Generalized binomial and negative binomial distributions of order<Emphasis Type="Italic">k</Emphasis> by the<Emphasis Type="Italic">l</Emphasis>-overlapping enumeration scheme |
| |
Authors: | Kiyoshi Inoue Sigeo Aki |
| |
Institution: | (1) Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, 560-8531 Osaka, Japan;(2) Present address: The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106-8569 Tokyo, Japan |
| |
Abstract: | In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The
probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution
of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration
scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number
of trials and derive the probability generating functions. The present work extends several properties of distributions of
orderk and leads us a new type of geneses of the discrete distributions. |
| |
Keywords: | Run waiting time binomial distribution negative binomial distribution Poisson distribution double generating function probability generating function Markov chain Markov chain imbedding method |
本文献已被 SpringerLink 等数据库收录! |
|