Home > wafo > trgauss > private > holmberg2.m

holmberg2

PURPOSE ^

Computes moments for higher order reliability methods.

SYNOPSIS ^

E=holmberg2(S,a,b,Q1,Q2)

DESCRIPTION ^

  HOLMBERG2 Computes moments for higher order reliability methods. 
  
  CALL: E=holmberg2(S,a,b,Q1); 
  
  Computation of the expectation of  
  sqrt(pi/2)*(b'*X)*(X'*Q1*X)(X'*Q2*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=holmberg2(S,a,b,Q1,Q2) 
02 % HOLMBERG2 Computes moments for higher order reliability methods. 
03 % 
04 % CALL: E=holmberg2(S,a,b,Q1); 
05 % 
06 % Computation of the expectation of  
07 % sqrt(pi/2)*(b'*X)*(X'*Q1*X)(X'*Q2*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 Q2=(Q2+Q2')/2; 
12 E=1/4*(4*holmquist2(S,Q1,Q2)*(a'*S*b)+8*holmquist2(S,Q1,Q2)*(a'*S*b)*(a'*S*a)+... 
13     4*holmquist2(S,Q1,Q2)*(a'*S*b)*(a'*S*a)^2+4*holmquist1(S,Q1)*(2*a'*S*Q2*S*b)+... 
14     8*holmquist1(S,Q1)*(2*a'*S*Q2*S*b)*(a'*S*a)+4*holmquist1(S,Q1)*(2*a'*S*Q2*S*b)*(a'*S*a)^2-... 
15     2*holmquist1(S,Q1)*(a'*S*b)*(2*a'*S*Q2*S*a)-2*holmquist1(S,Q1)*(a'*S*b)*(2*a'*S*Q2*S*a)*(a'*S*a)+... 
16     4*holmquist1(S,Q2)*(2*a'*S*Q1*S*b)+8*holmquist1(S,Q2)*(2*a'*S*Q1*S*b)*(a'*S*a)+... 
17     4*holmquist1(S,Q2)*(2*a'*S*Q1*S*b)*(a'*S*a)^2+4*1*(4*a'*(S*Q1*S*Q2*S+S*Q2*S*Q1*S)*b)+... 
18     8*1*(4*a'*(S*Q1*S*Q2*S+S*Q2*S*Q1*S)*b)*(a'*S*a)+4*1*(4*a'*(S*Q1*S*Q2*S+S*Q2*S*Q1*S)*b)*(a'*S*a)^2-... 
19     2*1*(2*a'*S*Q1*S*b)*(2*a'*S*Q2*S*a)-2*1*(2*a'*S*Q1*S*b)*(2*a'*S*Q2*S*a)*(a'*S*a)-... 
20     2*holmquist1(S,Q2)*(a'*S*b)*(2*a'*S*Q1*S*a)-2*holmquist1(S,Q2)*(a'*S*b)*(2*a'*S*Q1*S*a)*(a'*S*a)-... 
21     2*1*(2*a'*S*Q2*S*b)*(2*a'*S*Q1*S*a)-2*1*(2*a'*S*Q2*S*b)*(2*a'*S*Q1*S*a)*(a'*S*a)+... 
22     3*1*(a'*S*b)*(2*a'*S*Q1*S*a)*(2*a'*S*Q2*S*a)-2*1*(a'*S*b)*(4*a'*(S*Q1*S*Q2*S+S*Q2*S*Q1*S)*a)-... 
23     2*1*(a'*S*b)*(4*a'*(S*Q1*S*Q2*S+S*Q2*S*Q1*S)*a)*(a'*S*a))/(1+(a'*S*a))^(5/2); 
24 % Tested in test041104_1.m 
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Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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