VonMisesDistribution Class 
Namespace: Accord.Statistics.Distributions.Univariate
[SerializableAttribute] public class VonMisesDistribution : UnivariateContinuousDistribution, IFittableDistribution<double, VonMisesOptions>, IFittable<double, VonMisesOptions>, IFittable<double>, IFittableDistribution<double>, IDistribution<double>, IDistribution, ICloneable
The VonMisesDistribution type exposes the following members.
Name  Description  

VonMisesDistribution(Double) 
Constructs a vonMises distribution with zero mean.
 
VonMisesDistribution(Double, Double) 
Constructs a vonMises distribution.

Name  Description  

Concentration 
Gets the concentration κ (kappa) for this distribution.
 
Entropy 
Gets the entropy for this distribution.
(Overrides UnivariateContinuousDistributionEntropy.)  
Mean 
Gets the mean value μ (mu) for this distribution.
(Overrides UnivariateContinuousDistributionMean.)  
Median 
Gets the median value μ (mu) for this distribution.
(Overrides UnivariateContinuousDistributionMedian.)  
Mode 
Gets the mode value μ (mu) 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  

CircularUniform 
Creates a new circular uniform distribution by creating a
new VonMisesDistribution with zero kappa.
 
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.
(Overrides UnivariateContinuousDistributionDistributionFunction(Double).)  
DistributionFunction(Double, Double) 
Gets the cumulative distribution function (cdf) for this
distribution in the semiclosed interval (a; b] given as
P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.)  
DistributionFunction(Double, Double, Double) 
vonMises cumulative distribution function.
 
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Estimate(Double) 
Estimates a new vonMises distribution from a given set of angles.
 
Estimate(Double, VonMisesOptions) 
Estimates a new vonMises distribution from a given set of angles.
 
Estimate(Double, Double, VonMisesOptions) 
Estimates a new vonMises distribution from a given set of angles.
 
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, Int32, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)  
Fit(Double, Double, VonMisesOptions) 
Fits the underlying distribution to a given set of observations.
 
Generate 
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
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.)  
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.)  
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 logprobability density function (pdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionLogProbabilityDensityFunction(Double).)  
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.
(Overrides UnivariateContinuousDistributionProbabilityDensityFunction(Double).)  
QuantileDensityFunction 
Gets the first derivative of the
inverse distribution function (icdf) for this distribution evaluated
at probability p.
(Inherited from UnivariateContinuousDistribution.)  
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  

HasMethod 
Checks whether an object implements a method with the given name.
(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.)  
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 Matrix.) 
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:
// Create a new vonMises 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)