ON XEXPONENTIAL DISTRIBUTION: PROPERTIES, BAYESIAN ESTIMATION, GOODNESS-OF-FIT TEST AND APPLICATION

Abstract

This paper introduces a new probability model, the A special mixture of exponential and gamma models generate Xexponential model. The study explores the mathematical properties of this new model, including the moment generation function, moments, mode, and quantile function. The research evaluates various estimators to estimate the unknown parameter of the distribution using a Monte Carlo simulation. Also, the goodness-of-fit test is provided for this model. Additionally, the flexibility of the Xexponential model is compared to that of other commonly used models, such as gamma, exponential, Lindley, Shanker, Akash, Zeghdoudi, and Chris-Jerry, by applying the model to a real data set. The results indicate that the proposed model provides more flexibility and a better fit than other models. These findings suggest that the Xexponential model could be useful in modeling real-life data and may warrant further exploration in future research.