The Construction and Properties of Ellipsoidal Probability Density Functions

Abstract

[enter Abstract Body]A recipe for the construction of a multivariate probability density function from a normalized symmetric univariate function using a distance metric methodology is developed. A method to perform multivariate integration in a polar coordinate system in an arbitary number of dimensions is described. This method is then used to compute a constant that normalizes the multivariate p.d.f. constructed using the recipe specified here. The use of the Kolmogorov test, as applied to the univariate distribution of the square of the metric distance, for distributional identification is described. A summary of the general properties of the constructed p.d.f. is given including the computation of: the principal moments; Mardia's multivariate kurtosis measure; and, the characteristic and moment generatic functions. Some elements of maximum likelihood estimation are explored.