A Characterization of Convoluted Geometric Distributions.

Abstract

Let X be a nonnegative integer-valued random variable whose distribution is that of the sum of geometric variable Y with parameter theta and a nonnegative integer-valued random variable Z independent of Y whose distribution does not depend on theta. The class of all such distributions are characterized by a system of differential equations satisfied by their probability mass functions. The characterization is shown to be useful in maximum likelihood estimation of the parameter theta when the distribution of Z is known.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA042136

Entities

People

  • Francisco J. Samaniego

Organizations

  • University of California, Davis

Tags

DTIC Thesaurus Topics

  • Air Force
  • Binomials
  • California
  • Difference Equations
  • Differential Equations
  • Equations
  • Mathematics
  • Maximum Likelihood Estimation
  • Method Of Moments
  • Probability
  • Random Variables
  • Sequences
  • Statistical Samples
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Statistical inference.