Introducción T Student gráficas

Rubén Pizarro Gurrola

Objetivo

Representar visualmente distribución normal, distribución Z y distribución t Student con ggplot2 y visualize.

Librerías

library(dplyr)
library(mosaic)
library(ggplot2)  # Para gráficos
library(cowplot) #Imágenes en el mismo renglón
library(visualize)
options(scipen=999) # Notación normal

Cargar funciones

source("https://raw.githubusercontent.com/rpizarrog/probabilidad-y-estad-stica/master/2023/funciones/funciones%20para%20disribuciones%20de%20probabilidad.R")

Algunos datos

n <- 25
media <- 80
desv.std <- 5
gl <- n-1  # Grados de libertad (n-1)

n; media; desv.std; gl

[1] 25

[1] 80

[1] 5

[1] 24

Crea 25 valores aleatorios normal

xs <- rnorm(n = n, mean = media, sd = desv.std)
datos1 <- data.frame(x = xs, f.x = dnorm(x = xs, mean = media, sd = desv.std))

Visualizar Normal

g1 <- ggplot(data = datos1, aes(x = xs, y = f.x)) +
  geom_point(colour = "red") +
  geom_line(colour = 'blue') +
  ggtitle("Normal", subtitle = paste("media = ", media, "sd=", desv.std)) +
  labs(x = "X's", y= "Densidad")

Visualizar Normal

Convertir normal a normal Z

zs <- f.devolver.z(x = xs, media = media, desv = desv.std)
zs

 [1] -0.16765168 -1.72523432  0.20779676  1.65225582 -1.78543942  0.43232793
 [7] -0.44059901 -0.38187579  0.77509521  0.49721292  0.82692151  0.56166747
[13]  0.94420431  0.04123948 -0.46926042 -0.66205102 -0.63483318 -1.16538925
[19] -0.23043196 -1.83951661  2.30371881  0.76206009  0.22691028  1.01672222
[25] -0.91529437

datos2 <- data.frame(x = zs, f.x = dnorm(x = zs, mean = 0, sd = 1))

Visualizar Z

g2 <- ggplot(data = datos2, aes(x = zs, y = f.x)) +
  geom_point(colour = "red") +
  geom_line(colour = 'yellow') +
  ggtitle("Normal Z", subtitle = paste("media = ", 0, "sd=", 1)) +
  labs(x = "Z's", y= "Densidad")
# g2

Visualizar Z

Mismos valores de Z serán los de t

ts = zs
datos3 <- data.frame(x = ts, f.x = dt(x = ts, df = gl))
datos3

             x        f.x
1  -0.16765168 0.38907516
2  -1.72523432 0.09156328
3   0.20779676 0.38603729
4   1.65225582 0.10269547
5  -1.78543942 0.08305263
6   0.43232793 0.35832220
7  -0.44059901 0.35698785
8  -0.38187579 0.36601717
9   0.77509521 0.28984690
10  0.49721292 0.34733890
11  0.82692151 0.27789321
12  0.56166747 0.33534710
13  0.94420431 0.25025622
14  0.04123948 0.39445984
15 -0.46926042 0.35221288
16 -0.66205102 0.31487489
17 -0.63483318 0.32061572
18 -1.16538925 0.19840940
19 -0.23043196 0.38405200
20 -1.83951661 0.07591932
21  2.30371881 0.03249852
22  0.76206009 0.29281415
23  0.22691028 0.38437360
24  1.01672222 0.23305570
25 -0.91529437 0.25711170

Visualizar t

g3 <- ggplot(data = datos3, aes(x = ts, y = f.x)) +
  geom_point(colour = "red") +
  geom_line(colour = 'green') +
  ggtitle("t Student", subtitle = paste("media = ", 0, "sd=", 1)) +
  labs(x = "t's", y= "Densidad")

Visualizar t

Tres mismo renglón

plot_grid(g1, g2, g3, nrow = 1, ncol = 3)