Reliability estimation via length-biased transformation

The length-biased distribution arises as a weighted sampling distribution, via a process which distorts the probability of observations being selected. In this article we discuss estimation of reliability of the original distribution using information contained in length-biased sampling distribution. This could be achieved either by modeling the data with the length-biased version of the original random variable or by using a stochastic transformation which connects length-biased distribution to the original one. The first approach has been studied broadly in the literature, hence we present the latter.