Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Simple Geometric Approach to Evaluating a Bivariate Normal Orthant Probability

  • Lee, Kee-Won (Department of Statistics, Hallym University) ;
  • Kim, Yoon-Tae (Department of Statistics, Hallym University) ;
  • Kim, U-Jung (Department of Statistics, Hallym University)
  • Published : 1999.08.01
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Abstract

We present a simple geometric approach which uses polar transformation and elementary trigonometry to evaluating an orthant probability in a bivariate normal distribution. Figures are provided to illustrate the situation for varying correlation coefficient. We derive the distribution of the sample correlation coefficient from a bivariate normal distribution when the sample size is 2 as an application.

Keywords

References

  1. Encyclopedia of Statistical Sciences v.6 Samuel Kotz(ed.);Norman L. Johnson(ed.);Campbell B. Read
  2. American Statistician v.43 Bivariate Normal Orthant Probabilities Farebrother, R.W.
  3. Biometrika v.10 Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population Fisher, R.A.
  4. American Statistician v.43 A Note on Evaluating a Certain Orthant Probability Kepner, J.L.;Harper, J.D.;Keith, S.Z.
  5. American Statistician v.43 Normal Orthant Probabilities Stigler, S.M.