A new modified Sine-Weibull distribution for modeling medical data with dynamic structures

Biomedical data often exhibits complex structures characterized by skewness, kurtosis, and high variability, which pose challenges for traditional statistical models. To adequately address these challenges, asymmetrical statistical models are essential. This paper proposes a novel family of statistical distributions formed by Sine-G transformations. The family will be known as the Modified Sine-G (MoS-G) family. The new MoS-G family is utilized to propose the Modified Sine-Weibull (MoS-Weibull) distribution, as an extension of the classical Weibull distribution, which encompasses a greater variety of data features. The aim is to integrate a wider range of data features than the conventional Weibull distribution. The MoS-Weibull distribution demonstrates enhanced variability regarding skewness and kurtosis, rendering it appropriate for capturing diverse shapes. The shapes include reversed-J-shaped, right-skewed, heavy-tailed, and left-skewed distributions, commonly found in biomedical data. The maximum likelihood method is utilized to carry out the process of parameter estimation. It has been demonstrated through simulation tests conducted in various environments that the parameter estimates are reliable. Three real biological datasets demonstrate the practical applicability of the MoS-Weibull distribution. These datasets are the mortality statistics for the pathological clinic records, the COVID-19, and the acute bone cancer data. The results of this study suggest that the MoS-Weibull distribution has an edge over other models in terms of its capacity to capture the intricate patterns and variability that are present in these datasets. The findings of this study demonstrate that the MoS-Weibull distribution is an efficient tool for analysing complex biomedical data. It also offers significant insights and works to improve statistical modeling approaches in the field of biomedical research.