CVaR Deviation Normal Dependent (cvar_nd_dev)
Contents
CVaR Deviation Normal Dependent. Special case of the CVaR Deviation when all coefficients in Linear Loss function are mutually dependent normally distributed random values
Syntax
cvar_nd_dev(α, matrix_mn,matrix_cov) |
short call |
cvar_nd_dev_name(α, matrix_mn,matrix_cov) |
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_cov is a PSG matrix of covariance values:
where the header row contains names of variables. Other rows contain numerical data.
is a confidence level.
Mathematical Definition
CVaR Deviation Normal Dependent function is calculated as follows:
,
where
is CVaR Normal Dependent function,
,
is Loss Function (See section Loss and Gain Functions),
,
,
is a probability density function of the standard normal distribution,
,
is the standard normal distribution,
is an argument of function.
Remarks
| • | matrix_mn do not used in the calculation of CVaR Deviation for Loss Normal Dependent function. |
| • | matrix_cov have to be symmetric. |
Example
See also
CVaR Deviation for Gain Normal Dependent
CVaR,
CVaR Normal Independent, CVaR Normal Dependent,
CVaR Deviation, CVaR Deviation Normal Independent,
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