|
VonMisesDistribution Class |
von-Mises (Circular Normal) distribution.
Inheritance HierarchySystemObject
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
Accord.Statistics.Distributions.UnivariateVonMisesDistribution
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
The VonMisesDistribution type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | VonMisesDistribution |
Constructs a von-Mises distribution with zero mean and unit concentration.
|
| VonMisesDistribution(Double) |
Constructs a von-Mises distribution with zero mean.
|
| VonMisesDistribution(Double, Double) |
Constructs a von-Mises distribution.
|
Properties| 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.) |
Methods| 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.
(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.) |
| DistributionFunction(Double, Double, Double) |
von-Mises cumulative distribution function.
|
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
| Estimate(Double) |
Estimates a new von-Mises distribution from a given set of angles.
|
| Estimate(Double, VonMisesOptions) |
Estimates a new von-Mises distribution from a given set of angles.
|
| Estimate(Double, Double, VonMisesOptions) |
Estimates a new von-Mises 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(Random) |
Generates a random observation 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.
(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.) |
| InnerComplementaryDistributionFunction |
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.) |
| InnerDistributionFunction |
Gets the cumulative distribution function (cdf) for
this 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.
(Inherited from UnivariateContinuousDistribution.) |
| 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
this 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.) |
| 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).) |
Extension Methods| Name | Description | |
|---|---|---|
 | 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.) |
RemarksThe 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:
- Wikipedia, The Free Encyclopedia. Von-Mises distribution. Available on: http://en.wikipedia.org/wiki/Von_Mises_distribution
- Suvrit Sra, "A short note on parameter approximation for von Mises-Fisher distributions: and a fast implementation of $I_s(x)$". (revision of Apr. 2009). Computational Statistics (2011). Available on: http://www.kyb.mpg.de/publications/attachments/vmfnote_7045%5B0%5D.pdf
- Zheng Sun. M.Sc. Comparing measures of fit for circular distributions. Master thesis, 2006. Available on: https://dspace.library.uvic.ca:8443/bitstream/handle/1828/2698/zhengsun_master_thesis.pdf
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