The Joint Distribution of the Sum and the Maximum of IID Exponential Random Variables |
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| Authors: | Fares Qeadan Anna K. Panorska |
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| Affiliation: | 1. Department of Statistics and Probability , Michigan State University , East Lansing , Michigan , USA;2. Department of Mathematics and Statistics , University of Nevada , Reno , Nevada , USA |
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| Abstract: | The authors establish the joint distribution of the sum X and the maximum Y of IID exponential random variables. They derive exact formuli describing the random vector (X, Y), including its joint PDF, CDF, and other characteristics; marginal and conditional distributions; moments and related parameters; and stochastic representations leading to further properties of infinite divisibility and self-decomposability. The authors also discuss parameter estimation and include an example from climatology that illustrates the modeling potential of this new bivariate model. |
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| Keywords: | Bivariate distribution Generalized exponential distribution Geometric distribution Infinite divisibility Maximum likelihood estimation Peak to average ratio Precipitation Stochastic representation |
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