Recurrence algorithms of waiting time for the success run of length $k$ in relation to generalized Fibonacci sequences

Jungtaek Oh; Chongjin Park; Sungsu Kim

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arXiv · 2210.08797

Recurrence algorithms of waiting time for the success run of length $k$ in relation to generalized Fibonacci sequences

Jungtaek Oh·Chongjin Park·Sungsu Kim

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Abstract

Let $V(k)$ denote the waiting time, the number of trials needed to get a consecutive $k$ ones. We propose recurrence algorithms for the probability distribution function (pdf) and the probability generating function (pgf) of $V(k)$ in sequences of independent and Markov dependent Bernoulli trials using generalized Fibonacci sequences of order $k$. Maximum likelihood estimation (MLE) methods for the probability distributions are presented in both cases with simulation examples.

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BibTeX RIS

Jungtaek Oh, Chongjin Park, Sungsu Kim. 2022-10-17. Recurrence algorithms of waiting time for the success run of length $k$ in relation to generalized Fibonacci sequences. https://arxiv.org/abs/2210.08797

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