Integral representations and asymptotic expansions for Shannon and Renyi entropies
โ Scribed by C. Knessl
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 303 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
โฆ Synopsis
We derive integral representations for the Shannon and Renyi entropies associated with some simple probability distributions. These include the Poisson, binomial, and negative binomial distributions. Then we obtain full asymptotic expansions for the entropies.
๐ SIMILAR VOLUMES
Analyses of practical engineering problems often require the repeated evaluation of semi-inยฎnite integral transforms whereby a single variable is changed incrementally through a large range of values. Common examples include timeยฑhistory analyses of dynamical systems, and fatigue analyses of solid b
In this work we consider the eigenfunction V , t satisfying a condition at ลฝ . infinity of a singular second order differential operator on 0, qฯฑ . We give an < < asymptotic expansion of this solution with respect to the variable as ยช qฯฑ, which permits us to establish a generalized Schlafli integral