College of Computer Science and Mathematics

Discussion of a master’s thesis in the College of Computer Science and Mathematics – Department of Statistics and Informatics entitled:

“Survival Function Estimation for some Fuzzy Probability Distributions”

In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and Mathematics

Prof. Dr. Duha Bashir Abdullah The esteemed

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday 2/11/2023

Master’s thesis by student         Alan Adham Abdullah Bibani

, under the supervision of Prof. Dr. Zakariya Yahya Algamal

The study deals of survival data analysis receives wide and clear attention in most medical studies. The estimation of the survival function is one of the most important functions used in the analysis of survival data, through which the survival time variable is modeled when the values ​​of that variable are survival times with a known probability distribution. And since the process of estimating the survival function depends on observations, which in many cases cannot be recorded accurately, which leads to randomness and fuzziness being mixed in, and this in turn leads to the emergence of a state called fuzzy data. Like other data, survival data may contain fuzzy data, which negatively affects the accuracy of the survival function estimate and its simplicity in interpreting the results.

The study touched with estimating the survival function through fuzzy survival data, as a number of fuzzy distributions were used to model this data through simulation and a real application to the survival times of premature infants.

The study aims to propose estimating the survival function in the presence of fuzzy failure times that follow known probability distributions such as the exponential distribution, Weibull distribution, and Gompertz distribution, in order to be more efficient.

The Monte-Carlo simulation method was used to generate data that follows the three probability distributions depending on various factors such as the sample size, the values ​​of the parameters of that distribution, and the cutoff value. Two aspects of evaluating the performance of fuzzy estimation were relied upon: the first was the evaluation of the survival function estimate based on the information criteria through the Akaaki and Bayes information criteria, and the second was the reliance on the average time until failure. The simulation results showed the superiority of fuzzy estimation compared to normal estimation. In addition, these methods were applied to real Iraqi data, including survival time for premature infants. The results also showed the superiority of fuzzy estimation.

The discussion committee consists of