Statistical inference for geometric processes with gamma distributions

J.S.K. Chan, Y. Lam, Yin Ping Leung

Research output: Journal article publicationJournal articleAcademic researchpeer-review

29 Citations (Scopus)

Abstract

A stochastic process {Xi} is a geometric process if there exists a positive real number a such that {ai-1Xi} generates a renewal process. Under the assumption that X1 follows a Gamma distribution, the statistical inference problem for the geometric process is studied. The parameters a,? and ?2, where ? and ?2, are respectively, the mean and variance of X1, are estimated by parametric methods including maximum likelihood method along with some nonparametric methods previously proposed by Y. Lam such as the modified moment method. Limiting distributions for the maximum likelihood estimators are derived and this enables us to construct confidence intervals and perform hypothesis testing on parameters. Then some suggestions on the choice of methods are made based on simulation experiments and real data analysis. © 2004 Published by Elsevier B.V.
Original languageEnglish
Pages (from-to)565-581
Number of pages17
JournalComputational Statistics and Data Analysis
Volume47
Issue number3
DOIs
Publication statusPublished - 1 Oct 2004
Externally publishedYes

Keywords

  • Geometric process
  • Maximum likelihood estimate
  • Moment estimate
  • Renewal process

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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