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.
Original language | English |
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Pages (from-to) | 709-723 |
Number of pages | 15 |
Journal | Journal of Applied Mathematics and Informatics |
Volume | 42 |
Issue number | 3 |
DOIs | |
State | Published - 2024 |
Keywords
- Geometric distribution of order k
- modified geometric distribution of order k
- runs and patterns statistics
- weighted average