Probability Distributions

The Probability Distributions palette provides a selection of standard theoretical probability distributions as well as user-defined probability distributions.

Probability Distributions

Distribution Name

Description

UniformDistribution

Generates samples with a constant probability between minimum and maximum values.

TriangularDistribution

Generates samples from a triangular probability distribution between minimum and maximum values.  The distribution peaks at its mode.

NormalDistribution

Generates samples from a normal probability distribution.

ExponentialDistribution

Generates samples from a negative exponential probability distribution.

NonStatExponentialDist

Generates samples from a time-varying negative exponential probability distribution.  The correct ‘non-stationary Poisson process’ algorithm is used.

ErlangDistribution

Generates samples from an Erlang probability distribution.

GammaDistribution

Generates samples from a Gamma probability distribution.

BetaDistribution

Generates samples from a Beta probability distribution.

WeibullDistribution

Generates samples from a Weibull probability distribution.

LogNormalDistribution

Generates samples from a Log-Normal probability distribution.

LogLogisticDistribution

Generates samples from a Log-Logistic probability distribution.

DiscreteDistribution

Generates samples from a discrete set of values.

ContinuousDistribution

Generates samples over a continuous range of values.

BooleanSelector

Randomly selects true/false with a user-selectable probability of true.

Most probability distributions use the following inputs and outputs.

Distribution Inputs

Keyword

Description

UnitType

The unit type for the value returned by the distribution, e.g.  TimeUnit.  To keep the units consistent for other inputs, this input must be set first.

RandomSeed

Seed for the random number generator.  Must be an integer greater than or equal to zero.  The RandomSeed keyword works together with the GlobalSubstreamSeed under the Simulation object to determine the random sequence.  The GlobalSubstreamSeed keyword allows the user to change all the random sequences in a model with a single input.

MinValue

The minimum value that can be returned by the distribution.  A value less than the minimum is rejected and the distribution is re-sampled.

MaxValue

The maximum value that can be returned by the distribution.  A value greater than the maximum is rejected and the distribution is re-sampled.

Distribution Outputs

Output Name

Description

Value

The last value sampled from the distribution.  When used in an expression, this output returns a new sample every time the expression is evaluated.

CalculatedMean

The mean value for the distribution calculated directly from the inputs.  Ignores the values entered for the MinValue and MaxValue keywords.

CalculatedStandardDeviation

The standard deviation for the distribution calculated directly from the inputs.  Ignores the values entered for the MinValue and MaxValue keywords.

NumberOfSamples

The total number of samples returned by the Probability Distribution.

SampleMean

The average of the samples returned by the Probability Distribution.

SampleStandardDeviation

The standard deviation of the samples returned by the Probability Distribution.

SampleMin

The minimum of the samples returned by the Probability Distribution.

SampleMax

The maximum of the samples returned by the Probability Distribution.

The Probability Distributions were coded using algorithms adapted from "Simulation Modeling & Analysis", 4th Edition, by Averill M. Law.  Random numbers for these distributions are generated by the Multiple Recursive Generator developed by L'Ecuyer ("Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators", Operations Res., 47: 159-164 (1999a)).