The effect of exponentiating generalized models

Abstract

A common practice in statistical distribution theory involves exponentiating existing distribution functions to include some extra parameters that increase the flexibility of the distribution. This paper examines the effect of exponentiating some generalized models by adding three extra parameters to their probability distribution. Particularly, a new generalized distribution that is a member of the inverted Kumaraswamy family of distributions is considered. Afterward, three additional parameters are applied to enhance this generalized distribution, which results in a novel distribution referred to as the new generalized exponentiated generalized inverted Kumaraswamy Gompertz distribution (NGEGIKGD). Some of the statistical and mathematical characteristics of this distribution were derived. Additionally, parametric estimation of the new distribution parameters was considered using the maximum likelihood method. Several Monte Carlo simulation studies were conducted in order to explore the usefulness of the estimation method. The proposed distribution is then compared with its corresponding sub-models in order to assess the effects of the exponentiation. Further evaluation of the distribution is accomplished by comparing it to some relative distributions. Specifically, three real-world datasets were analyzed to demonstrate the potentiality of the suggested new modeling approach in enhancing the goodness of fit of the generalized models. Results indicate that exponentiating a generalized model significantly improves its fit compared to the non-exponentiating distributions.