Normal mean-variance Lindley Birnbaum-Saunders distribution

The generalization of Birnbaum-Saunders (BS) distribution has recently received considerable attention to provide accurate inferential results in dealing with survival data, reliability problems, fatigue life studies and hydrological data. This paper introduces a new extension of the BS distribution based on the normal mean-variance mixture of Lindley distribution. Since the proposed lifetime distribution can take positive and negative skewness and can have decreasing, increasing, upside-down bathtub, increasing-decreasing-increasing and decreasing-increasing-decreasing hazard rate functions, it may provide more flexible model than the existing extensions of BS distribution. Some properties of the new distribution are derived and the computationally analytical EM-type algorithm is developed for computing maximum likelihood estimates. Finally, the performance of the proposed methodology is illustrated through analyzing two real data sets.