dIW {RelDists}

The Inverse Weibull distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the inverse weibull distribution with parameters mu and sigma.

Usage

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

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

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

rIW(n, mu, sigma)

hIW(x, mu, sigma)

Arguments

x, q

vector of quantiles.

mu

scale parameter.

sigma

shape parameters.

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 inverse weibull distribution with parameters mu and sigma has density given by

f(x) = \mu \sigma x^{-\sigma-1} \exp(\mu x^{-\sigma})

for x > 0, \mu > 0 and \sigma > 0

Value

dIW gives the density, pIW gives the distribution function, qIW gives the quantile function, rIW generates random deviates and hIW gives the hazard function.

Author(s)

Johan David Marin Benjumea, [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.

Drapella A (1993). “The complementary Weibull distribution: unknown or just forgotten?” Quality and Reliability Engineering International, 9(4), 383–385.

Examples

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

## The probability density function
curve(dIW(x, mu=5, sigma=2.5), from=0, to=10,
      ylim=c(0, 0.55), col="red", las=1, ylab="f(x)")
#'
## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pIW(x, mu=5, sigma=2.5),
      from=0, to=10,  col="red", las=1, ylab="F(x)")
curve(pIW(x, mu=5, sigma=2.5, lower.tail=FALSE),
      from=0, to=10, col="red", las=1, ylab="R(x)")
            
## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qIW(p, mu=5, sigma=2.5), y=p, xlab="Quantile",
  las=1, ylab="Probability")
curve(pIW(x, mu=5, sigma=2.5), from=0, add=TRUE, col="red")
  
## The random function
hist(rIW(n=10000, mu=5, sigma=2.5), freq=FALSE, xlim=c(0,60),
  xlab="x", las=1, main="")
curve(dIW(x, mu=5, sigma=2.5), from=0, add=TRUE, col="red")

## The Hazard function
par(mfrow=c(1,1))
curve(hIW(x, mu=5, sigma=2.5), from=0, to=15, ylim=c(0, 0.9),
   col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters