R: Mean Distance Test for Poisson Distribution

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)
    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)

[Package energy version 1.7-6 Index]