# GAMMA3: Three-Parameter Gamma Distribution (also known as Pearson... In FAdist: Distributions that are Sometimes Used in Hydrology

## Description

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

## Usage

 ```1 2 3 4``` ```dgamma3(x,shape=1,scale=1,thres=0,log=FALSE) pgamma3(q,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE) qgamma3(p,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE) rgamma3(n,shape=1,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 gamma distribution (with shape and scale parameters), then X = Y+m has a 3-parameter gamma distribution with the same shape and scale parameters, and with threshold (or shift) parameter m.

## Value

`dgamma3` gives the density, `pgamma3` gives the distribution function, `qgamma3` gives the quantile function, and `rgamma3` generates random deviates.

## References

Bobee, B. and F. Ashkar (1991). The Gamma Family and Derived Distributions Applied in Hydrology. Water Resources Publications, Littleton, Colo., 217 p.

`dgamma`, `pgamma`, `qgamma`, `rgamma`

## Examples

 ```1 2 3 4``` ```thres <- 10 x <- rgamma3(n=10,shape=2,scale=11,thres=thres) dgamma3(x,2,11,thres) dgamma(x-thres,2,1/11) ```

### Example output

```  0.0326004734 0.0106116184 0.0132840252 0.0269172309 0.0077103519
 0.0030461017 0.0005155047 0.0315659821 0.0050922425 0.0235400470
 0.0326004734 0.0106116184 0.0132840252 0.0269172309 0.0077103519
 0.0030461017 0.0005155047 0.0315659821 0.0050922425 0.0235400470
```

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