Paper Info
Title
Coupling of probability distributions and an extremal problem for the divergence
Abstract
Let X and Y be discrete random variables having probability distributions P X and P Y , respectively. A necessary and sufficient condition is obtained for the existence of an α-coupling of these random variables, i.e., for the existence of their joint distribution such that Pr{X = Y} = α, where α, 0 ≤ α ≤ 1, is a given constant. This problem is closely related with the problem of determining the minima of the divergences D(P Z ‖ P X ) and D(P X ‖ P Z ) over all probability distributions P Z of a random variable Z given P X and under the condition that Pr{Z = X} = α. An explicit solution for this problem is also obtained.
Year
DOI
Venue
2015
10.1134/S003294601502009X
Probl. Inf. Transm.
Keywords
Field
DocType
Probability Distribution, Joint Distribution, Marginal Distribution, Information Transmission, Extremal Problem
Discrete mathematics,Combinatorics,Random variable,Joint probability distribution,Divergence,Coupling,Information transmission,Maxima and minima,Probability distribution,Marginal distribution,Mathematics
Journal
Volume
Issue
ISSN
51
2
1608-3253
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Vyacheslav V. Prelov114529.59