testdelta2_a: Pgf Test for Poisson Distribution Delta_2a

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

Description

Performs the empirical distribution function goodness-of-fit test of Poisson distribution with unknown parameter

Usage

testdelta2_a(x, n.boot, a)

Arguments

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

Details

The test of Poissonity Δ_2a was proposed by Puig and Weibb (2020). The test is based on some characterizations like the Binomial thinning operator for the probability generating function of a Poisson distribution. The test statistic is a weighted similarity measure based on the L2 norm.

\hat{Δ}_{2,a}=\int_{0}^{1} (\hat{g}(t) - [\hat{g}(t)(\frac{t+1}{2})]^2) ^2 t^a dt

\hat{g}(t) denotes the empirical pobability generating function of X.

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

Value

The function testdelta2_a 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

Puig, P and Weibb, C. H. (2020) Empirical-distribution-function goodness-of-fit tests for discrete models, Computational Statistics and Data Analysis Vol 144, 1-12 https://www.sciencedirect.com/science/article/pii/S0167947319302336

Examples

x <- rpois(20,2)
testdelta2_a(x, n.boot = 500, a = 3)

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