# RevWeibull: The Reverse Weibull Distribution In DescTools: Tools for Descriptive Statistics

## Description

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

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```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(x) = exp{-[-(z-a)/b]^s}

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`
 ```1 2 3 4 5 6 7``` ```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 ```