College of Computer Science and Mathematics

Discussion of the master’s thesis in the College of Computer Science and Mathematics -Department of Statistics and Informatics Department entitled: “Nonparametric Estimation of Probability Distribution Function Using Ranked Set Sampling with Application”

Master’s thesis by  Rami Saad Gharib

supervised by   Dr. Rikan Abdulazeez Ahmed

This thesis includes the important and primary issue in statistical applications is understanding the probability distribution of the population to be studied and knowing the characteristics of that population in order to represent it accurately through commonly used statistical methods. In most statistical inference problems, it is assumed that the probability distribution of the variable is known, while the parameters of that distribution are unknown. However, in practice, the functional form of the distribution is rarely known. Therefore, non-parametric and semi-parametric methods are employed to determine the probability distribution function, relying on little information or assumptions about the distribution under study.

The study addressed to estimate the cumulative distribution function (CDF) and measure the odds ratio, as well as the reliability estimation of stress and strength, relying on local polynomial regression of degree two and comparing it with the parametric estimation using the method of moments and maximum likelihood method. Additionally, the calculations of the mean squared error (MSE) and bias values for the ordered sample set (RSS) and the median ordered sample set (MRSS) will be conducted, along with studying the properties of the cumulative distribution function (CDF) based on local polynomial regression (LPR).

The study aims To estimate the probability distribution function (CDF) and measure the odds ratio, as well as to assess stress and strength reliability estimation under the principle of using the ranked sample set (RSS) and the median-ranked sample set (MRSS) based on the local polynomial regression approach

The discussion committee consists of

(Chairman)Dr. Haifa Abduljawad Said

(member) Dr. Raya Salem Muhammad Ali

(Member) Dr. Safwan Nazem Rasheed

(member and supervisor)  Dr. Rikan Abdulazeez Ahmed