A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications

Abstract

Trigonometric functions have gained considerable attention in recent studies for developing new lifetime distributions. This is due to their parsimonious framework, mathematical tractability, and flexibility of the newly developed distributions. In this paper, the Sine‐generated family is used to create a new bounded lifetime distribution, known as Sine‐Marshall–Olkin Topp–Leone distribution, for modeling data defined on the unit interval. Some statistical properties of the new bounded distribution, including quantile function, ordinary moments, incomplete moments, moment‐generating functions, inequality measures, Rényi entropy, and probability weighted moments are derived. Seven methods of parameter estimation, including maximum likelihood, ordinary least squares, weighted least squares, moment product spacing, Anderson–Darling, and Cramér–von Mises estimators are used to estimate the parameters of the new distribution. The behavior of the estimators obtained from the estimation methods are investigated using Monte Carlo simulation studies. The results show that the estimation methods are asymptotically efficient and consistent. The flexibility of the new bounded distribution is examined via data fitting using two proportional datasets. The results of the fittings show that the new bounded distribution performs significantly better than the competing bounded lifetime distributions. Finally, Sine‐Marshall–Olkin Topp–Leone regression model is presented as an alternative to the beta and Kumaraswamy regression models.