A Mathematics M.Sc. thesis develops a New Statistical Distribution for Survival Function Estimation and Its Application to Stroke Patient Data

The Department of Mathematics discusse’s a Master’s thesis in Pure Sciences submitted by researcher Mohammed Mahan Abd Farhan, entitled: “Estimate Survival Function of New Transmuted Rayleigh-Weibull Distribution” supervised by Asst. Prof. Dr. Maysaa Jalil Mohammed. The discussion committee comprised Prof. Dr. Baidaa Atiya Khalaf, Chair; Prof. Dr. Samaa Fouad Ibrahim, Member; and Asst. Prof. Ahmed Issa Abdul-Nabi, Member.
The study aimed to develop a new statistical distribution and estimate its survival function based on the Rayleigh-Weibull distribution and the quadratic rank transmutation approach. By introducing a new transformation parameter β, the proposed model provides greater flexibility for representing and analyzing data with different probabilistic characteristics.
The thesis derived and investigated a comprehensive set of mathematical and statistical properties of the proposed Transmuted Rayleigh-Weibull Distribution (TRWD), including the cumulative distribution function, probability density function, hazard function, and survival function. The study also examined the mode, raw moments, variance, skewness, kurtosis, characteristic function, moment-generating function, mean time to failure, quantile function, and median.
A major component of the research focused on estimating the parameters of the proposed distribution and its survival function using the Maximum Likelihood Estimation (MLE) and Ordinary Least Squares (OLS) methods. The performance of the two estimation approaches was assessed using the Mean Squared Error (MSE) criterion. To enhance the reliability of the findings, a simulation study was conducted using different sample sizes of 20, 30, 50, 100, and 200, with 1,000 and 2,000 replications.
The study further evaluated the performance of the proposed distribution by comparing the Transmuted Rayleigh-Weibull Distribution with several existing statistical distributions, including the Weibull, Rayleigh, T-Weibull, T-Rayleigh, and Rayleigh-Weibull distributions. The comparison was conducted using established statistical model-selection criteria, including the Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (AICc), Hannan–Quinn Criterion (HQ), and Bayesian Information Criterion (BIC).
To demonstrate the practical effectiveness and applicability of the proposed model, the research incorporated real-world stroke patient data collected from the records of Al-Kindi Teaching Hospital in the Al-Rusafa sector of Baghdad Governorate. The dataset covered the period from 1 January 2025 to 1 November 2025 and consisted of 17 stroke patients. The collected information included admission and discharge data as well as selected demographic characteristics. The data were statistically analyzed and modeled using the proposed distribution to evaluate its effectiveness in describing real-world survival-related observations.
The statistical modeling yielded positive results, supporting the potential usefulness of the proposed distribution as a flexible statistical model for analyzing survival data and other time-to-event datasets, particularly in applications where conventional probability distributions may not provide sufficient flexibility.
The significance of the research lies in its contribution to the development of modern statistical models and the advancement of mathematical and statistical approaches for addressing real-world problems. The study also highlights the potential of applied mathematics and statistics to support quantitative analysis in scientific and health-related research.
The research contributes to several United Nations Sustainable Development Goals, particularly:
SDG 3 – Good Health and Well-being: through the application of the proposed statistical model to real-world stroke patient data, supporting quantitative approaches to health-related data analysis.
SDG 4 – Quality Education: through advancing specialized academic knowledge and research in mathematics and statistics.
SDG 9 – Industry, Innovation and Infrastructure: through the development of an innovative statistical model and the application of simulation and quantitative analysis techniques.
SDG 17 – Partnerships for the Goals: through the use of real-world data from a healthcare institution to support academic research and the development of applied statistical models.