A new class of defective models based on the Marshall-Olkin family of distributions for cure rate modeling

Defective distributions model cure rates by changing the usual domain of its parameters in a way that their survival functions converge to a value p∈(0,1). A new way to generate defective distributions to model cure fractions is proposed. The new way relies on a property derived from the Marshall-Olkin family of distributions. To exemplify this new result we use the extended Weibull distribution and introduce ten new defective distributions. A regression approach for these models is also proposed. Estimation by maximum likelihood is discussed and their asymptotes verified through simulations. Practical use is illustrated by applications to four real data sets.