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

Autor: Gregory A. Tripsiannis, Afroditi A. Papathanasiou, Andreas N. Philippou
Jazyk: angličtina
Rok vydání: 2003
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2003, Iss 13, Pp 801-815 (2003)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
01611712
DOI: 10.1155/S0161171203207250
Popis: 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.
Databáze: Directory of Open Access Journals
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