NormalDistribution Class 
Namespace: Meta.Numerics.Statistics.Distributions
The NormalDistribution type exposes the following members.
Name  Description  

NormalDistribution 
Initializes a new standard normal distribution.
 
NormalDistribution(Double, Double) 
Initializes a new normal distribution with the given mean and standard deviation.

Name  Description  

ExcessKurtosis 
Gets the excess kurtosis of the distribution.
(Overrides UnivariateDistributionExcessKurtosis.)  
Mean 
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)  
Median 
Gets the median of the distribution.
(Overrides ContinuousDistributionMedian.)  
Skewness 
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)  
StandardDeviation 
Gets the standard deviation of the distribution.
(Overrides UnivariateDistributionStandardDeviation.)  
Support 
Gets the interval over which the distribution is nonvanishing.
(Inherited from ContinuousDistribution.)  
Variance 
Gets the variance of the distribution.
(Inherited from UnivariateDistribution.) 
Name  Description  

CentralMoment 
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)  
Cumulant 
Computes a cumulant of the distribution.
(Overrides UnivariateDistributionCumulant(Int32).)  
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
ExpectationValue 
Computes the expectation value of the given function.
(Inherited from ContinuousDistribution.)  
FitToSample 
Computes the normal distribution that best fits the given sample.
 
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetRandomValue 
Generates a random variate.
(Overrides ContinuousDistributionGetRandomValue(Random).)  
GetRandomValues 
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
Hazard 
Computes the hazard function.
(Inherited from ContinuousDistribution.)  
InverseLeftProbability 
Returns the point at which the cumulative distribution function attains a given value.
(Overrides ContinuousDistributionInverseLeftProbability(Double).)  
InverseRightProbability 
Returns the point at which the right probability function attains the given value.
(Overrides ContinuousDistributionInverseRightProbability(Double).)  
LeftProbability 
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)  
ProbabilityDensity 
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)  
RawMoment 
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)  
RightProbability 
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)  
ToString  Returns a string that represents the current object. (Inherited from Object.) 
A normal distribution is a bellshaped curve centered at its mean and falling off symmetrically on each side. It is a twoparameter 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 reparameterizing 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, after the mathematician Friedrich Gauss.