Normal distribution

The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields.

Specification of the normal distribution

There are various ways to specify a random variable. The most visual is the probability density function (plot at the top), which represents how likely each value of the random variable is. The cumulative density function is a conceptually cleaner way to specify the same information, but to the untrained eye its plot is much less informative (see below). Equivalent ways to specify the normal distribution are: the moments, the cumulants, the characteristic function, the moment-generating function, and the cumulant-generating function. Some of these are very useful for theoretical work, but not intuitive. See probability distribution for a discussion.

Related Topics:
Cumulant - Characteristic function - Moment-generating function - Generating function - Probability distribution

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All of the cumulants of the normal distribution are zero, except the first two.

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Probability density function

The probability density function of the normal distribution with mean mu and variance sigma^2 (equivalently, standard deviation sigma) is an example of a Gaussian function,

Related Topics:
Probability density function - Variance - Standard deviation - Gaussian function

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f(x;mu,sigma)

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