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NormalDistribution Class
Represents a normal (Gaussian) distribution.
Inheritance Hierarchy

Namespace:  Meta.Numerics.Statistics.Distributions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 3.1.0.0 (3.1.0.0)
Syntax
public sealed class NormalDistribution : Distribution

The NormalDistribution type exposes the following members.

Constructors
  NameDescription
Public methodNormalDistribution
Initializes a new standard normal distribution.
Public methodNormalDistribution(Double, Double)
Initializes a new normal distribution with the given mean and standard deviation.
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Properties
  NameDescription
Public propertyExcessKurtosis
Gets the excess kurtosis of the distribution.
(Overrides UnivariateDistributionExcessKurtosis.)
Public propertyMean
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)
Public propertyMedian
Gets the median of the distribution.
(Overrides DistributionMedian.)
Public propertySkewness
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)
Public propertyStandardDeviation
Gets the standard deviation of the distribution.
(Overrides UnivariateDistributionStandardDeviation.)
Public propertySupport
Gets the interval over which the distribution is nonvanishing.
(Inherited from Distribution.)
Public propertyVariance
Gets the variance of the distribution.
(Inherited from UnivariateDistribution.)
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Methods
  NameDescription
Public methodCumulant
Computes a cumulant of the distribution.
(Overrides UnivariateDistributionCumulant(Int32).)
Public methodEquals
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Public methodExpectationValue
Computes the expectation value of the given function.
(Inherited from Distribution.)
Public methodStatic memberFitToSample
Computes the normal distribution that best fits the given sample.
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetRandomValue
Returns a random value.
(Overrides DistributionGetRandomValue(Random).)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodInverseLeftProbability
Returns the point at which the cumulative distribution function attains a given value.
(Overrides DistributionInverseLeftProbability(Double).)
Public methodInverseRightProbability
Returns the point at which the right probability function attains the given value.
(Overrides DistributionInverseRightProbability(Double).)
Public methodLeftProbability
Returns the cumulative probability to the left of (below) the given point.
(Overrides DistributionLeftProbability(Double).)
Public methodMoment
Computes a raw moment of the distribution.
(Overrides DistributionMoment(Int32).)
Public methodMomentAboutMean
Computes a central moment of the distribution.
(Overrides DistributionMomentAboutMean(Int32).)
Public methodProbabilityDensity
Returns the probability density at the given point.
(Overrides DistributionProbabilityDensity(Double).)
Public methodRightProbability
Return the cumulative probability to the right of (above) the given point.
(Overrides DistributionRightProbability(Double).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

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 reparameterzing 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 to a normal distribution.

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

See Also