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6. Extreme Value B
Syntax
Real = EXTVALB( Stream, Locate,
Scale )
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
Probability Density Function
Figure 8—6. The Extreme Value B Distribution
7. Gamma
Syntax
Real = GAMMA( Stream, Locate,
Scale, Shape )
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.
Shape - The selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
Probability Density Function
Figure 8—7. The Gamma Distribution
Notes
The Gamma Distribution degenerates to the Exponential when the shape argument is 1. That is, Gamma( Stream, Locate, Scale, 1 ) is distributed as Exponential( Stream, Locate, Shape ).
For positive integer m, Gamma( Stream, 0, Scale, m ) is distributed as the m-Erlang(Scale) distribution.
8. Geometric
Syntax
Integer = GEOMETRIC(Stream,
Probability)
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Probability - The probability of success in each Bernoulli trial. Must be between 0 and 1. Required. Coerced to real. The argument must be Expression.
Return Value
Integer - The integer value generated as a single instance of the probability distribution.
Probability Mass Function
Figure 8—8. The Geometric Distribution
9. Inverse Gaussian
Syntax
Real = INVGAUSS(Stream,Locate,Scale,Shape
)
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.
Shape - The selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
Probability Density Function
Figure 8—9. The Inverse Gaussian Distribution
10. Inverse Weibull
Syntax
Real = INVWEIBULL( Stream, Locate, Scale, Shape )
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.
Shape - The selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
Probability Density Function
Figure 8—10. The Inverse Weibull Distribution
11. Laplace
Syntax
Real = LAPLACE( Stream, Locate,
Scale )
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
Probability Density Function
Figure 8—11. The Laplace Distribution
12. Logistic
Syntax
Real = LOGISTIC( Stream, Locate,
Scale )
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
Probability Density Function
Figure 8—12. The Logistic Distribution
13. LogLaplace
Syntax
Real = LOGLAPLACE( Stream, Locate, Scale, Shape )
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.
Shape - The selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
14. LogLogistic
Syntax
Real = LOGLOGIS( Stream, Locate, Scale, Shape )
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.
Shape - The selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
15. LogNormal
Syntax
Real = LOGNORMAL( Stream, Locate, Scale, Shape )
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.
Scale - The compression value used to expand or contract the distribution. Required. Coerced to real. The argument must be Expression.
Shape - The selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.
Return Value
Real - The real value generated as a single instance of the probability distribution.
Probability Density Function
Figure 8—15. The Lognormal Distribution
16. Negative Binomial
Syntax
Integer = NEGBINOM( Stream,SuccessCount,Probability)
Arguments
Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.
SuccessCount - The number of successful Bernoulli trials required before returning the failure count. Required. Coerced to integer. Must be strictly positive. The argument must be Expression.
Probability - The success probability of a Bernoulli trial. Must be between 0 and 1. Required. Coerced to real. The argument must be Expression.
Return Value
Integer - The integer value generated as a single instance of the probability distribution.
Probability Mass Function