testdelta1_a: Pgf Test for Poisson Distribution Delta_1a

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

testdelta1_a(x, a, n.boot)

Arguments

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

Details

The test of Poissonity Δ_1a 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 L1 norm.

\hat{Δ}^\star_{1,a} =\int_{0}^{1} |\hat{g}(t) - [\hat{g}(t)(\frac{t+1}{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 testdelta1_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
sample estimates	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)
testdelta1_a(x, a = 3, n.boot = 500)

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