33. Normal (Gaussian) Distribution

  1. Catherine Forbes1,
  2. Merran Evans1,
  3. Nicholas Hastings2 and
  4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch33

Statistical Distributions, Fourth Edition

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Normal (Gaussian) Distribution, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch33

Author Information

  1. 1

    Monash University, Victoria, Australia

  2. 2

    Albany Interactive, Victoria, Australia

  3. 3

    Brian Peacock Ergonomics, SIM University, Singapore

Publication History

  1. Published Online: 16 DEC 2010
  2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242



  • normal distribution;
  • parameter estimation;
  • probability density function;
  • random number;
  • variate


The normal distribution is applicable to a very wide range of phenomena and is the most widely used distribution in statistics. It was originally developed as an approximation to the binomial distribution when the number of trials is large and the Bernoulli probability p is not close to 0 or 1. It is also the asymptotic form of the sum of random variables under a wide range of conditions. This chapter illustrates probability density function of the standard N : 0, 1 variate, with the corresponding distribution and hazard functions. It discusses variate relationships, parameter estimation, random number generation and truncated normal distribution for the normal (Gaussian) distribution.

Controlled Vocabulary Terms

binomial distribution; control variate; normal distribution; probability density function