Abstract

Estimation of the probability density function for circular data is an important topic in statistical inference. In this thesis, I would like to introduce two transformation based methods for estimating probability density function in this context. One is derived from traditional kernel density estimator and the other one comes from the Bernstein polynomial estimator (Chaubey, 2017). We know both of the kernel density estimator (Silverman, 1986) and Bernstein polynomial estimator (Babu, Canty and Chaubey, 2002) are appropriate for the case of linear data, transformation of circular data to linear data would bring extreme simplicity to estimation of probability density function in the case of circular data by back transformation. I will conduct a simulation study to compare these methods with respect to their global and local errors. We find through our simulation study that transformed kernel density estimator has a stronger ability to alleviate the boundary problems than transformed Bernstein polynomial estimator, however, their overall performance is pretty much similar in the central part of the distribution. Therefore, in general we can say transformed kernel density estimator leads to a better method as compared to the transformed Bernstein polynomial estimator, however further research may be needed to study other transformations.