The cos-Lindley model with modeling to service times and failure times data

Abstract

ABSTRACT This paper makes a new contribution to distribution theory and application. In it, we develop and investigate a pliant three-parameter lifetime distribution based on a cosine weighting, called the cos-Lindley distribution. The idea of this weighting is to inject the oscillating behavior of the cosine function to flexibilize the functional capabilities of the Lindley distribution. The presence of a periodic hazard rate function elevates the new distribution in terms of applicability to real-world data sets. The main properties of the cos-Lindley distribution, such as the moments and moment generating function, are investigated. A maximum likelihood approach is considered for the study of the estimation of the model parameters. Three real-world data sets on the service times of the windshield and the lifetimes of fatigue fracture of Kevlar are taken into account to demonstrate the utility and robustness of the model. In particular, it is shown that the cos-Lindley model can outperform the Lindley, modified Lindley, and new exponential trigonometric models.