# Accession Number:

## ADA026851

# Title:

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

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## NORTH CAROLINA UNIV AT CHAPEL HILL

# Personal Author(s):

# Report Date:

## 1976-05-01

# Pagination or Media Count:

## 30.0

# 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 simulations 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.

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Computer Programming and Software