testCn: Edf Test for Poisson Distribution Cn

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

testCn(x, n.boot)

Arguments

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

Details

The edf test of Poissonity Cn was proposed by Henze (1996). The test is based on the similarity between the edf of the random variable X, F_{n}(k), and the cdf of Poisson distribution with parameter λ = \hat{X}, F(k,\hat{λ}_{n}). The test statistic is a Cramer-von-Mises type of distance.

C_{n} = n ∑_{k = 0}^{∞} [F_{n}(k) - F(k;\hat{λ}_{n})]^2 f(k,\hat{λ}_{n})

f(k,\hat{λ}_{n}) denotes the pmf of Poisson distribution with parameter λ. The test is implemented by parametric boostrap with n.boot replicates

Value

The function testCn 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

Henze, N. (1996) Empirical-distribution-function goodness-of-fit tests for discrete models, The Canadian Journal of Statistics Vol 24 No 1, 81-93 https://www.jstor.org/stable/3315691?seq=1

Examples

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

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