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