Average Kolmogorov-Smirnov Distance between Two Distributions (ksm_avg)
Contents
Average Kolmogorov-Smirnov Distance between Two Distributions. Kantorovich (or Average Kolmogorov-Smirnov) distance between a discrete distribution with variable probabilities of atoms and a fixed discrete distribution. This distance is calculated by taking the average of absolute values of differences between two distributions at atoms of the two discrete distributions with probabilities proportional to the distances between atoms.
Syntax
ksm_avg(α, matrix_kx, vector_yi, vector_qi) |
short call; |
ksm_avg_name(α, matrix_kx, vector_yi, vector_qi) |
call with optional name. |
Parameters
matrix_kx is a PSG matrix:
where the header row contains names of variables. The second row contains numerical data.
vector_yi is a PSG vector:
where the header row contains names of variables. Other rows contain numerical data.
vector_qi is a PSG vector:
where the header row contains names of variables. Other rows contain numerical data.
, 
.
is a confidence level.
Mathematical Definition
Average Kolmogorov-Smirnov Distance between Two Distributions function is calculated as follows:
,
where
is Average function for Loss Function 
(See section Loss and Gain Functions) with scenarios:
,
, 
, 
and probabilities:
,
where 
is an ascending order of elements in Z and 
, 
.
is an argument of function that satisfies the following conditions:
, 
.
Example
See also
Kolmogorov-Smirnov Distance between Two Distributions , Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions, CVaR Kolmogorov-Smirnov Distance between Two Distributions, CVaR Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions