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.

`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)
##  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
```

[Package evd version 2.2-4 Index]