A New Modified Extended Generalized Inverted Exponential (NMEGIEx) Distribution: A Distribution for Flexible and Accurate Data Analysis

Abstract

This study proposes and investigates a New Modified Extended Generalised Inverse Exponential (NMEGIEx) distribution, a novel distribution. The basic one-parameter inverse exponential distribution is extended in the new model. Four additional positive shape parameters are added to an extended Topp-Leone exponentiated a generalised family of distributions to create the new model, which simultaneously controls the centre and tail weights. The model’s asymptotic behaviour, explicit formulations for ordinary moments, mean, quantile function, hazard function, survival function, median, Moment Generating Function (MGF), and Probability Density Function (PDF) of lowest and highest order statistics were among the many statistical properties derived. Monte Carlo simulation is used to test the estimators of the proposed distribution. As predicted, as the sample size increases, the Root Mean Square Error (RMSE) and biases approach zero, and the estimated parameter values approach the true values of the parameters. Maximum Likelihood Estimation (MLE) is used to determine the values of the unknown parameters that make the observed data most likely under the assumed model. The superiority of the proposed NMEGIEx distribution is demonstrated through application to two real-world quality control engineering datasets, and it is clear that the proposed model fits the datasets better than competing distributions.