A New Extension of the Inverse Paralogistic Distribution using Gamma Generator with Application

Abstract

This study proposed a three-parameter model called the gamma inverse paralogistic (GiPL) distribution model. The probability density and cumulative distribution functions were presented together with the quantile function. Properties such as measures of reliability, the kth raw moment and moment-generating function, partial moments, order statistics, log-likelihood functions for maximum likelihood estimations, Renyi entropy and the ordering of random variables were provided. To test the performance of the parameters, a simulation study was conducted. The simulation result was assessed using the mean, bias and root mean square errors. Finally, the data set on the number of COVID-19-infected individuals per age was used to apply the model and compared with various recently developed distribution models. Results showed the superiority of the GiPL distribution model over these models.