HomeTechniques and Tips@RISK DistributionsWhich Distribution Should I Use?

# 3.1. Which Distribution Should I Use?

How do I know which probability distribution I should use?  Do you have some book you can refer me to?

Different industries tend to prefer a different selection of distributions.  We don't have any one book that directly addresses your question, but we do have a number of resources to offer, both within @RISK and externally.

One very powerful tool, assuming you have the Professional or Industrial Edition, is distribution fitting.  This lets you enter historical data; then @RISK attempts to fit every relevant distribution to the data.  You can instantly compare different distributions to see which one seems best suited to the data set.

If you're not fitting to existing data, here are some things to think about:

• Your first decision is whether you need a continuous or discrete distribution. Continuous distributions can return any values within a specified range, but discrete distributions can return only predefined values, usually whole numbers. The Define Distributions dialog has separate tabs for discrete and continuous distributions.

• Then ask whether your distribution should be bounded on both sides, bounded on the left and unbounded on the right, or unbounded on both sides. The thumbnails in Define Distributions will give you an idea of whether each distribution is bounded,

• Finally, do you have a general idea of the shape of distribution you want — symmetric or skewed? strong central peak or not? The shapes in Define Distributions are just a partial guide for this, because changing the numeric parameters of some distributions can change the shape drastically.

There's more than one way to specify a distribution. Every distribution has standard parameters that you can enter explicitly, as numbers or cell references. But you might prefer to specify distributions by means of percentiles, as a way of specifying those parameters implicitly. To do this, in Define Distributions select the Alt Parameters tab, and you'll see the distributions that can be specified by means of percentiles. On the other hand, if you know the mean, standard deviation or variance, skewness, and kurtosis that you want, the RiskJohnsonMoments distribution may be a good choice.

After you select a distribution, the Define Distribution window gives you instant feedback about the shape and statistics of the distribution as you alter the parameters or even the functions themselves.