Hassan, Siti Fatimah (2015) Confidence intervals (CI) for concentration parameter in von Mises distribution and analysis of missing values for circular data / Siti Fatimah binti Hassan. PhD thesis, University of Malaya.
Abstract
This study is on circular statistics that is also known as directional statistics. Directional statistics is a branch of statistics which deal with the data in angle form in which the method of analysis is different from linear data. For example, the distribution analogues to the normal distribution in linear data is known as circular normal distribution. This study comprises of four parts. The first part of the study focuses on the efficient approximation for the concentration parameter in von Mises distribution. Here, a new method of approximating the concentration parameter is proposed, and the performance of the proposed method is studied via simulation study. The second part of the study is on the confidence intervals (CI) for the concentration parameter in von Mises distribution. Several methods in constructing the CI for the concentration parameter are proposed including CI based on circular population, CI based on the asymptotic distribution of ˆ , CI based on the distribution of 휃 and 푅 and also CI based on bootstrap-t method. All proposed methods are validated via simulation study and the performance indicator such as an expected length and its coverage probability are evaluated. The third part of the study is on the derivation of the circular distance for circular data. From this derivation, we construct the CI for the concentration parameter. Three different methods will be considered in proposing the new CI including mean, median and percentile. The simulation studies carried out to assess the performance of each proposed method. The final part of this study is an analysis of missing values for circular variables. Missing values is a common problem that occurs in data collection. By ignoring the existence of missing values, leads to the biasness and lack of efficiency of a statistics. In this study, three imputation methods are considered namely expectation-maximization (EM) algorithm and data augmentation (DA) algorithm. All proposed methods are compared to the conventional methods. The analyses are conducted by doing the simulation studies by varying the value of the concentration parameter. All the proposed methods from this study are illustrated using the real data consisting of data in angle form found in the literature.
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