MultivariateNormalDistribution.DistributionFunction Method

public double DistributionFunction(
	Vector<double> x
)

Public Function DistributionFunction ( 
	x As Vector(Of Double)
) As Double

public:
double DistributionFunction(
	Vector<double>^ x
)

member DistributionFunction : 
        x : Vector<float> -> float 

Parameters

x  Vector<Double>

A number within the domain of the distribution

Return Value

The cumulative distribution function of a statistical distribution gives the probability that the components of a sample taken from the distribution are all less than the corresponding component of the specified vector.

For diagonal matrices, a product of 1D normal distribution functions is returned. For a bivariate distribution, an algorithm by Alan Genz is used. For three and four dimensions, numerical integration is used. Higher orders use randomized quasi-Monte Carlo integration, with a target absolute error estimate of 1e-6 and a nominal one-million-point work limit. Completing full batches can exceed that nominal count. The estimate is not a guaranteed error bound.

Independent covariance blocks of at most four coordinates each are evaluated separately and their probabilities multiplied. This deterministic path does not consume random values. Independence is recognized only when the covariances between blocks are exactly zero.

A NaN coordinate returns NaN. Any negative-infinite coordinate returns zero when all coordinates are non-NaN. If all coordinates are positive infinity, the result is one. Other positive-infinite coordinates are removed by evaluating the corresponding marginal.

Reference