RelDists (version 1.0.0)

dMOEW: The Marshall-Olkin Extended Weibull distribution

Description

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

Usage

dMOEW(x, mu, sigma, nu, log = FALSE)
pMOEW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
qMOEW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
rMOEW(n, mu, sigma, nu)
hMOEW(x, mu, sigma, nu)

Value

dMOEW gives the density, pMOEW gives the distribution function, qMOEW gives the quantile function, rMOEW

generates random deviates and hMOEW gives the hazard function.

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.

Author

Amylkar Urrea Montoya,

Details

The Marshall-Olkin Extended Weibull distribution mu, sigma and nu has density given by

\(f(x) = \frac{\mu \sigma \nu (\nu x)^{\sigma - 1} exp\{{-(\nu x )^{\sigma}}\}}{\{1-(1-\mu) exp\{{-(\nu x )^{\sigma}}\} \}^{2}},\)

for x > 0.

References

almalki2014modificationsRelDists

ghitany2005RelDists

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function
curve(dMOEW(x, mu=0.5, sigma=0.7, nu=1), from=0.001, to=1,
      col="red", ylab="f(x)", las=1)

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pMOEW(x, mu=0.5, sigma=0.7, nu=1),
      from=0.0001, to=2, col="red", las=1, ylab="F(x)")
curve(pMOEW(x, mu=0.5, sigma=0.7, nu=1, lower.tail=FALSE),
      from=0.0001, to=2, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qMOEW(p, mu=0.5, sigma=0.7, nu=1), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pMOEW(x, mu=0.5, sigma=0.7, nu=1),
      from=0, add=TRUE, col="red")

## The random function
hist(rMOEW(n=100, mu=0.5, sigma=0.7, nu=1), freq=FALSE,
     xlab="x", ylim=c(0, 1), las=1, main="")
curve(dMOEW(x, mu=0.5, sigma=0.7, nu=1),
      from=0.001, to=2, add=TRUE, col="red")

## The Hazard function
curve(hMOEW(x, mu=0.5, sigma=0.7, nu=1), from=0.001, to=3,
      col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters