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

Research output: Contribution to journalArticle

15 Scopus citations


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. / 1987 Biometrika Trust.

Original languageEnglish (US)
Pages (from-to)185-190
Number of pages6
Issue number1
StatePublished - Mar 1 1987

All Science Journal Classification (ASJC) codes

  • Agricultural and Biological Sciences(all)
  • Applied Mathematics
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Contingency table
  • Cross-product ratio
  • Discretized bivariate normal
  • Iterative proportional fitting algorithm

Cite this