Abstract
SUMMARY This paper is concerned with joint distributions, joint moments, and joint renewal functions in a stationary point process. The random variables considered are (a) the numbers of events in adjacent intervals of given lengths, located either arbitrarily in time or by an arbitrary event, and (b) the lengths of intervals measured to the various events, beginning either at an arbitrary point or at an arbitrary event. The different bivariate probability functions are related to each other by means of transforms. Moments are considered. In particular, the marginal moments of the number of events, counted by either method, are related to transforms of the multivariate renewal functions. Each product moment of the interval lengths is expressed as a multiple integral of the joint probability of certain numbers of events. A new theorem is proved, more general than in a previous paper, concerning the superposition of two independent stationary point processes. This theorem gives conditions under which the successive intervals between events can be independent in each of the constituent processes and also in the merged process.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of the Royal Statistical Society Series B: Statistical Methodology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
