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 |
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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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| _version_ | 1849305303358636032 |
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| author | Gregory A. Tripsiannis Afroditi A. Papathanasiou Andreas N. Philippou |
| author_facet | Gregory A. Tripsiannis Afroditi A. Papathanasiou Andreas N. Philippou |
| author_sort | Gregory A. Tripsiannis |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-081ccb437eca450ca1ab2681f2f28a71 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-081ccb437eca450ca1ab2681f2f28a712025-08-20T03:55:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-0120031380181510.1155/S0161171203207250Generalized distributions of order k associated with success runs in Bernoulli trialsGregory A. Tripsiannis0Afroditi A. Papathanasiou1Andreas N. Philippou2Department of Medical Statistics, Faculty of Medicine, Demokritos University of Thrace, Alexandroupolis 68100, GreeceDepartment of Medical Statistics, Faculty of Medicine, Demokritos University of Thrace, Alexandroupolis 68100, GreeceDepartment of Mathematics, University of Patras, Patras, GreeceIn 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.http://dx.doi.org/10.1155/S0161171203207250 |
| spellingShingle | Gregory A. Tripsiannis Afroditi A. Papathanasiou Andreas N. Philippou Generalized distributions of order k associated with success runs in Bernoulli trials International Journal of Mathematics and Mathematical Sciences |
| title | Generalized distributions of order k associated with success runs in Bernoulli trials |
| title_full | Generalized distributions of order k associated with success runs in Bernoulli trials |
| title_fullStr | Generalized distributions of order k associated with success runs in Bernoulli trials |
| title_full_unstemmed | Generalized distributions of order k associated with success runs in Bernoulli trials |
| title_short | Generalized distributions of order k associated with success runs in Bernoulli trials |
| title_sort | generalized distributions of order k associated with success runs in bernoulli trials |
| url | http://dx.doi.org/10.1155/S0161171203207250 |
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