Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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MODIFIED GEOMETRIC DISTRIBUTION OF ORDER k AND ITS APPLICATIONS

  • JUNGTAEK OH (Department of Biomedical Science, School of Medicine, Kyungpook National University, Clinical Omics Center, Kyungpook National University, The Institute of Industrial Technology, Changwon National University) ;
  • KYEONG EUN LEE (Department of Statistics, Kyungpook National University)
  • Received : 2024.01.23
  • Accepted : 2024.05.10
  • Published : 2024.05.30
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Abstract

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

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Acknowledgement

The author would like to thank Emeritus Prof. Dr. Chongjin Park whose comments led to significant improvements in this manuscript.

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