Comparison Of Expectations Of The Extreme Of Sums And The Sum Of Extremes From Gamma Distributions
This paper considers the expectations of the extremes from gamma distributions. An approximation to these expectations based on the limiting extreme value distribution is shown to give very good results. These results are applied to the problem of comparing the expected value of the maximum of a sum to the sum of the expected value of the maximums. That is, suppose a random variable is composed of a sum of r independent gamma variables. For a random sample of size n, how does the expected value of the maximum of the sum compare to the sum of the expected values of the maximums, based on samples of size n, from the individual gamma variables? Similar results are provided for comparing the sum of minimums to the minimum of a sum, for random samples of size n. The problem was motivated by considering the most efficient way to purchase electrical power when the rates for different meters were based on peak loads. © 1993, Taylor & Francis Group, LLC. All rights reserved.
L. J. Bain and G. Gan, "Comparison Of Expectations Of The Extreme Of Sums And The Sum Of Extremes From Gamma Distributions," Journal of Statistical Computation and Simulation, vol. 47, no. 3 thru 4, pp. 219 - 225, Taylor and Francis Group; Taylor and Francis, Oct 1993.
The definitive version is available at https://doi.org/10.1080/00949659308811531
Mathematics and Statistics
Keywords and Phrases
Expectations; Extreme value distribution; Gamma distribution; Maximums; Minimums
International Standard Serial Number (ISSN)
Article - Journal
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01 Oct 1993