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WaldDistribution Class

Represents a Wald (Inverse Gaussian) distribution.
Inheritance Hierarchy

Namespace:  Meta.Numerics.Statistics.Distributions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.1.4
Syntax
public sealed class WaldDistribution : ContinuousDistribution

The WaldDistribution type exposes the following members.

Constructors
  NameDescription
Public methodWaldDistribution
Initializes a new Wald distribution.
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Properties
  NameDescription
Public propertyExcessKurtosis
Gets the excess kurtosis of the distribution.
(Overrides UnivariateDistributionExcessKurtosis.)
Public propertyMean
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)
Public propertyMedian
Gets the median of the distribution.
(Inherited from ContinuousDistribution.)
Public propertyShape
Gets the shape parameter of the distribution.
Public propertySkewness
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)
Public propertyStandardDeviation
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.)
Public propertySupport
Gets the interval over which the distribution is non-vanishing.
(Overrides ContinuousDistributionSupport.)
Public propertyVariance
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.)
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Methods
  NameDescription
Public methodCentralMoment
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)
Public methodCumulant
Computes a cumulant of the distribution.
(Overrides UnivariateDistributionCumulant(Int32).)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodExpectationValue
Computes the expectation value of the given function.
(Inherited from ContinuousDistribution.)
Public methodStatic memberFitToSample
Determines the parameters of the Wald distribution that best fits a sample.
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRandomValue
Generates a random variate.
(Overrides ContinuousDistributionGetRandomValue(Random).)
Public methodGetRandomValues
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazard
Computes the hazard function.
(Inherited from ContinuousDistribution.)
Public methodInverseLeftProbability
Returns the point at which the cumulative distribution function attains a given value.
(Inherited from ContinuousDistribution.)
Public methodInverseRightProbability
Returns the point at which the right probability function attains the given value.
(Inherited from ContinuousDistribution.)
Public methodLeftProbability
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)
Public methodProbabilityDensity
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)
Public methodRawMoment
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)
Public methodRightProbability
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

The Wald distribution, also called the inverse Gaussian distribution, is the distribution of first passage times for Brownian motion.

In Brownian motion, a particle moves randomly so that its position at any given time is distributed normally with a mean that increases linearly and a standard deviation that increases with the square root of time. The first passage time is the earliest time that its position reaches a given level. This first passage time is Wald distributed with mean and shape parameters related to the drift, noise, and threshold.

This may appear a very obscure an technical relationship, but it turns out to have myriad applications: to stock prices, ballot counting, neurological response times, and earthquake prediction.

See Also