Construction of Confidence Interval of the Parameter in Von Mises Distribution using Bootstrap Methods

Abstract

Bootstrap method is a computer-based technique for making certain kind of statistical inferences which can simplify the often intricate calculations of traditional statistical theory. Recently, bootstrapping has been widely used for the parameter estimation of linear data. In this paper, we consider bootstrapping methods in the construction of the confidence interval of concentration parameter, for the von Mises distribution. The performances of confidence interval based on percentile bootstrap, bootstrap-t and calibration bootstrap are evaluated via simulation study. The numerical results found that confidence interval based on the calibration bootstrap is good in terms of coverage probability. Meanwhile, confidence interval based on the bootstrap-t method has a shorter expected length. The confidence intervals were illustrated using daily wind direction data recorded at maximum wind speed for four 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 values. The implication of the study is that confidence interval of the concentration parameter can be obtained using bootstrap as it provides good estimates. Keywords: bootstrap-t; calibration bootstrap; concentration parameter; percentile bootstrap; von Mises distribution