gp_test {goft}

Bootstrap test for the generalized Pareto distribution

Description

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

Usage

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 - \left[ 1 + \frac{\gamma x}{ \sigma } \right] ^ { - 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:

F(x) = 1 -exp\left(-x/\sigma \right).

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 [e-mail], 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

See Also

gp_fit for fitting a gPd to data.

Examples

# 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