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)

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)

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)

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