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