• Journal of the Korean Statistical Society
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• 제33권1호
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• pp.35-58
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• 2004

For fixed positive integers and $\textit{k}\;(n\;{\geq}\;{\textit{k}}\;+\;2)$, the exact probability distributions of non-overlapping and overlapping patterns of two failures separated by (i) exactly $textsc{k}$ successes, (ii) at least $\textit{k}$ successes and (iii) at most $\textit{k}$ successes have been obtained for Bernoulli independent and Markov dependent trials by using combinatorial technique. The waiting time distributions for the first occurrence and the $r^{th}$ (r > 1) occurrence of the patterns have also been obtained.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.709-723
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• 2024

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.

• 응용통계연구
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• 제23권1호
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• pp.123-138
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• 2010

총 28일에 걸친 매일의 불편감 증상점수에 근거하여 월경 전 증후군을 가린 후, 임상에서 의료인의 진단시 유용하게 사용될 수 있는 월경 전 증후패턴의 시작점을 추정한다. 이러한 추정에 앞서 불편감 증상점수가 과연 변화 추세를 보이는가의 검정이 우선되어야 하며, 모수적 단순회귀식에 의한 검정법과 비모수적 검정법을 적용한다. 실제 여성에게서 수집된 자료에 적용하여 분석한다. 증상점수의 직선적인 변화시점을 알아내는 단순회귀 방법과 직선 형태를 가정하지 않는 비모수적 검정법은 최적이 되는 상황이 서로 다를 것이며, 이를 모의실험으로 알아본다.