Some Discrete Lifetime Distributions with Bathtub-Shaped Hazard Rate Functions

ABSTRACT

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.

KEYWORDS:

• bathtub-shaped hazard rate
• continuous lifetime models
• discrete lifetime models
• statistical reliability

ACKNOWLEDGMENT

The partial support from the Ordered and Spatial Data Center of Excellence of the Ferdowsi University of Mashhad is acknowledged.

Notes

Bold values are related to the best model based on AIC.

Additional information

Notes on contributors

M. Shafaei Noughabi

Mohammad Shafaei Noughabi received his Ph.D in statistics from Ferdowsi University of Mashhad, Mashhad, Iran in 2012. Now, he is an assistant professor in Hakim Sabzevari University, Sabzevar, Iran. His research interests include applied probability and reliability theory.

A. H. Rezaei Roknabadi

Dr. A. H. Rezaei Roknabadi got his B.S. and MSc degree in statistics from Ferdowsi University of Mashhad in Iran and also, PhD in Statistics al Inference from Ferdowsi University of Mashhad, Mashhad, Iran in 2000. He is now a Professor in Staistics in Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Iran. His research is focused on reliability.

G. R. Mohtashami Borzadaran

Dr. G. R. Mohtashami Borzadaran got his B.S. degree in statistics from Faculty of Informatic and Statistics in Iran and MSc degree in statistics from Shahid Beheshti University in Iran and PhD in Statistical Inference from Sheffield University, Sheffield, England (UK) in 1997. He is now a Professor in Statistics in Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Iran. His research is focused on information theory and reliability.