Advances and Applications in Statistics
Volume 37, Issue 1, Pages 13 - 35
(November 2013)
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COMPARATIVE ANALYSIS OF DISPERSION MODELS
I. C. Kipchirchir
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Abstract: The negative binomial distribution has been widely used and to a lesser extent the Neyman Type A distribution, whereas the Pólya-Aeppli distribution has received no attention in modelling overdispersed (clustered) populations. On the other hand, the Poisson distribution is naturally used to model random populations.
The aim of this paper is to carry out a comparative analysis of the aforementioned distributions based on index of patchiness, correlation, skewness and kurtosis.
The study revealed that the negative binomial, the Neyman Type A and the Pólya-Aeppli distributions are equivalent in describing dispersion and they have Poisson as a limiting distribution as contagion breaks down to randomness. However, the distributions differ in terms of skewness and kurtosis, though the Pólya-Aeppli is closer to the negative binomial than the Neyman Type A. Degree of patchiness increases with degree of asymmetry and peakedness (skewness and kurtosis) of a distribution. However, index of patchiness depends on second order moments, hence does not discriminate overdispersion models in terms of skewness and kurtosis. |
Keywords and phrases: negative binomial, Neyman Type A, Pólya-Aeppli, Poisson, overdispersion, randomness, index of patchiness, correlation, skewness, kurtosis. |
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