# ProbDist - Custom continuous distribution using density points

Use these functions to specify a custom continuous probability distribution by specifying probability density points at selected values.

To use, you need to specify (p_i, r_i) points, where «p_i» is an array of relative non-negative densities indexed by «`I`

» and «r_i» is an increasing array of values, also indexed by «`I`

». The values in «p_i» are relative -- the function normalizes them so that the area under the distribution adds to 1.

It produces a density function using linear interpolation between the specified points on the density function.

Usually the first and last values in «p_i» are zero. If not, it extrapolates out for a distance equal to the spacing between the first two points (or last two points) before reaching zero.

The index parameter «`I`

» can be omitted if either «p_i» or «r_i» is itself an index (in which case the other is an array indexed by that).

## Functions

### ProbDist(p_i, r_i*, I, over*)

The distribution function. Use this to specify a quantity that has your custom distribution.

If you want to define independent and identically distributed quantities along one or more indexes, list those indexes in the optional «over» parameter.

### DensProbDist( x, p_i, r_i*, I, over*)

*, I, over*)

*New to Analytica 5.2*

The analytic density function. Computes the probability density at «x» according to your custom distribution, after any normalization has been applied.

### CumProbDist( x, p_i, r_i*, I, over*)

*, I, over*)

*New to Analytica 5.2*
The analytic cumulative density function. Computes the probability that a random outcome is less than or equal to «x».

### CumProbDistInv( p, p_i, r_i*, I, over*)

*, I, over*)

*New to Analytica 5.2*
The analytic inverse cumulative density function (aka *quantile function*). Computes the «p»^{th} fractile/quartile/percentile.

## See Also

- CumDist
- ProbTable
- ChanceDist -- the discrete distribution analog.
- Keelin distribution
- Custom continuous distributions
- Distribution Densities Library

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