A distribution that is confined to lie between two determined values is said to be *bounded*. Examples of bounded distributions are: Uniform - between minimum and maximum, Triangular - between minimum and maximum, Beta - between 0 and Scale, and Binomial - between 0 and *n*.

A distribution that is *unbounded* theoretically extends from minus infinity to plus infinity. Examples are: Normal, Logistic, and Extreme Value.

A distribution that is constrained at one or either end is said to be *partially bounded*. Examples are: Chi Squared (>0), Exponential (>0), Pareto (>*a*), Poisson (>=0) and Weibull (>0).

Unbounded and partially bounded distributions may, at times, need to be constrained to remove the tail of the distribution so that nonsensical values are avoided. For example, using a Normal distribution to model sales volume opens up the chance of generating a negative value. If the probability of generating a negative value is significant, and we want to stick to using a Normal distribution, we must constrain the model in some way to eliminate any negative sales volume figure being generated.

Truncating distributions

The Crystal Ball software provides truncation of any of its distributions (except the Custom Distribution) as explained here.

You can also build logic into the model that rejects nonsensical values. For example, using the IF function: A2:=IF(A1<0,ERR(),0) only allows values into cell A2 from cell A1 that are >=0 and produces an error in cell A2 otherwise.

If you are faced with the problem of needing to constrain the tail of a distribution, however, to avoid unwanted values, it is worth questioning whether you are using the appropriate distribution in the first place.

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