Bivariate Exponentiated Lomax Distribution Based on Marshall-olkin Method With a Real-life Application

Abstract This paper focuses on applying the Marshall-Olkin approach to generate a new bivariate distribution. The distribution is called the bivariate exponentiated Lomax distribution, and its marginal distribution is the exponentiated Lomax distribution. Numerous attributes are examined, including the joint reliability and hazard functions, the bivariate probability density function, and its marginal. The joint probability density function and joint cumulative distribution function can be stated analytically. Different contour plots of the joint probability density function, joint reliability, joint hazard rate functions of the bivariate exponentiated Lomax distribution are given. The unknown parameters, reliability, and hazard rate functions of the bivariate exponentiated Lomax distribution are estimated using the maximum likelihood method. Also, Bayesian technique is applied to derive the Bayes estimators, reliability and hazard rate functions of the bivariate exponentiated Lomax distribution. In addition, maximum likelihood and Bayesian two-sample prediction is considered to predict a future observation from a future sample of the bivariate exponentiated Lomax distribution. Finally, a numerical illustration is presented, including a simulation study to investigate the theoretical findings derived in this paper of the maximum likelihood and Bayesian estimation. Also, a simulation study is provided to evaluate the theoretical outcomes and performance of the maximum likelihood and Bayesian predictors. Furthermore, the real data set used in this paper is the scoring times from 42 American Football League matches that took place over three consecutive independent weekends in 1986. The results of utilizing the real data approves the practicality and flexibility of the bivariate exponentiated Lomax distribution in real-world situations and that the bivariate exponentiated Lomax distribution is suitable for modeling this bivariate data set. Mathematics Subject Classification: 62F10, 62F15, 62N05, 62E10, 62N0