A study on the new logarithmic-G family with statistical properties, simulations, and different data analysis

In probability theory, it is acknowledged that traditional probability distributions often struggle to represent real-world data characterized by non-monotonic hazard rate behaviour accurately. Researchers are actively working to enhance these distributions to better capture real-life datasets' complexities. This study presents an innovative modelling technique that utilizes logarithmic functions within a family of distributions, providing greater adaptability and potential. Various mathematical properties were investigated and defined for the proposed methodology. Several estimation methods were employed to estimate the model parameters. To assess the effectiveness of these estimators, a comprehensive Monte Carlo simulation was conducted, focusing on bias, mean square error and mean relative error. The New Log-Weibull (NLW) distribution was then applied to analyze multiple COVID-19 and engineering datasets and compare its performance against alternative distributions.