weibullness (version 1.24.1)

inverseWeibull: The inverse Weibull distribution

Description

Density function, distribution function, quantile function, random generation, raw moments and limited moments for the Inverse Weibull distribution with parameters shape and scale.

Usage

dinvweibull(x, shape, scale = 1, log = FALSE)
pinvweibull(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
qinvweibull(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
rinvweibull(n, shape, scale = 1)

Value

dinvweibull gives the density, pinvweibull gives the distribution function, qinvweibull gives the quantile function, and rinvweibull generates random deviates.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

shape, scale

parameters. Must be positive.

log, log.p

logical; if TRUE, probabilities or densities \(p\) are given as \(\log(p)\).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

Author

Chanseok Park

Details

The probability density function of the inverse Weibull distribution with parameters shape \(=\beta\) and scale \(= \theta\) is given by $$f(x) = \frac{\beta (\theta/x)^\beta e^{-(\theta/x)^\beta}}{x}$$ where \(x > 0\), \(\beta > 0\) and \(\theta > 0\).

The cumulative distribution function is given by $$F(X)=\exp(-(\theta/x)^\beta)$$

Examples

x = (-1):2
names(x) = letters[1:4]
dinvweibull(x, shape=2) 
exp( dinvweibull(x, shape=2, log=TRUE) )


pinvweibull (1, shape=2)
exp(pinvweibull (1, shape=2,  log=TRUE))

q = c(-1,0,1,2)
qinvweibull ( pinvweibull (q, shape=2), shape=2 )