مقارنة طرائق تقدير معلمات ودالة معولية توزيع كاما ذي المعلمتين في حالة البيانات المفقودة باستخدام المحاكاة == Comparing The Estimation Methods of The Parameters And The Reliability Function For The Two Parameters Gamma Distribution In Case of Missing Data By Using Simulation
Author name:
اوات سردار وادي
Supervisor name:
ظافر حسين رشيد النجار
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Master
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T3443 - p.pdf
Abstract:
ان اغلب طرائق التقدير الاحصائية تفترض توفر بيانات تامة المشاهدات للعينات المدروسة، وقد بنيت جميع الطرائق على هذا الاساس. ولكن في الكثير من الظواهر الطبيعية، والاقتصادية، والاجتماعية وغيرها تتعرض جزء من بيانات هذه الظواهر الى الفقدان وتختلف اسباب الفقدان ف | Most of the statistical estimation methods depend on the availability of the complete data of the observations of the samples under study. All the statistical methods are based on this basis. However, part of the data of most of the natural, economic and social phenomena is prone to be missed for several reasons. The missing of the data may happen intentionally because of the high costs, risks or the lack of capabilities or unintentionally because of the failure of the recorders, the lack of the necessary requirements of production, the natural disasters, wars etc. Regardless of the various reasons, the incomplete data gives arise to a complex problem, which must be resolved by using statistical methods that deal with the incomplete data.In most cases, the failure times data of the individual component in the system has missing observations. Most of the reasons of having missing data go back to the meter, which registers the failure times of the whole system instead of a single component. Furthermore, the maintenance employees and the operators, who register the data, are responsible for maintaining the systems or the engines which fail to operate; they are not responsible for registering the data. Hence, it is not possible to have a convenient distribution of failure times because of the missing data of the individual component during the registration and because the available data represent the whole number of the failure times and the accumulative number of the operating. Consequently, the familiar methods of estimation are inconvenient. Therefore, some researchers derive and develop certain methods to estimate the parameters and Reliability Function using this kind of non - standard data for the various distributions of failure times.The research studies the Two Parameters Gamma Distribution, which is considered one of the most important, applicable and widely used distributions in the reliability realm and Survival Theory. It is mostly used as a model to distribute the failure times of the electrical, mechanical and electromechanical systems. The estimation of the parameters and the Reliability Function of this distribution in case of missing data has been made by using two important methods : the Maximum Likelihood Method and the Shrinkage Method. The former one consists of three methods to solve the MLE non - linear equation by which the estimators of the maximum likelihood can be obtained : Newton - Raphson, Thom and Sinha methods. Thom and Sinha methods are developed by the researcher to be suitable in case of missing data. Furthermore, the Bowman, Shenton and Lam Method, which depends on the Three Parameters Gamma Distribution to get the maximum likelihood estimators, has been developed. A comparison has been made between the methods in the experimental aspect to find the best method through simulation by using the Monte Carlo Method. Several experimentations have been made by using two of the important statistical measures : Mean Square Error (MSE) and Mean Absolute Proportional Error (MAPE). Generally, the developed Thom Method is found to be the best one for the Reliability Function estimation because it has the minimum Integral Mean Square Error (IMSE) and the minimum Integral Mean Absolute Percentage Error (IMAPE) in comparison with the other methods.
