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

 WEIBULL3 R Documentation

## Three-Parameter Weibull Distribution

### 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

```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

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

FAdist documentation built on March 18, 2022, 5:24 p.m.