Distributions

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Distributions

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Vensim lets you choose from between a number of distributions in performing sensitivity analysis.  The VECTOR distribution simply runs through a series of increasing values.  The others all involve drawings from random distributions.  The distributions you choose should be based on the nature of the models you are working with and the parameters you are changing.

All of the random distributions are truncated by the minimum and maximum values you specify.  You can make these numbers as broad as you want, but for most models there are limits on Constant values beyond which model results begin to become less meaningful.  

NOTE The sensitivity RANDOM… distributions are identical to the random functions except that they do not take the final seed argument.  The RANDOM LOOKUP distribution also has a different argument order. The VECTOR distribution can only be used in sensitivity simulations – it is not part of the modeling language.

NOTE If min >= max then the function is ignored. Also, unlike in simulation, if no valid draw is made between min and max a uniform deviate is selected on the range specified by min and max.

RANDOM BETA(min,max,A,B,shift,stretch)

Draws a number from a beta distribution where the value for alpha is A and the value for beta is B.  The resulting number is multiplied by stretch and then shift is added.

RANDOM BINOMIAL(min,max,P,N,shift,stretch)

Draws a number from a binomial distribution where the underlying probability is P and there are N draws.  The RANDOM BINOMIAL distribution will always draw an integer value.  The resulting number is multiplied by stretch and then shift is added.

RANDOM EXPONENTIAL(min,max,shift,stretch)

Draws a number from an exponential distribution that starts at 0 and has mean 1.  Before the value is returned it is multiplied by stretch, and then shift is added to it.  Note that if min is bigger than shift only the middle of the distribution will be used.

RANDOM GAMMA(min,max,order,shift,stretch)

Draws a number from a Gamma distribution (where the underlying Poisson distribution has mean 1) of the specified order.  The value for order does not need to be an integer.  The draw from the distribution is multiplied by stretch, and then shift is added.

RANDOM LOOKUP(min,max,lookup,shift,stretch)

Draws a number from the arbitrary distribution defined by the Lookup function lookup. lookup  does not need to have an area of one as it will be normalized.  The output range for the random numbers being generated is defined by the input range of the Lookup.  

NOTE The name of the Lookup to be used is the third argument to this function while it is the first argument to the simulation function RANDOM LOOKUP.

RANDOM NEGATIVE BINOMIAL(min,max,draw prob,number success,shift,stretch)

Draws a number from a negative binomial distribution.  This is the number of tries required to achieve number success successful outcomes where each outcome has probability prob.  This is an integer before it is shifted and stretched.  The resulting number is multiplied by stretch and then shift is added.

RANDOM NORMAL(min,max,mean,standard dev)

Draws a number from a normal distribution with the specified mean and standard deviation.  In this case the shift and stretch parameters have a simple interpretation and so have been renamed.

RANDOM POISSON(min,max,mean,shift,stretch)

Draws a number from a Poisson distribution with the specified mean.  The resulting number is multiplied by stretch and then shift is added.

RANDOM TRIANGULAR(min,max,start,peak,stop)

Draws from a triangular distribution starting at start with the specified peak and stopping at stop.  By mixing the min, max, start, peak and stop values you can easily achieve tent like distributions.

RANDOM UNIFORM(min,max)

Draws from a uniform random distribution.

RANDOM WEIBULL(min,max,shape,shift,stretch)

Draws from a Weibull distribution starting at 0 with mean 1 and having the given shape.  Before the value is returned, it is multiplied by stretch and shift is added.  The Weibull distribution with shape 1 is the same as the exponential distribution.

VECTOR(min,max,increment)

Generates a sequence of numbers from min to max by increment.  This sequence of values is not random, but uniformly increasing.  VECTOR is most useful in univariate sensitivity testing, or performing an exhaustive grid search. Combining one VECTOR with other RANDOM distributions is not likely to be very useful, unless you need to select discrete values for a parameter.

When used in Multivariate and Latin Hypercube sampling, the order of VECTOR items is shuffled randomly.

VECTOR is not a available in the simulation language.

If the increment is 0, only the min and max points will be tested (avoiding the need for you to determine the increment).

If the increment is set to a negative value, only the min point will be tested.