Partial Moment Two Normal Independent (pm2_pen_ni)
Contents
Partial Moment Two Normal Independent. Expected squared Linear Loss in access of of some fixed threshold for Loss with independent normally distributed random coefficients.
Syntax
pm2_pen_ni(w,matrix_mn,matrix_vr) |
short call |
pm2_pen_ni_name(w,matrix_mn,matrix_vr) |
call with optional name |
Parameters
matrix_mn is a PSG matrix of mean values:
where the header row contains names of variables. The second row contains numerical data.
matrix_vr is a PSG matrix of variance values:
where the header row contains names of variables. The second row contains numerical data.
 | is a threshold value. |
Mathematical Definition
Partial Moment Two Penalty for Loss Normal Independent function is calculated as follows:
,
where
,
,
is the standard normal distribution,
is probability density function of the standard normal distribution.
is an argument of function.
Example
See also
Partial Moment Group, Partial Moment Two for Gain Normal Independent.