Special 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 probability for value 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.

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 probability for value 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.