# Bootstrap goodness-of-fit test for the generalized Pareto distribution

### Description

This function computes the bootstrap goodness-of-fit test by Villasenor-Alva and Gonzalez-Estrada (2009) for testing the null hypothesis
*H_0:* a random sample has a generalized Pareto distribution (gPd) with unknown shape parameter
*gamma*, which is a real number.

### Usage

1 | ```
gpd.test(x,J)
``` |

### Arguments

`x` |
numeric data vector containing a random sample from a distribution function with support on the positive real numbers. |

`J` |
number of bootstrap samples. This is an optional argument. Default |

### Details

The bootstrap goodness-of-fit test for the gPd is an intersection-union test for the hypotheses *H_0^-:* a random sample has a gPd with *gamma <0 *, and *H_0^+:* a random sample has a gPd with *gamma >=0*.
Thus, heavy and non-heavy tailed gPd's are included in the null hypothesis. The parametric bootstrap is performed on *gamma* for each of the two hypotheses.

We consider the distribution function of the gPd with shape and scale parameters *gamma* and *sigma* given by

* F(x) = 1 - [ 1 + gamma x / sigma ]^(-1/gamma)*

where *gamma* is a real number, *sigma > 0* and *1 + gamma x / sigma > 0*. When *gamma =
0*, we have the exponential distribution with scale parameter *sigma*:

*1-exp(-x/sigma)*

### Value

A list with the following components.

`boot.test` |
a list with class |

`p.values` |
the p-values of the tests of the hypotheses |

### Author(s)

Elizabeth Gonzalez Estrada egonzalez@colpos.mx, Jose A. Villasenor Alva

### References

Villasenor-Alva, J.A. and Gonzalez-Estrada, E. (2009). A bootstrap goodness of fit test for the generalized Pareto distribution. *Computational Statistics and Data Analysis*,**53**,11,3835-3841.

### See Also

`gpd.fit`

for fitting a gPd to data, `rgp`

for generating gPd random numbers.

### Examples

1 2 | ```
x <- rgp(20,shape = 1) ## Random sample of size 20
gpd.test(x) ## Testing the gPd hypothesis on x
``` |