Accession Number : AD0757068

Title :   Renewal Theory in Two Dimensions: Basic Results,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Hunter,Jeffrey J.

Report Date : FEB 1973

Pagination or Media Count : 43

Abstract : In the paper a unified theory for studying renewal processes in two dimensions is developed. Bivariate probability generating functions and bivariate Laplace transforms are the basic tools used in generalizing the standard theory of univariate renewal processes. Two examples involving the use of independent and correlated exponential distributions are presented. These are used to illustrate the general theory and explicit expressions for the two dimensional renewal density, the two dimensional renewal function, the correlation between the marginal univariate renewal counting processes, and other related quantities are derived. (Author)

Descriptors :   (*STOCHASTIC PROCESSES, DISTRIBUTION FUNCTIONS), RANDOM VARIABLES, EXPONENTIAL FUNCTIONS, INTEGRAL TRANSFORMS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE