Classical and Bayesian estimation for the extended odd Weibull power Lomax model with applications

Abstract

A new continuous distribution called the extended odd Weibull power Lomax (ExOW-POLO) distribution is introduced and studied. Numerous reliability and statistical features are derived. Additionally studied are point estimates using maximum likelihood, maximum product space, least square, weighted least square, and Bayesian estimation techniques. The mean square error and bias of the maximum likelihood and Bayesian parameter estimators are computed using simulation approaches, such as Markov chain Monte Carlo. Two intraocular pressure (IOP) real datasets were conducted between January 2015 and February 2018 on 49 patients (84 eyes) under the age of two who presented with primary congenital glaucoma to the Paediatric Ophthalmology Unit of the Mansoura Ophthalmic Center of Mansoura University in Egypt have been fitted the ExOW-POLO distribution. Comparing the properties of the proposed distribution’s fitting of the data to recognized extensions of the Lomax distribution. The analysis revealed that the most well-known extensions of Lomax distribution were made by the ExOW-POLO distribution outfit. In addition, the correlation measures and independent sample test for the two IOP real datasets are introduced with (A) Levene’s test for equality of variances for the two cases and (B) the t-test for equality of means. For Levene’s test for equality of variances: the null hypothesis is that equal variances are assumed and the alternative hypothesis is that equal variances are not assumed.