Distribution of Record Statistics in aq-Factorially Increasing Population
| Autor: | Ch. A. Charalambides |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
education.field_of_study Binomial (polynomial) Distribution (number theory) Population Probability density function Geometric distribution Riemann zeta function Combinatorics symbols.namesake Statistics symbols Probability distribution education Mathematics Sign (mathematics) |
| Zdroj: | Communications in Statistics - Theory and Methods. 38:2042-2055 |
| ISSN: | 1532-415X 0361-0926 |
| DOI: | 10.1080/03610920802711759 |
| Popis: | The probability function and binomial moments of the number N n of (upper) records up to time (index) n in a q-factorially increasing population are obtained in terms of the non central signless q-Stirling numbers of the first kind. As a corollary, the probability function of the time T k of the kth record is also expressed in terms of the non central signless q-Stirling numbers of the first kind. The mean of T k is obtained as a q-series with terms of alternating sign. Finally, the probability function of the inter-record time W k = T k − T k−1 is obtained as a sum of a finite number of terms of q-numbers. The mean of W k is expressed by a q-series. As k increases to infinity the distribution of W k converges to a geometric distribution with failure probability q. Additional properties of the non central q-Stirling numbers of the first kind, which facilitate the present study, are derived. |
| Databáze: | OpenAIRE |
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