# WEIBULL3: Three-Parameter Weibull Distribution In FAdist: Distributions that are Sometimes Used in Hydrology

## Description

Density, distribution function, quantile function and random generation for the 3-parameter Weibull distribution with shape, scale, and threshold (or shift) parameters equal to `shape`, `scale`, and `thres`, respectively.

## Usage

 ```1 2 3 4``` ```dweibull3(x,shape,scale=1,thres=0,log=FALSE) pweibull3(q,shape,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE) qweibull3(p,shape,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE) rweibull3(n,shape,scale=1,thres=0) ```

## Arguments

 `x,q` vector of quantiles. `p` vector of probabilities. `n` number of observations. `shape` shape parameter. `scale` scale parameter. `thres` threshold (or shift) parameter. `log,log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

## Details

If Y is a random variable distributed according to a Weibull distribution (with shape and scale parameters), then X = Y+m has a 3-parameter Weibull distribution with shape and scale parameters corresponding to the shape and scale parameteres of Y, respectively; and threshold parameter m.

## Value

`dweibull3` gives the density, `pweibull3` gives the distribution function, `qweibull3` gives the quantile function, and `rweibull3` generates random deviates.

`dweibull`, `pweibull`, `qweibull`, `rweibull`

## Examples

 ```1 2 3 4``` ```m <- 100 x <- rweibull3(10,3,1,m) dweibull3(x,3,1,m) dweibull(x-m,3,1) ```

### Example output

```  0.9545343 0.9704338 1.1311981 0.5664526 0.4372810 0.6580542 0.6557038
 1.1171193 0.4816011 0.8984930
 0.9545343 0.9704338 1.1311981 0.5664526 0.4372810 0.6580542 0.6557038
 1.1171193 0.4816011 0.8984930
```

FAdist documentation built on April 17, 2020, 1:24 a.m.