Probability of Exceedance Deviation for Gain Multiple (prmulti_dev_g)
Contents
Probability of Exceedance Deviation for Gain Multiple. There are M Linear Loss (every Linear Loss is defined by a Matrix of Scenarios). A new Maximum Gain Deviation is calculated by taking maximum for every scenario over M Linear Gain Deviations. Probability of Exceedance Deviation for Gain Multiple is the Probability of Exceedance of the Maximum Maximum Deviation for Gain Multiple scenarios.
Probability of Exceedance Penalty for Gain Multiple = 1-(Probability that all M -(Loss)+(Average Loss) functions are below the threshold).
Syntax
prmulti_dev_g(w, matrix_1,matrix_2,...,matrix_M) |
short call; |
prmulti_dev_g_name(w, matrix_1,matrix_2,...,matrix_M) |
call with optional name. |
Parameters
is a threshold value.
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
The Probability of Exceedance Deviation for Gain Multiple is calculated as follows:
,
where
is Probability of Exceedance Penalty for Loss function;
are scenarios of Maximum GAin Deviation Function;
, 
, are scenarios of Loss Function (See section Loss and Gain Functions);
is an argument of function.
Remarks
Input data is a set of Matrices of scenarios with equal number of scenarios (rows).
Probabilities of scenarios are taken form the first matrix in a list of the set (matrix_1). So an order of matrices in a list is essential.
Example
See also
Probability Group, Probability of Exceedance Deviation Multiple.