在删失数据的模型下，对于光滑未知的分布函数Ｆ０，文中提出了光滑化的方法去估计Ｆ０，得到了光滑ＰＬ估计Ｆｎ，并建立了Ｆｎ在Ｄ（－∞，Ｔ），Ｔ＜ＴＦ上的弱收敛和强相合的结果．同时也获得了光滑ＰＬ过程的强逼近和重对数律．

Weak convergence and strong consistency are established for a smooth version of the classical product-limit estimator of a distribution function when the data are subject to random censorship. The weak convergences oil D(I) = D(-∞,T] for T < TF=inf{x: F(x)=1} are shown to hold for the entire interval I under basically the same assumptions that have been used in the literature to establish the weak convergence of normalized estimator in D(I). Moreover,strong approximations and the laws of the iterated logarithm are proved.