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.

- trace

Sum of diagonal elements. |

- rqlf_asympt

Gives first two terms in an asymptotic expansion of the |

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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