Partial Moment Deviation Normal Dependent (pm_nd_dev)
Contents
Partial Moment Deviation Normal Dependent. Expected access of ( (Loss ) - (Average Loss )) over some fixed threshold for the Loss with mutually dependent normally distributed random coefficients.
Syntax
pm_nd_dev(w,matrix_mn,matrix_cov) |
short call |
pm_nd_dev_name(w,matrix_mn,matrix_cov) |
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_cov is a PSG matrix of covariance values:
where the header row contains names of variables. Other rows contain numerical data.
 | is a threshold value. |
Mathematical Definition
Partial Moment Deviation Normal Dependent function is calculated as follows:
,
where
is Partial Moment Penalty Normal Dependent function,
,
is Loss function (See section Loss and Gain Functions),
,
is the standard normal distribution,
is probability density function of the standard normal distribution.
is an argument of function.
Remarks
matrix_mn is not used in the calculation of Partial Moment Deviation Normal Dependent function.
Example
See also
Partial Moment Group, Partial Moment Gain Deviation Normal Dependent.