# gp.test: Bootstrap test for the generalized Pareto distribution In goft: Tests of Fit for some Probability Distributions

## Description

Test of fit for the generalized Pareto distribution (gPd) with unknown parameters by Villasenor-Alva and Gonzalez-Estrada (2009).

## Usage

 `1` ```gp_test(x, B = 999) ```

## Arguments

 `x` numeric data vector containing a random sample of positive real numbers. `B` number of bootstrap samples used to approximate p-values. Default is `B=999`.

## Details

This bootstrap test for the null hypothesis H_0: a random sample has a gPd with unknown shape parameter gamma 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.

The gPd function with unknown shape and scale parameters gamma and sigma is 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, F(x) becomes the exponential distribution with scale parameter sigma:

1-exp(-x/sigma).

## Value

A list with class `"htest"` containing the following components.

 `p.value` an approximated p-value of the test using parametric bootstrap. `method` the character string "Bootstrap test of fit for the generalized Pareto distribution". `data.name` a character string giving the name of the data set. `pvalues` approximated p-values of the tests for H_0^- and H_0^+

## Author(s)

Elizabeth Gonzalez-Estrada [email protected], 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. http://dx.doi.org/10.1016/j.csda.2009.04.001

`gp_fit` for fitting a gPd to data.
 ```1 2 3 4 5``` ```# Testing the gPd hypothesis on the excesses above the threshold 0.165 ppm of the ozone # levels given in the o3 data set data(o3) o3levels <- o3\$ozone_level - 0.165 # ozone levels minus the threshold 0.165 ppm gp_test(o3levels) # testing the gPd hypothesis ```