Distribuciones de Probabilidad

Distribución Normal

x = rnorm(10000, 5.0, 1.0)
hist(x, freq=FALSE, breaks=50, ylim=c(0, 0.6))
xx = seq(0, 9, 0.1)
lines(xx, dnorm(xx, 5.0, 1.0), col="blue")
alfa = 0.01
d1 = qnorm(alfa/2, 5.0, 1.0)
d2 = qnorm(1-alfa/2, 5.0, 1.0)
cat("d1=", d1, "d2=", d2, "\n")

## d1= 2.424171 d2= 7.575829

abline(v=d1)
abline(v=d2)
abline(v=5.0)

p1 = pnorm(d1, 5.0, 1.0)
p2 = pnorm(d2, 5.0, 1.0)
cat("p1=", p1, "p2=", p2)

## p1= 0.005 p2= 0.995

Distribución T-student

n = 10000
gl = 24
x = rt(n, gl)
hist(x, freq=FALSE, breaks=50, ylim=c(0, 0.6), main="Distribución t")
xx = seq(-4, 4, 0.1)
lines(xx, dt(xx, gl))
alfa = 0.05
d1 = qt(alfa/2, gl)
d2 = qt(1-alfa/2, gl)
cat("d1=", d1, "d2=", d2, "\n")

## d1= -2.063899 d2= 2.063899

abline(v=d1)
abline(v=d2)

p1 = pt(d1, gl)
p2 = pt(d2, gl)
cat("p1=", p1, "p2=", p2)

## p1= 0.025 p2= 0.975

Distribución F

gl1 = 14
gl2 = 14
n = 10000
x = rf(n, gl1, gl2)
hist(x, freq=FALSE, breaks=50, ylim=c(0, 1.2), main="Distribución F")
xx = seq(0, 8, 0.1)
lines(xx, df(xx, gl1, gl2))
alfa = 0.05
d1 = qf(1-alfa, gl1, gl2)
abline(v=d1)

cat("d=", d1, "\n")

## d= 2.483726

p = pf(d1, gl1, gl2)
cat("p=", p)

## p= 0.95

Distribución de Chi cuadrado

gl = 12
n = 10000
x = rchisq(n, gl)
hist(x, freq=FALSE, breaks=50, ylim=c(0, 0.15), main="Distribución Chi-cuadrado")
xx = seq(0, 35, 0.1)
lines(xx, dchisq(xx, gl), col="blue")
alfa = 0.05
d1 = qchisq(alfa/2, gl)
d2 = qchisq(1-alfa/2, gl)
cat("d1=", d1, "d2=", d2, "\n")

## d1= 4.403789 d2= 23.33666

abline(v=d1)
abline(v=d2)

p1 = pchisq(d1, gl)
p2 = pchisq(d2, gl)
cat("p1=", p1, "p2=", p2)

## p1= 0.025 p2= 0.975