The existence and the usefulness of discrete bathtub-shaped and upside down bathtubshaped distributions have been demonstrated in some papers of recent origin. However, the general properties of these two classes of distributions do not seem to have been discussed. This paper proposes to study some reliability properties of such distributions. We investigate the closure properties with reference to convolution, mixing, series and parallel systems, etc. and existence of bounds on reliability functions, moment properties and convergence.
There have been several works aimed at the determination of the shape of the hazard rate when lifetime is treated as continuous. In the present work, we establish some theorems, that enable the identification of the nature of discrete hazard rates. Further, some applications of the results to construct new discrete bathtub-shaped distributions are also proposed.
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