Average Partial Moment for Gain Normal Independent (avg_pm_pen_ni_g)
Contents
Average Partial Moment for Gain Normal Independent. Consider a mixture of (random) Linear Loss functions with positive weights summing up to one. Coefficients in all Linear Loss functions are independent normally distributed random values. Average Partial Moment for Gain Normal Independent is a weighted sum of Partial Moment for Gain Normal Independent functions over all Loss functions in the mixture. The weighs in the sum are taken from the mixture of Loss functions.
Syntax
avg_pm_pen_ni_g(w, matrix_mn, matrix_vr) |
short call; |
avg_pm_pen_ni_g_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. Other rows contain numerical data.
If "scenario_probability" column is absent or all 
then all weights are considered as equal to 1.
matrix_vr is a PSG matrix of variance values:
where the header row contains names of variables. Other rows contain numerical data.
 | is a threshold value. |
Mathematical Definition
The Average Partial Moment for Gain Normal Independent function is calculated as weighted mean of Partial Moment Penalty for Loss Normal Independent:
.
where
is Average Partial Moment Penalty for Loss Normal Independent function,
is Partial Moment Penalty for Gain Normal Independent function,
is normalized weight of m-th loss function,
,
,
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, Average Partial Moment Normal Independent.