CVaR for Mixture of Normal Independent. Consider a mixture of (random) Linear Loss functions with positive weights summing up to one. Coefficients in all  Linear Loss functions are independent normally distributed random values. avg_cvar_risk_ni is the CVaR of the mixture of Normally Independent random values.

 

Syntax

 
Parameters

matrix_mn        is a PSG matrix of mean values:

       

where the header row contains names of variables. Other rows contain numerical data.

 

matrix_vr        is a PSG matrix of variance values:

       

where the header row contains names of variables. Other rows contain numerical data.

 

       is a confidence level.

 

Mathematical Definition

CVaR for Mixture of Normal Independent function with confidence level is calculated by minimizing of the next expression which includes Average Partial Moment Penalty for Loss Normal Independent (avg_pm_pen_ni):

.

is an argument of function.

 

Example

 

See also

CVaR for Gain for Mixture of Normal Independent,

CVaR,

CVaR Normal Independent, CVaR Normal Dependent,

CVaR Deviation, CVaR Deviation Normal Independent, CVaR Deviation Normal Dependent,

CVaR Deviation for Mixture of Normal Independent

CVaR Max, CVaR Max Deviation,

CVaR for Discrete Distribution as Function of Atom Probabilities, CVaR for Mixture of Normal Distributions as Function of Mixture Weights