Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

`x` |
numeric data vector containing a random sample of positive real numbers. |

`B` |
number of bootstrap samples used to approximate p-values. Default is |

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).*

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 |

Elizabeth Gonzalez-Estrada [email protected], Jose A. Villasenor-Alva

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.

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goft documentation built on Nov. 17, 2017, 6:17 a.m.

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