Probability of Exceedance Deviation Multiple (prmulti_dev)
Contents
Probability of Exceedance Deviation Multiple. There are M Linear Loss (every Linear Loss is defined by a Matrix of Scenarios). A new Maximum Loss Deviation is calculated by taking maximum for every scenario over M Linear Loss Deviations. Probability of Exceedance Deviation Multiple is the Probability of Exceedance of the Maximum Maximum Deviation Multiple scenarios.
Probability of Exceedance Deviation Multiple = 1-(Probability that all M (Loss)-(Average Loss) functions are below the threshold).
Syntax
prmulti_dev(w, matrix_1,matrix_2,...,matrix_M) |
short call; |
prmulti_dev_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 Multiple is calculated as follows:
where
is Probability of Exceedance Penalty for Loss function;
are scenarios of Maximum Loss 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 for Gain Multiple.