On The Modeling of Biomedical Data Sets with a New Generalized Exponentiated Exponential Distribution

Introduction: Many experts in the field of distribution theory have focused on extending probability distributions utilizing extended families of continuous distributions to improve the modeling adaptability of the conventional probability distributions. Methods: This research employed a continuous family of probability distributions as introduced in the literature using the T-X methodology. Through this, some of statistical and mathematical properties of the model were derived and studied Results: This study had introduced a brand-new, five-parameter generalized exponentiated exponential distribution, which is a continuous probability distribution. With the aid of the quantile function, moments, moment generating function, survival function, hazard function, mean, and median, among other mathematical and statistical aspects, the new distribution's shape was deduced and researched. It was also possible to derive the probability density function for the minimum and maximum order statistics for this distribution. The method of maximum likelihood estimate was used to produce a conventional estimation of the unknown parameters. A simulation study was carried out to assess the efficiency and consistency of the estimation method used. To evaluate the fit and adaptability of the new model, it was applied to four real-world datasets in the field of medicine. Conclusion: The analysis's findings demonstrated that the new model performs better than its counterparts and offers a better fit than the Topp-Leone exponentiated exponential, Topp-Leone Kumaraswamy exponential, exponentiated exponential, and exponential distributions.