Descents following maximal values in samples of geometric random variables

Margaret Archibald, Aubrey Blecher, Charlotte Brennan and Arnold Knopfmacher

Statistics & Probability Letters, 2015, vol. 97, issue C, 229-240

Abstract: We consider samples of geometric random variables and find the average size of the descent after the first and last maximal values. These are asymptotically but not exactly equal, with the descent after the last maximum being slightly larger than that after the first. Thereafter we calculate the probability that the descent after the last maximum is equal to, greater than, or less than the descent after the first maximum. Finally we compute asymptotic expansions for these probabilities.

Keywords: Geometric random variable; Generating function; Rice’s method; Asymptotic approximation; Descent; Maximum (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2014.11.023

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