Accession Number : ADA185480

Title :   Error Bounds for Exponential Approximations to Geometric Convolutions.

Descriptive Note : Journal article,

Corporate Author : CITY COLL NEW YORK

Personal Author(s) : Brown, Mark

PDF Url : ADA185480

Report Date : 15 Aug 1986

Pagination or Media Count : 27

Abstract : This paper defines Y sub 0 to be a geometric convolution of X if Y sub 0 is the sum of N sub 0 i.i.d. random variables distributed as X, where N sub 0 is geometrically distributed and independent of X. It is known that if X is non-negative with finite second moment then as p approaches limit of 0, Y sub 0/EY sub 0 converges in distribution to an exponential distribution with mean 1. Derive is an upper bound for d(Y sub 0), the distance between Y sub 0 and an exponential with mean Y sub 0, namely for 0p or = 1/2, d(sub 0) or = cp where c = sq ex/sq (ex). This bound is asymptotically (p approaches limit of 0) tight.

Descriptors :   *EXPONENTIAL FUNCTIONS, *DISTRIBUTION THEORY, *CONVOLUTION, APPROXIMATION(MATHEMATICS), MOMENTS, RANDOM VARIABLES, CONVERGENCE, QUEUEING THEORY

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE