## Gaussian Normal Distribution Function

Continuous chance nodes in a HUGIN network can be specified to have a Gaussian normal distribution function. This text does not cover a mathematically description of the Gaussian normal distribution function but rather a description of how it can be used in HUGIN network nodes.

The Gaussian normal distribution function is defined on the complete real axis. Any Gaussian normal distribution function can be specified by its mean and variance parameter. In HUGIN, a continuous chance node can have a single Gaussian normal distribution function for each configuration of its discrete parents states (both discrete chance nodes and decision nodes). If a continuous chance node has one or more continuous chance node as parent, the mean can be linearly dependent of the state of the continuous chance node parents.

In figure 2 is shown an example of the specification of a Gaussian normal distribution function of a continuous chance node (C3) having one discrete chance node (C1) and one continuous chance node (C2) as parents (see figure 1).

Figure 1: An example of a Bbn where the continuous chance node C3 has one discrete chance node (C1) and one continuous chance node (C2) as parents.

Figure 2: The specification of a Gaussian normal distribution function for C3 having one discrete chance node (C1) and one continuous chance node (C2) as parents.

This specification gives a Gaussian normal distribution function for each of the states of C1 (where N(m,v) is the Gaussian normal distribution function with mean m and variance v):

- C1="State 0": N(1 + (-2.1 * C2), 3).
- C1="State 1": N(2 + (-2.2 * C2), 3.5).

The numeric values in the C2 row of the table in figure 2 are multiplied with C2 in to form C2's contribution to the mean of C3.

Only the mean depends linearly on a continuous parent node. The variance is constant for each configuration of the states of the discrete parents.

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