角度分布の概要

Directional data arise when one or more of the variables being observed is angular, and occur in fields as diverse as astronomy, ecology, medicine and the environmental sciences. Examples include the flight directions of migrating birds, the directions of fallen tree logs, the directions of wind or ocean currents, and the directions of fault lines in geological bedrock. When just one angle is measured, the resulting angular variable is referred to as being ``circular"; it being possible to represent each observation as a point on the circumference of the unit circle. In general, it is crucial that directional data are analyzed as such and not employing the statistical techniques designed for linear data (observed on the real line or throughout real space). ``Directional Statistics" deals with the methodology for analyzing directional data in general, whereas the term ``Circular Statistics" is employed when the data are, more specifically, circular (univariate angular data). Circular distributions arise as putative models for circular data, and numerous families of circular distributions have been proposed in the literature.

My research focuses on the distribution theory in Statistics, extension to the multivariate distributions using copula, modeling approaches in Mathematical Ecology, and algorithms for estimating parameters of the statistical models.

Historically the best known, and consequently the most often applied, model in circular statistics has been the von Mises distribution, also referred to somewhat misleadingly as the ``circular normal" distribution.

It is also frequently referred to as the circular normal distribution because various characterizations of it have much in common with those of the normal distribution. However, the von Mises distribution does not have the same properties of the normal distribution such as ``Reproductive Property".