Analysis, Estimation, and Practical Implementations of the Discrete Power Quasi-Xgamma Distribution

Abstract

In this study, we introduce a new three-parameter discrete power quasi-Xgamma (DPQXg) distribution. A detailed analysis of the mathematical and statistical properties of the DPQXg distribution demonstrates various important features. It has been observed that the DPQXg distribution can be used for analyzing both asymmetric and symmetric datasets exhibiting platykurtic and leptokurtic shapes. The hazard rate function of the distribution has both increasing and decreasing failure rates. Furthermore, the dispersion index of the DPQXg distribution indicates that the new statistical model can analyze both over- and underdispersed datasets. The parameter estimation of the statistical model is conducted using the maximum likelihood estimation approach. A simulation is carried out to assess the performance of the DPQXg estimator. Finally, real-world datasets from different fields are used to demonstrate the practical utility of the DPQXg distribution.