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

 GAMMA3 R Documentation

## Three-Parameter Gamma Distribution (also known as Pearson type III distribution)

### 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

```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.

### See Also

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

### Examples

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

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