R: The Reverse Weibull Distribution

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(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>

### 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

[Package DescTools version 0.99.28 Index]