A bivariate limiting distribution of tumor latency time

Svetlozar T. Rachev, Chufang Wu, Andrej Yu Yakovlev

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The model of radiation carcinogenesis, proposed earlier by Klebanov, Rachev, and Yakovlev [8] substantiates the employment of limiting forms of the latent time distribution at high dose values. Such distributions arise within the random minima framework, the two-parameter Weibull distribution being a special case. This model, in its present form, does not allow for carcinogenesis at multiple sites. As shown in the present paper, a natural two-dimensional generalization of the model appears in the form of a Weibull-Marshall-Olkin distribution. Similarly, the study of a randomized version of the model based on the negative binomial minima scheme results in a bivariate Pareto-Marshall-Olkin distribution. In the latter case, an estimate for the rate of convergence to the limiting distribution is given.

Original languageEnglish
Pages (from-to)127-147
Number of pages21
JournalMathematical Biosciences
Issue number2
StatePublished - Jun 1995


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