Master’s Degree Awarded to Ms. Fadwa Abdulqawi, Faculty of Commerce & Economics

Ms. Fadwa Abdulqawi Abdulmalik Al-Thari, a researcher from the Department of Statistics & Information, Faculty of Commerce & Economics, Sana’a University, was awarded a Master’s degree with an overall average of Excellent and a grade (96%) for her thesis entitled: “The Beta Exponentiated Power Distribution: Inference and Applications.”

The MA viva-voce committee comprised the following members:

• Assoc. Prof. Ahmed Ali Huraira (Main Supervisor)
• Prof. Abdullah Abdo Modhesh (External Examiner, Taiz University)
• Assoc. Prof. Mansour Ahmed Al-Amri (Internal Examiner, Sana’a University)

The defense was held on Thursday, Sha’ban 21, 1446 Hijri, corresponding to February 20, 2025.

The study’s objectives included:

• Developing and deriving a novel statistical distribution, the Beta Exponentiated Power (BEP) distribution, through the generalization of both the Exponentiated and Beta distributions.
  Inferring the parameters of the BEP distribution.
• Deriving the mathematical properties of the newly proposed (BEP) distribution.
• Estimating the parameters of the new distribution using Maximum Likelihood Estimation (MLE).
• Validating the statistical properties of the MLE estimators for the new distribution via simulation studies.
• Investigating the confidence intervals for the estimators of the (BEP) distribution regarding symmetry and the achievement of the nominal level through simulation.
• Comparing the estimation performance of likelihood ratio and Wald statistics for hypothesis testing in terms of size and power when applied to the (BEP) distribution.
• Applying the new distribution to three real-world datasets and comparing its fit with that of its sub-models to ascertain its flexibility and efficiency.

Key Findings of the Thesis:

This research introduced and analyzed a new statistical distribution generator, the BEP distribution, and compared it with its sub-models: Beta Power (BP), Exponentiated Power (EP), and Power (P). The study successfully derived several statistical properties of the BEP distribution, including the quantile function, moments, moment generating function, mean and median deviations, and Rényi entropy. Furthermore, the cumulative distribution function (CDF), probability density function (PDF), and hazard function were derived and illustrated graphically.

The Maximum Likelihood Estimation (MLE) method was employed to estimate the distribution’s parameters, and the properties of these estimators were evaluated through simulation studies. The findings indicated that the MLE estimators exhibited minimal bias across all considered scenarios, and the Mean Squared Error (MSE) consistently decreased with increasing sample size.

Hypothesis testing results for the Beta Exponentiated Power distribution demonstrated that the likelihood ratio statistic showed superior power performance compared to the Wald statistic.

Confidence intervals for the BEP distribution parameters were estimated for large samples, revealing symmetry in the lower and upper error probabilities and achieving the overall exponential error probabilities.

The study concluded with a number of recommendations, some of which are as follows:

• Exploring Alternative Parameter Estimation Methods: While this thesis utilized the maximum likelihood estimation method, the potential for iteration issues, particularly in models with a large number of parameters, suggests exploring alternative methods such as Probability Weighted Moments (PWM) and Minimum Distance Estimation Methods (MDM).
• Investigating Bayesian Parameter Estimation: Future research could explore parameter estimation using a Bayesian approach, including predictive analysis. Estimating the parameters of the proposed distribution based on censored data and establishing recurrence relations for single and product moments of order statistics are also recommended.
• Extending to Multivariate Analysis: This study focused on the univariate case of the power distribution. Future work could extend this to the multivariate setting, potentially leading to a multiple linear regression model based on the BEP distribution.
  The defense was well-attended by academics, researchers, colleagues, friends, and family members of Ms. Al-Thari.