Data Modelling and Analysis Using Odd Lomax Generalized Exponential Distribution: an Empirical Study and Simulation

This study is based on the formulation of a new probabilistic model called the generalized singular Lomax exponential distribution using the singular Lomax generator and the exponential distribution. The proposed distribution is very flexible in modelling age data with both decreasing and increasing (non-monotonic) shapes. We define the probability density function (pdf) and cumulative distribution function (CDF) for the proposed distribution. Some mathematical properties of the proposed distribution such as the quantum function and moments are derived and for the incomplete moments the Renyi entropy of the proposed distribution is also obtained. Furthermore, the paper discusses model parameters in three different techniques, with Monte Carlo simulations to determine the efficiency of estimating the HOLGE distribution, with a comparison with three benchmarks to determine the best estimation method. A practical application is also carried out on two types of data that include the survival times of 72 guinea pigs infected with virulent tuberculosis bacilli, where the efficiency of the HOLGE distribution analysis is determined by comparing it to six other distributions using 4 information criteria and 4 statistical measures, which demonstrated the efficiency and flexibility of the HOLGE distribution.