RevWeibull {DescTools} R Documentation

## 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)


### 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 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.

### 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.

### Note

Within extreme value theory the reverse Weibull distibution (also known as the negative Weibull distribution) is often referred to as the Weibull distribution. We 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.

### Author(s)

Alec Stephenson <alec_stephenson@hotmail.com>

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


[Package DescTools version 0.99.51 Index]