Geometric random variables: Descents following maxima

Margaret Archibald, Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher and Helmut Prodinger

Statistics & Probability Letters, 2017, vol. 124, issue C, 140-147

Abstract: We study descents from maximal elements in samples of geometric random variables and consider two different averages for this statistic. We then compare the asymptotics of these averages as the number of parts in the samples tends to infinity, and also find an asymptotic expression for the mean of the greatest descent after a maximum value in such a sample.

Keywords: Geometric random variable; Generating function; Rice’s method; Mellin transform; Asymptotic approximation (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.01.017

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