Probability of Exceedance for Gain Multiple Normal Dependent (prmulti_pen_nd_g)
Contents
Probability of Exceedance Penalty for Gain Multiple Normal Dependent. There are M Linear Loss functions with mutually dependent normally distributed random coefficients. Probability of Exceedance for Gain Multiple Normal Dependent = 1-(Probability that all M Linear Gain functions are below the threshold).
Syntax
prmulti_pen_nd_g(w,matrix_mn,matrix_cov_1,...,matrix_cov_M) |
short call; |
prmulti_pen_nd_g_name(w,matrix_mn,matrix_cov_1,...,matrix_cov_M) |
call with optional name. |
Parameters
is a threshold value.
matrix_mn is a PSG matrix of mean values of coefficients of Loss functions:
where the header row contains names of variables. Other rows contain numerical data.
matrix_cov_m is a PSG matrix of covariance values of coefficients of m-Loss function:
where the header row contains names of variables. Other rows contain numerical data.
,
Mathematical Definition
The Probability of Exceedance Penalty for Gain Multiple Normal Dependent is calculated as follows:
.
where
;
is average of Gain Functions;
is standard Deviation of Gain Functions;
is 
-th Gain Function (See section Loss and Gain Functions);
is an argument of function.
Example
See also
Probability Group, Probability of Exceedance Multiple Normal Dependent.