Estimation and Prediction Under Different Schemes for a Flexible Symmetric Distribution With Applications

This paper introduces a new probability distribution called the mixture symmetric gamma (MSG) distribution, which is defined as a mixture of two symmetric gamma distributions. Its statistical properties and applications are explored. We first examine its mathematical properties, including the possible shapes of the corresponding probability density function, as well as the moments, and the moment-generating function. We then look at parameter estimation using various frequentist and Bayesian methods, such as moment estimation, maximum likelihood method, least-squares method, and Bayesian approaches. In addition, the prediction of future observations under the MSG model is extensively covered, considering both frequentist and Bayesian perspectives, including median prediction, best unbiased prediction, and Bayesian prediction. A comprehensive simulation study is conducted to evaluate the performance of the proposed estimation and prediction techniques. Finally, the practical applicability of the MSG model is demonstrated through the analysis of four real-world datasets. It is shown to outperform several well-known competing models in terms of goodness-of-fit. The results highlight the inherent simplicity, efficiency, robustness, and intuitive interpretability of the MSG distribution, making it a compelling choice for modeling data with a symmetric pattern, with potential applications in diverse domains.