KS {gofgamma}

statistic of the Kolmogorov-Smirnov goodness-of-fit test for the gamma family

Description

This function computes the goodness-of-fit test statistic for the gamma family in the spirit of Kolmogorov and Smirnov. Note that this tests the composite hypothesis of fit to the family of gamma distributions, i.e. a bootstrap procedure is implemented to perform the test, see crit.values.

Usage

KS(data, k_estimator)

Arguments

data

a vector of positive numbers. NOTE: data has to be the rescaled data, i.e. devided by the estimated scale parameter!

k_estimator

value of the estimated shape parameter.

Details

The Kolmogorov-Smirnov test is computed as described in Henze et. al. (2012). Values of k_estimator are found by gamma_est.

Value

value of the test statistic

References

Henze, N., Meintanis, S.G., Ebner, B. (2012) "Goodness-of-fit tests for the Gamma distribution based on the empirical Laplace transform". Communications in Statistics - Theory and Methods, 41(9): 1543-1556. DOI

Examples

X=stats::rgamma(20,3,6)
KS(X,k_estimator=gamma_est(X)[1])