Entropy 2005, 7[2], 161-171
ISSN 1099-4300

On the Linear Combination of Exponential and Gamma Random Variables

Saralees Nadarajah and Samuel Kotz

Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA
Department of Engineering Management and Systems Engineering, The George Washington University, Washington, D.C. 20052, USA.

Received: 27 January 2005 / Accepted: 13 June 2005 / Published: 14 June 2005

Abstract: The exact distribution of the linear combination α X + β Y 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.

Keywords: entropy; exponential distribution; gamma distribution; linear combinations of random variables.

MSC 2000 codes: 33C90, 62E99.

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