set.seed(1122)
data1 <- rnorm(50,3,0.3)
data2 <- runif(50,(3-0.3*sqrt(3)),(3+0.3*sqrt(3)))

mean(data1)
mean(data2)
sd(data1)
sd(data2)

sim1 <- replicate(100, rnorm(30,3,0.3))
sim2 <- replicate(100, runif(30,(3-0.3*sqrt(3)),(3+0.3*sqrt(3))))

# Prueba normalidad Shapiro-Wilk
shapiro.sim1<- apply(sim1, 2, function(x) shapiro.test(x)$p.value)
table(shapiro.sim1<0.05)

shapiro.sim2<- apply(sim2, 2, function(x) shapiro.test(x)$p.value)
table(shapiro.sim2<0.05)

# Prueba de normalidad Anderson-Darlin
library(nortest)
ad.sim1<- apply(sim1, 2, function(x) ad.test(x)$p.value)
table(ad.sim1<0.05)

ad.sim2<- apply(sim2, 2, function(x) ad.test(x)$p.value)
table(ad.sim2<0.05)

cvm.sim1<- apply(sim1, 2, function(x) cvm.test(x)$p.value)
table(cvm.sim1<0.05)

cvm.sim2<- apply(sim2, 2, function(x) cvm.test(x)$p.value)
table(cvm.sim2<0.05)

set.seed(123)
data <- rnorm_multi(50,2,mu =c(4,5),sd= c(0.3,0.4),r=0.8,varnames = c("largo","ancho"))
medias <- colMeans(data)
plot(data$largo,data$ancho)
points(x = medias[1],y=medias[2], col= "darkred", pch = 16, cex = 2)

S <- cov(data)
S

eigen(S)

# 1. Preparación de datos (usando tu estructura)
library(faux)
set.seed(123)
data <- rnorm_multi(50, 2, mu = c(4, 5), sd = c(0.3, 0.4), r = 0.8, varnames = c("largo", "ancho"))
medias <- colMeans(data)
S <- cov(data)
e <- eigen(S)

# 2. Gráfico con relación de aspecto 1:1 para ver la ortogonalidad real
plot(data$largo, data$ancho, 
     asp = 1,
     main = "Vectores Propios Ortogonales",
     xlab = "Largo", ylab = "Ancho", 
     pch = 19, col = "gray")

# Centro de los datos
points(x = medias[1], y = medias[2], col = "darkred", pch = 16, cex = 2)

# 3. Dibujar vectores propios (Autovectores)
# Vector 1 (Columna 1 de e$vectors)
arrows(medias[1], medias[2], 
       medias[1] + e$vectors[1,1] * 0.5, 
       medias[2] + e$vectors[2,1] * 0.5, 
       col = "blue", lwd = 2, length = 0.1)

# Vector 2 (Columna 2 de e$vectors)
arrows(medias[1], medias[2], 
       medias[1] + e$vectors[1,2] * 0.5, 
       medias[2] + e$vectors[2,2] * 0.5, 
       col = "red", lwd = 2, length = 0.1)

valores = e$values
valores
S_val = sum(valores)
S_val
Explicado = (valores/S_val)*100
Explicado