Variance. Variance of Linear Loss scenarios calculated with Matrix of Scenarios or Covariance Matrix.

 

Syntax

 
Parameters

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.

 

matrix_cov        is a PSG matrix:

       

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

,

.

, .

 

Mathematical Definition

Variance function is calculated on the matrix of scenarios matrix as follows::

where

, ,

random vector has components and J vector scenarios, ,

random value , which is the i-th component of the random vector, , has J discrete scenarios ,

is probability of the scenario .

is Loss Function (See section Loss and Gain Functions).

Variance  is calculated on the covariance matrix matrix_cov as follows:

,

where

is a Quadratic function.

is an argument of Variance function.

 

Example

 

See also

Root Mean Squared Error, Root Mean Squared Error Normal Independent, Root Mean Squared Error Normal Dependent, Standard Risk, Standard Gain, Standard Risk Normal Independent, Standard Gain Normal Independent, Standard Risk Normal Dependent, Standard Gain Normal Dependent, Standard Deviation, Mean Square Error, Mean Square Error Normal Independent, Mean Square Error Normal Dependent