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VonMisesDistribution Class

von-Mises (Circular Normal) distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateVonMisesDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0
Syntax
[SerializableAttribute]
public class VonMisesDistribution : UnivariateContinuousDistribution, 
	IFittableDistribution<double, VonMisesOptions>, IFittable<double, VonMisesOptions>, 
	IFittable<double>, IFittableDistribution<double>, IDistribution<double>, 
	IDistribution, ICloneable
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The VonMisesDistribution type exposes the following members.

Constructors
  NameDescription
Public methodVonMisesDistribution
Constructs a von-Mises distribution with zero mean and unit concentration.
Public methodVonMisesDistribution(Double)
Constructs a von-Mises distribution with zero mean.
Public methodVonMisesDistribution(Double, Double)
Constructs a von-Mises distribution.
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Properties
  NameDescription
Public propertyConcentration
Gets the concentration κ (kappa) for this distribution.
Public propertyEntropy
Gets the entropy for this distribution.
(Overrides UnivariateContinuousDistributionEntropy.)
Public propertyMean
Gets the mean value μ (mu) for this distribution.
(Overrides UnivariateContinuousDistributionMean.)
Public propertyMedian
Gets the median value μ (mu) for this distribution.
(Overrides UnivariateContinuousDistributionMedian.)
Public propertyMode
Gets the mode value μ (mu) for this distribution.
(Overrides UnivariateContinuousDistributionMode.)
Public propertyQuartiles
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyStandardDeviation
Gets the Standard Deviation (the square root of the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertySupport
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.)
Public propertyVariance
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.)
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Methods
  NameDescription
Public methodStatic memberCircularUniform
Creates a new circular uniform distribution by creating a new VonMisesDistribution with zero kappa.
Public methodClone
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)
Public methodComplementaryDistributionFunction
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.)
Public methodCumulativeHazardFunction
Gets the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(Double)
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(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.)
Public methodStatic memberDistributionFunction(Double, Double, Double)
von-Mises cumulative distribution function.
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodStatic memberEstimate(Double)
Estimates a new von-Mises distribution from a given set of angles.
Public methodStatic memberEstimate(Double, VonMisesOptions)
Estimates a new von-Mises distribution from a given set of angles.
Public methodStatic memberEstimate(Double, Double, VonMisesOptions)
Estimates a new von-Mises distribution from a given set of angles.
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodCode exampleFit(Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, Int32)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, Int32, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)
Public methodFit(Double, Double, VonMisesOptions)
Fits the underlying distribution to a given set of observations.
Public methodGenerate
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Random)
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Random)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double, Random)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRange
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazardFunction
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.)
Protected methodInnerComplementaryDistributionFunction
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.)
Protected methodInnerDistributionFunction
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
Protected methodInnerInverseDistributionFunction
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.)
Protected methodInnerLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)
Protected methodInnerProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
Public methodInverseDistributionFunction
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.)
Public methodLogCumulativeHazardFunction
Gets the log of the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodQuantileDensityFunction
Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p.
(Inherited from UnivariateContinuousDistribution.)
Public methodToString
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(IFormatProvider)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String, IFormatProvider)
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodTo(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.)
Public Extension MethodToTOverloaded.
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.)
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Remarks

The von Mises distribution (also known as the circular normal distribution or Tikhonov distribution) is a continuous probability distribution on the circle. It may be thought of as a close approximation to the wrapped normal distribution, which is the circular analogue of the normal distribution.

The wrapped normal distribution describes the distribution of an angle that is the result of the addition of many small independent angular deviations, such as target sensing, or grain orientation in a granular material. The von Mises distribution is more mathematically tractable than the wrapped normal distribution and is the preferred distribution for many applications.

References:

Examples
// Create a new von-Mises distribution with μ = 0.42 and κ = 1.2
var vonMises = new VonMisesDistribution(mean: 0.42, concentration: 1.2);

// Common measures
double mean = vonMises.Mean;     // 0.42
double median = vonMises.Median; // 0.42
double var = vonMises.Variance;  // 0.48721760532782921

// Cumulative distribution functions
double cdf = vonMises.DistributionFunction(x: 1.4); // 0.81326928491589345
double ccdf = vonMises.ComplementaryDistributionFunction(x: 1.4); // 0.18673071508410655
double icdf = vonMises.InverseDistributionFunction(p: cdf); // 1.3999999637927665

// Probability density functions
double pdf = vonMises.ProbabilityDensityFunction(x: 1.4); // 0.2228112141141676
double lpdf = vonMises.LogProbabilityDensityFunction(x: 1.4); // -1.5014304395467863

// Hazard (failure rate) functions
double hf = vonMises.HazardFunction(x: 1.4); // 1.1932220899695576
double chf = vonMises.CumulativeHazardFunction(x: 1.4); // 1.6780877262500649

// String representation
string str = vonMises.ToString(CultureInfo.InvariantCulture); // VonMises(x; μ = 0.42, κ = 1.2)
See Also