Using the spherical inverse method to estimate the survival function of the semicircular Shanker distribution (with a practical application)
A letter submitted to the Council of the College of Economics and Administration at the University of Karbala
It is part of the requirements for obtaining a master’s degree in statistics
Submitted by the researcher
Hanan Jasab Muhammad
Under supervision
Assistant Prof.Dr. Sada Fayed Muhammad
Abstract
In many practical applications and in the reality of our lives, we may encounter data measured in angular units such as degrees or radians, and this data can fall within the full circular range, i.e. (0, 2π). Such data is called the circular data, as the supporting (Support) for circular data is the unit circle, but it falls in the circular range (0, 2π). This type of data is called circular data, and the term circular data is used for the purpose of distinguishing it from Cartesian plane data (x, y) that is often used in analyses. In the case of circular data, a distribution must be found for the purpose of studying and analyzing such data. Therefore, this thesis came to find the modified semi-circular spherical inverse Shanker Distribution (StereographicSemicircular Shanker Distribution) based on the (StereographicSemicircular Shanker Distribution) formula, which is concerned with converting normal (Cartesian) data into polar data (measured in angles) and then finding the statistical and structural properties of the proposed spherical inverse distribution. The semicircular average and then estimate the parameters of the new distribution based on three estimation methods, which are the Maximum Likelihood method, the Weighted Least Squares method (L S W)(Weighted Least Squares method), and the Cramer-Von Mises Minimum method. For the purpose of comparing methods for estimating parameters and the survival function, the Monte Carlo simulation method was employed using a program in the MATLAB language to conduct several experiments with different sample sizes (small (20), medium (50), and large (200,100)) and using the statistical criterion. Mean Square Integration Error (MSE) The results showed the superiority of the Cramer-von Mises method in calculating the survival function estimates for the new distribution at all sizes.
The method, which has been shown to be preferable to the applied side, was applied to real data of (101) observations representing the survival times of people with heart disease until death in the Holy Karbala Governorate, which were collected from the records of hospitalized patients in the Al-Hussein Teaching Hospital Department for the period 6/2/2020 until 2020. 8/12/2020, by applying these data to the transformed distribution (Stereographic Semicircular Shanker Distribution) to estimate the survival function using the Cramer-von Mises method and concluding that it is the best among the estimation methods used in calculating the survival function and according to the outputs of the experimental side, by relying on On Matlab program.
