DescTools (version 0.99.54)

RevWeibull: The Reverse Weibull Distribution

Description

Density function, distribution function, quantile function and random generation for the reverse (or negative) Weibull distribution with location, scale and shape parameters.

Usage

dRevWeibull(x, loc=0, scale=1, shape=1, log = FALSE)
pRevWeibull(q, loc=0, scale=1, shape=1, lower.tail = TRUE)
qRevWeibull(p, loc=0, scale=1, shape=1, lower.tail = TRUE)
rRevWeibull(n, loc=0, scale=1, shape=1)
dNegWeibull(x, loc=0, scale=1, shape=1, log = FALSE)
pNegWeibull(q, loc=0, scale=1, shape=1, lower.tail = TRUE)
qNegWeibull(p, loc=0, scale=1, shape=1, lower.tail = TRUE)
rNegWeibull(n, loc=0, scale=1, shape=1)

Value

dRevWeibull and dNegWeibull give the density function,

pRevWeibull and pNegWeibull give the distribution function,

qRevWeibull and qNegWeibull give the quantile function,

rRevWeibull and rNegWeibull generate random deviates.

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]

Author

Alec Stephenson <[e-mail]>

Details

The reverse (or negative) Weibull distribution function with parameters \(loc = a\), \(scale = b\) and \(shape = s\) 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 \(s > 0\).

See Also

rFrechet, rGenExtrVal, rGumbel

Examples

dRevWeibull(-5:-3, -1, 0.5, 0.8)
pRevWeibull(-5:-3, -1, 0.5, 0.8)
qRevWeibull(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rRevWeibull(6, -1, 0.5, 0.8)
p <- (1:9)/10
pRevWeibull(qRevWeibull(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