poisson.mtest {energy} | R Documentation |
Performs the mean distance goodness-of-fit test of Poisson distribution with unknown parameter.
poisson.mtest(x, R = 999) poisson.m(x)
x |
vector of nonnegative integers, the sample data |
R |
number of bootstrap replicates |
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.
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 |
Maria L. Rizzo mrizzo @ bgnet.bgsu.edu and Gabor J. Szekely gabors @ bgnet.bgsu.edu
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.
x <- rpois(20, 1) poisson.m(x) poisson.mtest(x, R = 199)