testTn: Pgf Test for Poisson Distribution Tn

In MMH1997/TestPoissonity: Goodness-of-fit test for Poisson Distribution.

Description

Performs the probability-generating function goodness-of-fit test of Poisson distribution with unknown parameter.

Usage

testTn(x, n.boot)

Arguments

x	vector of nonnegative integers, the sample data.
n.boot	number of bootstrap replicates.

Details

The pgf test of Poissonity Tn was proposed by Baringhaus and Henze (1992). The test is based on the similarity between the empirical probability-generating function of the random variable X and the pgf of a Poisson distribution with parameter mean of X. The test statistic is a square similarity measure.

T_{n} = \int_{0}^{1} [\bar{X}_{n} g_{n}(s) - g`_{n}(s)]^2 ds

g_{n}(s) denotes pgf of X.

The test is implemented by parametric boostrap with n.boot replicates.

Value

The function testTn returns a list with class htest containing:

	Description of test.
data	Description of data.
test statistic	Value of test statistic.
p-value	approximate p-value of the test.
mean	sample mean.

Author(s)

Manuel Mendez Hurtado [e-mail]

References

Baringhaus, L., Henze, N. (1992) A goodness of fit test for the Poisson distribution based on the empirical generating function Statist. Probab. Lett. Vol 13, 269-274 https://ideas.repec.org/a/eee/stapro/v13y1992i4p269-274.html

Examples

x <- rpois(20,2)
testTn(x, n.boot = 500)

MMH1997/TestPoissonity documentation built on Dec. 17, 2021, 2:11 a.m.