# General

General equations

General distribution is a non-parametric distribution (i.e. there is no underlying probability model) where {xi} is an array of x-values with probability densities {pi} and where the distribution falls between the minimum and maximum. In a simulation software package such as Crystal Ball where the general distribution is not specified, one has to use Crystal Ball's Custom Distribution to construct a General distribution. An example of the General distribution is given below:

General Distribution ({0,2,4,6,8,10},{0,1,3,2,4,0}),

constructed with Crystal Ball's Custom Distribution

Crystal Ball does not constrain the {pi} values that you provide to give an area under the curve of exactly 1. Instead, the Crystal Ball software will re-calibrate the probability scale for you during simulation.

#### Uses

##### 1. Modeling expert opinion

The General distribution is very useful for producing a fairly detailed distribution that reflects an expert's opinion. The General distribution is the most flexible of all of the continuous distribution functions. It enables the analyst and expert to tailor the shape of the distribution to reflect, as closely as possible, the opinion of the expert.

##### 2. Modeling distributions not available with the simulation software package

The General distribution can be used to construct a distribution not available with the simulation software package where you know the pdf or pmf.

##### 3. Modeling posterior distribution in Bayesian inference

If you use the construction method of obtaining a Bayesian posterior distribution, you will have two arrays: a set of possible values in ascending order; and a set of posterior weights for each of those values. If you leave the column in between "empty", this exactly matches the input parameters for a General distribution which can then be used to generate values from the posterior distribution. Examples: Turbine blades; Fitting a Weibull distribution.

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