Probability of Exceedance Normal Independent (pr_pen_ni)
Contents
Probability of Exceedance Normal Independent. Probability that Linear Loss exceeds some fixed threshold for the Loss with independent normally distributed random coefficients.
Syntax
pr_pen_ni(w, matrix_mn,matrix_vr) |
short call; |
pr_pen_ni_name(w, matrix_mn,matrix_vr) |
call with optional name. |
Parameters
is a threshold value.
matrix_mn is a PSG matrix of mean values of coefficients of Loss function:
where the header row contains names of variables. The second row contains numerical data.
matrix_vr is a PSG matrix of variance values of coefficients of Loss function:
where the header row contains names of variables. The second row contains numerical data.
Mathematical Definition
Probability of Exceedance Normal Independent is calculated as follows:
;
where
is a vector of random coefficients for Loss Function;
is average of Loss Function;
is standard deviation of Loss Function;
is a Loss Function (See section Loss and Gain Functions);
is standard normal distribution;
is an argument of function.
Example
See also
Probability Group, Probability of Exceedance for Gain Normal Independent.