Generalized distributions of order k associated with success runs in Bernoulli trials
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 nega...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203207250 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |