poisson.m {energy} | R Documentation |
Returns the mean distance statistic for a goodness-of-fit test of Poisson distribution with unknown parameter.
poisson.m(x)
x |
vector of nonnegative integers, the sample data |
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.
The value of the M-statistic for testing Poisson distribution is returned.
Maria Rizzo rizzo@math.ohiou.edu
Szekely, G. J. and Rizzo, M. L. (2004) Mean Distance Test of Poisson Distribution, Statistics and Probability Letters, to appear.
x <- rpois(20, 1) poisson.m(x)