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

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  • Gregory A. Tripsiannis
  • Afroditi A. Papathanasiou
  • Andreas N. Philippou

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.

Suggested Citation

  • Gregory A. Tripsiannis & Afroditi A. Papathanasiou & Andreas N. Philippou, 2003. "Generalized distributions of order k associated with success runs in Bernoulli trials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-15, January.
  • Handle: RePEc:hin:jijmms:749878
    DOI: 10.1155/S0161171203207250
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