Dirichlet distribution with views on geodesy and geophysics

Abstract

The Dirichlet distribution is one of the most important multivariate probability distributions with wide range of applications in various areas of statistics, probabilistic modelling, engineering and geosciences. Despite growing interest in the distribution, little appeared to be known of the Dirichlet distribution in the community of geodesy and geophysics. With these thoughts in mind, the present paper is an application-driven short and simplified introduction to the fundamental issues of the Dirichlet distribution and gives some useful representations of and bounds on the Dirichlet distribution function. A new polynomial representation for the bivariate Dirichlet distribution is established. In addition, we also shed a certain light on the astronomical, geodetic and geophysical background of the Dirichlet integral in historical context. The potential possibility of geodetic and geophysical applications of the Dirichlet distribution is briefly described within the framework of recent developments and trends of statistical science and applied probability.