CVaR Normal Independent (cvar_risk_ni)
Contents
CVaR Normal Independent. Special case of the CVaR when all coefficients in Linear Loss function are independent normally distributed random values.
Syntax
cvar_risk_ni(α, matrix_mn,matrix_vr) |
short call |
cvar_risk_ni_name(α, matrix_mn,matrix_vr) |
call with optional name |
Parameters
matrix_mn is a PSG matrix of mean values:
,
where the header row contains names of variables. The second row contains numerical data.
matrix_vr is a PSG matrix of variance values:
,
where the header row contains names of variables. The second row contains numerical data.
is a confidence level.
Mathematical Definition
VaR Normal Independent function is calculated as follows:
,
where
,
,
,
is a probability density function of the standard normal distribution,
,
is the standard normal distribution,
is an argument of function.
Example
See also
CVaR for Gain Normal Independent,
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, CVaR for Mixture of Normal Distributions as Function of Mixture Weights