On the Linear Combination of Exponential and Gamma Random Variables

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 p...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2005-06, Vol.7 (2), p.161-171
Main Authors: Nadarajah, Saralees, Kotz, Samuel
Format: Article
Language:English
Subjects:
entropy
exponential distribution
gamma distribution
linear combinations of random variables
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e7020161