An Innovative Technique for Generating Probability Distributions: A Study on Lomax Distribution with Applications in Medical and Engineering Fields

Abstract

In this paper, we propose and investigate a novel approach for generating the probability distributions. The novel method is known as the SMP transformation technique. By using the SMP Transformation technique, we have developed a new model of the Lomax distribution known as SMP Lomax (SMPL) distribution. The SMPL distribution, which is comparable to the Sine Power Lomax distribution, Power Length BiasedWeighted Lomax Distribution, Exponentiated Lomax and Lomax distribution have the desirable attribute of allowing the superiority and the flexibility over other well known existing models. Furthermore, the research article examines various aspects related to the SMPL , including the statistical properties along with the maximum likelihood estimation procedure to estimate the parameters. An extensive simulation study is carried out to illustrate the behaviour of MLEs on the basis of Mean Square Errors. To evaluate the effectiveness and flexibility of the proposed distribution, two real-life data sets are employed and it is observed that SMPL outperforms base model of Lomax distribution as well as other mentioned competing models based on Akaike Information Criterion, Akaike Information criterion Corrected, Hannan–Quinn information criterion and other goodness of fit measures.