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Quasi-negative binomial distribution: properties and applications. (English) Zbl 1328.62175

Summary: In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions, are investigated. It is shown that the moments do not exist in some situations and the limiting distribution of QNBD is the generalized Poisson distribution under certain conditions. A zero-inflated QNBD is also defined. Applications of QNBD and zero-inflated QNBD in various fields are presented and compared with some other existing distributions including Poisson, generalized Poisson and negative binomial distributions as well as their zero-inflated versions. In general, the QNBD or its zero-inflated version performs better than the other models based on the chi-square statistic and the Akaike Information Criterion, especially for the cases where the data are highly skewed, have heavy tails or excessive numbers of zeros.

MSC:

62F15 Bayesian inference
62E20 Asymptotic distribution theory in statistics
60E05 Probability distributions: general theory
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