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StudentDistribution Class

Represents the distribution of Student's t statistic.
Inheritance Hierarchy

Namespace:  Meta.Numerics.Statistics.Distributions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.1.4
Syntax
public sealed class StudentDistribution : ContinuousDistribution

The StudentDistribution type exposes the following members.

Constructors
  NameDescription
Public methodStudentDistribution
Initializes a new Student distribution.
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Properties
  NameDescription
Public propertyDegreesOfFreedom
Gets the number of degrees of freedom.
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 ContinuousDistributionMedian.)
Public propertySkewness
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)
Public propertyStandardDeviation
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.)
Public propertySupport
Gets the interval over which the distribution is non-vanishing.
(Inherited from ContinuousDistribution.)
Public propertyVariance
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.)
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Methods
  NameDescription
Public methodCentralMoment
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)
Public methodCumulant
Computes a cumulant of the distribution.
(Inherited from UnivariateDistribution.)
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 ContinuousDistribution.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRandomValue
Generates a random variate.
(Overrides ContinuousDistributionGetRandomValue(Random).)
Public methodGetRandomValues
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazard
Computes the hazard function.
(Inherited from ContinuousDistribution.)
Public methodInverseLeftProbability
Returns the point at which the cumulative distribution function attains a given value.
(Overrides ContinuousDistributionInverseLeftProbability(Double).)
Public methodInverseRightProbability
Returns the point at which the right probability function attains the given value.
(Inherited from ContinuousDistribution.)
Public methodLeftProbability
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)
Public methodProbabilityDensity
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)
Public methodRawMoment
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)
Public methodRightProbability
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

The mean of n independent standard-normal distributed variables, divided by their root mean square, is distributed according a Student distribution with n degrees of freedom. Since this is the form of the expression for the mean of a sample divided by its standard deviation, the Student distribution expresses the distribution of sample means arround the population mean, for a normally distributed population.

The origin of the name Student distribution is a nice bit of statistical trivia. William Gosset published a paper describing the distribution and its statistical applications in 1908. His employer, the Guiness Brewery, did not want other brewers to be tipped off to its application to comparing small samples of beer, so they asked him to publish under a pseudonym. He published the paper under the name "Student" and the distribution has been known by that name since.

See Also