The odd Lindley Nadarajah-Haghighi distribution

Abstract

In this paper, a new three-parameter model which can be used in lifetime data analysis is introduced. Its failure rate function can be decreasing, increasing, constant and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary moments, generating function, incomplete moments, order statistics, moment of residual life and reversed residual life. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimators are discussed in case of uncensored data. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and flexibility of the new model in modeling real data set.

https://doi.org/10.28919/jmcs/3417