WaldDistribution Class 
Namespace: Meta.Numerics.Statistics.Distributions
The WaldDistribution type exposes the following members.
Name  Description  

WaldDistribution 
Initializes a new Wald distribution.

Name  Description  

ExcessKurtosis 
Gets the excess kurtosis of the distribution.
(Overrides UnivariateDistributionExcessKurtosis.)  
Mean 
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)  
Median 
Gets the median of the distribution.
(Inherited from ContinuousDistribution.)  
Shape 
Gets the shape parameter of the distribution.
 
Skewness 
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)  
StandardDeviation 
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.)  
Support 
Gets the interval over which the distribution is nonvanishing.
(Overrides ContinuousDistributionSupport.)  
Variance 
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.) 
Name  Description  

CentralMoment 
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)  
Cumulant 
Computes a cumulant of the distribution.
(Overrides UnivariateDistributionCumulant(Int32).)  
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
ExpectationValue 
Computes the expectation value of the given function.
(Inherited from ContinuousDistribution.)  
FitToSample 
Determines the parameters of the Wald distribution that best fits a sample.
 
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetRandomValue 
Generates a random variate.
(Overrides ContinuousDistributionGetRandomValue(Random).)  
GetRandomValues 
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
Hazard 
Computes the hazard function.
(Inherited from ContinuousDistribution.)  
InverseLeftProbability 
Returns the point at which the cumulative distribution function attains a given value.
(Inherited from ContinuousDistribution.)  
InverseRightProbability 
Returns the point at which the right probability function attains the given value.
(Inherited from ContinuousDistribution.)  
LeftProbability 
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)  
ProbabilityDensity 
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)  
RawMoment 
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)  
RightProbability 
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)  
ToString  Returns a string that represents the current object. (Inherited from Object.) 
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.