Department of Statistics, University of Stockholm, S-106 91 Stockholm, Sweden

(Received April 19, 1993; revised April 18, 1994)

Abstract.    We study the class of renewal processes with Weibull lifetime distribution from the point of view of the general theory of point processes. We investigate whether a Weibull renewal process can be expressed as a Cox process. It is shown that a Weibull renewal process is a Cox process if and only if 0 < alpha < 1, where alpha denotes the shape parameter of the Weibull distribution. The Cox character of the process is analyzed. It is shown that the directing measure of the process is continuous and singular.

Key words and phrases:    Weibull, renewal process, point process, Cox process.

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