  In this article, we consider a useful product-limit estimator of distribution
function proposed by Huang & Qin(2011) when the observations are subject to
length-biased and right-censored data. The estimator retains the simple
closed-form expression of the truncation product-limit estimator with some good
properties. An almost sure representation for the estimator is obtained which
can be used to derive many properties of functional statistics based on this
product-limit estimator. The rate for the remainder in the representation is of
order $O(n^{-3/4}(\log(n)^{3/4}) $ a.s.
