Joint distribution of numbers of occurrences of countably many runs of specified lengths in a sequence of discrete random variables

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2025-09-25 DOI:10.1016/j.jspi.2025.106353

Kiyoshi Inoue

引用次数: 0

Abstract

In this paper, we consider the joint distribution of numbers of occurrences of countably many runs of several lengths in a sequence of nonnegative integer valued independent and identically distributed random variables through the generating functions. We propose a generalization of the potential partition polynomials, which gives effective computational tools for the derivation of probability functions. The waiting time problems associated with infinitely many runs are investigated and formulae for the evaluation of the generating functions are given. The results presented here provide a wide framework for developing the multivariate distribution theory of runs. Finally, we discuss several applications and numerical examples to show how our theoretical results are applied to the investigation of runs, as well as parameter estimation problems.

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离散随机变量序列中指定长度的可数多次运行的出现次数的联合分布

本文通过生成函数研究了非负整数值独立同分布随机变量序列中若干长度的可数多次运行的出现次数的联合分布。我们提出了一种潜在配分多项式的推广方法，它为概率函数的推导提供了有效的计算工具。研究了无限次运行的等待时间问题，给出了生成函数的求值公式。本文提出的结果为发展多变量运行分布理论提供了一个广泛的框架。最后，我们讨论了几个应用和数值例子，以显示我们的理论结果如何应用于研究运行，以及参数估计问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.