poisson.mtest {energy}R Documentation

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)

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

A list with class etest.poisson containing

method Description of test
statistic Observed value of the test statistic
p.value Approximate p-value of the test
n Sample size
lambda Sample mean
R Number of replicates
replicates Vector of replicates of the statistic

Author(s)

Maria L. Rizzo rizzo@math.ohiou.edu and Gabor J. Szekely gabors@bgnet.bgsu.edu

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.

See Also

poisson.m

Examples

 x <- rpois(20, 1)
 poisson.mtest(x)
 

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