  In this paper, we introduce a new approach to generate flexible parametric
families of distributions. These models arise on competitive and complementary
risks scenario, in which the lifetime associated with a particular risk is not
observable, rather, we observe only the minimum/maximum lifetime value among
all risks. The latent variables have a zero truncated Poisson distribution. For
the proposed family of distribution, the extra shape parameter has an important
physical interpretation in the competing and complementary risks scenario. The
mathematical properties and inferential procedures are discussed. The proposed
approach is applied in some existing distributions in which it is fully
illustrated by an important data set.
