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<α≤1, where α 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.
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Yannaros, N. Weibull renewal processes. Ann Inst Stat Math 46, 641–648 (1994). https://doi.org/10.1007/BF00773473
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DOI: https://doi.org/10.1007/BF00773473