Entropies of Sums of Independent Gamma Random Variables

被引：0

作者：

Chasapis, Giorgos ^{[1
]}

Singh, Salil ^{[1
]}

Tkocz, Tomasz ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Pittsburgh, PA 15213 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2023年 / 36卷 / 02期

关键词：

Entropy; Max-entropy; Gamma distribution; Weighted sums; Schur-convexity; BOUNDS; INEQUALITIES; PROBABILITY; SECTIONS; CUBE;

D O I：

10.1007/s10959-022-01192-y

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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 Renyi 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：16

共 50 条

[31] ON ORDER OF GROWTH OF SUMS OF INDEPENDENT RANDOM VARIABLES
PETROV, VV
DOKLADY AKADEMII NAUK SSSR, 1969, 185 (06): : 1236 - &
[32] THE DISTRIBUTION OF THE MAXIMUM OF SUMS OF INDEPENDENT RANDOM VARIABLES
KAC, M
POLLARD, H
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 55 (07) : 703 - 703
[33] ON THE NUMBER OF POSITIVE SUMS OF INDEPENDENT RANDOM VARIABLES
ERDOS, P
KAC, M
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1947, 53 (10) : 1011 - 1020
[34] On Sums of Conditionally Independent Subexponential Random Variables
Foss, Serguei
Richards, Andrew
MATHEMATICS OF OPERATIONS RESEARCH, 2010, 35 (01) : 102 - 119
[35] CONVERGENCE OF WEIGHTED SUMS OF INDEPENDENT RANDOM VARIABLES
ROHATGI, VK
PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1971, 69 (MAR): : 305 - &
[36] ON THE LOWER LIMIT OF SUMS OF INDEPENDENT RANDOM VARIABLES
CHUNG, KL
ERDOS, P
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1947, 53 (01) : 51 - 51
[37] On stochastic orders for sums of independent random variables
Korwar, RM
JOURNAL OF MULTIVARIATE ANALYSIS, 2002, 80 (02) : 344 - 357
[38] Learning Sums of Independent Integer Random Variables
Daskalakis, Constantinos
Diakonikolas, Ilias
O'Donnell, Ryan
Servedio, Rocco A.
Tan, Li-Yang
2013 IEEE 54TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS), 2013, : 217 - 226
[39] Note on "sums of independent fuzzy random variables"
Feng, YH
FUZZY SETS AND SYSTEMS, 2004, 143 (03) : 479 - 485
[40] ON THE EQUIDISTRIBUTION IN PROBABILITY OF SUMS OF INDEPENDENT RANDOM VARIABLES
KALLIANPUR, G
ROBBINS, H
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 59 (03) : 247 - 247

← 1 2 3 4 5 →