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On Concentration Functions of Random Sums of Independent Random Variables
Author(s) -
Ahmad Ibrahim A.
Publication year - 1980
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-21.1.189
Subject(s) - mathematics , random variable , sum of normally distributed random variables , independence (probability theory) , index (typography) , extension (predicate logic) , random function , multivariate random variable , statistics , random element , exchangeable random variables , function (biology) , variables , combinatorics , computer science , evolutionary biology , world wide web , biology , programming language
The purpose of this note is to give a result on the concentration function of a sum of random variables when the index is random and not necessarily independent of the observations. In this respect our result is an extension of those of Rosen ( Ark. Mat ., 4 (1962), 323–332) and Dunnage ( Proc. London Math. Soc. (3), 25 (1972), 183–191). The latter paper obtains results assuming the independence between the random index and the observations.