rweibull {evd} | R Documentation

## The Reversed Weibull Distribution

### Description

Density function, distribution function, quantile function and random generation for the reversed 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)

### 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 reversed 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

`drweibull` gives the density function, `prweibull` gives the distribution function, `qrweibull` gives the quantile function, and `rrweibull` generates random deviates.

### Note

Within extreme value theory the reversed Weibull distibution is usually referred to as the Weibull distribution. I 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

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