Probability of Exceedance Penalty for Gain Normal Independent (pr_pen_ni_g)
Contents
Probability of Exceedance Penalty for Gain Normal Independent. Probability that Linear Gain exceeds some fixed threshold for the Loss with independent normally distributed random coefficients.
Syntax
pr_pen_ni_g(w, matrix_mn,matrix_vr) |
short call; |
pr_pen_ni_g_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 Penalty for Gain Normal Independent is calculated as follows:
;
where
is Probability of Exceedance for Normal Independent function;
is a Gain Function (See section Loss and Gain Functions)
is a Loss Function (See section Loss and Gain Functions);
is average of Gain Function;
is standard Deviation of Gain Function;
is standard normal distribution;
is an argument of function.
Example
See also
Probability Group, Probability of Exceedance Normal Independent.