Estimating the Fuzzy Survival Function of the Bure III Distribution updated with the Application
A thesis is presented to the Council of College of Administration & Economics in University of Kerbalaa
As a part of MSc. Degree Requirements in Statistics
Presented by
Amal Mohammed Jawad Abdulkadhim Al Shaddood
Under supervision of
Asst. Prof.Dr. Moshtaq Kareem Abdulraheem Asst. Prof.Dr.Bahaa Abdulrazzaq Qasim
Abstract
Burr type III distribution with two parameters is deemed one of the most important continuous probability distributions to analyze survival time for several phenomenon such as (premise include birth, start a job, till ultimate event include pension or death). In consequence, it is debated herein the study of new modified Burr III distribution; i.e., NMBIII, after adding new parameter to Burr III Distribution function saving that we did not find the such new distribution but in one research work.
In this study, it is argued the characteristics of Mathematical statistic distribution in addition to the basic concepts for survival, risk, risk cumulative risk and the basic concepts of fuzzy sets, membership function and definition of fuzzy survival and then it is transferred to the empirical part of the study as it is accredited Mont0carlo Simulation Mode to generate data of different pattern sizes and study several hypothetical patterns for shape parameters(C,K) and scale parameter(l) for new modified Burr III distribution(NBMIII), as it is applied three modes to estimate parameters (Maximum Likelihood Estimation (MLE) ,Ordinary Least Square (OLS) and CVS methods). Then, its used parameters estimates were collected to find the estimation of survival function and the fuzzy survival functions through comparison with IMSE, Upon the results of simulation , it is concluded that the fuzzy survival; in case of accrediting NMBIII; which is estimated by MLE, is the best method rather than OLS and IMSE and CVM as it is given least integrated error of square means at the pattern of maximum size ( n=100). In regards to applied part, it is used a local real data form for a pattern consisted of 100 represent in survival times alive for breast cancer patients and after comparing the results of Goodness of fit tests, it is stated that data followed the distribution, and upon differentiation among distribution. It is found that distribution in case of fuzzy data is better than the same distribution in case of real data.
The study concluded several findings; the most important of which, the condition of died in case of that period of illness is increased. Thus, the researcher recommended to provide the required and best therapy by the concerned authorities include revealing the community with the importance of early test to avoid infection.
