Entropies of Sums of Independent Gamma Random Variables

被引：0

作者：

Giorgos Chasapis

Salil Singh

Tomasz Tkocz

机构：

[1] Carnegie Mellon University,

来源：

Journal of Theoretical Probability | 2023年 / 36卷

关键词：

Entropy; Max-entropy; Gamma distribution; Weighted sums; Schur-convexity; Primary 60E15; Secondary 94A17;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We establish several Schur-convexity type results under fixed variance for weighted sums of independent gamma random variables and obtain nonasymptotic bounds on their Rényi entropies. In particular, this pertains to the recent results by Bartczak–Nayar–Zwara as well as Bobkov–Naumov–Ulyanov, offering simple proofs of the former and extending the latter.

引用

页码：1227 / 1242

页数：15

共 50 条

[1] Entropies of Sums of Independent Gamma Random Variables
Chasapis, Giorgos
Singh, Salil
Tkocz, Tomasz
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2023, 36 (02) : 1227 - 1242
[2] Asymptotics of the Shannon and Renyi entropies for sums of independent random variables
D'yachkov, AG
Vilenkin, PA
[J]. 1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 1998, : 376 - 376
[3] On random variables stipulated by sums of independent random variables
Gnedenko, B.V.
Kudlaev, E.M.
[J]. Vestnik Moskovskogo Universiteta, Seriya 1 (Matematika Mekhanika), (05): : 23 - 30
[4] Comparing sums of independent bounded random variables and sums of Bernoulli random variables
Berger, E.
[J]. Statistics & Probability Letters, 34 (03):
[5] Comparing sums of independent bounded random variables and sums of Bernoulli random variables
Berger, E
[J]. STATISTICS & PROBABILITY LETTERS, 1997, 34 (03) : 251 - 258
[6] THE SEQUENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES
KALLIANPUR, G
ROBBINS, H
[J]. DUKE MATHEMATICAL JOURNAL, 1954, 21 (02) : 285 - 307
[7] ON OSCILLATIONS OF SUMS OF INDEPENDENT RANDOM VARIABLES
FELLER, W
[J]. ANNALS OF MATHEMATICS, 1970, 91 (02) : 402 - &
[8] On the growth of sums of independent random variables
Petrov V.V.
[J]. Journal of Mathematical Sciences, 2005, 127 (1) : 1763 - 1766
[9] ON FLUCTUATIONS OF SUMS OF INDEPENDENT RANDOM VARIABLES
FELLER, W
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1969, 63 (03) : 637 - &
[10] AN INEQUALITY FOR SUMS OF INDEPENDENT RANDOM VARIABLES
Offord, A. C.
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1945, 48 : 467 - 477

← 1 2 3 4 5 →