A New Exponentiated Siya Distribution and Its Biomedical Application

This article introduces a new exponentiated distribution called the Siya Distribution by incorporating a new parameter into the existing two-parameter Gamma distribution. It is a versatile three-parameter model designed to capture various data behaviors encountered in biological and environmental studies. Siya distribution accounts for data that exhibit variable degrees of skewness and kurtosis, making it suitable for complex datasets such as medical measurements, reliability analysis, and survival times. We derive fundamental properties including the probability density function (PDF), moments, the cumulative distribution function (CDF), and moment generating function (MGF), along with the hazard function to allow comprehensive analytical exploration of the distribution’s behavior. Parameter estimation is conducted using Maximum Likelihood Estimation (MLE), providing robust estimators for real-world applications. Model performance is evaluated using two real datasets against three alternative existing parameter distributions using the Akaike Information Criterion (AIC), Corrected AIC (AICc), and Bayesian Information Criterion (BIC), demonstrating that the Siya Distribution consistently achieves a superior fit, especially with highly skewed data. Empirical applications to biological and medical data illustrate the model’s adaptability and potential to improve data representation in fields requiring precise distribution modelling. The Exponentiated Siya distribution thus offers a significant tool for advanced statistical analyses in applied sciences, supporting more accurate and nuanced interpretation of complex data trends.