Abstract
In this paper, a new distribution called the Marshall-Olkin Rayleigh Lomax distribution is introduced and studied. Marshall and Olkin [1] proposed an interesting method of adding a parameter to well-known distributions, so we extended the Rayleigh Lomax distribution by the Marshall-Olkin method. For this new distribution, the probability density function, cumulative distribution function, hazard rate, survival function, moments and order statistics are derived. Then, maximum likelihood estimators and the confidence intervals of the model parameters by observed Fisher information matrix are obtained. Further, Bayes estimates under squared error and linear exponential loss functions using Markov Chain Monte Carlo methods are obtained. Finally, the comparative study of different method of estimations is carried out using Monte Carlo simulation method.