Category:Inverse cumulative probability functions

Inverse cumulative probability functions are also know as fractile functions or quantile functions. In Analytica, these functions are named according to the convention Cum«Dist»Inv(p, ...), where «Dist» is the name of the corresponding distribution function. For example, the inverse cumulative normal distribution function is CumNormalInv( p, m, sd ), which corresponds to the Normal( m, sd ) distribution function. Furthermore, they have the same parameters as their corresponding distribution function, but with a first parameter «p», which is the fractile/quantile level requested.

An inverse cumulative probability function returns the value x at which the probability of the true outcome being less than or equal to x is «p». They are said to compute the fractile, percentile, quantile, etc. They perform this computation analytically, so that there is no Monte Carlo sampling error in the result.

In general, it is possible to produce a sample from the corresponding distribution using

Cum«Dist»Inv( Uniform(0,1),...)

however, this is what the distribution function does, and the distribution function is usually a better option.

Inverse cumulative probability functions exist for both Continuous distributions and Discrete distributions, but only for Univariate distributions. They are the inverse of Cumulative distribution functions.