# CumDist - Custom continuous distribution using cumulative probabilities

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The `CumDist`

functions are used to specify an arbitrarily shaped distribution by specifying points (pi,ri) on the cumulative probability curve.

## Contents

## Functions

For each function below, the shape is described by two arrays, «p_i» and «r_i», each indexed by index «`I`

». These are points on the cumulative density (CDF) curve. «p_i» must be non-decreasing, «r_i» must be strictly increasing along «`I`

». The index «`I`

» may be omitted when either «p_i» or «r_i» is itself an index.

In addition, an optional boolean «smooth» parameter (defaults to true) causes the CDF to be smooth and the PDF to be continuous. When set to False, the CDF is piecewise linear, which implies the PDF is piecewise constant and discontinuous.

- Naming convention note

There is a convention that the Analytic functions use the names `Dens«Dist»()`

, `Cum«Dist»()`

and `Cum«Dist»Inv()`

, where «Dist» is the distribution function name. That convention is used with this function, but results in the repeated "CumCum" for two of the functions. Also, this convention is applied to the ProbDist distribution function also, so be careful not to confuse CumProbDist with CumDist, etc.

### CumDist(p_i, r_i*, I, over, smooth*)

The distribution function. Use this function to describe a quantity having the custom distribution described by («p_i», «r_i»). To specify independent by identically distributed quantities along additional indexes, list those other indexes in the «over» parameter.

### DensCumDist(x, p_i, r_i*, I, smooth*)

*, I, smooth*)

*New to Analytica 5.2*

Returns the probability density at each point in «x».

### CumCumDist(x, p_i, r_i*, I, smooth*)

*, I, smooth*)

*New to Analytica 5.2*

Returns the cumulative probability at «x» -- the probability that the quantity is less than or equal to «x».

### CumCumDistInv(p, p_i, r_i*, I, smooth*)

*, I, smooth*)

*New to Analytica 5.2*

The inverse cumulative probability. Returns the «p»^{th} fractile/quantile/percentile.

## History

- The analytic functions are new to Analytica 5.2.

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