Average Probability of Exceedance Normal Independent. 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 Probability of Exceedance Normal Independent is a weighted sum of Probability of Exceedance Normal functions over all Loss functions in the mixture. The weighs in the sum are taken from the mixture of Loss functions.

 

Syntax

 
Parameters

       is a threshold.

matrix_mn        is a PSG matrix of mean values:

       

where the header row contains names of variables. Other rows contain numerical data.

 

matrix_vr        is a PSG matrix of mean values of variance values of coefficients of Loss functions:

       

where the header row contains names of variables. Other rows contain numerical data.

 

 

Mathematical Definition

The Average Probability of Exceedance Normal Independent is calculated as follows:

 

,

where

is Probability of Exceedance Penalty for Loss Normal Independent function;

       is normalized weight of m-th Loss function;

,

is average of Loss Functions, ;

is standard Deviation of Loss Functions, ;

 is a -th Loss function, ;

is an argument of function.

 

Example

 

See also

Probability Group, Average Probability of Exceedance Penalty for Gain Normal Independent, Average Probability of Exceedance Deviation Normal Independent