Open Access
August 2015 The Burr XII power series distributions: A new compounding family
Rodrigo B. Silva, Gauss M. Cordeiro
Braz. J. Probab. Stat. 29(3): 565-589 (August 2015). DOI: 10.1214/13-BJPS234


Generalizing lifetime distributions is always precious for applied statisticians. In this paper, we introduce a new family of distributions by compounding the Burr XII and power series distributions. The compounding procedure follows the key idea by Adamidis and Loukas ( Statist. Probab. Lett. 39 (1998) 35–42) or, more generally, by Chahkandi and Ganjali ( Comput. Statist. Data Anal. 53 (2009) 4433–4440) and Morais and Barreto-Souza ( Comput. Statist. Data Anal. 55 (2011) 1410–1425). The proposed family includes as a basic exemplar the Burr XII distribution. We provide some mathematical properties including moments, quantile and generating functions, order statistics and their moments, Kullback–Leibler divergence and Shannon entropy. The estimation of the model parameters is performed by maximum likelihood and the inference under large sample. Two special models of the new family are investigated in details. We illustrate the potential of the new family by means of two applications to real data. It provides better fits to these data than other important lifetime models available in the literature.


Download Citation

Rodrigo B. Silva. Gauss M. Cordeiro. "The Burr XII power series distributions: A new compounding family." Braz. J. Probab. Stat. 29 (3) 565 - 589, August 2015.


Received: 1 June 2013; Accepted: 1 November 2013; Published: August 2015
First available in Project Euclid: 11 June 2015

zbMATH: 1326.62031
MathSciNet: MR3355748
Digital Object Identifier: 10.1214/13-BJPS234

Keywords: Burr XII distribution , information matrix , Kullback–Leibler divergence , order statistic , power series distribution

Rights: Copyright © 2015 Brazilian Statistical Association

Vol.29 • No. 3 • August 2015
Back to Top