The probability integrals of bivariate normal distributions: A contingency table approach

Abstract

SUMMARY After partitioning the plane into fine rectangular regions, the bivariate normal probability integrals over all the rectangular regions can be considered as a population contingency table. The row and column marginals of this contingency table are two discretized univariate normal distributions. The logarithm of the local cross-product ratios are approximately linear. Given the correlation coefficient of the bivariate normal, a contingency table with discretized normal marginals and proper cross-product ratios can be constructed which represents a table of probability integrals for the bivariate normal.