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Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family. (English) Zbl 1166.62009
Summary: We generalise the Poisson-inverse Gaussian distribution to a three-parameter family, which includes the Poisson and discrete stable distributions as boundary cases. It is flexible in modelling count data sets with different tail heaviness. Although the family only has a closed-form probability generating function, a recursive method is developed for statistical inferences based on the likelihood. As an example, this new family is applied to data sets of citation counts of published articles.

MSC:
62E10 Characterization and structure theory of statistical distributions
60E07 Infinitely divisible distributions; stable distributions
62F10 Point estimation
62F03 Parametric hypothesis testing
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