rweibull: The Reversed Weibull Distribution

Description

Density, distribution function, quantile function and random generation for the reversed Weibull distribution with location, scale and shape parameters.

Usage

drweibull(x, loc=0, scale=1, shape=1, log = FALSE) 
prweibull(q, loc=0, scale=1, shape=1, lower.tail = TRUE) 
qrweibull(p, loc=0, scale=1, shape=1, lower.tail = TRUE)
rrweibull(n, loc=0, scale=1, shape=1)

Arguments

x, q

vector of quantiles.

vector of probabilities.

number of observations.

loc, scale, shape

location, scale and shape parameters.

log

logical; if TRUE, the log density is returned.

lower.tail

logical; if TRUE (default), probabilities are P[X <= x],="" otherwise,="" p[x=""> x]

Value

drweibull gives the density, prweibull gives the distribution function, qrweibull gives the quantile function, and rrweibull generates random deviates.

Details

The reversed Weibull distribution function with parameters $\code{loc} = a$, $\code{scale} = b$ and $\code{shape} = s$ is $$G(z) = \exp\left{-\left[-\left(\frac{z-a}{b}\right) \right]^s\right}$$ for $z < a$ and one otherwise, where $b > 0$ and $s > 0$.

Examples

Run this code

drweibull(-5:-3, -1, 0.5, 0.8)
prweibull(-5:-3, -1, 0.5, 0.8)
qrweibull(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rrweibull(6, -1, 0.5, 0.8)
p <- (1:9)/10
prweibull(qrweibull(p, -1, 2, 0.8), -1, 2, 0.8)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

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