Special Functions

GoldSim provides the following specialized mathematical functions:

Function	Description
erf(U1)	Gauss error function of U1
erfc(U1)	Complementary Gauss error function of U1
if(C,E,F) or if(C then E else F)	If C is true then E else F
bess(U1,U2)	Bessel function of U1 of order U2
beta(U1,U2)	Beta function of U1 and U2
gamma(U1)	Gamma function of U1
normprob(U1)	Returns a value representing the cumulative probability level for the specified number of standard deviations (U1) away from the mean for a standard normal distribution. A negative argument represents values to the left of (less than) the mean.
normsds(P)	Returns a value representing the number of standard deviations away from the mean for the specified cumulative probability level (P) for a standard normal distribution. A negative output represents a value to the left of (less than) the mean .
tdist(P,nu)	Student’s t distribution for the specified cumulative probability level (P), with nu degrees of freedom.
tprob(X,nu)	Student’s t distribution, returns the cumulative probabilityforvalue X , with nu degrees of freedom .
ImpProb(Old,Target,Width)	Used for customized importance sampling for a given target probability and probability width. Takes a probability (Old) and returns a biased probability.
ImpWeight(Prob,Target,Width)	Used for customized importance sampling for a given target probability and probability width. Takes a biased probability (produced by ImpProb) and returns a weight.
ImpOld(Prob,Target,Width)	Used for customized importance sampling for a given target probability and probability width. Takes a biased probability (produced by ImpProb) and returns the unbiased probability. This is the inverse of ImpProb.
PDF_Value(D, P1)	Returns the value of the distribution at the specified cumulative probability level P1. The output has the same dimensions as the distribution being referenced.
PDF_CumProb(D, V)	Returns the cumulative probability of the distribution at the specified value V. The output is dimensionless.
PDF_Mean(D)	Returns the mean of the distribution. The output has the same dimensions as the distribution being referenced.
PDF_SD(D)	Returns the standard deviation of the distribution. The output has the same dimensions as the distribution being referenced.
PDF_CTE(D, P1)	Returns the conditional tail expectation of cumulative probability P1 (i.e., the expected value of the output given that it lies above a specified cumulative probability P1). This result represents the mean of the worst 100(1-P1)% of outcome. The output has the same dimensions as the distribution being referenced.
PDF_DiscreteProb(D, V)	Returns the discrete probability of the distribution at the specified value V. The output is dimensionless. This function returns 0 for continuous distributions (i.e., it should only be applied to discrete distributions).
changed(Z)	Returns a condition. True if the argument has changed since the last update (e.g., timestep). False if the argument has not changed. See Note below.
occurs(T)	Returns a condition. True if the argument has occurred this update (e.g., timestep). False if the argument has not occurred.

U1,U2: Must be a unitless value. Can be a scalar or an array.
D: A distribution output.
V: A scalar value.
X, Y: A value. Can be a scalar or an array.
E, F: A value or a condition. Can be a scalar or an array.
C: Must be a condition. C can be an array or scalar; if it is an array, then the “if” test is done on a term-by-term basis and either E or F (or both) must be an array with the same set of array labels as C. If C is scalar, E and F can be either scalar, arrays of the same order (entire array is then selected), or one can be an array and one can be a scalar (in which case the scalar is treated as an array of identical values).
P: A value between 0 and 1, inclusive. Can be a scalar or an array.
P1, Old, Target: A scalar value between 0 and 1, inclusive.
Width: A scalar value between 10-6 and 0.5, inclusive.
nu: A positive integer. Can be a scalar or an array.
Z: A value or a condition. Must be a scalar.
T: Must be a discrete event signal.

Note: If the argument to the changed() function is a Run Property that conceptually cycles (e.g., Hour), and your timestep is such that the actual value remains unchanged (e.g., Changed(Hour), with a 1 day timestep), GoldSim will still consider that the argument has changed (since the fact that it remains unchanged is simply an artifact of timestepping).

Note: The three importance sampling functions (ImpProb, ImpWeight and ImpOld) are used to carry out customized importance sampling of Stochastic elements.

Special Functions

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