The sampling distribution of the index of dispersion

Anderson, Jana C.; Siddiqui, M. M.

doi:10.1080/03610929408831294

Cited by 3 publications

(1 citation statement)

References 8 publications

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“…So, the result is only asymptotically valid and it does not work satisfactorily in practice. Anderson and Siddiqui (1994) derived the ®rst four moments of the index of dispersion for some discrete distributions. They also tried to develop the sampling distribution.…”

Section: The Variance Test (Or the Index Of Dispersion Test) And Relamentioning

confidence: 99%

A Simulation Comparison of Several Procedures for Testing the Poisson Assumption

Karlis

Xekalaki

2000

J Royal Statistical Soc D

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Summary. The importance of the Poisson distribution among the discrete distributions has led to the development of several hypothesis tests, for testing whether data come from a Poisson distribution against a variety of alternative distributions. An extended simulation comparison is presented concerning the power of such tests. To overcome biases caused by the use of asymptotic results for the null distribution of several tests, an extended simulation was performed for calculating the required critical points for all the tests. The results can be useful to researchers as a guide to selecting the appropriate test from several alternatives that are available.

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Section: The Variance Test (Or the Index Of Dispersion Test) And Relamentioning

confidence: 99%

A Simulation Comparison of Several Procedures for Testing the Poisson Assumption

Karlis

Xekalaki

2000

J Royal Statistical Soc D

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On the sampling distribution of Allan factor estimator for a homogeneous Poisson process and its use to test inhomogeneities at multiple scales

Serinaldi

Kilsby

2013

Physica A: Statistical Mechanics and its Applications

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An overview of goodness-of-fit tests for the Poisson distribution

Mijburgh

Visagie

2020

South African Statistical Journal

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The Poisson distribution has a large number of applications and is often used as a model in both a practical and a theoretical setting. As a result, various goodness-of-fit tests have been developed for this distribution. In this paper, we compare the finite sample power performance of ten of these tests against a wide range of alternative distributions for various sample sizes. The alternatives considered include, seemingly for the first time, weighted Poisson distributions. A number of additional tests are of historical importance although their power performance is not competitive against the remaining tests. These tests are discussed, but their powers are not included in the numerical analysis. The Monte Carlo study presented below indicates that the test with the best overall power performance is the test of Meintanis and Nikitin (2008), followed closely by the test of Rayner and Best (1990) (originally studied in Fisher, 1950).

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The sampling distribution of the index of dispersion

Cited by 3 publications

References 8 publications

A Simulation Comparison of Several Procedures for Testing the Poisson Assumption

A Simulation Comparison of Several Procedures for Testing the Poisson Assumption

On the sampling distribution of Allan factor estimator for a homogeneous Poisson process and its use to test inhomogeneities at multiple scales

An overview of goodness-of-fit tests for the Poisson distribution

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