Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions (ksm_max_ni)
Contents
Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions. Kolmogorov-Smirnov distance between a mixture of normal distributions with variable coefficients and a fixed discrete distribution (as function of variable coefficients). This distance is calculated by maximizing deference between two distributions.
Syntax
ksm_max_ni(matrix_mn, matrix_vr, vector_yi, vector_qi) |
short call; |
ksm_max_ni(matrix_mn, matrix_vr, vector_yi, vector_qi, vector_wt) |
short call with vector of weights; |
ksm_max_ni_name(...) |
call with optional name; |
Parameters
matrix_mn is a PSG matrix with mean values:
where the header row contains names of variables. The second row contains numerical data.
matrix_vr is a PSG matrix with variance values:
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.
, 
.
vector_wt is a PSG vector:
where the first row contains names of variables and it can not be empty. The other rows contain numerical data;
.
Remarks
vector_wt is optional and may be omitted. By the default 
.
Mathematical Definition
Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions function is calculated as follows:
,
where
, is a Mixture of Normal Independent Distributions 
with parameters 
and weights 
.
,
is empirical cumulative distribution function defined on the set of unique atoms 
with vector of probabilities 
.
is an argument of function.
Example
See also
Kolmogorov-Smirnov Distance between Two Distributions , CVaR Kolmogorov-Smirnov Distance between Two Distributions, CVaR Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions , Average Kolmogorov-Smirnov Distance between Two Distributions