C*********************************************************************** C THIS SUBROUTINE IS DESIGNED TO CALCULATE AN ESTIMATE OF DENSITY C AND ASSOCIATED STATISTICS. IT OUTPUTS POINT ESTIMATES OF F(0) C THE MODEL COEFFICIENTS AND DENSITY AND THEIR ASSOCIATED STATISTICS C C FUNCTIONS CALLED: TVALUE C*********************************************************************** SUBROUTINE PARAM (XN,DNSTY,VARD,LCL,UCL) C*********************************************************************** C DECLARATIONS C*********************************************************************** INCLUDE 'PARMTR.INC' CHARACTER*1 LABEL, HEAD, UL INTEGER CNT, STATUS REAL LCL, CORR(15) LOGICAL WARN C*********************************************************************** C COMMON STATEMENTS C*********************************************************************** COMMON /SOLN/ FZERO, VARF, FMAX, FMIN, FZ(100) COMMON /ALPHA/ LABEL(80), HEAD(30), UL(3,25) COMMON /PAGE/ IPAGE COMMON /IND/ IC, II, IREP, STATUS COMMON /NUM/ XL(MAXLIN), WIDTH, N, CNT, CONV(3), VARN, IDF, WARN DOUBLE PRECISION PAR, VCMAT, G, XLL COMMON /DPAR/ PAR(MAXPR2), VCMAT(MAXPAR,MAXPAR), G(MAXPAR), 1 XLL, NPAR, INDEX WRITE (6,70) WRITE (6,170) IF (NPAR.EQ.0) GO TO 20 C*********************************************************************** C FOR EACH PARAMETER IN THE MODEL WRITE OUT THE POINT ESTIMATE C STANDARD ERROR, COEFFICIENT OF VARIATION AND CONFIDENCE INTERVAL C*********************************************************************** DO 10 I=1,NPAR STERR=SNGL(DSQRT(MAX(0.D0,VCMAT(I,I)))) LCL=PAR(I)-1.96*STERR UCL=PAR(I)+1.96*STERR CV=0.0 IF (PAR(I).NE.0.0) CV=100.*STERR/PAR(I) CV=ABS(CV) WRITE (6,80) I,PAR(I),STERR,CV,LCL,UCL 10 CONTINUE C*********************************************************************** C WRITE OUT THE POINT ESTIMATE AND ASSOCIATED STATISTICS FOR F(0) C*********************************************************************** 20 STF=SQRT(MAX(0.E0,VARF)) LCL=FZERO-1.96*STF UCL=FZERO+1.96*STF CVF=STF/FZERO CV=CVF*100. CV=ABS(CV) WRITE (6,90) FZERO,STF,CV,LCL,UCL C*********************************************************************** C FOR THE DENSITY ESTIMATE WRITE OUT THE POINT ESTIMATE AND ASSOCIAT C STATISTICS C*********************************************************************** DNSTY=CONV(3)*XN*FZERO/(2.*XL(II)) CVN=VARN/(XN*XN) CVF=CVF**2 VARD=(CVN+CVF)*(DNSTY*DNSTY) VARD=SQRT(MAX(0.E0,VARD)) CVD=100.*VARD/DNSTY CVD=ABS(CVD) XMULT=1.96 IF (.NOT.WARN) XMULT=TVALUE(IDF) LCL=DNSTY-XMULT*VARD UCL=DNSTY+XMULT*VARD WRITE (6,100) DNSTY,VARD,CVD,LCL,UCL WRITE (6,170) WRITE (6,200) (UL(3,J),J=1,25) C*********************************************************************** C IF NPAR .GT.1 OUTPUT SAMPLING CORRELATION OF ESTIMATED PARAMETERS C THE DIMENSION OF COR SHOULD BE HALF OF THE ARRAY 'PAR'. C*********************************************************************** IF (NPAR.LE.1) GO TO 50 IF (NPAR.GT.11) CALL HEADER (1) WRITE (6,110) (J,J=1,NPAR) DO 40 I=1,NPAR DO 30 J=1,NPAR 30 CORR(J)=SNGL(VCMAT(I,J)/DSQRT(MAX(0.D0,VCMAT(I,I)*VCMAT(J,J)))) CORR(I)=1.0 40 WRITE (6,120) I,(CORR(J),J=1,NPAR) C*********************************************************************** C WRITE OUT THE VARIANCE COMPONENTS FOR DENSITY AND EXPLAIN THE C METHODS USED C*********************************************************************** 50 IF (NPAR.GT.6) CALL HEADER (1) WRITE (6,130) IF (WARN) WRITE (6,140) VARN IF (.NOT.WARN) WRITE (6,150) VARN,IDF,XMULT RATIO=100.*CVN/(CVN+CVF) WRITE (6,160) CVN,CVF,RATIO RETURN C*********************************************************************** C FORMAT STATEMENTS C*********************************************************************** C 60 FORMAT (2G15.7) 70 FORMAT (//14X,'Point',8X,'Standard',4X,'Percent Coef.',8X, 1 '95 Percent'/2X,'Parameter',3X,'Estimate',7X,'Error',6X, 2'of Variation',5X,'Confidence Interval') 80 FORMAT (4X,'A(',I2.2,')',3X,G12.4,1X,G12.4,3X, 1 F8.1,5X,G12.4,1X,G11.4) 90 FORMAT (4X,'F(0)',4X,G12.4,1X,G12.4,3X, 1 F8.1,5X,G12.4,1X,G11.4) 100 FORMAT (5X,'D',6X,G12.4,1X,G12.4,3X, 1 F8.1,5X,G12.4,1X,G11.4) 110 FORMAT ('0Sampling Correlation of Estimated Parameters'/ 1 8X,15(I2,6X)) 120 FORMAT (2X,I2,2X,15(F6.3,2X)) 130 FORMAT (/'0Notes on Variance Calculations and Confidence', 1' Intervals'/1X,55('-')) 140 FORMAT ('0All of the confidence intervals were constructed by', 1' assuming asymptotic'/ 2' normality and using the z-value of 1.96. It has been assumed', 3' that the number'/ 4' of observations N is a Poisson random variable. Thus the', 5' variance was esti-'/ 6' mated as Var(N) = N = ',F4.0,' This assumption is critical if', 7' the variance'/ 8' of N is the predominant portion of the variance of density.') 150 FORMAT ('0The confidence intervals for the coefficients A(i)', 1' and F(0) were constructed'/ 2' by assuming asymptotic normality and using the z-value 1.96. ', 3' The variance of'/ 4' N was estimated using replicate line lengths (Var(N) = ',G10.3, 5'). The'/ 6' confidence interval for density was constructed with a t', 7' distribution with'/ 8' the degrees of freedom equal to the number of line lengths - 1.' 9,' The t-value'/ A' with ',I3,' degrees of freedom is ',F7.3) 160 FORMAT (/6X,'Squared Coefficient of Variation for N = ',3X,G11.4/ 1 6X,'Squared Coefficient of Variation for F(0) = ',G11.4/ 2 6X,'Percent of the variation of density attributable to the'/ 3 6X,'sampling variance of N = ',F6.2) 170 FORMAT (2X,9('-'),2X,11('-'),2X,11('-'),2X,14('-'),2X,22('-')) 200 FORMAT ('0Density (D) units are numbers/',25A1) END