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| Titel: |
Polya, Inverse Polya, and Circular Polya Distributions of Order k for l-Overlapping Success Runs |
| Auteur: |
Makri, Frosso S. Philippou, Andreas N. Psillakis, Zaharias M. |
| Verschenen in: |
Communications in statistics |
| Paginering: | Jaargang 36 (2007) nr. 4 pagina's 657-668 |
| Jaar: |
2007-03 |
| Inhoud: |
The Polya-Eggenberger sampling scheme is considered, i.e., a ball is drawn at random from an urn containing w white (success) balls and b black (failure) balls, its color is observed, and then it is returned to the urn along with s additional balls of the same color of the ball drawn. This scheme is repeated n times, and Nn, k, l, s denotes the number of l-overlapping success runs of length k. If the balls drawn are arranged on a circle, the number of l-overlapping success runs of length k is denoted by [image omitted]. Finally, Wr, k, l, s denotes the number of drawings according to the Polya-Eggenberger sampling scheme until the rth occurrence of the l-overlapping success run of length k. Polya, inverse Polya, and circular Polya distributions of order k for l-overlapping success runs of length k are introduced as the distributions, respectively, of Nn, k,l, s, Wr, k, l, s, and [image omitted]. These distributions include as special cases known and new distributions of order k. Exact formulae are derived for their probability distribution functions and means, which generalize several results on well-known distributions of order k. Asymptotic results of the new distributions are also given, relating them, respectively, to the binomial, negative binomial, and circular binomial distributions of order k for l-overlapping success runs of length k. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 14 van 16 gevonden artikelen
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