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Entropy 2005, 7(2), 161-171; doi:10.3390/e7020161

On the Linear Combination of Exponential and Gamma Random Variables

1
Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA
2
Department of Engineering Management and Systems Engineering, The George Washington University, Washington, D.C. 20052, USA
*
Author to whom correspondence should be addressed.
Received: 27 January 2005 / Accepted: 13 June 2005 / Published: 14 June 2005
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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 entropy; exponential distribution; gamma distribution; linear combinations of random variables
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Nadarajah, S.; Kotz, S. On the Linear Combination of Exponential and Gamma Random Variables. Entropy 2005, 7, 161-171.

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