CVaR for Mixture of Normal Distributions as Function of Mixture Weights (wCVaR_ni)
Contents
CVaR for Mixture of Normal Distributions as Function of Mixture Weights. This function calculates CVaR for a mixture of normal distributions as a function of variable weights in this mixture.
Syntax
wcvar_ni(α, matrix_mn, matrix_vr) |
short call; |
wcvar_ni_name(α, matrix_mn, matrix_vr) |
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 first row contains names of variables. The second row contains non-negative numerical data.
is a confidence level.
Mathematical Definition
Weighed CVaR for Normal Independent function with confidence level 
is calculated as follows:
,
where
is varying threshold;
is Partial Moment Penalty Normal Independent function with fixed parameters (means and variances) and varying threshold.
is an argument of CVaR for Mixture of Normal Distributions as Function of Mixture Weights.
Example
See also
CVaR,
CVaR Normal Independent, CVaR Normal Dependent,
CVaR Deviation, CVaR Deviation Normal Independent, CVaR Deviation Normal Dependent,
CVaR for Mixture of Normal Independent, CVaR Deviation for Mixture of Normal Independent
CVaR for Discrete Distribution as Function of Atom Probabilities