Average Max Deviation for Gain (avg_max_dev_g)

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

 

Syntax

avg_max_dev_g(matrix_1,matrix_2,...,matrix_M)

short call

avg_max_dev_g_name(matrix_1,matrix_2,...,matrix_M)

call with optional name

 

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 for Gain 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 for Gain function.

 

Example

Calculation in Run-File Environment
Calculation in MATLAB Environment

 

See also

Average Loss, Average Gain, Average Max, Average Max for Gain, Average Max Deviations