# Interval estimation of the concentration parameter and missing value imputation in the von mises distribution / Nor Hafizah Moslim

Nor Hafizah , Moslim (2022) Interval estimation of the concentration parameter and missing value imputation in the von mises distribution / Nor Hafizah Moslim. PhD thesis, Universiti Malaya. PDF (The Candidate's Agreement) Restricted to Repository staff only Download (212Kb) PDF (Thesis PhD) Restricted to Repository staff only until 31 December 2023. Download (656Kb)

## Abstract

This study focuses on the construction of confidence interval for parameters and analysis of missing values for circular variables. The scope of the study is the von Mises distribution where it is also known as circular normal distribution. It is worthwhile to note that statistical theories for straight line and circle are different from one to another because the circle is a closed curve but line is not. The study is on the construction of the confidence interval (CI) for the concentration parameter of von Mises distribution. Here, the proposed methods is CI based on calibration bootstrap and compared with the present methods to achieve the best confidence interval for the concentration parameter. The present methods involve in the study are CI based on percentile bootstrap, CI based on asymptotic distribution of ˆ _ and CI based on bootstrap-t. The coverage probability and expected length values from each method are examined. The simulation study shows that CI based on the calibration bootstrap is good in terms of coverage probability with reasonable expected length. Next, the study is on the derivation of a new statistic based on circular distance for circular data. From the simulation study, the new statistic is approximated to the chi-squared distribution for large concentration parameter, _. Based on the new statistic, a CI for the concentration parameter is constructed as well. Numerical results suggest the CI based on 32nd percentile gives the most efficient performance. The final part of the study is analysing the missing values for the circular variables. The simulated data are assigned to six different percentages of missing values. Then, the missing data are imputed with two methods; mean imputation and bootstrap-t. Three indicators namely mean, estimate bias (EB) and estimate root mean square error (ERMSE) are used to measure the performance of concentration parameter for each method. Through the simulation study, we observe that the bootstrap-t method performs better than the other method to impute missing values. For illustration, real data consisting of data in angle form found in literature are used.

Item Type: Thesis (PhD) Thesis (PhD) – Institute of Advanced Studies, Universiti Malaya, 2022. Parameter; Confidence interval (CI); Estimate root mean square error (ERMSE); Circular distance; Asymptotic distribution Q Science > Q Science (General)Q Science > QA Mathematics Institute of Advanced Studies Mr Mohd Safri Tahir 10 May 2023 04:29 10 May 2023 04:29 http://studentsrepo.um.edu.my/id/eprint/14395

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