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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.

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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