test.CM {gofgamma}

The Cramer-von Mises goodness-of-fit test for the gamma family

Description

This function computes the goodness-of-fit test for the gamma family in the spirit of Cramer and von Mises. 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.

Usage

test.CM(data, boot = 500, alpha = 0.05)

Arguments

data

a vector of positive numbers.

boot

number of bootstrap iterations used to obtain critical value.

alpha

level of significance of the test.

Details

The Cramér-von Mises test is computed as described in Henze et. al. (2012). Critical values are obtained by a parametric bootstrap procedure, see crit.values.

Value

a list containing the value of the test statistic, the approximated critical value and a test decision on the significance level alpha:

$T.value

the value of the test statistic.

$cv

the approximated critical value.

$par.est

number of points used in approximation.

$Decision

the comparison of the critical value and the value of the test statistic.

$sig.level

level of significance chosen.

$boot.run

number of bootstrap iterations.

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

test.CM(stats::rgamma(20,3,6),boot=100)