An improved extension of Xgamma distribution: Its properties, estimation and application on failure time data.

A new, more flexible model, the power quasi-Xgamma (PQXg) distribution, is introduced by adding an extra shape parameter using the power transformation approach. The PQXg distribution is more flexible due to its variable failure rate shapes. We derived its various theoretical properties including moments and its associated measures. Some reliability measurements include the survival function, hazard rate, mean residual life, Rényi and Tsallis entropy, and stress-strength reliability. Five approaches are used for parameter estimation: maximum likelihood, Anderson-Darling, Cramér-von Mises, ordinary, and weighted least squares. A Monte Carlo simulation is used to determine the effectiveness of these estimators for different sample sizes. The use of derived distribution is investigated utilizing symmetrical and asymmetric data sets from real-world fields. When compared to other competing distributions considered, the new distribution performed better.