# poisson.mtest: Mean Distance Test for Poisson Distribution In energy: E-Statistics: Multivariate Inference via the Energy of Data

## Description

Performs the mean distance goodness-of-fit test of Poisson distribution with unknown parameter.

## Usage

 1 2 poisson.mtest(x, R) poisson.m(x) 

## Arguments

 x vector of nonnegative integers, the sample data R number of bootstrap replicates

## Details

The mean distance test of Poissonity was proposed and implemented by Szekely and Rizzo (2004). The test is based on the result that the sequence of expected values E|X-j|, j=0,1,2,... characterizes the distribution of the random variable X. As an application of this characterization one can get an estimator \hat F(j) of the CDF. The test statistic (see poisson.m) is a Cramer-von Mises type of distance, with M-estimates replacing the usual EDF estimates of the CDF:

M_n = n sum [j>=0] (\hat F(j) - F(j; \hat λ))^2 f(j; \hat λ).

The test is implemented by parametric bootstrap with R replicates.

## Value

The function poisson.m returns the test statistic. The function poisson.mtest returns a list with class htest containing

 method Description of test statistic observed value of the test statistic p.value approximate p-value of the test data.name description of data estimate sample mean

## Author(s)

Maria L. Rizzo mrizzo @ bgsu.edu and Gabor J. Szekely

## References

Szekely, G. J. and Rizzo, M. L. (2004) Mean Distance Test of Poisson Distribution, Statistics and Probability Letters, 67/3, 241-247. http://dx.doi.org/10.1016/j.spl.2004.01.005.

## Examples

 1 2 3 4  x <- rpois(20, 1) poisson.m(x) poisson.mtest(x, R = 199) 

energy documentation built on Aug. 12, 2018, 1:04 a.m.