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WEIBULL RENEWAL PROCESSES

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NIKOS YANNAROS

*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.

**Source**
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