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.


Mathematics and Statistics

Keywords and Phrases

Expectations; Extreme value distribution; Gamma distribution; Maximums; Minimums

International Standard Serial Number (ISSN)

1563-5163; 0094-9655

Document Type

Article - Journal

Document Version


File Type





© 2023 Taylor and Francis Group; Taylor and Francis, All rights reserved.

Publication Date

01 Oct 1993