Encyclopedia of Machine Learning

2010 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Gaussian Distribution

  • Xinhua Zhang
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30164-8_323



The simplest form of Gaussian distribution is the one-dimensional standard Gaussian distribution, which can be described by the probability density function (pdf):
$$\begin{array}{rlrlrl} p(x) = \phi (x) = \frac{1} {\sqrt{2\pi }}{e}^{-{x}^{2}/2 }, & & \end{array}$$
This is a preview of subscription content, log in to check access.


  1. Bernardo, J. M., & Smith, A. F. M. (2000). Bayesian theory. Chichester: Wiley.MATHGoogle Scholar
  2. Bishop, C. (2006). Pattern recognition and machine learning. New York: Springer.MATHGoogle Scholar
  3. Casella, G., & Berger, R. (2002). Statistical inference (2nd ed.). Pacific Grove, CA: Duxbury.Google Scholar
  4. Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). Springer series in statistics. New York: Springer.Google Scholar
  5. Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate analysis. London: Academic Press.MATHGoogle Scholar
  6. Miller, J., Aldrich, J., Cabilln, J. G., de Arajo, C. C., Landau, J. A. Earliest known uses of some of the words of mathematics. http://jeff560.tripod.com/mathword.html

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Xinhua Zhang
    • 1
  1. 1.Australian National UniversityCanberraAustralia