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The Cumulative distribution in Crystal Ball can be constructed using Crystal Ball's Custom distribution, and requires two arrays of data, *{xi} and* *{P**i}*) where *{xi}* is an array of *x*-values with cumulative probabilities *{Pi}* and where the distribution falls between the minimum and maximum. The figure below shows the Cumulative distribution using data ({0,1,4,6,10},{0,0.1,0.6,0.8,1.0}) as it is defined in its cumulative form and how it looks as a relative frequency plot.

#### Uses

##### 1. Empirical distribution of data

The Cumulative distribution is very useful for converting a set of data values into a first or second order empirical distribution that can be sampled by Crystal Ball.

##### 2. Modeling expert opinion

The Cumulative distribution can be used to construct uncertainty distributions when using some classical statistical methods. Examples: p in a Binomial process; l in a Poisson process.

##### 3. Modeling expert opinion

The Cumulative distribution is used in some texts to model expert opinion. The expert is asked for a minimum, maximum and a few percentiles (e.g. 25%, 50%, 75%). However, we have found it largely unsatisfactory because of the insensitivity of its probability scale. A small change in the shape of the Cumulative distribution that would pass unnoticed produces a radical change in the corresponding relative frequency plot that would not be acceptable. The figure below provides an illustration:

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