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

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

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

energy documentation built on Sept. 15, 2017, 1:02 a.m.