In this paper we proposed a new long-term distribution derived from the exponentiated complementary exponential geometric distribution (LECEG). The LECEG distribution is obtained straightforwardly from the exponentiated complementary exponential geometric (ECEG) and accommodates decreasing and unimodal hazard functions in a latent complementary causes scenario, where only the maximum lifetime among all causes is observed. We derive the density, quantile, survival and failure rate functions for the proposed distribution, as well as some proprieties such as the characteristic function, mean, variance and r-th order statistics. The estimation is based on maximum likelihood approach. A simulation study is performed in order to assess the performance of the maximum likelihood estimates. The practical importance of the new distribution was demonstrated in three real datasets.
exponentiated complementary exponential geometric distribution; latent competing risks; long-term survivals
