Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 1.5.0.0 (1.5.0.0)
Syntax
| C# | Visual Basic | Visual C++ |
public class ChiSquaredDistribution : Distribution
Public Class ChiSquaredDistribution _ Inherits Distribution
public ref class ChiSquaredDistribution : public Distribution
Members
| All Members | Constructors  | Properties  | Methods |
 Public Protected | Instance Static  | Declared Inherited | XNA Framework Only  .NET Compact Framework Only  |
| Member | Description | |
|---|---|---|
| ChiSquaredDistribution(Int32) |
Initializes a new χ2 distribution.
|
| DegreesOfFreedom |
Gets the number of degrees of freedom ν of the distribution.
|
| Equals(Object) | (Inherited from Object.) |
| ExpectationValue(Function<(Of <(Double, Double>)>)) |
Computes the expectation value of the given function.
(Inherited from Distribution.) |
 | Finalize()()() |
Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
(Inherited from Object.) |
| GetHashCode()()() |
Serves as a hash function for a particular type.
(Inherited from Object.) |
| GetRandomValue(Random) |
Returns a random value.
(Inherited from Distribution.) |
| GetType()()() |
Gets the Type of the current instance.
(Inherited from Object.) |
| InverseLeftProbability(Double) |
Returns the point at which the cumulative distribution function attains a given value.
(Overrides Distribution..::.InverseLeftProbability(Double).) |
| LeftProbability(Double) |
Returns the cumulative probability to the left of (below) the given point.
(Overrides Distribution..::.LeftProbability(Double).) |
| Mean |
Gets the mean of the distribution.
(Overrides Distribution..::.Mean.) |
| Median |
Gets the median of the distribution.
(Overrides Distribution..::.Median.) |
| MemberwiseClone()()() |
Creates a shallow copy of the current Object.
(Inherited from Object.) |
| Moment(Int32) |
Returns the given moment of the distribution.
(Overrides Distribution..::.Moment(Int32).) |
| MomentAboutMean(Int32) |
Returns the given moment of the distribution, about the mean.
(Overrides Distribution..::.MomentAboutMean(Int32).) |
| ProbabilityDensity(Double) |
Returns the probability density at the given point.
(Overrides Distribution..::.ProbabilityDensity(Double).) |
| RightProbability(Double) |
Return the cumulative probability to the right of (above) the given point.
(Overrides Distribution..::.RightProbability(Double).) |
| Skewness |
Ges the skewness of the distribution.
(Overrides Distribution..::.Skewness.) |
| StandardDeviation |
Gets the standard deviation of the distribution.
(Inherited from Distribution.) |
| Support |
Gets the interval over which the distribution is nonvanishing.
(Overrides Distribution..::.Support.) |
| ToString()()() | (Inherited from Object.) |
| Variance |
Gets the variance of the distribution.
(Overrides Distribution..::.Variance.) |
Remarks
A chi squared distribution is an asymmetrical distribution ranging from zero to infinity with a peak near its number of degrees of freedom ν. It is a one-parameter distribution determined entirely by the parameter nu.
The figure above shows the χ2 distribution for ν = 6, as well as the normal distribution with equal mean and variance for reference.
The sum of the squares of ν independent standard-normal distributed variables is distributed as χ2 with ν degrees of freedom.
The χ2 distribution appears in least-squares fitting as the distribution of the sum-of-squared-deviations under the null hypothesis that the model explains the data. For example, the goodness-of-fit statistic returned by the model our model fitting methods (FitToFunction(Function<(Of <(array<Double>[]()[], T, Double>)>), array<Double>[]()[]), FitToLinearFunction(array<Function<(Of <(T, Double>)>)>[]()[]), FitToLine()()(), and others) follows a χ2 distribution.
Inheritance Hierarchy
Meta.Numerics.Statistics..::.Distribution
Meta.Numerics.Statistics..::.ChiSquaredDistribution
See Also
