On a Waiting Time Distribution in a Sequence of Bernoulli Trials
نویسنده
چکیده
Abs t rac t . In the present article we investigate the exact distribution of the waiting time for the r-th non-overlapping appearance of a pair of successes separated by at most k 2 failures (k > 2) in a sequence of independent and identically distributed (rid) Bernoulli trials. Formulae are provided for the probability distribution function, probability generating function and moments and some asymptotic results are discussed. Expressions in terms of certain generalised Fibonacci numbers and polynomials are also included.
منابع مشابه
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Runs and patterns in a sequence of Bernoulli trials and multi-state trials have broadly been used for various purposes and in many areas of statistics and applied probability. Recently, Fu and Koutras (1994) developed a new method based on finite Markov chain imbedding technique to study the exact distributions for the number of specified runs and patterns in a sequence of Bernoulli trials. In ...
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تاریخ انتشار 2004