dGMW {RelDists}

The Generalized modified Weibull distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the generalized modified weibull distribution with parameters mu, sigma, nu and tau.

Usage

dGMW(x, mu, sigma, nu, tau, log = FALSE)

pGMW(q, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)

qGMW(p, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)

rGMW(n, mu, sigma, nu, tau)

hGMW(x, mu, sigma, nu, tau, log = FALSE)

Arguments

x, q

vector of quantiles.

mu

scale parameter.

sigma

shape parameter.

nu

shape parameter.

tau

acceleration 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 generalized modified weibull with parameters mu, sigma, nu and tau has density given by

f(x)= \mu \sigma x^{\nu - 1}(\nu + \tau x) \exp(\tau x - \mu x^{\nu} e^{\tau x}) [1 - \exp(- \mu x^{\nu} e^{\tau x})]^{\sigma-1},

for x>0.

Value

dGMW gives the density, pGMW gives the distribution function, qGMW gives the quantile function, rGMW generates random deviates and hGMW gives the hazard function.

Examples

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

## The probability density function
curve(dGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5), from=0, to=0.8,
      ylim=c(0, 2), col="red", las=1, ylab="f(x)") 
 
## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5),
      from=0, to=1.2, col="red", las=1, ylab="F(x)")
curve(pGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5, lower.tail=FALSE),
      from=0, to=1.2, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qGMW(p, mu=2, sigma=0.5, nu=2, tau=1.5), y=p, xlab="Quantile",
    las=1, ylab="Probability")
curve(pGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5), from=0, add=TRUE, col="red")
 
## The random function
hist(rGMW(n=1000, mu=2, sigma=0.5, nu=2,tau=1.5), freq=FALSE,
    xlab="x", main ="", las=1)
curve(dGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5),  from=0, add=TRUE, col="red")
 
## The Hazard function
par(mfrow=c(1,1))
curve(hGMW(x, mu=2, sigma=0.5, nu=2, tau=1.5), from=0, to=1, ylim=c(0, 16),
      col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters