Abstract
In this paper, we discuss discrete compound distributions, in which the counting distribution is a weighted Poisson distribution. The over- and under-dispersion of these distributions are then discussed by analyzing the Fisher index of dispersion as well as a newly introduced factorial moment to mean measure. Several cases of compounding distributions and weight functions are subsequently examined in detail.
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Acknowledgments
The first author was partially supported by the Bulgarian NSRF grant DDVU 0290/2011. The second author thanks the Natural Sciences and Engineering Research Council of Canada for funding this research, and for facilitating the visit of the first author to McMaster University during the summer of 2011. Finally, the authors express their sincere thanks to an anonymous reviewer for some useful comments and suggestions which led to this improved version of the manuscript.
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Minkova, L.D., Balakrishnan, N. Compound weighted Poisson distributions. Metrika 76, 543–558 (2013). https://doi.org/10.1007/s00184-012-0403-y
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DOI: https://doi.org/10.1007/s00184-012-0403-y