# Probabilistic calculation

Analytica can calculate the value of each variable deterministically -- generating its Mid value -- or probabilistically, generating a probability distribution -- its Prob value -- if the definition of the variable or any of its predecessors contains a probability distribution. It does probabilistic calculation as a random sample of values from the actual probability distribution for each uncertain quantity. Each probabilistic value is represented internally as a sample, an array of the sample values indexed by Run. Run is a system index variable that identifies each sample iteration by an integer from 1 to Samplesize.

You can display a probabilistic value using a variety of uncertainty views — including mean, statistics, probability bands, probability density (or mass function), cumulative distribution function, and Sample view. All these views are derived or estimated from the underlying sample array, which you can see directly in the Sample view. For example, with a Samplesize = 6, here is the probabilistic value of A:

Example

A := Normal(10, 2) →
Iteration (Run) ▶
1 2 3 4 5 6
10.74 13.2 9.092 11.44 9.519 13.03
Tip
The values in a sample are generated at random from the distribution; if you try this example and display the result as a table, you might see values different from those shown here. To reproduce this example, reset the random number seed to 99 and use the default sampling method and random number method (see Uncertainty Setup dialog.

For each sample run, a random value is generated from each probability distribution in the model. Output variables of uncertain variables are calculated by calculating a value for each value of Run.

Example

B := Normal(5, 1) →
Iteration (Run) ▶
1 2 3 4 5 6
5.09 4.94 4.65 6.60 5.24 6.96
C := A + B →
Iteration (Run) ▶
1 2 3 4 5 6
15.83 18.13 13.75 18.04 14.76 19.99

Notice that each sample value of C is equal to the sum of the corresponding values of A and B. To control the probabilistic simulation, as well as views of probabilistic results, use the Uncertainty Setup dialog.

Tip
If you try to apply an array-reducing function to a probability distribution across Run, Analytica returns the distribution’s mid value.

Example:

X := Beta(2, 3)
Mid(X) &arr; 0.3857
Max(X, Run) → 0.3857

To evaluate the input parameters probabilistically and reduce across Run, use Sample().

Example:

Max(Sample(X), Run) &arr; 0.8892