摘要：在很多实际应用中，个体寿命时间可能被同时左截断与右截断。

Abstract: in many applications involving follow-up studies, individuals' lifetimes may be subject to both left and right censoring.

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传统的乘积限估计法只能处理寿终数据和右删失数据，对左截断数据则无能为力。

The traditional product limit estimation method can only deal with complete data and right censored data, but can not deal with left truncated data.

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在左截断右删失数据下，我们基于乘积限估计给出了分位密度估计，获得了分位密度估计及其导数的重对数律。

In this paper laws of the iterated logarithm for quantile density estimator and its derivative estimators are established when data are subject to left-truncated and right-censored observations.

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