rweibull {evd}R Documentation

The Reversed Weibull Distribution

Description

Density function, 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.
p Vector of probabilities.
n Number of observations.
loc, scale, shape Location, scale and shape parameters (can be given as vectors).
log Logical; if TRUE, the log density is returned.
lower.tail Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The reversed Weibull distribution function with parameters loc = a, scale = b and shape = s is

G(x) = exp{-[-(z-a)/b]^s}

for z < a and one otherwise, where b > 0 and s > 0.

Value

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

Note

Within extreme value theory the reversed Weibull distibution is usually referred to as the Weibull distribution. I make a distinction to avoid confusion with the three-parameter distribution used in survival analysis, which is related by a change of sign to the distribution given above.

See Also

rfrechet, rgev, rgumbel

Examples

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

[Package evd version 2.2-4 Index]