Error Bounds for Exponential Approximations to Geometric Convolutions.

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 0<p < or = 1/2, d(sub 0) < or = cp where c = sq ex/sq (ex). This bound is asymptotically (p approaches limit of 0) tight.

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Document Details

Document Type
Technical Report
Publication Date
Aug 15, 1986
Accession Number
ADA185480

Entities

People

  • Mark O. Brown

Organizations

  • City College of New York

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Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Age Distribution
  • Classification
  • Convergence
  • Convolution
  • Engineering
  • Inequalities
  • Mathematics
  • New York
  • Probability
  • Random Variables
  • Security
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  • Stationary
  • Statistical Sampling
  • Statistics
  • Stochastic Processes
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Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.