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