New defective models based on the Topp-Leone generated family of distributions

Abstract

This paper proposes two new defective models based on the Topp-Leone (TL) gen-erated family of distributions. Unlike most of the cure rate models, the advantage of the defective model is that the cure rate can be modeled without adding any addi-tional parameters to the model. The maximum likelihood function (MLE) is discussed for these models, and the asymptotic property of MLE is verified by simulation. The applications of this method are illustrated by three real data sets.