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

Area of Science:

• Statistics
• Probability Distributions
• Reliability Engineering

Background:

• Traditional statistical distributions often lack the flexibility to model complex real-world data.
• Variable failure rates in reliability analysis require adaptable probability models.

Purpose of the Study:

• Introduce a novel, more flexible statistical model: the power quasi-Xgamma (PQXg) distribution.
• Investigate the theoretical properties and reliability measurements of the PQXg distribution.
• Evaluate the performance of the PQXg distribution against competing models using real-world data.

Main Methods:

• Developed the PQXg distribution by incorporating an additional shape parameter via power transformation.
• Derived key theoretical properties, including moments and reliability measures (survival function, hazard rate, entropy, stress-strength reliability).
• Employed five parameter estimation techniques: maximum likelihood, Anderson-Darling, Cramér-von Mises, ordinary least squares, and weighted least squares.
• Utilized Monte Carlo simulations to assess estimator performance across various sample sizes.

Main Results:

• The PQXg distribution exhibits enhanced flexibility due to its variable failure rate shapes.
• Parameter estimation methods were evaluated for their effectiveness.
• The PQXg distribution demonstrated superior performance when applied to both symmetrical and asymmetrical real-world datasets compared to other distributions.

Conclusions:

• The proposed power quasi-Xgamma (PQXg) distribution is a valuable and flexible addition to the statistical modeling toolkit.
• The PQXg distribution offers improved performance for analyzing diverse real-world data, particularly in reliability contexts.
• The study validates the utility and effectiveness of the new distribution and its estimation methods.