On Modeling the Medical Care Insurance Data via a New Statistical Model

Abstract

Proposing new statistical distributions which are more flexible than the existing distributions have become a recent trend in the practice of distribution theory. Actuaries often search for new and appropriate statistical models to address data related to financial and risk management problems. In the present study, an extension of the Lomax distribution is proposed via using the approach of the weighted T-X family of distributions. The mathematical properties along with the characterization of the new model via truncated moments are derived. The model parameters are estimated via a prominent approach called the maximum likelihood estimation method. A brief Monte Carlo simulation study to assess the performance of the model parameters is conducted. An application to medical care insurance data is provided to illustrate the potentials of the newly proposed extension of the Lomax distribution. The comparison of the proposed model is made with the (i) Two-parameter Lomax distribution, (ii) Three-parameter models called the half logistic Lomax and exponentiated Lomax distributions, and (iii) A four-parameter model called the Kumaraswamy Lomax distribution. The statistical analysis indicates that the proposed model performs better than the competitive models in analyzing data in financial and actuarial sciences.