TY - JOUR
T1 - A bivariate limiting distribution of tumor latency time
AU - Rachev, Svetlozar T.
AU - Wu, Chufang
AU - Yakovlev, Andrej Yu
PY - 1995/6
Y1 - 1995/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0029003125&partnerID=8YFLogxK
U2 - 10.1016/0025-5564(94)00043-Y
DO - 10.1016/0025-5564(94)00043-Y
M3 - Article
C2 - 7795315
AN - SCOPUS:0029003125
VL - 127
SP - 127
EP - 147
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 2
ER -