# GenPARETO: Generalized Pareto Distribution In FAdist: Distributions that are Sometimes Used in Hydrology

 GenPARETO R Documentation

## Generalized Pareto Distribution

### Description

Density, distribution function, quantile function and random generation for the generalized Pareto distribution with shape and scale parameters equal to `shape` and `scale`, respectively.

### Usage

```dgp(x,shape=1,scale=1,log=FALSE)
pgp(q,shape=1,scale=1,lower.tail=TRUE,log.p=FALSE)
qgp(p,shape=1,scale=1,lower.tail=TRUE,log.p=FALSE)
rgp(n,shape=1,scale=1)
```

### Arguments

 `x,q` vector of quantiles. `p` vector of probabilities. `n` number of observations. `shape` shape parameter. `scale` scale 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 X is a random variable distributed according to a generalized Pareto distribution, it has density
f(x) = 1/scale*(1-shape*x/scale)^((1-shape)/shape)

### Value

`dgp` gives the density, `pgp` gives the distribution function, `qgp` gives the quantile function, and `rgp` generates random deviates.

### References

Coles, S. (2001) An introduction to statistical modeling of extreme values. Springer

### Examples

```x <- rgp(1000,-.2,10)
hist(x,freq=FALSE,col='gray',border='white')