Properties of the Bivariate Normal Cumulative Distribution

摘要

The key position of the normal distribution, both in probability and statistics, has led to extensive theory and applications of this density function. This paper investigates special properties of equi-distributional contours, defined as a functional relationship between lower limits on the range of integration for the upper bivariate normal cumulative distribution with fixed value. Although theory developed in the following sections pertains to the bivariate case, these results may be generalized to a larger number of variables. (Author)