Acta Electronica Malaysia (AEM)

Modelling heavy-tailed and skewed data presents substantial challenges in statistical analysis, especially when dealing with mixed-type variables and complex distributional structures. This study proposes a novel and flexible distributional model, the Generalized Exponential Power Distribution with Modified Variance Transformation (GEPDMVT), to address these challenges. The GEPDMVT extends the classical Exponential Power Distribution by incorporating distinct shape and scale parameters along with a variance transformation mechanism that enhances its flexibility in modelling diverse hazard rate shapes, including increasing, decreasing, and bathtub forms. The study derives key statistical properties of the GEPDMVT such as the probability density function, cumulative distribution function, moments, survival function, and hazard function, providing analytical tractability and robustness. Through extensive Monte Carlo simulations across a range of sample sizes, the model’s performance is evaluated in terms of bias, root mean square error (RMSE), and flexibility. Additionally, the model is empirically validated using secondary datasets comprising public health expenditure in Nigeria and Ghana (1995–2014), renal transplant graft survival times, tax revenue data, and daily COVID-19 case counts in Nigeria. Comparative analyses with existing exponential-based distributions demonstrate the superior fit, versatility, and robustness of the GEPDMVT under varied data conditions. This study contributes to the advancement of statistical modelling by offering a unified and interpretable distribution that enhances prediction accuracy and inferential reliability in heavy-tailed and skewed data contexts.