R: The Reverse Weibull Distribution

rweibull {evd} | 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

    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)

    dnweibull(x, loc=0, scale=1, shape=1, log = FALSE)
    pnweibull(q, loc=0, scale=1, shape=1, lower.tail = TRUE)
    qnweibull(p, loc=0, scale=1, shape=1, lower.tail = TRUE)
    rnweibull(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 \code{loc} = a, \code{scale} = b and \code{shape} = s is

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

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

### Value

`drweibull` and `dnweibull` give the density function, `prweibull` and `pnweibull` give the distribution function, `qrweibull` and `qnweibull` give the quantile function, `rrweibull` and `rnweibull` 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.

### 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 2.3-3 Index]