Description Usage Arguments Details Value Author(s) References Examples

Performs the mean distance goodness-of-fit test of Poisson distribution with unknown parameter.

1 2 | ```
poisson.mtest(x, R)
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 @ bgsu.edu and Gabor J. Szekely

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.

1 2 3 4 | ```
x <- rpois(20, 1)
poisson.m(x)
poisson.mtest(x, R = 199)
``` |

energy documentation built on Sept. 15, 2017, 1:02 a.m.

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