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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 probabilistic values random variables in a data stream and provides algebraic operator (+, *, -, /) to perform probabilistic addition, subtraction, multiplication, division, and exponentiation.

SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) + ToProbabilisticDouble([4.0,0.25;5.0,0.75]) FROM Stream
=> (6.0:0.0625;7.0:0.375;8.0:0.5625)
SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) - ToProbabilisticDouble([4.0,0.25;5.0,0.75]) FROM Stream
=> (-3.0:0.1875;-2.0:0.625;-1.0:0.1875)
SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) * ToProbabilisticDouble([4.0,0.25;5.0,0.75]) FROM Stream
=> (15.0:0.5625;12.0:0.1875;10.0:0.1875;8.0:0.0625)
SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) / ToProbabilisticDouble([4.0,0.25;5.0,0.75]) FROM Stream
=> (0.75:0.1875;0.6:0.5625;0.5:0.0625;0.4:0.1875)
SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75])^2 FROM Stream
=> (4.0:0.25;9.0:0.75)
SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) + 2 FROM Stream
=> (4.0:0.25;5.0:0.75)
SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) - 2 FROM Stream
=> (0.0:0.25;1.0:0.75)
SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) * 2 FROM Stream
=> (6.0:0.75;4.0:0.25)
SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) / 2 FROM Stream
=> (1.5:0.75;1.0:0.25)

SQRT(Probabilistic Number)

Computes the probabilistic square root of the given probabilistic value.

sMIn(Probabilistic Number, Probabilistic Number)

Computes the minimum of two probabilistic values.

sMax(Probabilistic Number, Probabilistic Number)

Computes the maximum of two probabilistic values.

ToProbabilisticDouble(Matrix)

Constructs a discrete probabilistic value using the first column of the given matrix for the values and the second column of the matrix for the probabilities for each value.

SELECT ToProbabilisticDouble([2.0,0.25;3.0,0.75]) FROM Stream
=> (3.0:0.75;2.0:0.25)

DoubleToByte(Probabilistic Number)

Converts the given probabilistic double value to a probabilistic byte value

DoubleToShort(Probabilistic Number)

Converts the given probabilistic double value to a probabilistic short value

DoubleToInteger(Probabilistic Number)

Converts the given probabilistic double value to a probabilistic integer value

DoubleToLong(Probabilistic Value)

Converts the given probabilistic double value to a probabilistic long value

DoubleToFloat(Probabilistic Number)

Converts the given probabilistic double value to a probabilistic float value

...

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.

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.

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.

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.

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