Arctangent Zubair‐G Family of Distributions: Properties and Applications to Biomedical Data

The Zubair‐G family provides a simple yet effective approach to introduce an extra parameter to extend current distributions. In this study, we proposed a modified version, termed the arctangent Zubair‐G (AZ‐G) family of distributions. We examined its fundamental statistical properties and estimated the model parameters using various estimation techniques. The probability density function (PDF) plots revealed that the proposed family exhibits symmetric, reversed J, and symmetric shapes, while the hazard function demonstrated increasing, decreasing, and bathtub‐shaped behaviors. We further assessed the behavior of the maximum likelihood estimators through a Monte Carlo simulation. The results confirmed the consistency of the estimators, showing that parameter estimates converge to their true values as the sample size increases. To validate the applicability of the proposed model, we applied it to three biomedical datasets. The empirical results demonstrated that the AZ‐G distribution provides a superior fit compared to competing distributions, highlighting its potential in real‐world data modeling. These findings contribute to the development of generalized probability distributions, offering statisticians and practitioners a flexible tool to analyze complex data.