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# spec2dplus

## PURPOSE

Calculates an upper bound of the damage intensity explicitly

## SYNOPSIS

d = spec2dplus(S,bet)

## DESCRIPTION

  SPEC2DPLUS Calculates an upper bound of the damage intensity explicitly

CALL:  d = spec2dplus(S,bet)

d = an upper bound of the damage intensity

S = a spectral density (structure array)
bet = the parameter beta

The upper bound of the damage intensity can be calculated explicitly and is
given by

d^+ = 2^{3*beta/2}*sqrt(lam2)*(lam0)^{(beta-1)/2}*gamma(1+beta/2)/(2*pi)

## CROSS-REFERENCE INFORMATION

This function calls:
 spec2mom Calculates spectral moments from spectrum gamma Gamma function.
This function is called by:
 itmkurs_lab3 Script to computer exercises 3

## SOURCE CODE

01 function d = spec2dplus(S,bet)
02 % SPEC2DPLUS Calculates an upper bound of the damage intensity explicitly
03 %
04 % CALL:  d = spec2dplus(S,bet)
05 %
06 %        d = an upper bound of the damage intensity
07 %
08 %        S = a spectral density (structure array)
09 %      bet = the parameter beta
10 %
11 % The upper bound of the damage intensity can be calculated explicitly and is
12 % given by
13 %
14 %       d^+ = 2^{3*beta/2}*sqrt(lam2)*(lam0)^{(beta-1)/2}*gamma(1+beta/2)/(2*pi)
15 %
16
17 % Example
18 %  S = oscspec; bet = 3:0.2:5;
19 %  dplus = spec2dplus(S,bet)
20
21 % Tested on: Matlab 5.3
22 % History:
23 % By jr 12.01.2000
24
25 lam = spec2mom(S); l0 = sqrt(lam(1));, l2 = sqrt(lam(2));
26
27 d = (2.^(bet/2)).*(l0.^(bet-1)).*gamma(bet/2+1)*l2/2/pi;
28

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

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