Fractiles

Fractiles(x: Array Number Ascending)

This creates a probability distribution treating the elements of x as fractiles (percentiles) with equal probability spacing. The first element of x is the zeroth fractile (i.e. minimum), the last element is the 1.0 fractile (100th percentile, i.e. maximum). If x has n+1 elements, the ith value is the (i/n) fractile. The distribution is piecewise uniform -- that is, it assumes a uniform distribution between each pair of adjacent fractiles.

If you have a distribution specified by a set of fractiles (percentiles), it is usually best to use CumDist, that let's you specify an arbitrary (not just equal probability-spaced) fractiles, and interpolates the density function as linear between specified fractiles (or equivalently, interpolates the cumulative function as quadratic). Fractiles is rarely of value. We retain it in Analytica simply for compatibility with any (very old) models that may have used it in the past.