Discrete distributions with bathtub-shaped hazard rates

Discrete distributions with bathtub shaped hazard rates have recently become of interest in reliability modelling and analysis. In the present work, we address the problem of obtaining distributions having such hazard rates when the lifetime is discrete. The methods considered here include discretising continuous bathtub models, construction using the score function, construction from decreasing hazard rate distributions and some other methods currently available in the continuous case. We discuss properties and applications of the discretised quadratic hazard model which has a bathtub shaped hazard rate. Keywords: Bathtub hazard rate, Discrete distribution, Quadratic hazard model, Score function, Upside down bathtub hazard rate