The Department of Mathematics at the College of Science held a discussion of the M.Sc. thesis submitted by Shahad Kareem Taher Mahmoud, entitled: “A New Hybrid Algorithm for Estimating the Survival Function of the Mixture Distribution”
The thesis was supervised by Prof. Dr. Baidaa Atiyah Khalaf. The discussion committee consisted of Asst. Prof. Dr. Sadad Khalil Ibrahim, Chair, and members Asst. Prof. Dr. Ali Talib Mohammed and Asst. Prof. Ahmed Issa Abdul Nabi.
The study aimed to develop novel probabilistic models and hybrid optimization algorithms to improve the efficiency and accuracy of survival function estimation within mixture distribution models, thereby enhancing the applicability of advanced statistical and computational approaches to survival and time-to-event data analysis.
The research addressed survival analysis as an important statistical methodology widely applied in several fields, particularly medicine, reliability engineering, and risk assessment. It focused on developing flexible probabilistic models capable of representing survival-time data with greater accuracy.
Two new mixture distributions were proposed: the Mixture Komal-Komal Distribution (MKKD) and the Mixture Inverse Rayleigh-Inverse Gompertz Distribution (MIRIGD). The study derived and analyzed several fundamental statistical properties of the proposed distributions, including the survival function, hazard function, r-th moment, mean, variance, skewness, kurtosis, moment-generating function, and mode.
Furthermore, two novel hybrid optimization algorithms were introduced for estimating the survival functions of the proposed models. The first algorithm, PSOMO, combines the local exploitation capability of the Monkey Optimization (MO) algorithm with the global search efficiency of Particle Swarm Optimization (PSO). The second algorithm, CABA, integrates the echolocation mechanism of the Bat Algorithm (BA) with the adaptive exploratory behavior of the Camel Algorithm (CA).
The proposed algorithms were designed to establish an effective balance between exploration and exploitation, thereby improving estimation accuracy and convergence speed.
A comprehensive simulation study was conducted to evaluate the performance of the proposed algorithms using the Mean Squared Error (MSE) criterion across different sample sizes, namely 10, 20, 30, 40, 50, 75, 100, and 120 observations. All computational procedures were implemented using MATLAB R2022a. In addition, real-world datasets were analyzed to assess the flexibility and practical applicability of the proposed distributions, with the resulting survival functions compared against those of relevant existing distributions.
The simulation results demonstrated that the proposed hybrid algorithms, PSOMO and CABA, achieved superior performance compared with standard optimization algorithms in estimating the survival functions of the proposed models. This superiority was reflected in consistently lower Mean Squared Error (MSE) values across the different sample sizes considered.
The proposed hybrid approaches also outperformed conventional optimization algorithms, including PSO, Genetic Algorithm (GA), and Bat Algorithm (BA), confirming their effectiveness in improving estimation accuracy and computational performance.
The findings indicate that integrating the proposed MKKD and MIRIGD distributions with the newly developed hybrid optimization algorithms provides a more flexible and robust statistical-computational framework for modeling time-to-event data. This integration can contribute to improving the reliability and accuracy of survival analysis models in applications requiring precise estimation of survival functions.
Scientific Contribution and Sustainable Development Goals
The thesis represents a scientific contribution to the fields of mathematical statistics, computational methods, and optimization algorithms through the development and application of hybrid computational approaches for more accurate survival-function estimation.
The outcomes of the study are particularly aligned with Sustainable Development Goal 4 (SDG 4): Quality Education, by supporting advanced research and the development of knowledge and skills in mathematics, statistics, and computational sciences. The study also contributes to Sustainable Development Goal 9 (SDG 9): Industry, Innovation and Infrastructure, through the development of innovative computational methodologies with potential applications in scientific and engineering analysis and data-driven decision-making.
The thesis highlights the importance of applied mathematical research in developing advanced statistical and computational tools capable of efficiently addressing complex datasets and strengthening the role of modern optimization algorithms in scientific research and future applications.
