Specialized Functions That Operate on Distributions

GoldSim provides several specialized functions that can be used to reference the Distribution output type and return properties of the distribution. The Distribution output is a complex output representing all the distribution information. It can be produced by a Stochastic element An element that can be used to quantitatively represent the uncertainty in a model input., a Spreadsheet element, or a SubModel A specialized element that allows you embed one complete GoldSim model within another GoldSim model. This facilitates, among other things, probabilistic optimization, explicit separation of uncertainty from variability, and manipulation of Monte Carlo statistics..

These functions all require as the first argument a Distribution output. Some require an additional output:

PDF_Value(Distribution, P): The value of the distribution at the specified cumulative probability level P. The output has the same dimensions as the distribution being referenced.

PDF_CumProb(Distribution, V): The cumulative probability of the distribution at the specified value V. The output is dimensionless.

PDF_Mean(Distribution): The mean of the distribution. The output has the same dimensions An output attribute for an element that defines the dimensionality (in terms of Length, Time and other fundamental dimensions) of the output. as the distribution being referenced.

PDF_SD(Distribution): The standard deviation The square root of the variance of a distribution. The variance is the second moment of the distribution and reflects the amount of spread or dispersion in the distribution. of the distribution. The output has the same dimensions as the distribution being referenced.

PDF_CTE(Distribution, P): The conditional tail expectation of cumulative probability P (i.e., the expected value of the output given that it lies above a specified cumulative probability P). This result represents the mean of the greatest 100(1 - P)% of outcomes. The output has the same dimensions as the distribution being referenced.

Note: Calculation of the Conditional Tail Expectation is discussed in detail in Appendix B of the GoldSim User’s Guide.

PDF_Density(Distribution, V): The probability density or discrete probability of the distribution at the specified value V. If the distribution is continuous, the result is the probability density of the specified value. The dimensions are the inverse of the distribution itself. If the distribution is discrete, the result is the discrete probability of the specified value, in which case it is dimensionless.

Note: For Boolean distributions, the value argument V must be a condition. Note, however, that if a condition-type result is passed out through a SubModel interface, it must be either 1 or 0.

Note: In some cases, GoldSim cannot compute a direct solution for a statistic (e.g., computing the standard deviation for a truncated Weibull). In this case, the function returns an error.

Since these functions simply return the key properties of a probability distribution, in most cases, there would be no value in using these functions directly on Stochastic elements. However, there are two primary applications for these functions:

• When the definition of a Stochastic distribution is changing dynamically during a simulation (either by making the defining parameters functions of time, or via simulated Bayesian updating), these functions can be used to query the current shape and characteristics of the distribution.

• When exporting a distribution result from a Monte Carlo SubModel, these functions can be used to query the current shape and characteristics of the distribution in the parent model.