Probability of Exceedance (pr_pen)
Contents
Probability of Exceedance. Probability that Linear Loss exceeds some fixed threshold.
Syntax
pr_pen(w, matrix) |
short call; |
pr_pen_name(w, matrix) |
call with optional name. |
Parameters
is a threshold value.
matrix 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 is calculated as follows
;
where
is a vector of random coefficients for Loss Function:
, 
, are scenarios of Loss Function (See section Loss and Gain Functions);
;
is an argument of function.
Example
Case Studies with Probability of Exceedance
See also
Probability Group , Probability of Exceedance Penalty for Gain (pr_pen_g).