Introduction letter to
Council of the College of Business and Economics / University of Karbala, which is part of the requirements for obtaining a master’s degree in statistics
Submitted by the researcherBy
Huda Abdul Hussen Awda Al-Khafaji
Supervised By
Prof. Awad Kadim Shaalan AL-Khalidi
Abstract
Circular data is one of the most relevant and important applied techniques in many
fields such as physical sciences, medical sciences, meteorology, psychology and
other sciences that fall within the full circular range (0, 2π). Such data is called
circular data. A model must be found for the purpose of studying and analyzing such
data. Therefore, this message came in which the circular wrapped distribution rule
was relied upon, so that the distribution (zeghdoudi Distribution) is adopted as a
basic distribution to obtain the distribution (Wrapped zeghdoudi Distribution), which
is concerned with converting regular linear data into circular polar data (measured by
angles), and then finding most of the statistical and structural properties of the
proposed distribution (Wrapped zeghdoudi Distribution) as a probability and
cumulative density function, survival and risk function, in addition to other statistical
properties, and then estimating the parameters and survival function of the new
distribution based on three estimation methods, which are the usual maximum
likelihood method (Maximum Likelihood), the least squares method (LS), and the
weighted least squares method (WLS). For the purpose of comparing the methods of
estimating the parameters of the proposed distribution, the Monte Carlo simulation
method was employed using a program in the (Mathematica) language to conduct
several experiments with different sample sizes. Small (30-20-10), medium (75-50)
and large (,100)) based on the statistical criterion of the mean square error (MSE), as
the simulation results showed the superiority of the weighted least squares method in
calculating the parameters and survival function estimates for the distribution
(Zeghdoudi Distribution Wrapped) in a way, and the distribution was applied to real
data of (100) observations representing the angles of the spinal deflection of people
“suffering from scoliosis” by applying this data to the proposed distribution to
estimate the parameters and the survival function using the weighted least squares
method, which showed its superiority in the experimental aspect among the
estimation methods used in calculating the parameters and the survival function,
based on the outputs of the program Mathematical.
