Probabilidad en R

# Simulación de datos de una distribución Binomial

# Generación de números aleatorios

rbinom(10,8,0.7)

#Gráfica función de densidad con n=10 y p=0.8

x <- 1:10

plot(x, dbinom(x, size=10, prob=0.8), xlab="Number of Successes",

ylab="Probability Mass", main="Binomial Distribution: Trials = 10, Probability of

success = 0.8", type="h")

points(x, dbinom(x, size=10, prob=0.8), pch=16)

abline(h=0, col="gray")

#Grafica función de distribución n=10 y p=0.8

x <- 1:10

pbinom(x, size=10, prob=0.8)

cbind(x, round(pbinom(x, size=10, prob=0.8), 4))

plot(x, pbinom(x, size=10, prob=0.8), type="p", pch=16)

x <- rep(x, rep(2, length(x)))

plot(x[-1], pbinom(x, size=10, prob=0.8)[-length(x)], xlab="Number of Successes",

ylab="Cumulative Probability", main="Binomial Distribution: Trials = 10, Probability

of success = 0.8", type="l")

abline(h=0, col=1, lty=2)

x <- 3:10

points(x, pbinom(x, size=10, prob=0.8), pch=16)

#Gráfica función de densidad con n=10 y p=0.5

x <- 0:10

plot(x, dbinom(x, size=10, prob=0.5), xlab="Number of Successes",

ylab="Probability Mass", main="Binomial Distribution: Trials = 10, Probability of

success = 0.5", type="h")

points(x, dbinom(x, size=10, prob=0.5), pch=16)

abline(h=0, col="gray")

#Grafica función de distribución n=10 y p=0.5

x <- 0:10

x <- rep(x, rep(2, length(x)))

plot(x[-1], pbinom(x, size=10, prob=0.5)[-length(x)], xlab="Number of Successes",

ylab="Cumulative Probability", main="Binomial Distribution: Trials = 10, Probability

of success = 0.5", type="l")

points(x, pbinom(x, size=10, prob=0.5), pch=16)

abline(h=0, col="gray")

#Gráfica función de densidad con n=20 y p=0.2

x <- 0:11

plot(x, dbinom(x, size=20, prob=0.2), xlab="Number of Successes",

ylab="Probability Mass", main="Binomial Distribution: Trials = 20, Probability of

success = 0.2", type="h")

points(x, dbinom(x, size=20, prob=0.2), pch=16)

abline(h=0, col="gray")

#Grafica función de distribución n=20 y p=0.2

x <- 0:11

x <- rep(x, rep(2, length(x)))

plot(x[-1], pbinom(x, size=20, prob=0.2)[-length(x)], xlab="Number of Successes",

ylab="Cumulative Probability", main="Binomial Distribution: Trials = 20, Probability

of success = 0.2", type="l")

abline(h=0, col="gray")

points(x, pbinom(x, size=20, prob=0.2), pch=16)

#####################################################

# Simulación de datos de una distribución Poisson #

#####################################################

#Generación de números aleatorios

rpois(5,2)

#Gráfica función de densidad media=2

x <- 0:8

plot(x, dpois(x, lambda=2), xlab="x", ylab="Probability Mass", main="Poisson

Distribution: Mean = 2", type="h")

points(x, dpois(x, lambda=2), pch=16)

abline(h=0, col="gray")

#Grafica función de distribución media=2

x <- 0:8

x <- rep(x, rep(2, length(x)))

plot(x[-1], ppois(x, lambda=2)[-length(x)], xlab="x", ylab="Probability Mass",

main="Poisson Distribution: Mean = 2", type="l")

abline(h=0, col="gray")

points(x, ppois(x, lambda=2), pch=16)

#Gráfica función de densidad media=4

x <- 0:8

plot(x, dpois(x, lambda=4), xlab="x", ylab="Probability Mass", main="Poisson

Distribution: Mean = 4", type="h")

points(x, dpois(x, lambda=4), pch=16)

abline(h=0, col="gray")

#Grafica función de distribución media=4

x <- 0:12

x <- rep(x, rep(2, length(x)))

plot(x[-1], ppois(x, lambda=4)[-length(x)], xlab="x", ylab="Probability Mass",

main="Poisson Distribution: Mean = 4", type="l")

abline(h=0, col="gray")

#Gráfica función de densidad media=10

x <- 2:22

plot(x, dpois(x, lambda=10), xlab="x", ylab="Probability Mass", main="Poisson

Distribution: Mean = 10", type="h")

points(x, dpois(x, lambda=10), pch=16)

abline(h=0, col="gray")

points(x, ppois(x, lambda=4), pch=16)

#Grafica función de distribución media=10

x <- 2:22

x <- rep(x, rep(2, length(x)))

plot(x[-1], ppois(x, lambda=10)[-length(x)], xlab="x", ylab="Probability Mass",

main="Poisson Distribution: Mean = 10", type="l")

abline(h=0, col="gray")

points(x, ppois(x, lambda=10), pch=16)

########################################################

# Simulación de datos de una distribución Geométrica #

########################################################

#Generación de números aleatorios

rgeom(10,0.5)

#Gráfica función de probabilidad p=0.5

x <- 0:10

plot(x, dgeom(x, prob=0.5), xlab="Number of Failures until Success",

ylab="Probability Mass", main="Geometric Distribution: Prob of success = 0.5",

type="h")

points(x, dgeom(x, prob=0.5), pch=16)

abline(h=0, col="gray")

#Grafica función de distribución p=0.5

x <- 0:10

x <- rep(x, rep(2, length(x)))

plot(x[-1], pgeom(x, prob=0.5)[-length(x)],

xlab="Number of Failures until Success", ylab="Cumulative Probability",

main="Geometric Distribution: Probability of success = 0.5", type="l")

abline(h=0, col="gray")

#Gráfica función de densidad p=0.95

x <- 0:2

plot(x, dgeom(x, prob=0.95), xlab="Number of Failures until Success",

...