Date: Thu, 7 Jul 2022 09:59:41 +0200 (CEST) Message-ID: <94021326.905.1657180781883@odysseus.offis.uni-oldenburg.de> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_904_953038238.1657180781883" ------=_Part_904_953038238.1657180781883 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Probabilistic Functions

# Probabilistic Functions

To use these functions, the Probabilistic Feature is required.

The probabilistic feature provides arbitrary functions to work with disc= rete and continuous random variables in a data stream and provides algebrai= c operator (+, *, -, /) to perform probabilistic addition, subtraction, mul= tiplication, division, and exponentiation.

### = |)">Int(<ProbabilisticDouble x, Number a, Num= ber b>|<Vector xyz, Vector a, Vector b>)

Estimates the multivariate normal distribution probability with lower an= d upper integration limit.

### as2DVector(ProbabilisticDouble x, ProbabilisticDouble y)

Converts the two object into a 2D vector.

### as3DVector(ProbabilisticDouble x, Probabi= listicDouble y, ProbabilisticDouble z)

Similar to the as2DVector function, this function creates a 3D vector wi= th the given objects.

### |)">Distance(<ProbabilisticDouble p, Number x>|<Vect= or p, Vector x>)

Calculates the Mahalanobis distance bet= ween the distribution and the value. The value can be a scalar value or a v= ector.

Example
=20
```SELECT =
distance(as3DVector(x, y, z), [1.0;2.0;3.0]) FROM stream```
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### |)">KL(<ProbabilisticDouble p1, ProbabilisticDo= uble p2>|<Vector p1, Vector p2>)

Calculates the Kullback-Leib= ler divergence of the two given probability distributions.

Example
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```SELECT =
kl(as3DVector(x, y, z), as3DVector(a, b, c)) FROM stream```
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### LogLikelihood(Vector points, ProbabilisticDouble p)

Calculates the log Likelihood between the given points and the prob= ability distribution.

Example
=20
```SELECT =
loglikelihood([1.0;2.0;3.0], x) FROM stream```
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