Estimation of stress-strength reliability based on unit generalized Gompertz distribution

Abstract

Although the investigation of the stress-strength parameter has a long history due to its importance, the investigation of this parameter in distributions with a limited range, such as (0, 1), has received less attention. Thus, in this article, we study the stress-strength parameter for Unit Generalized Gompertz (UGG) distribution, which can cover a variety of data, including data skewed ones. Considering the flexibility of the shape of the density function and its hazard rate function, we expect that this distribution would possess more applicability and can be fitted to different data sets. With this aim, we discuss the parameter R for the UGG distribution and obtain different methods of parameter estimation such as maximum likelihood, bootstrap, and Bayesian. The performance of the estimators has been done by simulation, and finally, the presented content has been applied to a real data set.