Testing for Size-Biased Sampling in Lifetime Data

Abstract

Size-biased sampling is a phenomenon that arises in many disciplines and it is common with “survival”, or “lifetime” data. This type of sampling occurs when the probability of a population element being sampled is proportional to some weight function that depends on the observed value of that element. This alters the assumed (“base”) distribution of the sample data to a “weighted distribution”. In practice, it is often not known if size-biased sampling has been used, so there is a need for formal testing to select between the “base” distribution and the “weighted” distribution. We consider two variants of a particular such test in the context of distributions from the generalized gamma family. A Monte Carlo simulation experiment is used to generate critical values for the tests, and to evaluate their power properties. The tests are illustrated in two empirical applications using real-life data.