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holmberg1

PURPOSE ^

Computes moments for higher order reliability methods.

SYNOPSIS ^

E=holmberg1(S,a,b,Q1)

DESCRIPTION ^

  HOLMBERG1 Computes moments for higher order reliability methods. 
  
  CALL: E=holmberg1(S,a,b,Q1); 
  
  Computation of the expectation of  
  sqrt(pi/2)*(b'*X)*(X'*Q*X)*(2*normcdf(a'*X)-1) 
  if S is normally distributed with mean zero and covariance matrix 
  S.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

01 function E=holmberg1(S,a,b,Q1) 
02 % HOLMBERG1 Computes moments for higher order reliability methods. 
03 % 
04 % CALL: E=holmberg1(S,a,b,Q1); 
05 % 
06 % Computation of the expectation of  
07 % sqrt(pi/2)*(b'*X)*(X'*Q*X)*(2*normcdf(a'*X)-1) 
08 % if S is normally distributed with mean zero and covariance matrix 
09 % S. 
10 Q1=(Q1+Q1')/2; 
11 term1=a'*S*b*trace(S*Q1); 
12 term2=2*a'*S*Q1*S*b; 
13 term3=-(a'*S*b)*(a'*S*Q1*S*a)/(1+a'*S*a); 
14 E=(term1+term2+term3)/sqrt(1+a'*S*a); 
15

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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