The Flexible Weibull Extension distribution

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

Usage

dFWE(x, mu, sigma, log = FALSE)

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

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

rFWE(n, mu, sigma)

hFWE(x, mu, sigma)

Arguments

x, q: vector of quantiles.
mu: parameter.
sigma: 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.

Value

dFWE gives the density, pFWE gives the distribution function, qFWE gives the quantile function, rFWE generates random deviates and hFWE gives the hazard function.

Details

The Flexible Weibull extension with parameters mu and sigma has density given by

\(f(x) = (\mu + \sigma/x^2) \exp(\mu x - \sigma/x) \exp(-\exp(\mu x-\sigma/x))\)

for x>0.

Examples

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

## The probability density function
curve(dFWE(x, mu=0.75, sigma=0.5), from=0, to=3, 
      ylim=c(0, 1.7), col="red", las=1, ylab="f(x)")


## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pFWE(x, mu=0.75, sigma=0.5), from=0, to=3, 
      col="red", las=1, ylab="F(x)")
curve(pFWE(x, mu=0.75, sigma=0.5, lower.tail=FALSE), 
      from=0, to=3, col="red", las=1, ylab="R(x)")


## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qFWE(p, mu=0.75, sigma=0.5), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pFWE(x, mu=0.75, sigma=0.5), from=0, add=TRUE, col="red")

## The random function
hist(rFWE(n=1000, mu=2, sigma=0.5), freq=FALSE, xlab="x", 
     ylim=c(0, 2), las=1, main="")
curve(dFWE(x, mu=2, sigma=0.5), from=0, to=3, add=TRUE, col="red")


## The Hazard function
par(mfrow=c(1,1))
curve(hFWE(x, mu=0.75, sigma=0.5), from=0, to=2, ylim=c(0, 2.5), 
      col="red", ylab="Hazard function", las=1)


par(old_par) # restore previous graphical parameters