Rachev S T, Wu C
Department of Statistics and Applied Probability, University of California, Santa Barbara 93106, USA.
Math Biosci. 1995 Jun;127(2):127-47. doi: 10.1016/0025-5564(94)00043-y.
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.
克莱巴诺夫、拉切夫和雅科夫列夫[8]早前提出的辐射致癌模型证实了在高剂量值下采用潜伏时间分布的极限形式是合理的。这种分布出现在随机极小值框架内，两参数威布尔分布就是一个特例。该模型的当前形式不考虑多部位致癌的情况。如本文所示，该模型自然的二维推广形式为威布尔 - 马歇尔 - 奥尔金分布。类似地，基于负二项极小值方案对该模型的随机化版本进行研究，得到了双变量帕累托 - 马歇尔 - 奥尔金分布。在后一种情况下，给出了收敛到极限分布的速率估计。
