Entropy of the Sum of Two Independent, Non-Identically-Distributed Exponential Random Variables
Andrew W. Eckford, Peter J. Thomas
TL;DR
This paper derives a simple, closed-form expression for the differential entropy of the sum of two independent, non-identically distributed exponential random variables, filling a gap in the existing literature.
Contribution
It provides the first concise, closed-form formula for the entropy of the sum of such exponential variables, with practical examples demonstrating its usefulness.
Findings
Closed-form entropy expression derived
Examples illustrate the application of the formula
Fills a gap in information theory literature
Abstract
In this letter, we give a concise, closed-form expression for the differential entropy of the sum of two independent, non-identically-distributed exponential random variables. The derivation is straightforward, but such a concise entropy has not been previously given in the literature. The usefulness of the expression is demonstrated with examples.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Stochastic processes and statistical mechanics · Bayesian Modeling and Causal Inference