Generalized distributions of orderkassociated with success runs in Bernoulli trials
2003 ◽
Vol 2003
(13)
◽
pp. 801-815
Keyword(s):
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 orderk, typeI, which extends to distributions of orderk, the generalized negative binomial distribution of Jain and Consul (1971), and includes as a special case the negative binomial distribution of orderk, typeI, 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.
2002 ◽
Vol 29
(12)
◽
pp. 727-736
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1978 ◽
Vol 34
(2)
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pp. 223-224
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2021 ◽
Vol 10
(1)
◽
pp. 77-84
1980 ◽
Vol 39
(2)
◽
pp. 231-237
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1997 ◽
Vol 18
(1)
◽
pp. 189-198
1986 ◽
Vol 40
(3)
◽
pp. 141-144
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