CVaR2 Error (cvar2_err)
Contents
CVaR2 Error. CVaR (Superquantile) Error, which is an element of CVaR (Superquantile) quadrangle (see [1])
Syntax
cvar2_err(α, matrix) |
short call; |
cvar2_err_name(α, matrix) |
call with optional name . |
Parameters
is a confidence level.
matrix is a Matrix of Scenarios:
where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.
Output
When function CVaR2 Error is used in optimization or calculation problems PSG automatically calculates and includes in the solution report two outputs:
pseudo_R2_function_name |
|
contributions(function_name) |
Mathematical Definition
CVaR2 Error function is calculated as follows:
,
where
is Average function,
is an integral of CVaR (see CVaR2 Risk function),
is a confidence level such, that 
:
,
where 
is Buffered Probability of Exceedance.
Example
References
[1] Rockafellar,R. T. , Royset, J. O., and S. I. Miranda (2014): Superquantile Regression with Applications to Buffered Reliability, Uncertainty Quantification and Conditional Value-at-Risk. European J. Operations Research 234 (2014), 140-154.
See also