The Distributions of the Peak to Average and Peak to Sum Ratios Under Exponentiality

Tomasz J. Kozubowski (), Anna K. Panorska and Fares Qeadan
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Tomasz J. Kozubowski: University of Nevada, Department of Mathematics and Statistics, MS 084

Chapter Chapter 9 in Advances in Directional and Linear Statistics, 2011, pp 131-142 from Springer

Abstract: Abstract Let E 1, E 2, …, E N be independent and identically distributed exponential random variables, and let $$Y = \vee _{i = 1}^N$$ and S = ∑ i = 1 N E i be their maximum and sum, respectively. We review distributional properties of the peak to sum and peak to average ratios, R = Y ∕ S and $$\tilde{R} = Y/(S/N)$$ respectively, with deterministic N, and provide an extension to the case where N is itself a random variable, independent of the {E j }. Our results include explicit formulas for the relevant density and distribution functions, which apply to any distribution of N, as well as a particular example with geometrically distributed N. An example from climatology shows modeling potential of these models.

Keywords: Probability Density Function; Flood Risk Management; Exponential Random Variable; Deterministic Number; Potential Climate Change Impact (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2628-9_9

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DOI: 10.1007/978-3-7908-2628-9_9

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