Statistical Modelling of Positive Continuous Data Using the Gamma Distribution: A Simulation and Real-Life Data Study

The Gamma distribution is a flexible continuous probability distribution widely used for modelling positive, right-skewed data in engineering, reliability, medicine, and biological sciences. This study evaluates the applicability of the Gamma distribution to ten real-life datasets, including ball bearings, air conditioning, Boeing, analgesic, accelerated life test, strain level, strength of glass, vinyl chloride, RT_CT, and virulent tubercle bacilli data, alongside simulated datasets with sample sizes of 100, 200, 300, 400, 500, and 1000. Parameters were estimated using the Maximum Likelihood Estimation (MLE) method, while model adequacy was assessed through goodness-of-fit measures and graphical diagnostics implemented in R. A simulation study was conducted to examine the performance of the MLE across varying sample sizes. The results showed that the Gamma distribution achieved improved model fit with increasing sample size, demonstrating favourable large-sample properties. Among the real-life datasets, the analgesic dataset provided the best fit according to the selected goodness-of-fit criteria. Most datasets exhibited positive skewness and varying degrees of kurtosis, supporting the suitability of the Gamma distribution for modelling non-negative, asymmetric data. The findings demonstrate that the Gamma distribution is an effective model for positively skewed data and performs particularly well for simulated datasets and selected real-life applications. The study highlights the usefulness of Maximum Likelihood Estimation for parameter estimation and reinforces the Gamma distribution as a valuable tool for statistical modelling in reliability, engineering, and biomedical research.