Mean Distance Test for Poisson Distribution

Description

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

Usage

poisson.mtest(x, R = 999)
poisson.m(x)

Arguments

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

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

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

Results