الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
In multiple scientific fields, measurements are often expressed in angles. As a result, circular distributions are frequently utilized to broaden the scope of applications in these domains, incorporating diverse characteristics. Several approaches can be employed to establish a circular distribution, among which the technique known as “wrapping” is particularly prominent. The text is structured into four chapters, which are outlined below:
Chapter One:
Chapter 1 explores the wide-ranging applications of circular data across var- ious scientific disciplines. It delves into the utilization and significance of circular data in fields such as medicine, physics, image analysis, geography, economic time series, and biology.
By examining the diverse applications of circular data, this chapter high- lights the importance and relevance of circular data analysis in different do- mains. It demonstrates how circular data plays a vital role in addressing specific challenges and extracting meaningful insights in various scientific disciplines.
Chapter Two:
Chapter 2 serves as an introductory foundation for our primary results by providing an overview of fundamental definitions and theorems. Further- more, it offers a concise review of the existing literature on circular distri- butions, directional analysis, and the wrapping approach used to generate circular distributions.
The main objective of this chapter is to establish the necessary theoretical background that enables a comprehensive understanding of the subsequent discussions and findings presented in the study. By familiarizing readers with
key concepts and prior research in the field, we lay the groundwork for the development and interpretation of our primary results.
Chapter Three:
Chapter 3 of our study introduces the Wrapped XLindley (WXL) distribu- tion, a circular distribution characterized by a single parameter. We provide expressions for the trigonometric moments, characteristic function, and other important descriptive metrics associated with this distribution.
We employ a maximum likelihood, least squares, and weighted least squares methods to estimate the unknown parameter of the WXL distribu- tion. These methods have been proven effective in estimating the parameters of the WXL distribution, as evidenced by our simulation study.
Additionally, we apply the suggested WXL model to fit two real-world circular datasets. To evaluate the goodness-of-fit of our proposed model, we compare it with several other circular distributions, including the wrapped Lindley, wrapped modified Lindley, Von Mises, Jones-Pewsey, and Kato- Jones distributions.
Chapter Four:
Chapter 4 of our study introduces a novel two-parameter power wrapped exponential (PWE) distribution and provides a comprehensive analysis of its properties. We delve into various aspects such as the mode, hazard rate function, trigonometric moments, skewness and kurtosis measures, quantile function, order statistics, and R´enyi and Shannon entropies for this distribu- tion.
In terms of parameters estimation, we derive expressions for maximum likelihood, Bayesian, least squares, weighted least squares, percentile, maxi- mum product spacings, Cram´er-von-Mises, and Anderson-Darling methods. To assess the performance of the estimation methods, we conduct an extensive simulation study. This study examines important metrics such as
biases and mean square errors for each estimated parameter.
Lastly, we apply the newly proposed PWE distribution to three real data sets. We compare its goodness of fit with that of several well-known circular distributions, thereby providing insight into the distribution’s suitability for practical applications.