# rweibull: The Reverse Weibull Distribution In evd: Functions for Extreme Value Distributions

## 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``` ```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.

`rfrechet`, `rgev`, `rgumbel`

## Examples

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

### Example output

```[1] 0.005386194 0.016885315 0.058502349
[1] 0.005102464 0.015101477 0.048246445
[1] 1.969986 1.923317 1.862180 1.784071
[1] -2.141003 -1.152556 -1.385156 -1.979736 -1.269373 -1.105807
[1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
```

evd documentation built on May 1, 2019, 10:11 p.m.