ESTIMATION OF THE TRANSITION DISTRIBUTIONS OF A MARKOV RENEWAL PROCESS

Abstract

The present paper is concerned with the estimation of the transition distributions of a Markov renewal process with finitely many states, which extends and unifies some aspects of the results in the special cases of discrete and continuous parameter Markov chains. A natural estimator of the transition distributions is defined and shown to be consistent. Limiting distributions of this estimator are derived. A density for a Markov renewal process is developed to permit the definition of maximum likelihood estimators for a renewal process and for a Markov renewal process.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1964
Accession Number
AD0607350

Entities

People

  • Erin H. Moore
  • Ronald Pyke

Organizations

  • Boeing

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Data Science
  • Distribution Functions
  • Estimators
  • Geometry
  • Information Science
  • Markov Chains
  • Markov Processes
  • Mathematical Analysis
  • Mathematics
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Regression Analysis.