Probability of Exceedance for Gain Multiple (prmulti_pen_g)
Contents
Probability of Exceedance for Gain Multiple. There are M Linear Loss (every Linear Loss is defined by a Matrix of Scenarios). A new Maximum Gain is calculated by taking maximum for every scenario over M Linear Gains. . Probability of Exceedance for Gain Multiple is Probability of Exceedance of the Maximum -Loss scenarios.
Probability of Exceedance for Gain Multiple = 1-(Probability that all M Linear -(Loss) functions are below the threshold).
Syntax
prmulti_pen_g(w, matrix_1,..., matrix_M) |
short call; |
prmulti_pen_g_name(w, matrix_1,..., 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 for Gain Multiple is calculated as follows:
,
where
is Probability of Exceedance function;
are scenarios of Maximum Gain 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