On the Linear Combination of Exponential and Gamma Random Variables

Authors

Saralees Nadarajah, University of Nebraska-LincolnFollow
Samuel Kotz, George Washington University, Washington, DC

Document Type

Article

Date of this Version

2005

Citation

Entropy 2005, 7[2], pp. 161-171.

Comments

Copyright © 2005, the authors. Licensee MDPI, Basel, Switzerland. Open access, Creative Commons Attribution license 4.0.

Abstract

The exact distribution of the linear combination αX + βY is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide computer programs for generating tabulations of the percentage points associated with the linear combination. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing and other areas of computer science.