Estimation of Convolution Tails

Abstract

Several classes of distribution functions (d.f.) are originated by considering distributions whose tailfunctions satisfy special asymptotic relations. A large class sharing this property is provided by a certain subexponential class, in which case the asymptotic relation involves tails of convolution powers. This paper introduces a statistic which estimates the asymptotic behaviour of convolution tails of a given d.f. and it is shown that this statistic is strongly consistent and asymptotically normal under appropriate conditions. Furthermore, the statistic can be used to test the hypothesis that a d.f. is in the exponential class being described.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1987
Accession Number
ADA190323

Entities

People

  • Eric Willekens

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Convolution
  • Data Science
  • Distribution Functions
  • Information Science
  • Normality
  • North Carolina
  • Order Statistics
  • Probability
  • Probability Distributions
  • Random Variables
  • Scientific Research
  • Sequences
  • Statistics
  • Stochastic Processes
  • Universities
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Statistical inference.