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# Statistical Distributions Overview

Each Random Variable that you define for a Probabilistic Analysis must have a Statistical Distribution selected. The following Statistical Distributions are available in RocSlope:

The type of Statistical Distribution, together with the statistical parameters of the distribution (mean, standard deviation, minimum and maximum values), defines a "probability density function" for the Random Variable. A "probability density function" is commonly referred to as a PDF.

The PDF describes the distribution of possible values that the Random Variable may assume, for a hypothetical, infinite set of observations of the variable.

In most cases very limited data is available on which to decide what Statistical Distribution and standard deviation to use. Therefore, the engineer must often rely on "best estimates" when defining the PDF for a Random Variable.

## Normal Distribution

A Normal Distribution is commonly used for statistical analysis in geotechnical engineering. When the true distribution of a variable is not known, a Normal Distribution is often assumed. By making a best estimate of the minimum and maximum values of the variable, a standard deviation can be estimated. This is described in the Normal Distribution topic.

## Other Distributions

Although a Normal Distribution is most commonly used, the user should become familiar with the properties and advantages of using other Statistical Distributions.

For example, variables which can only have positive values (such as Cohesion, for example), often have PDFs which are NOT well modelled by a Normal Distribution. Such variables may have non-symmetric distributions, with a peak in the distribution at low values and a gradual tapering off at higher values. For such variables, it is often more appropriate to use a Lognormal or Gamma distribution rather than a Normal distribution.

Other variables may be best modelled with an Exponential distribution. For example, the level of a Water Table might be modelled using an Exponential distribution if high Water Tables are expected only rarely due to infrequent rainfall.

A Uniform distribution can be useful if you wish to specify an equal probability of the variable, taking on any value between the minimum and maximum values.
The Statistical Distributions available in RocSlope are briefly described in the following topics. For further information, you should consult one of the many reference works which are available on the subject.

A Fisher distribution is applicable for orientation data in RocSlope. See the Define Synthetic Joints and Fisher Distribution topics for more information.