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# holmquist3

## PURPOSE

Computes moments for higher order reliability methods.

## SYNOPSIS

E=holmquist3(S,Q1,Q2,Q3)

## DESCRIPTION

`  HOLMQUIST3 Computes moments for higher order reliability methods.`

## CROSS-REFERENCE INFORMATION

This function calls:
 trace Sum of diagonal elements.
This function is called by:
 holmberg3 Computes moments for higher order reliability methods. rqlf_asympt Gives first two terms in an asymptotic expansion of the

## SOURCE CODE

```01 function E=holmquist3(S,Q1,Q2,Q3)
02 % HOLMQUIST3 Computes moments for higher order reliability methods.
03
04 S=.5*(S+S');
05 Q1=.5*(Q1+Q1');
06 Q2=.5*(Q2+Q2');
07 Q3=.5*(Q3+Q3');
08 E1=0;
09 E1=8*trace(Q1*S*Q2*S*Q3*S);
10 E1=E1+2*trace(Q1*S*Q2*S)*trace(Q3*S)+2*trace(Q1*S*Q3*S)*trace(Q2*S)+ ...
11   2*trace(Q2*S*Q3*S)*trace(Q1*S);
12 E=E1+trace(Q1*S)*trace(Q2*S)*trace(Q3*S);
13```

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

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