      large 0.07374631   0.0025916399
## 4 very_large 0.01002950   0.0009880758

6.3 Intervalo de confianza del 95 %

# ==========================================
# Valor crítico para un nivel de confianza
# del 95 %
# ==========================================

z <- qnorm(0.975)


z

## [1] 1.959964

# ==========================================
# Límite inferior
# ==========================================

limite_inferior <- proporcion_muestral -

  z * error_estandar


# ==========================================
# Límite superior
# ==========================================

limite_superior <- proporcion_muestral +

  z * error_estandar


# ==========================================
# Ajuste de límites al intervalo [0,1]
# ==========================================

limite_inferior <- pmax(

  0,

  limite_inferior

)


limite_superior <- pmin(

  1,

  limite_superior

)


# ==========================================
# Incorporación a la tabla
# ==========================================

tabla_inferencia$Limite_inferior <- limite_inferior

tabla_inferencia$Limite_superior <- limite_superior


tabla_inferencia

##    Categoria Proporcion Error_estandar Limite_inferior Limite_superior
## 1      small 0.27207473   0.0044129299     0.263425546      0.28072391
## 2     medium 0.64414946   0.0047475185     0.634844494      0.65345442
## 3      large 0.07374631   0.0025916399     0.068666792      0.07882583
## 4 very_large 0.01002950   0.0009880758     0.008092906      0.01196609

6.4 Presentación de la inferencia estadística

# ==========================================
# Tabla de presentación
# ==========================================

tabla_inferencia %>%

  gt() %>%

  tab_header(

    title = md("**Tabla N° 2**"),

    subtitle = md(

      "Estimación puntual e intervalos de confianza para las proporciones del tamaño de los deslizamientos"

    )

  ) %>%

  cols_label(

    Categoria = "Tamaño del deslizamiento",

    Proporcion = "Proporción",

    Error_estandar = "Error estándar",

    Limite_inferior = "Límite inferior (95 %)",

    Limite_superior = "Límite superior (95 %)"

  ) %>%

  fmt_number(

    columns = c(

      Proporcion,

      Error_estandar,

      Limite_inferior,

      Limite_superior

    ),

    decimals = 4

  ) %>%

  tab_style(

    style = list(

      cell_fill(color = "#6D213C"),

      cell_text(

        color = "white",

        weight = "bold"

      )

    ),

    locations = cells_column_labels()

  ) %>%

  tab_source_note(

    source_note = md(

      "Autor: Grupo 1 – Carrera de Geología"

    )

  )

Tamaño del deslizamiento	Proporción	Error estándar	Límite inferior (95 %)	Límite superior (95 %)
Tabla N° 2
Estimación puntual e intervalos de confianza para las proporciones del tamaño de los deslizamientos
small	0.2721	0.0044	0.2634	0.2807
medium	0.6441	0.0047	0.6348	0.6535
large	0.0737	0.0026	0.0687	0.0788
very_large	0.0100	0.0010	0.0081	0.0120
Autor: Grupo 1 – Carrera de Geología

7. CÁLCULO DE PROBABILIDADES

7.1 Probabilidad observada

# ==========================================
# Categoría de interés
# ==========================================

categoria_interes <- "medium"


categoria_interes

## [1] "medium"

# ==========================================
# Búsqueda de la categoría
# ==========================================

fila_categoria <- tabla_inferencia %>%

  filter(

    Categoria == categoria_interes

  )


fila_categoria

##   Categoria Proporcion Error_estandar Limite_inferior Limite_superior
## 1    medium  0.6441495    0.004747518       0.6348445       0.6534544

# ==========================================
# Probabilidad observada
# ==========================================

probabilidad <- fila_categoria$Proporcion


probabilidad

## [1] 0.6441495

7.2 Intervalo de confianza de la probabilidad

# ==========================================
# Intervalo de confianza
# ==========================================

limite_inferior <- fila_categoria$Limite_inferior

limite_superior <- fila_categoria$Limite_superior


limite_inferior

## [1] 0.6348445

limite_superior

## [1] 0.6534544

7.3 Interpretación

plot(

  1,

  type = "n",

  axes = FALSE,

  xlab = "",

  ylab = ""

)


texto <- paste0(

  "Estimación del intervalo de confianza\n\n",

  "Para la categoría:\n\n",

  "'",

  categoria_interes,

  "'\n\n",

  "la proporción observada fue de ",

  round(probabilidad * 100, 2),

  "%.\n\n",

  "Con un nivel de confianza del 95 %, se estima\n",

  "que la proporción poblacional se encuentra\n",

  "entre ",

  round(limite_inferior * 100, 2),

  "% y ",

  round(limite_superior * 100, 2),

  "%."

)


text(

  x = 1,

  y = 1,

  labels = texto,

  cex = 1.20,

  font = 2

)

8. CONCLUSIÓN

# ==========================================
# Categoría con mayor probabilidad
# ==========================================

indice_maximo <- which.max(

  tabla_inferencia$Proporcion

)

categoria_mayor <- tabla_inferencia$Categoria[

  indice_maximo

]

probabilidad_mayor <- round(

  tabla_inferencia$Proporcion[indice_maximo] * 100,

  2

)

lim_inf <- round(

  tabla_inferencia$Limite_inferior[indice_maximo] * 100,

  2

)

lim_sup <- round(

  tabla_inferencia$Limite_superior[indice_maximo] * 100,

  2

)

# ==========================================
# Presentación de la conclusión
# ==========================================

plot(

  1,

  type = "n",

  axes = FALSE,

  xlab = "",

  ylab = ""

)


texto <- paste0(

  "Conclusión\n\n",

  "La categoría '",

  categoria_mayor,

  "' presentó la mayor proporción observada\n",

  "de deslizamientos, con un valor de ",

  probabilidad_mayor,

  "%.\n\n",

  "Con un nivel de confianza del 95 %, la\n",

  "proporción poblacional para esta categoría\n",

  "se estima entre ",

  lim_inf,

  "% y ",

  lim_sup,

  "%.\n\n",

  "Estos resultados permiten inferir que esta\n",

  "categoría constituye la más representativa\n",

  "dentro del conjunto de deslizamientos\n",

  "analizados."

)

text(

  x = 1,

  y = 1,

  labels = texto,

  cex = 1.15,

  font = 2

)

VARIABLE CUALITATIVA ORDINAL: TAMAÑO DEL DESLIZAMIENTO

Geología Grupo 1

2026-07-13

1. CARGA DE DATOS Y LIBRERÍAS

2. PREPARACIÓN DE LA VARIABLE

2.1 Definición del orden de las categorías

2.2 Conversión de la variable a factor ordenado

2.3 Extracción de la variable de análisis

2.4 Eliminación de valores faltantes

2.5 Tamaño de la muestra

3. DISTRIBUCIÓN DE PROBABILIDAD

3.1 Frecuencia absoluta

3.2 Probabilidad simple

3.3 Construcción de la distribución de probabilidad

3.4 Probabilidad acumulada

4. TABLA DE DISTRIBUCIÓN DE PROBABILIDAD

4.1 Tabla simple de distribución

4.2 Tabla de presentación

5. GRÁFICAS DE LA DISTRIBUCIÓN DE PROBABILIDAD

5.1 Distribución de probabilidad

5.2 Distribución acumulada

6. ESTADÍSTICA INFERENCIAL

6.1 Estimación puntual de la proporción

6.2 Error estándar de la proporción

6.3 Intervalo de confianza del 95 %

6.4 Presentación de la inferencia estadística

7. CÁLCULO DE PROBABILIDADES

7.1 Probabilidad observada

7.2 Intervalo de confianza de la probabilidad

7.3 Interpretación

8. CONCLUSIÓN