A new extension of the Gumbel distribution with biomedical data analysis

In the field of biomedical research, data characteristics often exhibit significant variability, challenging the applicability of classical Gumbel distribution for biomedical data modeling. To address this, this paper introduces a novel extension of the Gumbel model known as the odd beta prime Gumbel (OBP-Gum) model. Derived from the odd beta prime family, the new distribution exhibits greater kurtosis compared to the traditional Gumbel distribution. Importantly, the proposed distribution is designed to capture right-skewed, left-skewed, and nearly symmetric density functions, as well as increasing, decreasing, constant, and upside-down bathtub shapes for its hazard rate function, providing excellent curvature features for creating flexible statistical models for biomedical research. We derive the fundamental features of the OBP-Gum model, such as the quantile function, linear representations, moment generating function, moments, skewness, kurtosis, incomplete moments, and Rényi and Tsallis entropies. Parameter estimation for this new model is conducted using the maximum likelihood estimation method. A simulation study demonstrates the performance of the model parameters. The empirical findings, based on applications to two biomedical datasets, suggest that the OBP-Gum distribution outperforms existing models, particularly in handling extreme observations. Instead of relying on conventional models for decision-making, this research provides relevant stakeholders with an improved statistical distribution for more accurate biomedical data modeling.