The Linear Combination of Logistic and Gumbel Random Variables

Article type: Research Article

Authors: Nadarajah, Saralees | Kotz, Samuel

Affiliations: Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA. E-mail: [email protected] | Department of Engineering Management and Systems Engineering, The George Washington University, Washington, D.C. 20052, USA. E-mail: [email protected]

Abstract: The exact distribution of the linear combination αX + βY is derived when X and Y are independent logistic and Gumbel random variables. A measure of entropy of the linear combination is investigated. Computer programs are provided for generating tabulations of the percentage points associated with the linear combination. The work is motivated by problems in automation, control, fuzzy sets, neurocomputing and other areas of computer science.

Keywords: Entropy, Gumbel distribution, Linear combinations of random variables, Logistic distribution

Journal: Fundamenta Informaticae, vol. 74, no. 2-3, pp. 341-350, 2006