A combinatorial problem from sooner waiting time problems with run and frequency quotas

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:321

Article

Gao, Tangan ; Wu, Mengnien

关键词: combinatorial counting problem;    multinomial coefficients;    Markov dependent trials;    waiting time random variables;    probability generating functions;   

DOI  :  10.1016/j.jmaa.2006.03.071

来源: Elsevier

【 摘 要 】

In this paper. we study the problem of finding the number of integer solutions solving z(1) + (.) (.) (.) + z(k) <= w, 1 <= z(i) <= r, i = 1, . . . . , k, 1 <= k < f for given f, r, w is an element of N with w >= max (f, r). This problem is naturally from calculating exact distributions of some sooner waiting time random variables of run and frequency quotas in statistics. We present several solutions to the problem and develop an algorithm for the sooner waiting time problems. Numerical results are given to show the efficiency of our algorithm for calculating the exact distributions of the sooner waiting time random variable. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free