Maximum Likelihood Estimation of the Distribution of the Sum of Three Independent Exponential Random Variables

Abstract

This paper describes a procedure for computing the maximum likelihood estimates of the parameters of the distribution of the sum of three independent exponential random variables. By fitting sample interevent time data from a real system to this distribution, one can create a simulation of the system that exploits the regenerative representation of queueing systems to analyze the simulation's output by relatively elementary statistical methods. The paper also describes computation of the sample asymptotic covariance matrix and an implementation of the likelihood ratio for testing six hypotheses that are special cases of interest. A set of FORTRAN subroutines for executing these procedures appears in the Appendix.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1976
Accession Number
ADA026851

Entities

People

  • George S. Fishman

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computations
  • Covariance
  • Data Science
  • Hypotheses
  • Information Science
  • Maximum Likelihood Estimation
  • Normal Distribution
  • North Carolina
  • Operations Research
  • Probability
  • Probability Density Functions
  • Procedures (Computers)
  • Random Variables
  • Simulations
  • Statistical Analysis
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Modeling and Simulation
  • Mathematical Modeling and Probability Theory.