A Comparison of Asymptotic and Bootstrapping Approach in Constructing Confidence Interval of the Concentration Parameter in von Mises Distribution

Bootstrap is a resampling procedure for estimating the distributions of statistics based on independent observations. Basically, bootstrapping has been established for the use of parameter estimation of linear data. Thus, the used of bootstrap in confidence interval of the concentration parameter, κ in von Mises distribution which fitted the circular data is discussed in this paper. The von Mises distribution is the ’natural’ analogue on the circle of the Normal distribution on the real line and widely used to describe circular variables. The distribution has two parameters, namely mean direction, μ and concentration parameter, κ, respectively. The confidence interval based on the calibration bootstrap method will be compared with the existing method, confidence interval based on the asymptotic to the distribution of . Simulation studies were conducted to examine the empirical performance of the confidence intervals. Numerical results suggest the superiority of the proposed method based on measures of coverage probability and expected length. The confidence intervals were illustrated using daily wind direction data recorded at maximum wind speed for seven stations in Malaysia. From point estimates of the concentration parameter and the respective confidence interval, we note that the method works well for a wide range of κ values. This study suggests that the method of obtaining the confidence intervals can be applied with ease and provides good estimates.