Geology Reference
In-Depth Information
CALL GAMI(GP,A(N),XARG)
C Find logarithm of current term.
TERMLN=W(IJ)+W(JJ)+W(KJ)
1 +(A(1)-1.D0)*XIJ(I,IJ)+(A(2)-1.D0)*XIJ(J,JJ)
2 +(A(3)-1.D0)*XIJ(K,KJ)+DLOG(GP)
3 +BMA(I)+BMA(J)+BMA(K)
C Find current term.
TERM=DEXP(TERMLN)
C Add current term to sum of previous terms.
CDF=CDF+TERM
15 CONTINUE
C Revert to Z from the logarithm of Z.
Z=DEXP(ZLOG)
C Divide by triple product of gamma functions in front of integrals.
CDF=CDF*DEXP(-ALOGAM(A(1))-ALOGAM(A(2))-ALOGAM(A(3)))
RETURN
END
We will later require the cumulative distribution function for the product of
four spectra found from four, five, seven and eight segments with 75% overlap.
From Table 2.1 these are found to have 5.8522880, 7.1850360, 9.8583334 and
11.1968478 degrees of freedom, respectively. The resulting cumulative distribu-
tion function is shown plotted in Figure 2.18.
Iteration on the cumulative distribution function F ( z ) allows the calculation of
confidence intervals for the product spectrum. For z
=
292.22, F ( z )
=
0.025, and for
z
0.975, giving a 95% confidence interval of 1.824 on logarithmic
plots of the product spectrum.
=
19,500, F ( z )
=
1.0
0.8
0.6
0.4
0.2
0.0 0
5
10
Product z (in units of 10 3 )
15
20
25
30
Figure 2.18 The cumulative distribution function F ( z ) for the product of four
spectral density estimates based on four, five, seven and eight segments with 75%
overlap, respectively. Iteration on this function gives a 95% confidence interval of
1.824 on logarithmic plots of the product spectrum.
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