FDistribution Class |
Namespace: Accord.Statistics.Distributions.Univariate
[SerializableAttribute] public class FDistribution : UnivariateContinuousDistribution, ISampleableDistribution<double>, IDistribution<double>, IDistribution, ICloneable, IRandomNumberGenerator<double>
The FDistribution type exposes the following members.
Name | Description | |
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FDistribution |
Constructs a F-distribution with
the given degrees of freedom.
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FDistribution(Int32, Int32) |
Constructs a F-distribution with
the given degrees of freedom.
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Name | Description | |
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DegreesOfFreedom1 |
Gets the first degree of freedom.
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DegreesOfFreedom2 |
Gets the second degree of freedom.
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Entropy |
Gets the entropy for this distribution.
(Overrides UnivariateContinuousDistributionEntropy.) | |
Mean |
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.) | |
Median |
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.) | |
Mode |
Gets the mode for this distribution.
(Overrides UnivariateContinuousDistributionMode.) | |
Quartiles |
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.) | |
StandardDeviation |
Gets the Standard Deviation (the square root of
the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |
Support |
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.) | |
Variance |
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.) |
Name | Description | |
---|---|---|
Clone |
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.) | |
ComplementaryDistributionFunction |
Gets the complementary cumulative distribution function
(ccdf) for this distribution evaluated at point x.
This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.) | |
CumulativeHazardFunction |
Gets the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |
DistributionFunction(Double) |
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |
DistributionFunction(Double, Double) |
Gets the cumulative distribution function (cdf) for this
distribution in the semi-closed interval (a; b] given as
P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.) | |
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
Fit(Double) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |
Fit(Double, IFittingOptions) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |
Fit(Double, Double) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |
Fit(Double, Int32) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |
Fit(Double, Double, IFittingOptions) |
Not available.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).) | |
Fit(Double, Int32, IFittingOptions) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |
Generate |
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |
Generate(Random) |
Generates a random observation from the current distribution.
(Overrides UnivariateContinuousDistributionGenerate(Random).) | |
Generate(Int32) |
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |
Generate(Int32, Double) |
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |
Generate(Int32, Random) |
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |
Generate(Int32, Double, Random) |
Generates a random vector of observations from the current distribution.
(Overrides UnivariateContinuousDistributionGenerate(Int32, Double, Random).) | |
GetHashCode | Serves as the default hash function. (Inherited from Object.) | |
GetRange |
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.) | |
GetType | Gets the Type of the current instance. (Inherited from Object.) | |
HazardFunction |
Gets the hazard function, also known as the failure rate or
the conditional failure density function for this distribution
evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |
InnerComplementaryDistributionFunction |
Gets the complementary cumulative distribution
function evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerComplementaryDistributionFunction(Double).) | |
InnerDistributionFunction |
Gets the cumulative distribution function (cdf) for
the F-distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).) | |
InnerInverseDistributionFunction |
Gets the inverse of the cumulative distribution function (icdf) for
this distribution evaluated at probability p. This function
is also known as the Quantile function.
(Overrides UnivariateContinuousDistributionInnerInverseDistributionFunction(Double).) | |
InnerLogProbabilityDensityFunction |
Gets the log-probability density function (pdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).) | |
InnerProbabilityDensityFunction |
Gets the probability density function (pdf) for
the F-distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).) | |
InverseDistributionFunction |
Gets the inverse of the cumulative distribution function (icdf) for
this distribution evaluated at probability p. This function
is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.) | |
LogCumulativeHazardFunction |
Gets the log of the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |
LogProbabilityDensityFunction |
Gets the log-probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ProbabilityDensityFunction |
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |
QuantileDensityFunction |
Gets the first derivative of the
inverse distribution function (icdf) for this distribution evaluated
at probability p.
(Inherited from UnivariateContinuousDistribution.) | |
Random(Int32, Int32) |
Generates a random observation from the
F-distribution with the given parameters.
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Random(Int32, Int32, Int32) |
Generates a random vector of observations from the
F-distribution with the given parameters.
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Random(Int32, Int32, Random) |
Generates a random observation from the
F-distribution with the given parameters.
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Random(Int32, Int32, Int32, Double) |
Generates a random vector of observations from the
F-distribution with the given parameters.
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Random(Int32, Int32, Int32, Random) |
Generates a random vector of observations from the
F-distribution with the given parameters.
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Random(Int32, Int32, Int32, Double, Random) |
Generates a random vector of observations from the
F-distribution with the given parameters.
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ToString |
Returns a String that represents this instance.
(Inherited from DistributionBase.) | |
ToString(IFormatProvider) |
Returns a String that represents this instance.
(Inherited from DistributionBase.) | |
ToString(String) |
Returns a String that represents this instance.
(Inherited from DistributionBase.) | |
ToString(String, IFormatProvider) |
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).) |
Name | Description | |
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HasMethod |
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.) | |
IsEqual |
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.) | |
To(Type) | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) | |
ToT | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) |
In probability theory and statistics, the F-distribution is a continuous probability distribution. It is also known as Snedecor's F distribution or the Fisher-Snedecor distribution (after R.A. Fisher and George W. Snedecor). The F-distribution arises frequently as the null distribution of a test statistic, most notably in the analysis of variance; see FTest.
References:
The following example shows how to construct a Fisher-Snedecor's F-distribution with 8 and 5 degrees of freedom, respectively.
// Create a Fisher-Snedecor's F distribution with 8 and 5 d.f. FDistribution F = new FDistribution(degrees1: 8, degrees2: 5); // Common measures double mean = F.Mean; // 1.6666666666666667 double median = F.Median; // 1.0545096252132447 double var = F.Variance; // 7.6388888888888893 // Cumulative distribution functions double cdf = F.DistributionFunction(x: 0.27); // 0.049463408057268315 double ccdf = F.ComplementaryDistributionFunction(x: 0.27); // 0.95053659194273166 double icdf = F.InverseDistributionFunction(p: cdf); // 0.27 // Probability density functions double pdf = F.ProbabilityDensityFunction(x: 0.27); // 0.45120469723580559 double lpdf = F.LogProbabilityDensityFunction(x: 0.27); // -0.79583416831212883 // Hazard (failure rate) functions double hf = F.HazardFunction(x: 0.27); // 0.47468419528555084 double chf = F.CumulativeHazardFunction(x: 0.27); // 0.050728620222091653 // String representation string str = F.ToString(CultureInfo.InvariantCulture); // F(x; df1 = 8, df2 = 5)