Stereographic Semicircular ThreeParameters Lindley(SSTL) With practical application

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistics

Presented by researcher

NAJWAA TURKI AWAD

Supervised By

Ass. Prof. Dr. Sada Fayed Mohammed

Abstract

In many practical applications and in the reality of our daily lives, we may encounter data measured in units of circular angular measurement, such as degrees, and this data can fall within the full circular range, i.e. (0, 2π). Such data is called circular data, which can be described as data that They are in the form of vectors collected by a single point of origin and are measured by the angular measure, as the distance of each vector from the vector specified by the zero direction and the direction of rotation represents the amount of the angle that indicates the direction of that vector, and that the minimum possible amount for this angle is zero degrees and the highest amount is 360 degrees.

In the case of circular data, a model must be found for the purpose of studying and analyzing such data. Therefore, this thesis came to present a study on finding a new distribution linking the random variable known as the Cartesian plane (x, y) and the circular space (r, θ) by finding the proposed model and then estimating The parameters of the new distribution are based on three estimation methods, namely the Maximum Likelihood ML method, the Least Squares method (LS), and the Maximum Product of Spacing Estimation Method. For the purpose of comparing the methods of estimating the parameters for the proposed distribution, Employing the Monte Carlo simulation method to conduct several experiments with different sample sizes ((30), (50), (150, 100)) based on the statistical criterion Mean Square Error (MSE). The results showed the superiority of the Maximum Possibility method in calculating the estimates of the stereographic distribution parameters. Semicircular Lindley) (in general in estimating the size distribution parameters, and the distribution was applied to real data with (116) observations representing the “survival times” of people with kidney failure measured in weeks until “death” in the Holy “Karbala” governorate, which were collected from the records of “inpatients in the hospital.” Al-Hussein Teaching Hospital Department for the period 9/2/2014 until 4/3/2023, by applying these data “to the transformed distribution to estimate the survival function” using the maximum potential method, which showed its superiority in the experimental aspect among the estimation methods used. In calculating the retention function.

Stereographic Semicircular ThreeParameters Lindley(SSTL) With practical application

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistics

Presented by researcher

NAJWAA TURKI AWAD

Supervised By

Ass. Prof. Dr. Sada Fayed Mohammed

Abstract

In many practical applications and in the reality of our daily lives, we may encounter data measured in units of circular angular measurement, such as degrees, and this data can fall within the full circular range, i.e. (0, 2π). Such data is called circular data, which can be described as data that They are in the form of vectors collected by a single point of origin and are measured by the angular measure, as the distance of each vector from the vector specified by the zero direction and the direction of rotation represents the amount of the angle that indicates the direction of that vector, and that the minimum possible amount for this angle is zero degrees and the highest amount is 360 degrees.

In the case of circular data, a model must be found for the purpose of studying and analyzing such data. Therefore, this thesis came to present a study on finding a new distribution linking the random variable known as the Cartesian plane (x, y) and the circular space (r, θ) by finding the proposed model and then estimating The parameters of the new distribution are based on three estimation methods, namely the Maximum Likelihood ML method, the Least Squares method (LS), and the Maximum Product of Spacing Estimation Method. For the purpose of comparing the methods of estimating the parameters for the proposed distribution, Employing the Monte Carlo simulation method to conduct several experiments with different sample sizes ((30), (50), (150, 100)) based on the statistical criterion Mean Square Error (MSE). The results showed the superiority of the Maximum Possibility method in calculating the estimates of the stereographic distribution parameters. Semicircular Lindley) (in general in estimating the size distribution parameters, and the distribution was applied to real data with (116) observations representing the “survival times” of people with kidney failure measured in weeks until “death” in the Holy “Karbala” governorate, which were collected from the records of “inpatients in the hospital.” Al-Hussein Teaching Hospital Department for the period 9/2/2014 until 4/3/2023, by applying these data “to the transformed distribution to estimate the survival function” using the maximum potential method, which showed its superiority in the experimental aspect among the estimation methods used. In calculating the retention function.