Cvar Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions (ksm_cvar_ni)
Contents
Cvar Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions. CVaR 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 taking CVaR of absolute values of differences between two distributions at atoms of the fixed discrete distribution.
Syntax
ksm_cvar_ni(α, matrix_mn, matrix_vr, vector_yi, vector_qi) |
short call; |
ksm_cvar_ni(α, matrix_mn, matrix_vr, vector_yi, vector_qi, vector_wt) |
call with vector of weights; |
ksm_cvar_ni(α, matrix_mn, matrix_vr, vector_yi, vector_qi,vector_wt,vector_pi) |
call with vector of weights and vector of probabilities of loss functions scenarios; |
ksm_cvar_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 header row contains names of variables. Other rows contain numerical data.
.
vector_pi is a PSG vector:
where the header row contains names of variables. Other rows contain numerical data.
, 
.
is a confidence level.
Remarks
| • | vector_wt is optional and may be omitted. By the default  . |
| • | vector_pi is optional and may be omitted. By the default  . |
Mathematical Definition
Cvar Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions function is calculated as follows:
,
where
is CVaR Risk function for Loss Function 
(See section Loss and Gain Functions) with scenarios:
,
, 
,
is an ascending order of elements in Z
is a Normal Distributions with parameters 
,
Probabilities for scenarios are:
,
is an argument of function.
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, Average Kolmogorov-Smirnov Distance between Two Distributions