Normal distribution

In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution.

Description

Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

The normal distribution is useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of random variables is sufficiently large. Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal.

Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.

The normal distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student's t, and logistic distributions).

The terms Gaussian function and Gaussian bell curve are also ambiguous because they sometimes refer to multiples of the normal distribution that cannot be directly interpreted in terms of probabilities.

See also

• Behrens–Fisher problem — the long-standing problem of testing whether two normal samples with different variances have same means;
• Bhattacharyya distance – method used to separate mixtures of normal distributions
• Erdős–Kac theorem — on the occurrence of the normal distribution in number theory
• Gaussian blur—convolution, which uses the normal distribution as a kernel
• Sum of normally distributed random variables
• Normally distributed and uncorrelated does not imply independent
• Tweedie distribution — The normal distribution is a member of the family of Tweedie exponential dispersion models
• Z-test — using the normal distribution
• Rayleigh distribution
• Multivariate normal distribution — a generalization of the normal distribution in multiple dimensions

External links

• Normal distribution @ Wikipedia.org