Distribution Functions

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Distribution Functions

Distribution functions are built-in functions which, in conjunction with streams, return random values according to a statistical distribution. The following table is a summary of available distribution functions. They are valid in any numeric expression.

Distribution	Syntax	Individual Components
Beta	B(a,b,c,d{,<s>})	a=shape value 1, b=shape value 2, c=lower boundary, d=upper boundary
Binomial	BI(a,b{,<s>})	a=batch size, b=probability of “success”
Erlang	ER(a,b{,<s>})	a=mean value, b=parameter
Exponential	E(a{,<s>,<ax>})	a=mean
Gamma	G(a,b{,<s>,<ax>})	a=shape value, b=scale value
Geometric	GEO(a{,<s>})	a=probability of “success”
Inverse Gaussian	IG(a,b{,<s>,<ax>})	a=shape value, b=scale value
Lognormal	L(a,b{,<s>,<ax>})	a=mean, b=standard deviation
Normal	N(a,b{,<s>})	a=mean, b=standard deviation
Pearson5	P5(a,b{,<s>,<ax>})	a=shape value, b=scale value
Pearson6	P6(a,b,c{,<s>,<ax>})	a=shape value 1, b=shape value 2, c=scale value
Poisson	P(a{,<s>})	a=quantity
Triangular	T(a,b,c{,<s>})	a=minimum, b=mode, c=maximum
Uniform	U(a,b{,<s>})	a=mean, b=half range,
User-defined	<name>({<s>})	Name of a user-defined distribution as defined in the User Distribution section
Weibull	W(a,b{,<s>,<ax>})	a=shape value, b=scale value

General Components

<s> The optional stream to use in conjunction with the distribution’s probabilities. If this option is omitted, ProModel will use stream one. For more information on streams, see Streams.

<ax> An optional axis shift. The distributions, E, G, W, L, IG, P5, and P6 all normally have a minimum value of zero. Use an axis shift to alter the distribution’s minimum value and at the same time shift the entire distribution. Any time an axis shift is specified, a stream must be specified also.

Any negative value returned by a distribution that is used for a time expression will be automatically converted to zero.