Generalized Polya-Eggenberger model of order \(k\) via lattice path approach. (English) Zbl 1021.62006
Summary: In this paper, based on the Polya-Eggenberger model, we have developed a generalized Polya-Eggenberger model of order \(k\) via a lattice path approach. It generates a generalized Polya Eggenberger distribution [K. Sen and A. Mishra, Sankhyā, Ser. A 58, 243-251 (1996; Zbl 0889.60009)]. It generates a number of other new discrete distributions of order \(k\), namely, uniform distribution of order \(k\), beta-binomial distribution of order \(k\), factorial distribution of order \(k\), beta-Pascal distribution of order \(k\), and Haight distribution of order \(k\) [F. A. Haight, Biometrika 48, 167-173 (1961; Zbl 0095.12603)] as particular cases, besides the already known ones. Distributions of order \(k\) can be applied in obtaining reliability of some complex systems, viz, consecutive-\(k\)-out-of-\(n\): \(F\) systems.
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
| 60C05 | Combinatorial probability |
Keywords:
distributions of order k; lattice-path approach; Polya-Eggenberger sampling scheme; balls-into-cells techniqueReferences:
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