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)).