dLW {RelDists}

The Log-Weibull distribution

Description

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

Usage

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

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

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

rLW(n, mu, sigma)

hLW(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.

Details

The Log-Weibull Distribution with parameters mu and sigma has density given by

f(y)=(1/\sigma) e^{((y - \mu)/\sigma)} exp\{-e^{((y - \mu)/\sigma)}\},

for - infty < y < infty.

Value

dLW gives the density, pLW gives the distribution function, qLW gives the quantile function, rLW generates random deviates and hLW gives the hazard function.

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32–55. doi:10.1016/j.ress.2013.11.010.

E.J G (1958). Statistics of extremes. Columbia University Press. ISBN 10:0231021909.

Examples

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

## The probability density function
curve(dLW(x, mu=0, sigma=1.5), from=-8, to=5,
      col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pLW(x, mu=0, sigma=1.5),
      from=-8, to=5,  col="red", las=1, ylab="F(x)")
curve(pLW(x, mu=0, sigma=1.5, lower.tail=FALSE),
      from=-8, to=5, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qLW(p, mu=0, sigma=1.5), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pLW(x, mu=0, sigma=1.5), from=-8, to=5, add=TRUE, col="red")

## The random function
hist(rLW(n=10000, mu=0, sigma=1.5), freq=FALSE,
     xlab="x", las=1, main="")
curve(dLW(x, mu=0, sigma=1.5), from=-15, to=6, add=TRUE, col="red")

## The Hazard function
par(mfrow=c(1,1))
curve(hLW(x, mu=0, sigma=1.5), from=-8, to=7,
      col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters