Thetype exposes the following members.
Initializes a new standard normal distribution.
Initializes a new normal distribution with the given mean and standard deviation.
Gets the excess kurtosis of the distribution.(Overrides UnivariateDistributionExcessKurtosis.)
Gets the mean of the distribution.(Overrides UnivariateDistributionMean.)
Gets the median of the distribution.(Overrides DistributionMedian.)
Gets the skewness of the distribution.(Overrides UnivariateDistributionSkewness.)
Gets the standard deviation of the distribution.(Overrides UnivariateDistributionStandardDeviation.)
Gets the interval over which the distribution is nonvanishing.(Inherited from Distribution.)
Gets the variance of the distribution.(Inherited from UnivariateDistribution.)
Computes a cumulant of the distribution.(Overrides UnivariateDistributionCumulant(Int32).)
Computes the expectation value of the given function.(Inherited from Distribution.)
Computes the normal distribution that best fits the given sample.
Serves as a hash function for a particular type.(Inherited from Object.)
Returns a random value.(Overrides DistributionGetRandomValue(Random).)
Gets the Type of the current instance.(Inherited from Object.)
Returns the point at which the cumulative distribution function attains a given value.(Overrides DistributionInverseLeftProbability(Double).)
Returns the point at which the right probability function attains the given value.(Overrides DistributionInverseRightProbability(Double).)
Returns the cumulative probability to the left of (below) the given point.(Overrides DistributionLeftProbability(Double).)
Computes a raw moment of the distribution.(Overrides DistributionMoment(Int32).)
Computes a central moment of the distribution.(Overrides DistributionMomentAboutMean(Int32).)
Returns the probability density at the given point.(Overrides DistributionProbabilityDensity(Double).)
Return the cumulative probability to the right of (above) the given point.(Overrides DistributionRightProbability(Double).)
Returns a string that represents the current object.(Inherited from Object.)
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.