Normalizing constant: Difference between revisions

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{{Use American English|date = March 2019}}

{{Short description|Constant a such that af(x) is a probability measure}}

{{Lead too short|date=March 2014}}

The concept of a '''normalizing constant''' arises in [[probability theory]] and a variety of other areas of [[mathematics]]. The normalizing constant is used to reduce any probability function to a probability density function with total probability of one.

For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution. In Bayes' theorem, a normalizing constant is used to ensure that the sum of all possible hypotheses equals 1. Other uses of normalizing constants include making the value of a Legendre polynomial at 1 and in the orthogonality of orthonormal functions.

==Definition==