Accession Number : AD0683322

Title :   ON DISTRIBUTION FUNCTION - MOMENT RELATIONSHIPS IN A STATIONARY POINT PROCESS,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Leadbetter,Malcolm R. ; Serfling,Robert J.

Report Date : FEB 1969

Pagination or Media Count : 21

Abstract : Let G sub n (t) denote the distribution function for the time to the n-th event in a stationary regular point process, and F sub n (t) the corresponding distribution function, conditional on an event having occurred 'at' t = 0. (i.e., F sub n (t) represents the distribution of the time from an 'arbitrary event' to the n-th subsequent event). Let N(o, t) denote the number of events in (o, t). Relationships between the distribution functions G sub n, F sub n, and the moments (unconditional and conditional) of N(o, t) are obtained. Specifically, series are given for G sub n (t) in terms of factorial moments of N(o, t), and for F sub n (t) in terms of such moments, conditional on the occurrence of an event 'at' t = 0. (Author)

Descriptors :   (*DISTRIBUTION FUNCTIONS, STOCHASTIC PROCESSES), DISTRIBUTION THEORY, COMBINATORIAL ANALYSIS, SERIES(MATHEMATICS), THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE