poisson.m {energy}R Documentation

Mean Distance Statistic for Testing Poisson Distribution

Description

Returns the mean distance statistic for a goodness-of-fit test of Poisson distribution with unknown parameter.

Usage

poisson.m(x)

Arguments

x vector of nonnegative integers, the sample data

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 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).

See Szekely and Rizzo (2004) for the computing formula.

Value

The value of the M-statistic for testing Poisson distribution is returned.

Author(s)

Maria Rizzo rizzo@math.ohiou.edu

References

Szekely, G. J. and Rizzo, M. L. (2004) Mean Distance Test of Poisson Distribution, Statistics and Probability Letters, to appear.

See Also

poisson.mtest

Examples

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

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