title: A bivariate limiting distribution of tumor latency time.
abstract: 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.
authors.affiliation: Department of Statistics and Applied Probability, University of California, Santa Barbara 93106, USA.
authors.forename: S T
authors.initials: ST
authors.lastname: Rachev
authors.forename: C
authors.initials: C
authors.lastname: Wu
authors.lastname: Yakovlev AYu
mesh_terms: D000818:Animals; D003043:Cocarcinogenesis; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D009369:Neoplasms / Q000209:etiology*; D013269:Stochastic Processes; D013997:Time Factors