Journal of Probability and Statistics
Volume 2013 (2013), Article ID 502159, 12 pages
Research Article

The Complementary Exponentiated Exponential Geometric Lifetime Distribution

1Department of Applied Mathematics and Statistics, ICMC, University of São Paulo, 13560-970 São Carlos, SP, Brazil
2Department of Statistics, Federal University of São Paulo, 13565-905 São Carlos, SP, Brazil
3London School of Hygiene and Tropical Medicine, University of London, Keppel Street, London WC1E 7HT, UK

Received 8 August 2012; Revised 17 November 2012; Accepted 26 November 2012

Academic Editor: Gauss M. Cordeiro

Copyright © 2013 Francisco Louzada et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We proposed a new family of lifetime distributions, namely, complementary exponentiated exponential geometric distribution. This new family arises on a latent competing risk scenario, where the lifetime associated with a particular risk is not observable but only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments, rth moment of the ith order statistic, mean residual lifetime, and modal value. Inference is implemented via a straightforwardly maximum likelihood procedure. The practical importance of the new distribution was demonstrated in three applications where our distribution outperforms several former lifetime distributions, such as the exponential, the exponential-geometric, the Weibull, the modified Weibull, and the generalized exponential-Poisson distribution.