Statistics and Its Interface

Volume 12 (2019)

Number 4

Destructive power series long-term survival model with complex activation schemes

Pages: 561 – 571



Diego I. Gallardo (Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Chile)

Heleno Bolfarine (Institute of Mathematics and Statistics, University of São Paulo, Brazil)

Antonio C. Pedroso-de-Lima (Institute of Mathematics and Statistics, University of São Paulo, Brazil)

Jose S. Romeo (SHORE and Whariki Research Centre, College of Health, Massey University, New Zealand)


A new destructive cure rate model is introduced based on a family of power series distribution for the number of concurrent causes related to the event of interest. A mixture of first and last activation schemes is considered. For parameter estimation a classical approach based on maximum likelihood methodology is implemented. The performance of estimation procedure is evaluated based on a small scale simulation study. The model is also considered on a real data example, involving congestive heart failure patients.


cure rate models, competing risks, power series distribution

2010 Mathematics Subject Classification

Primary 62N01. Secondary 62N02.

The first author has been partially supported by FONDECYT (Fondo Nacional de Desarrollo Científico y Tecnológico) Grant 11160670.

Received 2 January 2019

Accepted 29 April 2019

Published 18 July 2019