dGIW function

The Generalized Inverse Weibull distribution

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

dGIW(x, mu, sigma, nu, log = FALSE)

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

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

rGIW(n, mu, sigma, nu)

hGIW(x, mu, sigma, nu)

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.

Returns

dGIW gives the density, pGIW gives the distribution function, qGIW gives the quantile function, rGIW

generates random deviates and hGIW gives the hazard function.

Details

The Generalized Inverse Weibull distribution mu, sigma and nu has density given by

$f(x) = \nu \sigma \mu^{\sigma} x^{-(\sigma + 1)} exp \{-\nu (\frac{\mu}{x})^{\sigma}\},$

for x > 0.

Examples

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

## The probability density function
curve(dGIW(x, mu=3, sigma=5, nu=0.5), from=0.001, to=8,
      col="red", ylab="f(x)", las=1)

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pGIW(x, mu=3, sigma=5, nu=0.5),
      from=0.0001, to=14, col="red", las=1, ylab="F(x)")
curve(pGIW(x, mu=3, sigma=5, nu=0.5, lower.tail=FALSE),
      from=0.0001, to=14, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qGIW(p, mu=3, sigma=5, nu=0.5), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pGIW(x, mu=3, sigma=5, nu=0.5),
      from=0, add=TRUE, col="red")

## The random function
hist(rGIW(n=1000, mu=3, sigma=5, nu=0.5), freq=FALSE,
     xlab="x", ylim=c(0, 0.8), las=1, main="")
curve(dGIW(x, mu=3, sigma=5, nu=0.5),
      from=0.001, to=14, add=TRUE, col="red")

## The Hazard function
curve(hGIW(x, mu=3, sigma=5, nu=0.5), from=0.001, to=30,
      col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters

References

Rdpack::insert_ref(key="almalki2014modifications",package="RelDists")

Rdpack::insert_ref(key="gusmao2009",package="RelDists")

Author(s)

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co