RelDists (version 1.0.0)

dExW: The Extended Weibull distribution

Description

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

Usage

dExW(x, mu, sigma, nu, log = FALSE)
pExW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
qExW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
rExW(n, mu, sigma, nu)
hExW(x, mu, sigma, nu)

Value

dExW gives the density, pExW gives the distribution function, qExW gives the quantile function, rExW

generates random deviates and hExW 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 Extended Weibull distribution with parameters mu, sigma and nu has density given by

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

for x > 0.

References

almalki2014modificationsRelDists

Zhang2007RelDists

Examples

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

## The probability density function
curve(dExW(x, mu=0.3, sigma=2, nu=0.05), from=0.0001, to=2,
      col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pExW(x, mu=0.3, sigma=2, nu=0.05),
      from=0.0001, to=2, col="red", las=1, ylab="F(x)")
curve(pExW(x, mu=0.3, sigma=2, nu=0.05, 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=qExW(p, mu=0.3, sigma=2, nu=0.05), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pExW(x, mu=0.3, sigma=2, nu=0.05), 
      from=0, add=TRUE, col="red")

## The random function
hist(rExW(n=10000, mu=0.3, sigma=2, nu=0.05), freq=FALSE,
     xlab="x", ylim=c(0, 2), las=1, main="")
curve(dExW(x, mu=0.3, sigma=2, nu=0.05),
      from=0.001, to=4, add=TRUE, col="red")

## The Hazard function
curve(hExW(x, mu=0.3, sigma=2, nu=0.05), from=0.001, to=4,
      col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters