dMOLE: The Marshall-Olkin logistic-exponential distribution

In vagarciave/pruebas: pruebas

Description

Density, distribution function, quantile function, random generation and hazard function for the Marshall-Olkin logistic-exponential distribution with parameters mu, sigma, and nu .

Usage

dMOLE(x, mu, sigma, nu, log = FALSE)

pMOLE(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

qMOLE(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

rMOLE(n, mu, sigma, nu)

hMOLE(x, mu, sigma, nu)

Arguments

x, q	vector of quantiles.
mu	parameter.
sigma	parameter.
nu	parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
p	vector of probabilities.
n	number of observations.

Details

The Marshall-Olkin logistic-exponential Distribution with parameters mu, sigma, and nu has density given by

f(x)=\ μ σ ν \exp^{ν x}[\exp^{ν x}-1]^{-μ-1} / [1 + σ [\exp^{ν x}-1]^{-μ}]^2

for x > 0

Value

dMOLE gives the density, pMOLE gives the distribution function, qMOLE gives the quantile function, rMOLE generates random deviates and hMOLE gives the hazard function.

Examples

## The probability density function
par(mfrow=c(1, 2))
 curve(dMOLE(x, mu=0.6, sigma=5.5, nu=1), from=0, to=8,
 ylim=c(0, 0.3), col="red", las=1, ylab="f(x)")

 curve(dMOLE(x, mu=3, sigma=15, nu=1.2), from=0, to=3,
 ylim=c(0, 1.5), col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pMOLE(x, mu=0.6, sigma=5.5, nu=1),
      from=0, to=15,  col="red", las=1, ylab="F(x)")
curve(pMOLE(x, mu=0.6, sigma=5.5, nu=1, lower.tail=FALSE),
      from=0, to=15, col="red", las=1, ylab="S(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qMOLE(p, mu=0.6, sigma=5.5, nu=1), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pMOLE(x, mu=0.6, sigma=5.5, nu=1), from=0, add=TRUE, col="red")

## The random function
hist(rMOLE(n=10000, mu=0.6, sigma=5.5, nu=1), freq=FALSE,
     xlab="x", las=1, main="")
curve(dMOLE(x,  mu=0.6, sigma=5.5, nu=1), from=0, add=TRUE, col="red")

## The Hazard function
par(mfrow=c(1,1))
curve(hMOLE(x,  mu=0.6, sigma=5.5, nu=1), from=0, to=8,
      col="red", ylab="Hazard function", las=1)

vagarciave/pruebas documentation built on July 2, 2019, 12:17 a.m.