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To use these functions, the Probabilistic Feature is required.

The probabilistic feature provides arbitrary functions to work with discrete and continuous random variables in a data stream and provides algebraic operator (+, *, -, /) to perform probabilistic addition, subtraction, multiplication, division, and exponentiation.

Int(<ProbabilisticDouble x, Number a, Number b>|<Vector xyz, Vector a, Vector b>)

Estimates the multivariate normal distribution probability with lower and upper integration limit.

as2DVector(ProbabilisticDouble x, ProbabilisticDouble y)

Converts the two object into a 2D vector.

as3DVector(ProbabilisticDouble x, ProbabilisticDouble y, ProbabilisticDouble z)

Similar to the as2DVector function, this function creates a 3D vector with the given objects.

Similarity(ProbabilisticDouble p1, ProbabilisticDouble p2)

Calculates the Bhattacharyya distance between two distributions.

Example
SELECT similarity(as2DVector(x1,y1), as2DVector(x2,y2)) FROM stream

Distance(<ProbabilisticDouble p, Number x>|<Vector p, Vector x>)

Calculates the Mahalanobis distance between the distribution and the value. The value can be a scalar value or a vector.

Example
SELECT distance(as3DVector(x, y, z), [1.0;2.0;3.0]) FROM stream

KL(<ProbabilisticDouble p1, ProbabilisticDouble p2>|<Vector p1, Vector p2>)

Calculates the Kullback-Leibler divergence of the two given probability distributions.

Example
SELECT kl(as3DVector(x, y, z), as3DVector(a, b, c)) FROM stream

LogLikelihood(Vector points, ProbabilisticDouble p)

Calculates the log Likelihood between the given points and the probability distribution.

Example
SELECT loglikelihood([1.0;2.0;3.0], x) FROM stream
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