Bayesian and classical inference of univariate maximum Harris extended Rayleigh model with applications

Abstract

In the literature, modifying the baseline distributions and proposing novel approach of the existing probability models play an important role in the analysis of real-world phenomena as well as the development of new distributions essentially stems from the need to adequately characterize environmental and lifetime events. In this paper, we introduce a new model by applying maximum compound technique to the baseline distributions for modeling more types data used in different case of studies including symmetric, asymmetric, skewed and complex data sets. The proposed model called univariate maximum Harris extended Rayleigh distribution and three parameters characterize it, and it is regarded as strong competitor for widely applied symmetrical and non symmetrical models. The paper offers varied fundamental distributional and mathematical properties of the suggested distribution, such as conditional probability and its expectation, as well as quantile and moment-generating functions. The model’s parameters are estimated by applying numerous procedures including maximum likelihood estimation, Expectation–Maximization iterative method and Bayesian approach. Bayesian estimation is performed via various loss functions such as square error, Linex and general entropy functions. As well as, approximate and Bootstrap methods are used to construct the confidence interval for the unknown parameters of the proposed model. Additionally, we illustrated different extensive simulation experiments to see the potential of the suggested estimation methods which give satisfactory performance results. In the end, we applied two real data sets for illustrative purposes. In our illustration, we have compared the practicality of the recommended model with several well-known competing distributions.