TY - JOUR T1 - General Proportional Reversed Hazard Rate Frailty Model and It's Applications in the Analysis of Lung Cancer Data TT - مدل شکنندگی نرخ خطر معکوس متناسب تعمیم‌یافته و استفاده از آن در تحلیل داده‌های مربوط به سرطان ریه JF - JSS JO - JSS VL - 13 IS - 2 UR - http://jss.irstat.ir/article-1-602-en.html Y1 - 2020 SP - 405 EP - 425 KW - ‎Frailty Models‎ KW - ‎Reversed Hazard Rate Model‎ KW - ‎Left Censored‎ KW - ‎Stochastic Orders‎ KW - ‎Likelihood Function. N2 - In survival studies‎, ‎frailty models are used to explain the unobserved heterogeneity hazards‎. ‎In most cases‎, ‎they are usually considered as the product of the function of the frailty random variable and baseline hazard rate‎. ‎Which is useful for right censored data‎. ‎In this paper‎, ‎the frailty model is explained as the product of the frailty random variable and baseline reversed hazard rate‎, ‎which can be used for left censored data‎. ‎The general reversed hazard rate frailty model is introduced and the distributional properties of the proposed model and lifetime random variables are studied‎. ‎Some dependency properties between lifetime random variable and frailty random variable are investigated‎. ‎It is shown that some stochastic orderings preserved from frailty random variables to lifetime variables‎. ‎Some theorems are used to obtain numerical results‎. ‎The application of the proposed model is discussed in the analysis of left censored data‎. ‎The results are used to model lung cancer data‎. M3 10.29252/jss.13.2.405 ER -