A presmooth estimator of unbiased distributions with length-biased data

In this paper, we propose a presmooth product-limit estimator to draw statistical inference on the unbiased distribution function representing the population of interest. The strong consistency of the estimator proposed is investigated. The finite sample performance of the proposed estimator is evaluated using simulation studies. It is observed that the proposed estimator exhibits greater efficiency in comparison with the alternative method in de Uña-Álvarez (Test 11(1):109–125, 2002).