Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 67--76

ON A STUDY OF SOME PROPERTIES OF POINT PROCESSES

By

WEN JANG HUANG and JYH MING SHOUNG, National Sun Yat-sen University

SUMMARY. In this article we study some interesting properties of point processes. First we provide an elementary proof of the characterization of point processes with the order statistics property. Then we give certain characterization results for point processes with both the Markov and exchangeable properties. Among others, we also give a discrete time version of the order statistics property and obtain a characterization of the mixed geometric process.

AMS (1991) subject classification. Primary 62E10; secondary 60G55.

Key words and phrases. Characterization, exchangeable property, exponential distribution, geometric distribution, Markov property, order statistics property, Poisson process, renewal process.

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