In this paper, we introduce a new three-parameter distribution by compounding the Nadarajah-Haghighi and geometric distributions, which can be interpreted as a truncated Marshall-Olkin extended Weibull. The compounding procedure is based on the work by Marshall and Olkin 1997. We prove that the new distribution can be obtained as a compound model with mixing exponential distribution. It can have decreasing, increasing, upside-down bathtub, bathtub-shaped, constant and decreasing-increasing-decreasing failure rate functions depending on the values of the parameters. Some mathematical properties of the new distribution are studied including moments and quantile function. The maximum likelihood estimation procedure is discussed and a particle swarm optimization algorithm is provided for estimating the model parameters. The flexibility of the new model is illustrated with an application to a real data set.
Marinho, P. R. D., Bourguignon, M., Silva, R. B., & Cordeiro, G. M. (2019). A new class of lifetime models and the evaluation of the confidence intervals by double percentile bootstrap. Anais Da Academia Brasileira de Ciencias, 91(1). https://doi.org/10.1590/0001-3765201920180480