Generalized distributions of order k associated with success runs in Bernoulli trials

Gregory A. Tripsiannis, Afroditi A. Papathanasiou and Andreas N. Philippou

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-15

Abstract:

In a sequence of independent Bernoulli trials, by counting multidimensional lattice paths in order to compute the probability of a first-passage event, we derive and study a generalized negative binomial distribution of order k , type I , which extends to distributions of order k , the generalized negative binomial distribution of Jain and Consul (1971), and includes as a special case the negative binomial distribution of order k , type I , of Philippou et al. (1983). This new distribution gives rise in the limit to generalized logarithmic and Borel-Tanner distributions and, by compounding, to the generalized Pólya distribution of the same order and type. Limiting cases are considered and an application to observed data is presented.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:749878

DOI: 10.1155/S0161171203207250

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