NormalDistribution Class

public sealed class NormalDistribution : ContinuousDistribution

Public NotInheritable Class NormalDistribution
	Inherits ContinuousDistribution

public ref class NormalDistribution sealed : public ContinuousDistribution

[<SealedAttribute>]
type NormalDistribution = 
    class
        inherit ContinuousDistribution
    end

Inheritance

Object    UnivariateDistribution    ContinuousDistribution    NormalDistribution

A normal distribution is a bell-shaped curve centered at its mean and falling off symmetrically on each side. It is a two-parameter distribution determined by giving its mean and standard deviation, i.e. its center and width. Its range is the entire real number line, but the tails, i.e. points more than a few standard deviations from the means, fall off extremely rapidly.

A normal distribution with mean zero and standard deviation one is called a standard normal distribution. Any normal distribution can be converted to a standard normal distribution by re-parameterizing the data in terms of "standard deviations from the mean", i.e. z = (x - μ) / σ.

Normal distribution appear in many contexts. In practical work, the normal distribution is often used as a crude model for the distribution of any continuous parameter that tends to cluster near its average, for example human height and weight. In more refined theoretical work, the normal distribution often emerges as a limiting distribution. For example, it can be shown that, if a large number of errors affect a measurement, then for nearly any underlying distribution of error terms, the distribution of total error tends toward a normal distribution.

The normal distribution is often called a Gaussian, after the mathematician Friedrich Gauss.

Reference

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