Probabilistic calculation

Analytica performs probabilistic evaluation of probability distributions through simulation — by computing a random sample of values from the actual probability distribution for each uncertain quantity. The result of evaluating a distribution is represented internally as an array of the sample values, indexed by Run. Run is an 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 view options (page 29) — the mean, statistics, probability bands, probability density (or mass function), and cumulative distribution function. All these views are derived or estimated from the underlying sample array, which you can inspect using the last uncertainty view, Sample.

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” on page 257).

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)

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 (page 257).

Tip: If you try to apply an array-reducing function (page 194) to a probability distribution across Run, Analytica returns the distribution’s mid value.

Example:

X:= Beta(2, 3)

Mid(X) → 0.3857 and Max(X, Run) → 0.3857

To evaluate the input parameters probabilistically and reduce across Run, use Sample() (page 301).

Example:

Max(Sample(X), Run) → 0.8892