Average Max Deviation. There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Deviation scenarios function is calculated by maximizing losses over (Linear Loss) -  (Average Linear Loss over scenarios) functions (over M functions for every scenario).  Average Max Deviation is calculated by averaging Maximum Deviation scenarios.

 

Syntax

 

Parameters

matrix_m        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.

.

 

Mathematical Definition

Average Max Deviation function is calculated as follows

,

where:

is Average Loss function,

M =  number of random Loss Functions ,

 = vector of random coefficients for m-th Loss Function;

 = j-th scenario of the random vector ,

is a random function with scenarios .

 

Every Loss Function is defined by a separate matrix of scenarios and has an equal number of scenarios J.

Probability of scenario  is defined by the first matrix.

 

is an argument of Average Max Deviation function.

 

Example

 

See also

Average Loss, Average Gain, Average Max, Average Max for Gain, Average Max Deviation for Gain