Some Discrete Lifetime Distributions with Bathtub-Shaped Hazard Rate Functions

Unlike continuous distributions, discrete models capable of modeling failure times with bathtub-shaped hazard rate functions have not received deserving attention in the statistical reliability literature. In this article, we show that the shape of the hazard rate function of a continuous lifetime model is partially preserved under the usual discretization of the model. Then, two continuous distributions with bathtub-shaped hazard rates are discretized, and some properties of the obtained discrete versions are studied. Graphical methods are utilized to obtain initial estimates of the parameters that are necessary for calculation of the maximum likelihood estimator. Finally, we fit the studied models along with some other proper discrete models to a set of real data and show that these models may be good candidates for describing discrete lifetime data.