A Weibull-based score test for heterogeneity

The Weibull distribution is a natural starting point in the modelling of failure times in reliability, material strength data and many other applications that involve lifetime data. In recent years there has been a growing interest in modelling heterogeneity within this context. A natural approach is to consider a mixture, either discrete or continuous, of Weibull distributions. A judicious choice of mixing distribution yields a tractable and flexible generalization of the Weibull distribution. In this note a score test for detecting heterogeneity in this context is discussed and illustrated using some infant nutrition data.