Discrim: a computer program using an interactive approach to dissect a mixture of normal or lognormal distributions

Conpvtrrr k Gmchu Vd. 6. pp. MI-396 @Pc.mmmRarLfd..1910. PriedinGnrlBli&

DISCRIM: A COMPUTER PROGRAM USING AN INTERACTIVE APPROACH TO DISSECT A MIXTURE OF NORMAL OR LOGNORMAL DISTRIBUTIONS NANCYJ. BRIDGES U.S. GeologicalSurvey, Denver, CO 80225U.S.A. and RICHARD B. MCCAMMON U.S. GeologicalSurvey, Reston.VA22Q92, U.S.A. (Recked 19July 1979) A~~~M-DWRI~~ is an interactive computer graphics program that dissects mixtures of normal or lognormal distributions. The program was written in an effort to obtain a more satisfactory solution 10 the dissection problem than that offered by a graphical or numerical approach alone. It combines graphic and analytic techniques using a Tektronix’ terminalin a tune-sharecomputingenviromncnt.The main programand subroutineswerewritten in the FORTRAN language. Key M&K

Computergraphics,Mixturesof distributions,Dissection. tNTRoDucnoN

graphics terminal. This decision was made because the

The dissection of a mixed frequency distribution long has been a problem for statisticians. Two basic approaches to solving this problem have existed-one numerical and the other graphical. Each of these approaches had its own disadvantages, which are summarized here. A more detailed explanation was given by McCammon(1976a,1976b). The numerical approaches met with dirticulty in that prior knowledge of the number of subpopulations or initialparameter estimates were required. These methods were complicated, and estimate selection became a critical factor. Methods to eliminate the problem of initial estimation met with severe problems also. Even when calculationswere done by a large computer, the methods did not work with complex data. Graphical approaches provided solutions in which the theoretical distributions were hard to compare. Goodnessqf-fit tests were difficult to evaluate because they required calculations.These problems introduced a large degree of uncertainty to the dissection. For this reason, the approach was less than ideal. The graphical and numerical approaches were combined in DISCRIM in an attempt to eliminate some of the major problems encountered in the individual approaches. DISCRIM first was written in I%9 by R. B. McCammon. It was rewritten later for use on INFONET with a Princeton 801 graphics terminal. In 1977,it was decided that the program should be rewritten for use on the Honeywell Multics System using a Tektronix 4014

Princeton 801 was not available widely in the U.S. Geological Survey and because part of the Survey had converted to the Honeywell MulticsSystem. The details of the method and applicationsof DISCRIMin geological problems have been described previously (McCammon, 1976a,1978; McCammonand others, 1979).The purpose of this paper is to provide a description of the dissection program, a current listing, and a worked example.

‘Any trade names in this report purposes only and do not. constitute Geological Survey.

are used for descriptive endorsement by the U.S.

DATA INPUC PoluuT

DISCRIMrequires the followinginformationabout the input data: (1) the total number of observations, (2) the observed proportion of observations, and (3) the corresponding endpoints of the interval in the original histograms. To provide this information, a program was written (Appendix)that accepts the original data to be dissected and generates an output filt that contains this information. Four option types are available for calculating proportions of observations and the associated endpoints. Option 1: the endpoints are calculated for a standard set of observed proportions. Option 2: for situations where the number of observations is large or where it is necessary to dissect populationshavinga high degreeof overlap,the use of an expandedset of proportions of observationsis recommended.Option 3: if the data are reported as grouped observations, the proportions of observationsare selected on the basis of grouped interval bouadPrie~.Option4:aptesekctednum&r(n)ofobsmed proportionsof observationsis entered. For example,if you wantedto use observed proportions(expressedas percentages) of 25,50,75,90,95, and 98, you would enter 6.

361

N. J. Bruffi~s

362

and R. B. MCCAMMON

location, the user types a character followed by a carriage return. The following is a brief explanation of the menu: a

The display generated on the screen of the terminal is designed to keep the user informed at all times of the status of a particular dissection (Fig. 1). The screen is divided into four sections. The upper left section is for messages. Messages are displayedto verify that an action has been taken, to note an error, or to prompt the user. The upper right section contains the name of the data set and a code indicatingwhether the data are assumed to be a mixture of normal or lognormal distributions. Both pieces of informationare suppliedby the user prior to dissection. The main leftmost part of the screen is reserved for plotting. It is used initially to display the cumulative frequency function for the original data. The endpoints of the intervals in the originalhistogramare plotted along the abscissaand the observed proportion of observations are plotted along the ordinate. The axes are left unmarke< as the user does not need to he concerned with the actual values. Later, computed curves and other options requested by the user are plotted on this part of the screen. The rightmost section of the screen contains the “menu.” The “menu” is a list of labels used to describe the options available.By selectingdifferent combinations of labels.the user defines a particularoption. To select a label, the user positions the crosshair cursor on the label name and signalsthat location to the computer. To signal

Components a

d b e c

Eachcomponentdistribution is identifiedby analphabetic character.Components maybc selectedin any orderbut mustbe arranged

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in alphabetic sequence for dissection. Parameters Parameters associated with each component. Estimates are entered as graphic input, either as a scalar or vector quantity.

intltction pt threshold

display erase delete

Display, erase, or delete the graphic estimates of parameters for specified components.

Brafit

Fit a theoretical curve based on the current set of graphic estimates.

besfitfn)

Fit a theoretical curve with the current graphic estimates by nonlinear least-squares analysis.

pdf cdf

Display the probability-density curves or cumulative frquency curves of the components.

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Figure 1. Initial display.

DISCRIM a computer statistics(d)

restart next end

program of normal or lognormal distributions

Clear the work space and provide a statistical summary of the dissection or a more detailed summary. Restart the dissection process, ask for next set of data, or end the procedure.

PROGRAMUSE

DISCRIMwas

designed

to: (1) provide a graphic display of a cumulative frequency curve on an arithmetic (or logarithmic) probability scale, (2) permit the graphic estimation of initial values of parameters, (3) allow the selective display, erasure, or deletion of graphic estimates, (4) permit the selection of an arbitrary number of normal (or lognormal) components, (5) generate a graphic display of the theoretical compound distribution for a specifkd number of components, given the values of the parameters of the distribution, (6) produce an algorithm

363

for a least-squares solution which determines an acceptable fit nearest to a set of initial estimates of the parameters, (7) produce a graphic display of component probability density and cumulative-frequency curves, (8) allow a graphic input of threshold values for determining the separability of inferred subpopulations, (9) produce a statistical summary which displays the final values of the parameters, the results of goodness-of-fit test, and the quantitative measures of the separability of the subpopulations, and (10) provide the ability to restart, to advance to the next set of data, or to end the program. As a result, the use of the program is highly flexible. The flowchart (Fig. 2) gives an overview of the basic logic used in dissecting any given curve. A detailed system description (Fig. 3) shows the actual interrelation of the FORTRAN subroutines. A more detailed explanation of the different routines is given later.

Figure 2. Flowchart of DISCRIM

program.

Figure 3. Detailed system description.

DISCRIM

a computer program of normal or lognormal distributions

INlTlALCUAPElCINpvIANDANDl’lON

The dissection process begins with the input of the graphic estimate of the slope of each subpopulation. The program assumes that the leftmost distribution will be labeled component a, the next b, and so on. The assumed input order is: the component label; the chosen parameter, in this example the slope: and the location of two representative points on the screen. As mentioned previously, the information to be input is indicated by the cursor. The user positions the crosshair cursor at the desired location, then signals this location by typing a character and then returning the carriage. The slope, represented by a line, then is displayed on the screen. If the user has assumed a single population, this completes the graphic input. For two or more populations, the slopes of each subpopulation must be estimated in the same manner. For two or more populations, estimates of inflection points are required. To input an inflection point, the user selects a component label, the inflection point parameter, and the screen location that he thinks indicates an inflection point on the curve. The leftmost inflection is associated with component a, the next with component b, and so forth. Once the graphic estimates of the slopes and inflection points have been made, the grafit subroutine is executed. This routine calculates a theoretical cumulative curve using the estimated slopes and inflection points to obtain initial estimates of the mean, standard deviation, and mixing fraction of each subpopulation. The curve is superposed on the data set and allows the user to judge the fit between the estimated curve and the data. The trial fit should be reasonably good because the nonlinear least-squares algorithms require reasonably accurate initial values. If the solution is judged to be unsatisfactory, the graphic estimates are adjusted and new fits are obtained until one fit is judged satisfactory. NoNLWEULEAsr-sQuAuESFlT Two nonlinear least-squares routines exist. The fist is the routine originally used by McCammon (1969). To use this routine, the option besfit is chosen. The second routine is one described by Clark (1977). To use this routine, the option (n) to the right of besfit is chosen. Either routine can be used to obtain a least-squares solution for any given data. Experience has shown that when the distributions have thin tails, McCammon’s routine generally gives the better solution. When the distributions have fatter tails, Clark’s routine is preferable. The curve resulting from either routine is superposed on the original data expressed as points on the screen. If the fit is adequate, the user can proceed by requesting the summary statistics; otherwise, the user trys again to make suitable initial graphics estimates. OTBER INFORMATION If the fit is judged to be adequate, the user can obtain other graphic information. The user can request a display of the probability-density curves by moving the cursor to the label pdf and signailing that location. Further, the user can request a display of the cumulative probability-

365

distribution curve by moving the cursor to the label cdf and signalling that location. If pdf is chosen first and cdf is chosen second, the curves are produced simultaneously on the screen. Another graphics option is available to assess the separability of the inferred sub populations. To do this, threshold values must be chosen. Threshold values are chosen in the same manner as inflection points. The cursor is positioned at the point of separability after indicating the components and threshold parameter on the menu. STATISTICAL

SUMMARY

Once dissection is performed, the summary statistics can be evaluated. When the statistics option on the menu is selected, the mode, median, mean, standard deviation, and mixing fraction for each subpopulation are displayed. The results of a chi-square goodness-of-fit test are also provided. These results consist of the &i-square value, the number of degrees of freedom, the p-value of the chi-square distribution, and the critical value at the 95 percent confidence level. Additional details of the besfit solution are available as an option. To exercise this option, the user moves the cursor to the label (d), which immediately follows the label statistics, then signals this location. The detailed summary provides information on the least-squares fit of the data. The initial and final estimates of the parameters, the mean, the standard deviation, and the mixing fraction of each subpopulation are displayed. Also, the initial and the final error sum-of-squares and the number of iterations for the iterative least-squares fit is provided. In addition, the observed and calculated values for each reported interval for the &i-square goodness-of-fit test are displayed. CiUPmfJCAPAmLJTW At different stages of a dissection, the user may wish to recall the graphics performed earlier, to erase parts of the displayed graphics, or to delete the graphics entirely. Three commands can be used in combination with the appropriate components and parameters to display, erase, or delete any graphics element. The order of input is: (1) enter command (display, erase, or delete), (2) enter corresponding component when applicable, then (3) enter corresponding parameter. For exampk, if the user wished to display the besfit curve along with the prob ability-density-function curves, the display label and the besfit label would be selected. WORKED_ The

following is a sample dissection applied to a set of geochemical data derived from altered rock &ples collected near Ely, Nevada. The data were studied in an effort to understand the zoning patterns associated with a porphyry-type copper deposit. Figure 4 is a plot of the data for the manganese content in gossan material. The x-axis represents the manganese content expressed as the logarithm of the concentration and the y-axis represents the cumulative frequency expressed on an arithmetic normal-probability scale. The first step in the dissection process involves esti-

N. J. BR~DGE.S and R. B. MCCAMMON

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Figure4. Initialplot of manganesecontent.

the standard deviation for a single population. The graphic estimate of the standard deviation obtained by choosing a particular slope is indicated by the line in FIgure 5 labeled a. On the basis of this estimate, a theoretical cumulativecurve of the distributionis shown beside the slope. The graphic estimate is used as an initial estimate, and a least-squaressolution obtained by usingthe besfit is shown in Figure 6. In this example, the change in slope is slight. To test the hypothesis that a single lognormal distribution provides an adequate fit to the data, a goodnessof-fit test is performed by using the statistics command. The results are given in Figure 7. For the 258 samples,a chi-squarevalue of 15.41based on 7 degrees of freedom is obtained. Because the critical value at the 95 percent confidence level is 14.07,the hypothesis is rejected. To see what caused the hypothesis to be rejected, a more detailed statistical summary shown in Figure 8 can be displayed. The more detailed summary shows that intervals three, five, and eight contribute most to the total &i-square statistic. With such information,the user can decide where best to position an assumed second population. From the original data, graphic estimates of the standard deviationsof two subpopulationsare obtained along with the selection of the inflection point which best separates the two populations. The theoretical curve produced by these estimates is shown in Figure 9. Note that subpopulation(I has been located to accomodatethe

mating

third interval which had a large chi-square contribution. The Clark algorithmfor nonlinearleast-squareswas used to obtain a best fit. The result is shown in Figure IO.The fit seems to be acceptable. A next step is to obtain the probabilitydensity-function curves shown in Figure 1I. In addition, a threshold value is selected and is represented by the location la&led A in Figure Il. The threshold a best separates the two populations. Figure 12 contains the statistical summary. Because the chi-square value is 8.25 with 4 degrees of freedom and the critical value is 9.49, the hypothesis that the observed distributionis a mixture of two longnormalpopulations is accepted. Moreover, the detailed statistical summary shown in Figure 13 reveals that the third, fifth, and eight intervals contribute considerably less than before. Althoughthe hypothesis of two subpopulationscan be accepted, further study of the data would be necessary to verify the geological meaningfulnessof such a conclusion. Such a study, however, is beyond the scope of this paper. LtMlTArtoNs The user should be aware of complications that can arise when running the program. For instance, grouped data are treated differently from ungrouped data. If the user treats the data as being ungroupedwhen, in fact, the data are grouped, an acceptable solution is unlikely to result.

DISCRIMa computerprogramof normalor lognormaldistributions

367

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Figure6. Least-squans solution for one-populationhypothesis.

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369

DISCRIM a computerprogramof normal or lognormaldistributions

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Figure 9. Theoretical curve for two-populationshypothesis.

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N. J. BRIDGES and R. 8. MCCAMMON

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for two-populationshypothesis.

Secondly, a problem arises when the user attempts to dissect a mixture when the data are grouped into a few intervals. It can happen, for instance, that the degrees of freedom will vanish. The calculated degrees of freedom is the number of intervals minus three times the number of subpopulationsminustwo.Thecurrentprogramprovides for up to 30 intervals in the originalhistogramand up to 6 subpopulationsinto which a mixed popu@ion can be dissected. Third, the-user must decide beforehand upon the type of subpopulations.At present, the program is written to handle data for mixtures of either normal or lognormal distributions.Thus, the user is required to specify which of these two mixtures are present. Fourth, the program uses two commercial software packages: IMSL (InternationalMathematicaland Statistical Libraries, Inc., 1976)and Plot 10 TCS (terminal control software) (Tektronix, Inc., 1977).If the user’s facility does not have these available, much rewritingof the program will be necessary.

DISCRIMis a graphic-analyticapproach to dissection that successfullycombinesinteractive computer graphics with an analytic method of solution to the problem of mixed-frequencydistributions.It offers a rapid, accurate,

and convenient method for handlii a di@cultproblem frequently encountered in data analysis. The Appendixcontains the FORTRANcoding for the program and subprogramsused.

Ckuk, I., 1977,ROKE, A computerprogmmfor nonlinearkastsquaresdecomposition of mixtures of distributions: Cornputers & Geos&nces, v. 3, no. 2, p. 245-256. International Mathemakl and Statktical Libraries, Inc., 1976, SWoutks m&h, n&hi, mdnttr, and a&is, in IMSL Library (3rded.): Houston,Texas, 3 vols, misc. pr&a&. McCammon,R. B., 1969,FORTRANIV programfor no&near estimation:Kansas Geol. Survey ComputerConk v. 34,20 p. McCammon,R. B., 1976a.An interactive computer Brapbics approach for dissectinga mixtureof normal(or loswrmal) dhhtions, in Pm. %dArm. Cord. on ComputerGraph&, Interactive Techniaues. and Imafre Processina. SIGGRAPH -’ 76: ComputerGra&c;. v. IO,p. i12. McCammon,R. B., 1978, An interactive computer graphics program for dissecting a mixture of normal (or lognormal) distriins, in Proc. 9th Interface Symp. on Computer Scienceand Statistics:Harvard Univ. and M.I.T.,p. 3614. McCammon.R. B., Bridges,N. J., M-y, J. H., Jr., and Gott, G. B.. 1979,E&mate of mixed ge&amkd popukticms in rocks at Ely, NevadazGeochemkal Exploration 1978.Proc. 7th Intern. Geochem.Exul. Assoc.ExD~.Gc~cbcmi~ts. . Symo.. p. 385-390.’ Tektronix, Inc., W77,4OlOAOl PLOT 10Terminal Control System: Tektronix,Inc., Beaverton,Oregon,71 p.

N. J. Brums

372

and R. B. MCCAMMON

APPENDIX1

Program listing

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DISCRIM a computer promm of normal or lognormal distributions 79

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26

ENTERED

NP=ITYP YRITE (TERWOUTARS) FORMAT(lX.“ENTER PERCENTAGES: ‘) READ(TERMIN,75)(PROB(I),~=l,NP) D9 27 I=l#NP PROR(I)=PROR(I)/lOtl. XD=N+l DO TO I=l#N Y(I)=I/XD Jfl K=l IF(PROS(J).GT.Y(K))GO TO 34 P(Jq=X(K) J+J*l GO TO 32 U=K+l DO 40 I+JeNP IF(PROB(I).GT.Y(K))GO TO 36 P~I~=X~K-l~+~X~K~-X~~-l~~~~PRO~~I~-Y~K-l~~/~Y~K~-Y~K-l~~ GO TO LO IF(K.EO.N)GO TO 38 U=K+l GO TO 35 P(I)=X(K) CONTlNUE

64

5n c c c 52 55

TO

OPTION

TO

LOOP

BACK

WRITE (TERMOIIT,55) FORMAT{1 X,” DO READ(TERMINt1003)4NS FORFlAT CALL CLSFLE(IlJNIN) CALL CLSFLE(IUOU) IF(ANS.EQ.YES)GO STOP EN0

TO

YOU

THE

WISH

TO

2

RI

DISCRIM

DATA

SET

NAME:

“1

“)

BEGINNING

TO

ENTER

MORE

DATA?“)

313

N. J. Bnmm and R. B. MCCAMMON

314

APPENDIXII 1

c

2 3 L 5 6 7 a 0 10 11 12 13 14 15 16 17 18 19 7C 21 22 23 2c 2s 26 27 28 29 3u 31 32 33 3c 3s 36 37 38 39 co 41 42 L3 44 LS Lb 47

c C c c c c c c c

49 so 51 s2 53 54 5s 56 57

c c c c c c c c c

59 60 61 62 63 64 65 66 67 68 b9 70 71 72 73

c C c c c c c c c c C c c C c

7c 7s

c c

DISCRIH.FORTRAN

THIS IS THE MAIN PROGRAM IT CURVt I’ISSECTING PPOCESS. THE TEKTRDNIX TERMINAL CONTROL

C&TA DATA c c c c c c c i c c c c c

ca c

58 c

AND

1CHA~/97r9A,99.100~101,102/,KCHAR/6~,66~6?,68,69,70/ JYL/3069~2331r2190~2046/rIPARIZOL6r1758r1611~1~70/ VARIABLE

DESCRIPTION

JYL--SCREEN LOCATIONS --USED IN DETERMINING UHICH COMPONENTS CHCSEN IPAR--SCREEN LOCATIONS --USED IN DETERMINING YHICH PARAMETERS CHOSEN LOL--SCREEN LOCATIONS--USED IN DETERMINING WHICH OPTION CHOSEN FIRST’!---USED TO STORE STATUS OF DRAYING OF AXES8 PANEL, MENU, AND KCMD--3SEO TO STORE STATUS OF OPTION CHOSEN OFF OF MENU KSEL--USED TO STORE STATUS OF COMPONENT ENTERED KCAL--USED TO STORE STATUS OF MESSAGES TO BE PRINTED OUT ISL--USED TO STORE STATUS OF SLOPES INPUTTED ISLD--USED 10 STORE STATUS OF SLOPES DRAUN IFL--USED TO STORE STATUS OF INFLECTION POINTS INPUTTED IFLD--USED TO STORE STATUS OF INFLECTION POINTS DRAUN ITH--JSED TO STORE STATUS OF THRESHOLD POINTS INPUTTED ITHD--USED TO STORE STATUS OF THRESHOLD POINTS DRAUN KPAR--USED TO STORE STATUS OF PARAMETER CMOSEN ILOG--USED TO STORE DATA TYPE--LOGNORMAL OR NORMAL IAXD--USED TO STORE STATUS OF AXES DRAUING IPTD--USED TO STORE STATUS OF POINTS DRAYINC N--NUMBER Of POINTS IN ORIGINAL DATA X--DATA INPUT PROB--CUMULATIVE PERCENTILES P--INTERVAL ENDPOINTS PRlS--STANDARD PERCENTILE TABLE PRZT--EXPANDED PERCENTILE TABLE PVB--USED TO STORE STATUS Of THREE OPTIONSCbISPLAYrERASEIDELETE) ICHAR--CHARACTERS USED FOR LAOELLING SLOPES AND INFLECTION POINTS KCHAR--CHARACTERS USED FOR LANELLING THRESHOLDS NP--NUWBER OF INTERVALS IPXIIPY--SCALED AND TRANSFORMED POINTS FOR PLOT CRV--USED TO STORE STATUS OF CURVE CREATION CRVD--USED TO STORE STATUS OF CURVE ORAYING IFCR--USED TO STORE STATUS OF PDF CREATION IFCRD--USED TO STORE STATUS OF PDF DRAYING ISSCl)--INITIAL ERROR SUM OF SPUARES ISSC2)--FINAL ERROR SUM OF SQUARES IFCMR--USED TO STORE STATUS OF CDF CREATION IFCMRD--USED TO STORE STATUS OF CDF DRAUING

76 77

c 78 c

USED AS THE DRIVER IN THE USES THE IMSL SUAROUTINFS SOFTWARE.

ERR=.FALSi. SET

UP

THE

SIZE

OF

THE

PLOTTING

AREA

ON

THE

SCREEN

POINTS

375

DISCRIMa computerprogramof normalor lognormaldistributions 79 80

c YBRrYBZ-Y61 XBR=XB2-XBl URITE(TERbO’JT,l) READ(TERCIN,ll)ITERP CALL INITT(ITERM) fORMAT(lXr”ENTER TERr;INAL FORFAT (V) CALL TERM<2140961 JRITE(TER~OllT~200l) FORMAT (1 X,“ENTER DATASET kEAD(TERMIN,1033)FILENA~E FDRMAT (A81 IF(FILENAIE.EP.PllIT)STOP CALL OPNFLE (IUNITrFILENANE,“SI READ(IUNITrlOOl)N,NDATIorl=)rNDAT) FORMAT(V)

81 82 83 84 a5 E6 67 88 t; 91 92 93 94 95 96 97 PA 99 lOti 101 102 103 104 105 106 107 108 109 110 111 112 113 114 11s 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 13s 136 137 13b 139 14G 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157

1 11 2 2oci1 1033

1001 c c c c c c 2002

CONVERT

PROM

6

9 587 012 585 5867 5866 1003

CALL

TO

I’ISL

CALL

“)

TO

PERCENTILE NDAT IS IS NDAT VlJST

OR BE

27

SETTING

ROUTINE--

DECIMAL

587

~=LOCNORMALI

COMPUTES

PROBABILITY

INVERSE

NORNAL

SCALE

MDbRIS(PROB(1 )rYl NDNRIS(PROB(NP)ry2eIDUfl) UP

SCALING

FACTORS

YDIF=YZ-Yl YSC’YBRlYDIF DO 10 I=lrNP CALL YDNRIS(PROB(I),TINORM~IDUM) IPY(I)=Y~.~+YSC*(TINORM-yl) TRANSFORM

O=NORCIAL”)

MDN~IS(PROB(I)rIYT(I)~IDU~)

TRANSFORR CALL CALL

10 c c c

PERCENT

PROB(K)=XCI)/l00. P(K)=X(I+l) GO TO 585 NP=NDAT DO 6 I=lrNP +(1)=x(I) IF(NP.EP.27)tO TO DO 9 I=leNP PROB(I)=PRlS(I) GO TO 585 DO 812 I’lrNP PROBCI)=PR27(1) CONTINUE YRITE(TERROUTISW~) FORMAT(lX,“ENTER* READCTERMINI~~~~)ILOG FORMAT EYC0DE(DATN~1003)FILENAME FORMAT (A81 IF(PROB(l).EP.O)PROB(l~=~./(N*l) DO 8 I=lrNP IXT(I)=P(I) IF(ILOG.EQ.l)IXT(I)‘ALOG~P(I))

4

c c c

“)

ITYP=HOD(~QDAT,~)*~ G3 TO (3rb)ITYP NP=NDAT/Z K=O DO S I=lrNDATat U=K*l

5

c c C e C c c

NAME:

30r120r960rETC.“)

CHECK TO SEE IF USING THE STANDARD OR EXPANDED TARLES OR ENTERING PERCEkTILES DIRECTLY----IF THEN IT REFERS TO PERCENTILE TABLES, OTHERUISE EVE& AND PERCENTILES ARE ENTERED DIRECTLY.

3

C c c

SPEED.

PERCENTILES

l IDUN)

FOR

THE

Y-AXIS.

PROBABILITY

DISTRIBUTION

376

N. J. BRIDGESand R. B. MCCAMMON

158 159 160 161 lb2 163 164 lb5 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 la3 184 la5 la6 187 168 18.9 190 191 192 193 19L 195 196 107

c C c

SETTING

20 C C C ae

RESTART

12 120 121 c C

SCALING

FACTORS

FOR

THE

X-AXIS.

iDIF=X2-Xl xSC'XYR/XDIF DO 20 I=lrNP IPX(I)=XBl+XSc*(IXT(x~-xl) OPTION

CALL RESET CALL ERASE CALL PANEL CALL MENU CALL AXES STX=.FALSi. IAXD=.TRUE. CALL POIN~S(IPXIIPY~NP) IPTD=.TRUE. FIRSTI=.TRUE. CRV=.FALSZ. CRVD=.FALSE. KCTIl KCAL'l DO 12 I=lr6 IFLD(I)*.FALSE. ISLD(I)'.FALSE. IFCR(I)'.FALSE. IFCRD(I)=.FALSE. IFC?lR(I)=.FALSE. IFCMRD(I)=.FALSE. IlH(I)=.FALSE. IlHD(I)=.FALSE. ISL(I)=.FALSE. IFL(I)=.FALSE. CALL '~ESSAGE~KCALIPVB) FIRSTY=.FALSE. FIRST

c 1vm 304

199 200 201 202 203 204 705 226 7U 7 2UR 2 (J 9 210 211 212 213 214 215 716 217 218 219 220 221 222 223 22L 225 226 227 228 229 230 231 232 233 23C 235 236

UP

CURSOR

INPUT

CALL SCURSR(ISCRIJX~~JYI) IF(JXl.NE.O.AND.JYl.NE.O)GO TO 305 KCAL*7 CALL ERASE CALL RESTORE CALL YESSAGE(KCALIPVB) GO TO 3OC DO 317 I=lrlZ IF((JY~.GT.LF!L(I)).OI?.~JY~.LT.LRL~I+~~~)GO

305

TO

317

KC’lC’I

342 J=1r3 IF(PVB(J))
3L2 317

c c C 318

COMPONENT

TO

SEE

UHICH

COMPONENT

03 307 I=lr3 IF((JYl.GT.JYL(I)).OR.~JY1.LT.JYL~I+1)))GO KSEL=I GO TO 309 C3KTINUE

307 c

c

IkPJT--CHECK

CHECK

FOR

GRAFIT

WAS

TO

Et+TERED

307

OPTION

C IF((JYl.LE.LPL(6)).AND.(JYl.GE.LbL(7)))CO C C C 309 705

CHECK

FOR

BESFIT

145

TO

Cl2

OFTIOh

IF((JYl.LE.LBL(7)).ARD.tJYl.GE.LBL(A)))CO JXl.GT.27CO)KSELfKSEL*3 CALL SCURSR(ISCRIJXZIJYZ) IF(JX2.Nt.O.AND.JY2.t4E.0~GO TO 706 KCAL.7 CALL ERASE CALL RESTORE CALL MESSAGE(KCALePV8) ti0 TO 705 IF(

TO

DISCRIM 237 23P. 239 2&O 241 242 243 2&L 245 246 247 2L8 249 250 251 252 253 254 25 5 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 2so 2bl 282 283 284 285 286 287 28P 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315

706 C C c

311 c c c

DO CHECK

SEE

UHICH

PARAMETER

SELECTED

IFCCJY2.GT.IPARCI)).OR.CJY2.Ll.IPARCI*l)~~GO hPAR=I GO TO Cl30,140,114)KPAP CONTINUF CHECK

FOR

INCDRRECT

TO

PROBABILITY

C C C 312 c c C A12

414 C C c

DENSITY

TO

FUNCTION

319

ROUTINE

CALL PDFCKPDF) CALL RESTORE GO TO 121 KCALf3 CALt RESTORE GO TO 121

319

c C C 313

311

CHOICE

IFCCJY2.GT.LBLC8)).0R.(JYZ.LT.LBL(9)))GO KPDF=KSEL IFCJXZ.GT.2?00)KPDF=KPDF+? C c C

3n

I=103

311 TO

a computer program of normal or lognormal distributions

ERROR

MESSAGE

FOR

INCORRECT

SELECTION

OF

PARAUETERS

KCAL=4 CALL RESTORE GO TO 121 DISPLAY

OPTION--SET

STATUS

TO

TRUE

THEN

RETURN

FOR

MORE

INFO

PVBCl)=.TRUE. GO TO 304 BESFIT

OPTION--NONLINtAR

LEAST

SQUARES

ROUTINES

IFCJXl.GE.2850)CAtL BESFITZ IFCJXl .LT.ZISO)CALL BESFIT IFCKCAL.EP.5)CAtL RESTORE IFCKCAL.ER.S)GO TO 121 DO 41C I=183 IFCPVBCI))CALL RESTORE IFCPVBCI))GO TO 121 CONTINUE ENTRY

INTO

GRAFIT

ROUTINE

CALL GRABSF CALt RESTORE GO TO 121 C C C 712

STATISTICS

IFCNCPT.EP.O)GO KSEL=0 IFCJXl .GE,2850)KSEt=1 CALL STATCKSEL) STX=.TRUE. KCAL=3 GO TO 716 KCAL=5 CALL RESTORE GO TO 121

715 716 c C c 857 c c C 858 c C c 912

OPTION--BOTH

ERASE

OPTION--SET

TYPES TO

715

STATUS

TO

TRUE

THEN

RETURN

FOR

MORE

INFO

PVBCZ)=.TRUE. GO TO 304 DELETE

OPTION--SET

STATUS

TO

TRUE

THEN

RETURN

FOR

FlORE

INFO

PVBC3)=.TRUE. GO TO 304 NEU

OPTION--DELETE CALL CALL

ERAS: CLSFLECIUNIT)

ALL

REFERENCES

TO

OLD

DATASET

AND

REENNTER

N. J. BIUEGES andR. B. MCCMNON

378 FILENAME'BLANK GO TO 2

316 317

318

c

319 320 321 322 323 324 325 326 327 328 329 3'0 331 332 333 334 335 336 337 338 339 34c 341 312 3L3 341, 345 346 347 348 349 350 351 352 353 35L 355 356 357 356 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 3&O 3P.l CP2 3P3 3ec 3c5 IPt 31,7 359 3P.9 3Vcl 391 3v2 393 594

c C 130

SLOPE

INPlJT

250 C c c 252 299 c c C

TkO

DATA

POINTS

FOR

SLOPE

C4LL SCURSR(ISCRIJX~(KSEL),JY~(KSEL)) IF(JX3(KSiL).NE.O.AND.JY3(KSEL).NE.O)CO KCAl_=7 CALL ERASE C4LL RESTORE CALL YESS~GE(KCALIPVB) LO TO 736 CALL SC'JRSR(ISCRIJX~(KSEL)~J~~(KSEL)) IF(JX4(KSIL).NE.0.AND.JrC(KSEL).NE.O)CO KCAL'7 C4LL ERAS: CALL RESTORE CALL !lFSS4GE(KCAL,PVB) GO TO 237

237

c c c 2377 2&O

SELECTED

J'1 DO 135 I=163 IF(PVB(I))J=I*1 CONTINUE CO TO (236r299r23br239)J

135 c c C 236

PARAMETER

DRAUS

282

c c C 239

224 2Sb

c c c 160

2bC

237

TO

2377

SLOPE ISL(KSEL)=.TRUE. CALL flOVA6S(JX3(KSEL)rJV3(KSEL)) CALL DRUA~SCJX~(KStL)rJYC(KSEL)) CALL AfdCHO(ICHAR(kSEL)) ISLD(KSFL)'.TRUE. D3 252 I=lr3 RESET

DISPLAYr

ERASE,

PJB(I)=.FALSE. GO TO 304 IF(ISL(KS:L))GO OPTIOY

TO

TO

DISPLAY

AND

DELETE

240

SLOPE

KCAL=5 CALL RESTORE G3 TO 121 C C C 238

TO

OPTION

TO

ERASE

SLOPE

IF(ISL(KSEL))GO UCAL=3 CALL RESTORE GO TO 121 ISLD(KSEL)'.FALSE. CALL RESTORE GO TO 304 OPTION

TO

DELETE

TO

SLOPE

IF(ISL(KSEL))GO TO KCAL=5 CALL RESTORE GO TO 121 IF(.NOT.ISLD(KSEL))GO ISCD(KSEL)=.FALSE. ISL(KSEL)=.FALSE. &CAL=6 C4LL RESTORE GO TO 121 INFLECTIOV

PCINT

282

284

PAPAKETER

J=l DO 260 I=lr3 IF(Pva(I))J=I*l CJ:TINUE C3 TO (3~br138e33br333)J

TO

296

SELECTED

STATUS

CHECKS

DISCRIM 39s ‘96 397 39.5 399

c c c 336

coo 401 4u2

4G3 434 405 406 4117 4LR 409 410 411 412 413 414 415 416 417 41b 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 L42 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473

337 440 c c c

13.5 c c c

338 c c C

380

382

c c c 339

3a4 386

c c c 144

560

INPUT

a computer program of normal or lognormal distributions

INFLECTION

POINT

CALL SCUHSRCISCR,JJXCKSEL)rJJI(KSEL)) IfCJJXCKS:L).hE.O.AUD.JJYCKSEL).NE.0)GO LCAL'7 CALL tRASE CALL RESTORE CALL MESS~GECKCALIPVR) 60 TO 330 IFLCKSEL)=.TRUE. CALL YOVABSCJJXCKStL)rJJYCKSEL)) INFLECTIOV

POINT

TO

337

DRAWN

CALL ANCHOCICHARCLSEL)) IFLDCKSEL)=.lRUE. GO TO 250 IFCIFLCKSEL))GO TO 440 OFTION

TO

DISPLAY

KCAL=5 CALL RESTORE GO TO 121 IFCIFLCKSEL))GC' OPTION

TO

ERASE

TO

TO

DELETE

TO

THRESHOLD

POINT

382

INFLECTION

IFCIFLCrSEL))GO 10 KCAL'5 CALL RESTORE GO TO 121 IFC.NOT.IFLDCKSEL))GO IFLDCKSEL)=.FALSE. IFLCKSEL)=.FALSE. KCAL'6 CALL RESTORE GO TO 121 ROUTINE

POINl

3RO

INFLECTION

KCAL=S CALL RESTORE GO TO 121 1FCIFLDCKSEL))GO KCAL=3 CALL RESTORE GO TO 121 IFLDCKSEL)=.FALSE. CALL RESTORE to TO 304 OPTION

INFLECTION

POINT

362

PARAHETER

TO

386

SELECTED

J=l DO 560 I=183 IFCPVBCI))J=I+l CONTINUE GO TO (5368537#538#539)J

c C

INPUT

THRESHOLD

POINT

c 536

5366

CALL SCURSRCISCR,JJX2CKSEL)rJJIZ(KSEL)) IFCJJXZCKSEL).NE.O.AND.JJY2CKSEL).NE.O)CO KCAL'f CALL ERASE CALL RESTORE CALL MESSAGECKCALIPVR) GO TO 536 ITHCKSEL)=.TRUE.

c C C 540

c

DISPLAY

THRESHOLD

POINl

CA-L 'lOVABSCJJX2CKSEL)rJJIZ(KSEL)) CALL ANCWOCKCHARCKSEL)) ITHDCKSEL)'.TRUE. GO TO 250

TO

5366

379

380

N. J. BIUDGES and R. B.

47b b75

c c

676 477

537

482 463 Lab Aa5 486 ca7 Aaa ba9 APO 491 492 493 494 495 496 497 498 499 500 501 502 so3 504 SO5 506 507 50s 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 52a 529 530 531

c 53b

478 479 LAO c 401 c

100 105 c C c 110

C C C 604

5 6

c C

c c 4 c

:: 13 14 15 lb 17 18

TO

OPTION

THRESHOLD

ERASE

TU

TO

TO

GRAFIT

POIhl 580

TO

DELETE

582

THRESHOLD TO

POINT

540

THRESHOLD

IFCITHCKSEL))GO KCAL=5 CALL RESTORE GO TO 121 IF~.NOT.IIHD~KSEL~~GO ITHDCKSEL)=.FACSE. ITHCKSEL)*.FALSE. KCAL=b CALL RESTORE GO TO 121

586

c c c 145

DISPLAY

IFCITHCKS:L))GO KCAL’C, CALL RESTORE GO TO 121 1FCITWDCKSEL))GO KCALM3 CALL RESTORE GO TO 121 ITHOCKSEL)=.FALSh. CALL RESTORE GO TO 304

584

c

10

OPTION

582

c c C 539

TO

IFCITHCKSEL))GO KCAL’5 CALL RESTORE GO TO 121

5ao

1 2 3

x 0

OPTION

hkch&lON

POINT

584

10

586

OPTION CALL GRAFIT CALL RESTORE GO TO 121 NRITECfERHOltT,105) F3RMAT Cl XI” ERROR

PROBABILITY

DENSITY

IN

TINORH”)

FUNCTION

AN0

CUMULATIVE

FREPUENCY

CURVE

KPD FM0 IFCJXl .GT.270O)KPDF=? IFCJX2.GT.2700)KPOF=f CALL PDF CKPDF) CALL RESTORE GO 10 121 END

OPTION CALL CALL CALL STOP END

RESET CLSFLECIUNIT) FINITTCO~O)

THE PANEL AREA FROM

SURROUTINE THE MESSAGE

SUBROUTINE PANEL CALL NOVABSCOI~) CALL bRuABS(3ObVrO) CALL DRYA8SC3obVr3069) CALL DRYABSCoe3069) CALL DRYABSC~I~) CALL MOVABSCoe2700) CALL DRYABS(3ObV~2700) CALL MOvABSC24OOr3069) CALL DRUAtJSC2Aoo~o) RETURN EYD

DRAUS AND

LINES TO SEPARATE MENU AREAS.

THE

GRAPHICS

DISCRIM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3c 31

c c c c c c

THIS SUBROUTINE PRINTS THAT THE USER CHOOSES THESE ARE PRINTED OUT

OUT THE NAMES OF ALL THE OPTIONS FROM PLUS THE FILENAME AND DATA TYPE. ON THE RIGHT SIDE OF THE SCREEN.

~llrIPT~4/8O,68r?0r32,32,32,32~6?,68~?~~~IPTl5f83~8~~6S~8~t?3~83~0~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IPT18/69r?8,681r1PT19176r78/rlPT20~?8~ CALL CHRSIZO) CALL MOVABSC~SOOI~~~~) CALL AOUTSTC6rOATN) CALL MOVABSC2500,2?04) IFCILOC.EQ.l)CALL ANSTRCZIIPTT~) IFCILOG.EQ.O)CALL ANSTR(lrIPT20) CALL YOVABSC2500r2568) CALL ANSTRClO#IPTl) CALL MOVA~SC25?2,2424) CALL ANSTRC~IIPTZ) CALL MOVAbSC2572t2280) CALL ANSTRC6rIPT3) CALL MOvAbSC25?2,2136) CALL A?JSTRC6rIPT4) CALL MOVABSC2500r1992) CALL ANSTRC~OIIPTS) CALL MOVAbSC25?281F,&8) CALL ANSTRCSrIPT6) CALL YOVAbSC25?2,1?01) CALL ANSTEC13rIPT7) CALL NOVABSC2572~1560) CALL ANSTRCP,IPTI) CALL MOVABSCZS00,1416) CALL ANSTRC?,IPTP) CALL MOVABSC2SOOrl252)~ CALL ANSTRCSrIPTlO) CALL NOVABSC2SOOr1128) CALL ANSTRC6rIPTll) CALL MOVAbSC2500r984) CALL ANSTRC6,IPTlZ) CALL MOVABSC2500,840) CALL ANSTRC13rIPT13) CALL NOVABSC2500r696) CALL ANSTRClO,IPTlL) CALL MOVA8SC2500,552) CALL ANSTRC13rIPTlS) CALL MOVABSC25CJOrL08) CALL ANSTRC?,IFT16) CALL NOVAbSC2500r264) CALL ANSTRC4rIFT17) CALL MOVAbSC2500~120) CALL ANSTRC3rIPT18) RETURN END

:: 34 35 36 37 38 39 40 41 42 43 44 45 16 17 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

1c 2 3 4 5 6 7 8 9 10 11

a computer program of normal or lognormal distributions

c c c c

DRAYS

DATA

AXES

011 THE

SUbROUTINE AXES CALL MOVAbSC2250,3CIC) CALL DRUAHSC~OCI~~OCJ) CALL DRUAbSC3O!lr21UU) RETURN END

SCREEN

381

N. J. BRICGESand R. B. MCCMN 1c 2 3 L 5 b 7 A 9 10 11 12 13 1L

c c c c c c

1c

1c 2 3 4 5 6 7 8 9 10 11 12 13 11 15 lb 17 18 19 20 21 22 23 21 25 26 27 28 29 30 31 32 33 34 3s 36

1c 2 3 cc 5 6 7 8 9 10 11 12 13 1C 1s lb 17 1R 19 20 21 22 ?3 2L 25

THIS ROUTINE PLOTS OUT THE DATA POINTS RtPRESENlS TIIE INTERVCLS AND THE Y-AXIS CuIV,Ul_ATIVE PERCENTILES.

c c c c c

10 2i-J 30 cc 50 60 65 70 80

c c c c c C

WHERE THE REPRESENTS

X-AXIS THE

SuBROUTINE POINTSCIPX,IPYrNP) DIXENSION IPX(301rIPYC30) DO 10 I=lrNP CALL PNTAdS(IPXCI)sIPY(I)) C3NTINUE RETURN tND

ROUTINE WHICH PRINTS OUT ANY TOP LEFT CORNER OF THE PANEL.

FESSAGES

AT

THE

CALL *OVABS(lOFe2784) GO TO C10,20,30rlO.50rb0rbS)YCAL CALL ANSTR(35rIMSl) GO TO 70 ,CALL ANSTRClY,IMS2) GO TO 70 CALL ANSTRC?rIMS3) GO TO 70 CALL ANSTRCZlrIflS4) GO TO 70 CALL ANSTR(Z~IIMSS) GO TO 70 CALL ANSTRClSrI!'lSb) GO TO 70 CALL ANSTRCPIIKS~) DO 80 I=lr3 PVB(I)=.FALSE. RETURN END

THIS ROUTINE CHECKS THE STATUS OF ALL POSSIBLE OPTIONS FOR OUTPUT ONTO THE SCREEN. IT WAS WRITTEN TO RESTORE OUTPUT AFTER A CHANGE IN THE MESSAGE TO BE DISPLAYEDa A DELETION OR ERASURE OF SOME PORTION OF THE GRAPH.

DISCRIM 26 27 2h 29 30 31 32 33 3-i 35 36 37 38 39 40 41 L2 43 CL 45 Lb L7 4F L9 50 51 52 53 54 55 56

lfi

20

30

LO 50

60

70 Bf!

10 11 12 13 14 15 lb

17 1E 19 cc' !, 21 22 23 24 25 26 27 1:I

;s ,'c 3c 31 32 33 34 35 36 37 3E 39 LO 41 &2 L3 LL 25 46

15

21

c c c 2L 2s

a computer program of normal or lognormal distributions

CALL MFNU IF(IPTD)CALL POINTS(IPXIIPYINP) IFCIAXD)CALL AXES CALL -+ESSAGECKCALtPVR) DO 60 K=lrb IF(.NOT.ISLDCK))CO TO II-I CALL NOVARS(JX3CK)rJY3(K)) GILL DRWAdS(JX4CK)rJY4CK)) CALL ANChOCICHARCK)) IFC.NOT.IFLD(K))GO TO 20 CALL MOVAeSCJJXCK)rJJYCK)) CALL ANCHOCICHARCk)) IFC.NOT.ITHDCK))GO TO 30 CALL MOVAtiSCJJXZ(K)rJJYZ(K)) CALL ANCHOCKCHARCK)) IFC.NOT.IFCRDCK))GO TO 50 CALL ~OVABSCIXFCRCK,l)rIYFCR(K~l~) DO 40 I=Z#NTOT CALL DRUABSCIXFCRCKrI)rIYFCR~K~I~) IFC.NOT.IFCHRD(K))GO TO 60 CALL MOVABS(IXFCMRCK,l)rIYFCMR~K~?)) GILL DRU66SCIXFCMR(K,2)rIYFCMttCK~2)) C3NTINUE IFC.NOT.CHUD)GC TO 80 CALL MOVABSCIX(l)~IYCl)) DO 70 I=ZtNPLT CALL DRWABSCIXCI)rIYCI)) CONTINUE CONTINUE RETURN EVD

PR00C30~rlPTDISCAL/XBl,X~2,Y~l,Y~2,YER~X~R,YSC~XSC~ YlrY2,XlrX2~YDIF,XDIF INTEGER TEQWOUT LOGICAL IFL,ISL,IFLD,ISLD,CRV,CRVD,IFCR,IFCRD~IPTD~PVR~FIRST~~ ITH,IT~'P,STX,IAXDIIFC~~~,IFCMRDIERR DhTA TCR'lGLIT/6/ i kQR=.FALSE. IFCNCPT.&ti.J)GP TO h KCAL'S kETURN IFC.NOT.STx)GC TO 18 CALL RESET C9LL ERAS; CALL PANkL C4LL MENU STX=.FALSI. FIRSTM=.THUE. CO:JTINUE IFCKSEL.Ed.3)GO TO lo lFCKSFL.ka.7)GO TG 30 J=l 00 15 I=lr3 lF(PVY(I))J'I*' C3NTINUE IFCKSEL.tiE.7)GO TO 31 GO TO ClO,2lr27,22)J 1FCIFCRCKSEL))CO TO 26 kCAL=5 RETURN PLOTS

PDF

CURVE

CALL ROVA~SCIXFCRCKSEL,l)rIrFCRCKSEL,l)) DO 25 1+2,'1TOT CALL DQW4BSCIXFCR(kSEL,I)rIrFCRCKSELII)) IFCRDCKSEL)=.TRUE. GO TO 180

383

N. J. Brumies and R. B. MCCAMMC~ 47 LP 49 50 51 52 53 54 55 56 57 59 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 7s 76 77 78 79 80 a1 a2 a3 a4 as 86 a7 aB 09 9c 91 92 93 94 95 96 97 98 99 100 1Gl lC2 103 104 lil5 106 11)? 108 109 110 111 112 113 114 115 ?lb 117 118 119 120 121 122

c c

ERASES

C 26

35 33

C C C 36

ERASES

CDF

21

CJRvE

TO

35

TO

36

CURVE

IFCHRD(KSLL-?)=.FALSE. GO TO 180 FWAX=PF(l)/STD(l) DO 150 J=lrNCPT FTrP=PF(J)/STD(J) IF~FTNP.GT.F~AX~C~AX=FTMP CONTINUE YSCF=YBR/FIAX IF(.NOT.(CRV.AND.CRVD))GO CRVD=.FALSE. IF(NCPT.EQ.l)GO TO 161 NCPTl=NCPT-1 DO 159 I=lrNCPTl IF(.NOf.IFLD(I))GO TO IFLD(I)=.FALSE. IF(.NOT.ISLD(I))GO TO ISLD(I)+.FALSE. CDNTINUE IF(.NOT.ISLD(NCPf))GO ISLD(NCPTl=.FALSE. IF(KSEL.GE.?)GO TO 74 DO 72 I=116 IF(.NOT.IFCR(I))GO TO IFCR(I)*.FALSE. CONTINUE

10

1so 30 157

163 159 161 164

72 C c c

PDF

TO

IFCRD(KSEL)=.FALSE. GO TO lb(J GO TO (30r32133r33)J IF(IFCHR(KSEL-?))GO KCAL=5 RETURN IFCMRD(KSiL-?)'.TRUE. GO TO 180 IF(IFCMR(KSEL-?))GO YCAL=5 RETURN

31 32

CALCULATES

TO

157

163 159

TO

164

72

PDF

DO 160 J=lrNCPT DO 170 I'l#NTOT lXFCR(J,I)'(XBltXSCr(X(I)-X1)) CHECK=(-((X(I)-XMN(J))/STD(J))~~2/2.) IF(CHECK.LE. -8a.O)CHECK=-85. IF(PF(J).LT.o.)PF(J)=O. IF(PF(J).GT.l.)PF(J)=l. IYFCR(J,I)'(YBltYSCF*PF~J~+EXP(tHECK)ISTD~J~~ CONTINUE IFCR(J)=.TRUE. IFCRD(J)=.TRUE. CDNTINUE GO TO 85 DO 75 1x186 IF(.NOT.IFCMR(I))GO TO 75 IFCFR(I)=.FALSE. CONTINUE DO 178 J=lrNCPT XC=XBl*XSC'(XCN(J)-Xl)

170

160 74

75

c

c

IMSL

ROUTINE

TO

COPPUTE

THE

C CALL PDNRIS(.S,TINORMrIDUM) YC=YtIl+YSC+(TINORM-Yl) XD=XBltXSi*(XilN(J)tSTb(J)-X1) CALL UDNRIS(.8413rTINORMrIDUM) YD=Y01tYSC*(TINORM-Ii) XA=(YD-YC)/(XD-XC) XB=((YDtYC)-XA+(XDtXC))IZ.

123 124 12s

IF(IFCR(KSEL))60 KCAL'5 PETURN

27

c c

CALCULATED

CDF

CURVE

INVERSE

NORMAL

PROB.

DEN.

FUNCTION

DISCRIM 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141

1 2 3 4 s 6 7 a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 21 25 26 27 ?S 29 3c 31 32 33 34 35 36 37 38 39 Ire 41 42 43 L4 &5 C6 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61

a computer program of normal or lognormal distributions

385

c IXFCMR(Jcl)*300

178 a5 180

IF(IYFCMR(J,l).EG.30O)IXFCMR~J,l)=~~3OO.-XB~/XA~ IXFCNR(Je2)'2280 IYFCFdR(J,Z)=(XA*2280.+XB) IF(IYFCMR(J,2).GT.24OCl~IYFCMR~J~2~=24BU IF(IYFCMR(J,2).EQ.2400)1XFCMR(J,2~=((2~~O.-XB~/XA~ IFCFtR(J)*.TRUE. IFCMRD(J)=.TRUE. CDNTINUE CONTINUE KCAL=3 RETURN END

SUBROUTINE c c c c

PROGRAM CLARK'S

BESFITZ

10 ESTIMATE METHOD

PARAMETERS

BY

NONLINEAR

LEAST

SQUARES

LOGICAL ISFL~ISLIIFLD.ISLDICRV~CRVD~IFCRDIIPTD~PVB~ F1RSTRrITH~ITHDrSTX~IAXDIIFCnRlIFCnRD REAL IXT DOUBLE PRECISION AIBICIRFIFRACIRDCIXV~U~YV~U~F.?~F~FYILONST~PU rDFrAN,BMrV,FS,UF,EZ,EX,CHECKlftHECK,TCHECK2

68

c c c

99

163

c c c

167 16C

CAGE0 Vd. 6. No. 4-E

EZ(A,BIC)=DEXP(-((A-B)/C)~~~/~.DO) EX(AnBeC)=(A-B)/C DATA NTIM/SO/rNRDI9frFRAC/l.DO~,RDC/3.Dtl/ DATA CONSTf.39R94228040143268DGl IF(NCPT.EP.O)GO TO 74 IF(.NOT.STX)GO TO 68 CALL RESET CALL PANEL CALL MENU STX=.FALSE. FIRSTH=.TRUE. CALL AXES IAXD=.TRUE. CDNTINUE IF(.NOT.PJB(l))GO TO 163 IF(.NOT.CRJ)GO TO 167 IF(CRVD)GO TO 164 DISPLAYS

CURVE

CALL MOVABS(IX(l)rIY(T)) DO 99 I=Z#NPLT CALL DRUABS(IX(I)rIY(I)) CDNTINUE CRVD=.TRUE. GO TO 164 IF(.NOT.(PVB(Z).OR.PVB())))GO IF(.NOT.CRV)GO TO 167 IF(.NOT.C?VD)GO TO 164 ERASES

CURVE

CRVD=.FALSE. CALL RESTORE GO TO 164 KCAL=S RETURN KtAL'3 RETURN

TO

165

USING

386

N. b2

165

03

c

64

c

65

c

RESETS

PDF

STATUS

69

CHECKS

03

67

If(.NOT.IFCRD(I))GO

68

IFCRD(I)=.FALSE. C4LL

69

I=lr6

RESTORE

DO

9

K=Z,NRD

CF(K)=RF(K-l)/RDC

9

74

KCPTl=NCPT-1

75

NUY=NP

76

NPRM=3*NCPT-1

77

NPRMl=NPRM+l

7 h

DO

79

~=3*1-2

En

U(J)=XMN(I)

10

I'lrNCPT

U(J+l)=STD(I)

$1

lJ(J+2)=PF(I)

1n

53

FL=O.DO

84

D3

85

F=O.DO

1)6

DO

87

J=3*K-2

88

CHECKt((lXT(Il-U(J))/U(J+l))

12

I=lrNUfi

14

C=lrNCPf

-8t?.DOjCHECK=-85.00

89

IF(CHECK.LE.

90

CHK=SNGL(CHECK)

91

c

92

C

93

c

IMSL

SUOROUTINE C4LL

94 9s

69

tiF(l)=FRAC

72

82

TO

C3NTINUE

69

71 73

R.B.MCCAMMON

CONTINUE

66

70

J.B~m~sand

14

TO

EVALUATE

THE

NORMAL

PROB.

'!DNOR(CHK,RNORM)

F=F+U(J+2)*RNORM

FY(I)=F z12

FZ=FZ+~PRO6~I~-FY~I~~'tZ

98

XSS(l)=FZ

99

xss(2)=xss(1)

100

DO

101

PJ(K,3'NCPT)=U(3'NCPT) DO

102 103

16

K=lrNRD J+lrVPRM

16

PJ(K,J)=U(J)

24

IF(ITN.EU.NTIM)GO

104 105

16

ITN=O TO

106

DO

30

I=lr'iJY

107

DO

32

J=lrNCPT

108

K=3*J-2

109

TCNECKZ=((IXT(I)-U(K))/U(K+l))

1lC

CHECK=(-TCHECK2**2/2.Dr)

111

IF(CHECK.LE.

112

TCHECK=DEXP(CHECK)

113

CHK=SNGL(TCHECKZ)

74

-8R,DO)CHECT=-85.00

174

CALL

11s

DF(I,K)=

YDNOR(CHK,RNORA)

116

LF(IrKtl)=-

117

IF(J.EQ.hCPT)GO

11F

TCHECKZ=((IXT(I)-U(NPRP-l))/U(NPRM))

-U(K+2)+CONST+TCHECK/U(K+l~**2 U(K*Z)*(IXT(I)-U(K))*CONST*TCHECK/c(Ktl)**3

119

IF(TCHECKZ.LE

120

TCHKZ=SNGL(TCHECKZ) CALL

121

TO

.-!B.uO)TCHECKZ=-ES.DO

YDNOR(TCHK~,R~OR~'I~)

122

32

DF(I,KtZ)=(RNORR-RNORMZ)

123

30

C3kTINUE

124

co

34

I=lrP1PA~'

125

PO

33

J=lrNPRM

120

A*(I,J)=O.DO b0

127 128

33

33

K=lr'tJM

AY(I,J)=AM(I,J)tDF(CII)'DF(KIJ) J~(I)=C!.DL

129

DO

13v 131

34

34

K=lrVUY

LY(I)=P~(I)+DF(K,I)'(PPO~(K)-FY(K))

132

IECR=O

133

CALL

134

IF(IERR.NE.3)GO

135

lr3

130

v(I)=zl.Dc D3

137

~ATTITTAA,~JPRI~~rIFCP~ 42 42

I'lr'JPR" J=l,'lPRb

139

~~(I)=V(I)*AF(I,J)'L.~(J) CO 60 K=l,NRIa

14G

DO

138

30

42

60

J=l,NPRF:

TO

53

DEN.

FUNCTION

DISCRIM a computer program of normal or lognormal distributions 141 6C 142 163 164 lL5 lL6 b3 147 b2 l4E lL9 150 151 152 153 156 22 155 156 157 15R 159 160 lb1 162 lb3 161 165 t7 166 167 65 168 169 26 170 20 171 172 173 174 175 176 177 25 178 179 1RO 36 161 182 183 38 184 lR5 39 186 187 188 53 189 190 191 192 193 72 104 195 196 74 197 198

1 2 3 4 5 6 7 R 9 10 11 12 13 14 15 16 17 18 19

PJ(K,J)DFJCK.J)*RF(K)~V(J) D3 62 K=lrNRb PJCK,NPt?Ml)fT.DB IFCNCPT.EQ.l)GO TO 62 DO 63 I=lrNCPTT P~CK,NPRFll)=PUCUrNPRrl)-PU(KIJ+I) CONTINUE DO 20 K=lrNRD FSCK)+O.DO DO 22 I=lrNCPT ~=3*1-2 IFCPUCK,J+T).LE.O.DU)GD TO 26 IFCPUCY,J*2).LF.O.DB)GO TO 26 CONTINUE IFCFUCK,3*NCPT).GT.l.DC)tO 10 DO L5 J'lrNUY F=I;.D3 DO 67 JI=lrNCPT I=3*JI-2 CHECK=C(lXT(J)-PU(krI))/PU(KII*1)) -8e.DB)CO TO 61 IFCCHECK.LE. CHW=SNGLCCHECK) CALL '~DNORCCHKIRNORM) F=F+PUCK,I+2)+RNORM CONTINUE kFCKrJ)=F FS(K).FS(K)+(PWOBCJ)-UF(K,J))~~2 GO TO 20 FSCK)=FZ+l.DO CDNTINUE PIN=0 GO 25 K=lrNRD IFCFSCK).GE.FZ)tO TO 25

387

26

NIN=K FZ=FSCK) XSSCZ)=FZ CDNTINUE IFCMIN.EQ.O)GO DO 36 J=l,NPRWl UCJl=PUCFtIN,J) DO 38 K=l#NRD DO 38 J=lrNPRMl PJCKrJ)=UCJ) DO 39 K=lrNUM FYCK)'UFCMINIK) ITN=ITN+l GO TO 2L IFCITN.EO.3)tO DO 72 I*lrNCPT J=3*I-2 XMNCI)=UCJ) STDCI)=UCJ+l) PFCI)=UCJ+Z) KCAL=3 RETURN KCALf5 RETURN END

SUBROUTINE

TO

53

TO

74

BESFIT

c c

c

PROGRAM TO HCCAPFlON'S

ESTIMATE METHOD

PARARETERS

BY

NONLINEAR

LEAST

SWARES

c

DDiJBLE

PRECISION

A~B~C,RF~FRACIRDCIXV~U~YV~U~FZ~F~FY~CONST~PU

USING

N. J. BRIDGES and R. B. MCCAMMON

388

,DF,AMrI3HrV,FS,YF,EZIErrCHECKITCnECK~TCHECK2 DIMENSICN RF~9~rXV~3O~rU~30~~Vv~3O~rU~l~~~PU~9~la~~ DF~30,1?~,A~~17,17~,FY~30~,V~17~rTS~9~,UF~9~3~~~~~~17~ EZ(A,B,C)=DEXP(-((A-B)IC)+CZ/Z.DO) EX(AIBIC)=(A-B)/C DATA NTIMi50/rNRD/9/,FRACfl.DOlrADC13.bOl DATA CONSTf.39a9422a0401C32b8DOl IF(NCPT.EP.O)GO TO 74 IF(.NOT.STX)C9 TO 68 CALL RESET CALL PANEL CALL MENU STX=.FALSE. FIRSTM=.TRUE. CALL AXES IAXD=.TRUE. CONTINUE IF(.NOT.PVB(l))GO TO lb3 IF(.NOT.CRV)GO TO lb7 IF(CRVD)GO TO 164

20 21 22 23 24 2s 26 27 2a

29

30 31 32 33 34 35

36 37 38 39 40 41 42 43 44

68

c c c

45 46 L? Aa

49

50 51 s2 53 54 55 56 57 58 59 6@ 61 62 63 64 65 66 67

ba 69 70 71 72 73 74 7s 76 77 78 79 a0 a1 82 a3 a4 85 86 67

99

163

DRAYS

THE

CURVE

CALL MOVABS(IX(l)rIYC1)) CO 99 I'ZINPLT CALL DRYABS(IX(I)rlY(I)) CDNTINUE CRVD=.TRUE. CO TO 164 IF(.NOT.(PVB(2).OR.PVB(3))))GO IF(.NOT.CRV)GO TO 167

c IF(.NOT.CRVD)GO c c c

167 lb4 165

09

9

a

10

;"p 90 Pi 92 93 94 14 9s 96 12 97 98

ERASES

THE

TO

164

CURVE

CRvD=.FALSE. CALL RESTORE LO TO 164 kCAL=S hETURN KCAL=3 RETURN CIt!TINUE DO 09 I=lr6 IF(.NOT.IFCRD(I))GO TO 69 IFCRD(I)=.FALSE. CALL RESTORE CGNTINUE RF(l)=FRAC DO 9 K=Z,NRD RF(K)=RF(K-l)/RDC NCPTl=NCPT-l NiJMfNP-1 NPRM=S*NCPT-l NPHMl=NPRM+l F=G.DO DO 8 I=lrNUJ XV~I~=~IXT~I+~~+IXT~I~~/~.DO h(I)=IXT(I+l)-IXT(I) YV(~)=PROB(I+~)-PROB[I) F=F+YV(I) DO 10 I=lrNCPT J=3*1-2 U(J)=XMN(I) U(J*l)=STD(I) U(J+2)=PF(I) FL=O.DO DO 12 I=lrNUM F=O.DO DD 14 K=lrNCPT J=3*K-2 CHECK=(-((XV(I)-U(J))/U(J+l))~~2/2.DO) IF(CHECK.LE.8R.bO)CHECK=-85.00 F=F+U(J+2)*DEXP(CHECK)/UtJ+l) FY(I)=CONST*Y(I)*F FZ=FL+(YV(I)-FY(I))+rZ XSS(l)-FL XSS(2)=xSS(l)

TO

165

DlSCRlM DO

99

program

of

normal or bgnormai

distributions

K=l,NRD

16

CO

16

J=lrNPRM

16

PJ(K,J)=U(JI

24

IF(ITN.EId.NTIP)GO

IT\=0

10 3 lr,4

CbmpuIer

PJ(K,ScNCPf)rU(S~NCPf)

100 ICI 1 1'22

a

TO

11:s

DD

30

I=l,::il!l

lli6

~'0

32

J=l,?CPT

lC7

<=3*

74

J-2

1i;r;

CHECK=(-((XV(I)-U(~))/~(~+~))~~~/~.DO)

III Q

IF(CHECK.LF

110

TCHECKzDEXP(CNECK)

111

Df~I,K~=C3VST+~~l~'U~K*2~~EX~XV~l~,U~K~rU~Ktl~~~lCHECK/U~K+l~~~2

.-bR.DO)CHECK=-RS.DO

112

LF~~,U*l~=C3NST+Y~1~~U~K+2~~TCHECKI((EX~XV~l~,

113

U(K),U(K+l)))'C2-l.D~)/U(K+l)~~2 TC

3@

114

If1J.EO.CCPl)GO

115 IlL

TCHECK2+~-~~Xv~I~-U~NPRF-I))/U~NPRw~)~~2/2.D~~ IF(TChECKL.LF.-SB.DO)TCHECK2=-85.00

117

32

DF~l,K*2~=CCNST+~~I~~~TCH~CK/U~X+l~-DEXP~TC~ECK2~/U~NPRW~~

110 119 12c 121 122 123 124 12s 126 127 128 129 130 131 132 133 134 135

?,r)

COkT

136

61:

IPIIJE

LO

34

l=lrNPRR

DO

33

J=l,'lPRW

AY(IeJ)=O.DG 00

33

33

K=lrNU?

A~~I,J~=Al~lrJ~*DF~K,l~~DF~K,J~ ~~(l)+o.DG DO

34

34

KMlrNUM

~M(I)=9*(I)iDf(K,I)'(YV(K)-FYK)) ItRP=U CALL

IATI~~TLAMINPRY~IERR)

lF(IERR.NE.OIGO I,:, 42

TO

53

TO

62

l=l,NPRN

V(I)=D.DC' D3

42

42

J'lrVPRM

v(I)=~(I)+Aw(I,J)~~W(J) DO

60

KwlrNRD

DO

60

J'lrNPRT'

PJ(K,J)=PJ(KrJ)*Rf(K)~V(J)

137

DO

13e

PJ(K,NPRMII=~.DO

62

K=lrNRD

139

lF(NCPT.EU.l)GD

140

DO

63

l=lrNCPTl

141

63

PJ(K,NPRYl)=PU(K,NPRMlI-PU(K,3*1)

142 143 l&4 145

b2

CONTINUE

146 147 148 149

20 K=lrNRD FS(K)*O.DU DO 22 I=lrNCPT J=3*1-2 IF(PU(KrJ*l).LE.O.DO)GO IF(PU(KIJ+Z) .CE.O.DO)CO COhTlNUE lF(PU(Ke3*NCPT).GT.t.DC)GO DO 65 J’lrNUM F=C.DO DO 67 JI=lrNCPT DO

22

150 IS1 152 IS3

TO TO

26 26 TO

154 1ss

156 is7 158 159 160

67 65

161 162

26

163

20

164 165

166 167 168 lb9 l7O

171 172 173 ‘176

25

36

175

316 f77

38

-8d.D0)60 TO 67 IF(CHECK.LE. F=F+PU~K.I*2~~EZ~XV~J~~PU~K~I~~PU~K~~+l~~/PU~K~I+l~ COW1 INUE YF(KrJ)=C>NST*Y(J)*F FS(K)=fS(K)*(IV(J)-YF(K~J))r+Z GO TO 20 FS(K)=FZ*l.DO CONTINUE MIN=O DO 25 K=lrNRD IF(FS(K).GE.FL)tO TO 25 MlN=K FL=FS(K:) XSS(Z)=fZ CONTINUE IF(WlN.EO.O)CO TO 53 DO 36 J=lrNPR*l U(J )=PU(MINIJ) DO 38 K=lrNRD DO 38 J*leNPRWl PJ(krJ)=ll(J) DO 39 K=l.NUW

26

389

N. J. BRIDGESand R. B. MCCAMMON 178 179 180 181 182 183

39

53

104 185 186 187 188 la9 190 191

1 2 3 c 5 6 I 9 9 rn 11 12 13 14 15 16

72

74

c c c c

801

802

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 CO 41 42 43 44 45 46 47 co c9 50 51 52 53 54 55 56 57 58 59 60 61 62 63

803 8Ob

805

806

801

808

a09 810 811 812

813

811 a15 816

al7

FV(K)=YF(MIhrK) ITN=ITN+l GO TO 24 IF(ITN.LP.D)GO DO ?2 I’lrNCPT J=S*I-2 XMN(I)=U(J) SfD(I)=U(J+l) PFCI)=lJ(J*Z) KCAL=3 RETURN KCALIS RETURN END

USED IN FITTING

TO

CALCULATIONS ROUTINE.

74

FOR

SUIROUTILE BATINTCDIN~N,IERR) DOUbLE PRECISION 6rDIN LINENSION D:N~1?,17~rLC~17~,LR(17~ DO 801 I’lrk LC(I)=I LR( I)=1 DO 813 I-1rN B=O.DO DO a03 K’lrN 00 803 J=IrN ~F(DA9S~DIN(KrJ))-tt)803~aO2,RO2 KL=K JL=J B=DABS(DIN(KeJ)) CONTINUE IF(0)701~701r804 J=LR(I) LR(I)=LR(JL) LR(JLl=J K=LC(I) LC(I)=LC(KL) LC(KL)=K DO 805 J=lrN B=DIN
NON-LINEAR

LEAST

SQUARES

DISCRIM 64 65 66 c7 6.5 69

818 701

a computer program of normal or lognormal distributions

LCCJ)'LCCJl) LCCJl)=Jl co 70 815 CONTINUE RETURN IERR=l RETURN EYD

70 71

2 3 4 S

6 7 a 9 10 11

12 13 14 1s lb 17 18 19 2c 21 22 23 :: 26 27

28 29 30 31 32 33 34 3s 36 37 c '3e c 39 c 40 41 42 43 44 45 46 12 47 46 49 St 51 999 52 53 54 5s

56 57 58 59

60 61 62 63 b4 65 :; 60

1G

ERASE

ALL

GRAPHICS

PRESENTLY

co 12 1=lrb IFCIFLDCI))IFLDCI)+.FALSE. IFCISLDCI))ISLDCl)=.FALSE. 1FCIFCRDCI))IFCRDCI)r.FALSE. IFCITHDCI))ITHDCI)=.FALSE. lFCIFCRROCI))IFCRRDCI)=.FALSE. CDNTINUE CALL CHRSIZC3) CALL ERASE DO 999 I=lrb CALL RESET CONTINUE CALL PANE, CALL RENU FIRSTR=.TRUE. XMNCT=S. IFCN.LE.lOO)XRNCT=3. CALL ROVABSC540r256U) IFCKSEL.EP.O)GO TO CALL ANSTRC16rIRSGl) CALL 'TOVABSC250.2424) CALL ANSTRC7rIRSG2) CALL ROVRELCllOOrO) CALL ANSTRCSrIRSG3) CALL ROVABSC130r2352) CALL ANSTRC56rIRSG4) GO TO 11 CONTINUE CALL ANSTRClPsIRSGb)

10

ON

SCREEN

391

N.J. BRIDGES and R. B. MCCAMMON

392 69 70 71

CALL 11

ANSTRCS6rIMSG7)

ITEnP=2352 DO

72

73 74 75 76 77 7s 73 8 t'

LO

I=l,NCPT

IF(ILOG.EQ.l)GO

TO

41

XYOD=XMN(I) XIED=XMN(I) XYEAN=XMh(I) bXMEAN=BXMN(I) XSTD=STD(I) BXSTD=RSTD(I)

91

82 83 54 R5 A6 Y7

NOVABS(130e23S2)

CALL

GO

c c c c 41

TO

42

CALCULATE

YEAF!r

INITIAL

AND

f'?ObE#

FINAL

STANDARD

XqOD=EXP(XHN(I)-STD2)

Bd

XYED=EXP(XYN(I))

69 9(1

XflEAN=EXP(XMN(I)+STD2/2.)

91

dXSTD=SQRT(EXP(2~BXMN(I)+~SlD2)~(EXP(BSTD2)-1))

92 93 9L 95

aX,~EAN=EXPC3XnN(I)+BSTD2/2.) XSTD=SQRT(EXP(2'XMI~(I)+SlD2~*(EXP(STDZ)-l~~

42

IF(KSEL.EQ.l)GO

TO

43

tYCODE(~LINE~3R)ICHLRCI)8X~OO~XMED

38

F3CkATCAL,Fll.2,F13.2)

9b

ITEMP=ITE!lP-72

97 96 9v

CALL

'!OVAbSC13C~ITt~Pl

C4LL

AOUTST(2A,MLINE)

lllti

EYCODE(MLINE~37)XMEAN,XSlC~PF(Il

37

FORYAT(F13.21F10.2~f8.3)

11: 1

CALL

1 (12

GO

43 Iti& 44

EVCODE(MLINEIC~)ICHAR(I)~~~XMEAN,PXSTD,~PF~I~

l('3

AOUTST(35,YLIfiE) TO

40

FOkMATCAL.F10.2,F9.2,F~.3)

1 ('5 106

CALL

YOVAuS(13LeITFFP)

li7

C4LL

AOUTST(3lr~:LICE)

1 c 1?

fYCODE(~LINE,37?)X!"EAh,XSlD,PF(I)

103

ITEPP=ITf??P-72

377 co

AOUTSTC3lr'lLI::E)

C~~~TINUE IFtKSEL.:E.l)GO

112 113

c

11L

c

115

c

110 117

FORXATCFlG.2,F1~.2,FR.3) CALL

1 1 il 111

PRINT

TO

OIJT tIOTcc

ITEMP=ITE?P-72 YOVAUSC13PrITiMP)

120

CALL

4OUTST(2C,MLINE)

121

EVCODEC"LINtr471XSSC2) c7

CALL

tiOVkEL(400rU)

124

CALL

AOUTST(IZ,I"LI~E)

125

E'JCODE(PLINEaLC)ITh 49

fakMAT('*wfiOCR

OF

127

ITtMP=ITtr:P-l&C

12b

CALL

~OVAEJS(lLC.ITEPP,

129

LALL

AOlJTST(26rPLIkE)

1P

DC

131

70

133

CO

134

XC=(IXT(I)-XPN(J))/STD(J)

70

CALL 70

J=lrNCPT flDNOH(XC,RNORP)

Y(I)=Y(I)*P~(J)~RI~oR~

137

lVDX(l)=l

138

K=C

139

YU'Y(1)

140

co

lL1

YDIF=Y(I)-YU

75

I=Z,*%P

162

IFCCN*YDlF).LT.XMkCT)GO

163

K=K+l

l&L

INOX(K+l)=I

lL5

YU=Y(I)

107

75

=

I=lrNP

Y(l)=o.

135

ITEBFTIONS

ClNTIh'UE

132

166

SQUARES

FORNAT(E12.5)

123

136

OF

FOkWAT("SS"rlOX,El2.5) CALL

130

SUN

~~C~DE(~~LIZE~~~)XSS(~) C6

119

126

48

ERROR

11F

122

DEVIATION

CURVES

C3NTINUE ItiTRL'K

TO

75

*#,13)

OF

BOTH

DISCRIM 148 14Y 150 151 152 153 l5L 155 154 157 158 15Y 1tc lb1 162 lb3 %tL lb5 164 167 l*b lb9 17c 171 172 173 17L 175 176 177 178 179 180 181 182 183 lE& lb5 1st lb7 18C l&9 190 191 '192 193 19l 195 lV6 197 198 199

77 c c c

393

INDx(K+~ I=NP C’!AX=U. CHI 2=0. DO ?? I=lrK EXPT=Y(INDX(I+l))-t(INDX(I)) OBS=PROB(INDX(I+l))-PROB(lNDX(I1) CHIZT=N*(EXPT-OBS)*(EXPT-OBSI/EXPT XCT(Irl)=N*OBS XCT(IrZ)‘N*EXPT XCT (Ir3I’CHIZT IF(CHI2T.GT.CFlAX)CMAX=CHI2T LHI2=CHI2*CtlI2T CALCULATES

MAXIMUM

PERCENT

CONTRIBUTION

CYPX=lOO.*C4AX/CHI2

c c c

CALCdLATES

TWf

NUMBED

OF

DEGREES

OF

FREEDOM

NDF’XNTRL-(3*NCpT-l 1-l KNDF=FLDAT(NDFI IF(RNDF.LT.O.5IRNOF=O.5 IF(Ri~DF.6T.2OOCOO.)RI~DF=2OBOOB. IF(CHI2.LT.O.)CHI2=0. c c c

1ciu 7h

92

91 95 33

200 201 202 203 2OL 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 2 2 L; 221 222 223 224 225 226

a computer program of normal or lognormal distributions

34

35

32

31

56

IMSL

ROUTINE

UHICH

CALCULATES

CALL ~DCH(CHI~IRNDF,CHIIIER) PVAL=l .-CNI ALPH=.C’S A~Pttl+l .-ALPH CALL 4DCHl~ALP~lrRf~Of,CRITIIER~ CD TO 78 CALL ANSTR(ZOIIMSG~I CDNTINUE ITEMPtlTEMP-14C CALL ~OVAYS(~O~‘~ITEMP) CALL ANSTR(lS,IRSGYI IF(KSEL.Lt.11GO TO 95 ITEFlP=ITEMP-l&L CALL ?!OVABS(13~rITEMPI CALL ANSTR(36rIMSGlU) DO 91 I=lrK EYCODE(MLINE,P~)II(XCT(I#J),J=~#~I F3RMAT(IC,2F9.lrF10.2) ITCMP+ITEMP-72 CALL YOVAUS(lSG,ITEMP) CALL LOUTST(~ZIMLINE) CGNTINUE GO TO 57 EVCODE(MLINE,33IN FDRMAT(“S\MPLE SIZE = “015) ITERP’ITEWP-72 CALL MOVABS(ZOGIITEMP) CALL AOUTST(lPaMLINE) EYCODE(MLINE,3~1CHIZ F3RMAT (“CHI-SPUARE VALUE = ITEMP=ITtMP-72 CALL MOVABS(ZOOIITEMP) CALL AOUTST(ZI?rMLlNEI EYCODE(MLINEr35)NDF FORKATC”YITH”rI7,” D.F.“) CALL MOVREL (10810) CALL AOUTST(18eMLIhEI EHCODE(MLINE,32)CMAX FDCfAT(“EAX, PCT, CONTRIBe ITEMP=ITtvP-72 CULL “IOVAUS(~O~!~ITEMP) CALL AOUTST(26~MLINFI EvCOOE(MLINE,~~)K FDRNAT (“FOR”, 13,” INTERVALS”) CALL ‘ICVRELOOPI~JI CULL AOUtST(17,MLIt.E) E\ICODE (MLINEr36)PVAL FDRYAT(*‘P-V4LUE = “rF7 . 5) ITEMP=ITEMP-72 :~LL MOVABS(ZOC,ITEF!P) CALL AOUTST(lfrMLINEI C’ICODE (MLINE,39)CRIT

THE

CHI-SPUARED

“rF9.2)

=

“rF5

. 1)

PROBABILITY

N. J. BRIDGES and R. B. MCCAMMON

394 227 2 2
39

F3RYATCnCRITIC41.

VALUE

=

"rF9.2)

lTtMP=ITt#P-72 C4LL

YC'VAt~SC2@f!,ITECP)

CALL

AOUTSTC2brf'LINF)

FVCODE(~lLINE,45)AL~H

45

FDR~ATC"FOR

P-V4LUE

CALL

YOVRELC1UR,O)

C4LL

ADUTSTC19rMLINE)

=

"rFS.3)

THPR=.FALSE. DO

80

I=lrNCPT

IF~IT~~I~~THD~I~=X1+~JJX2~I~-X~l~/XSC IF(ITHCI))THPP=.TRUE.

FI?

CDNTINUE IFC.NOT.ITH(l))GO

TO

PL

XC=(THDCl)-XYNCl))/STDCl)

c c c

1'1s~

ROUTINE

CALL

WHICH

CALCULATES

THE

NORMAL

PROB.

DIST.

MDNORCXC,RNORF)

ES(l)=(l.-RYORM)r~F(l) t?R=ERCl) IFCNCPT.LE.l)GO DO

82

TO

84

1=20NCPT

XC=(THD(I-l~-X~N~I~~/STD(I~ CALL

'lDNORCXC,RNORM)

ERCI)=RNORM*PFCI) IFCI.ER.NCPT)GO

TO

b2

XC=CTHDCI)-XMNCI))/STDCI) CALL

fiDNOR(RNORMrXC)

E~(I)=ER(I)+(l.-RNORn)+PF(I)

a2 L4

E?R=ERR+E?C.I) CDNTINUE IFC.NOT.THPR)GO

TO

57

ITENP=ITEfiP-144 CALL

'4OVABSC130rITEMP)

CALL

ANSTRC~~IIMSG~~)

ITEMP+ITEMP-164 CALL

MOVAUSC350rITEMP)

CALL

ANSTRC22,IRSGl2)

266

;'0 7

ITEMP=ITEMP-72 C4iL

L(.t!

ClLL A'JSTdCL7rI'"SblT) ~3 55 I'lr'lCPT IF(I.tC.f~C~T)GO Tu 5P XC=THO(I) IF~IL@~.E~.l~XC=E~t~CT~~~I~~

269

_

27': ill 272

"OvnusC35~rlTEr~P)

LUCL~DE~~~LI~~E~~~~KCHAR~I~~XC~ER~I~ F3W?eATC4C,Fll.Z,Fl2.3) ITtvP=ITE'lP-72 C4LL

wOVA~~SC13~,ITt"P)

CALL GO

ACUTSTC27rk~L11.E) TU

55

ITC*P=ITCUP-72 C4LL

'OVAoS(1:I'rITtCP)

CALL

rfC~tlTST(27rMLIfiE)

Clf.TIt.UE EYCCDECXLINE,5l)ERd FDht.ATCFi3.3) ITCbP=ITt*P-72 C4LL

~c?VAiSClhSrITtMP)

CALL

AOUTSTC23rMLIf.E)

C 3 t.T I !Jllt IAXD=.TPUE. IPlL=.TRUt. RETURN E?dC

1c ?

c

THIS

I

C

FOR

L

c

SU~~CIUTINE FITHER

OF

CALCULATES THE

NON-LIf.EAR

THE

"STARTING LEAST

POINTS"

SQUARES

NECESSARY

SOLUTIONS.

5

SU~ROUTI~IE

c

C>TulOQ

7

PJ3~;~rSTXrIAXDrILCGr!:rDATll/CURVt/NTOTrNPLTrIXO00~rIY~l00~r

8 9

CS~rCRVD/PARAh/~JCPT~Y~~b~,X~~~~6~~PF~b~~IFL~6~,ISL~6~,ICHAR~6~,

GRAFIT ICUTRL/FIRST~FI~ST~~KCAL~IDU~~JYL~~~,L~L~~~~,IPAR~~~,

IXfCR~hrlJ~~rIYFCR~L,l~~~~,IXFC~R~6.l~J~~,IYFC~R~6,lOO~,X~lOO~,Y~l~O~,

FUNCTION

DISCRIM a computer program of normal or lognormal distributions 1 I: 11

,

12 13 14 15 16 17 1% 19 2 (, 21

22 23 24 25

26 27 21 6E 29 SO 31

32 c 33 c 34 c 35 36

37 38

626

39 4e 41

63

42 43 44 45 46 47 46 49 50 51 52

c c C

67 64

53 65 54 55 56 57 5R 59 6C 61 02 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 7F 79 80 81

82 83 84 85 86 a7 88

72

78

147 146

148

JXlrJYlrJk2,JY2rJX3~l)rJr30~1JX4(6~rJrCC6~~JJXC6~~JJYC6~,JJX2~6~, JJY2C6~rSTDC6~rIFLDCL)rISLD(6~~IFCRC6~~IFCROC6~~ITH~6~,ITHDC6~. ~ChPR~6~rdX~~N~~~,~STD~6~,@PF~6~,IlN,XSSC2~~IFCNRC6~,IFC~RDC6~/PCl/NP, IPX~30~,IPY~3C~rIXToO)rllT(30)rY(50)rPROBC3O~,IPlD/SCAL/XGl, k~2rYDlrY~2,YbP,XGR,YSC,XSC,Yl~Y2~Xl,X2,YDIF,XDIF h'iAL IXT,IYT IFITlGER TERMOUT LOGICAL ~FLIISLI~FLDIISLD,CRV~CRVD~IFCR~IFCRD~IP~O,PVE,FIRS~~, ITH,ITHD,STX,IAXD,IFC~R~IFC~RD,ERR bIYEFISlON PA(L) DATA TERFluU7/6/ fRR=.FALS:. IF(.NOT.STX)GO TO 68 CALL ERASE CALL PANEL CALL MENU STX*.FALSE. FIRSTR=.TRUE. CONTINUE IFC.NOT.PJBCl))GO TO 63 IFC.NOT.CRV)GO TO 67 1FCCRVD)GO TO 64

DISPLAYS

THE

GRAFIT

CURVE

CALL MOVAGSCXXCl)rIYCl)) DO 688 I=ZeNPLT CALL DRYABSCIXCI)rIYCI)) CONTINUE CRVD=.TRUE. GO TO 64 IFCC.NOT.PVBC2,,.OR.C.NOT.PVR(S)))CO IFC.NOT.CRV)GO TO 67 IFC.NOT.CRVD)GO TO 64 ERASES

THE

CURVE

CRVD=.FALSE. CD TO 64 KCAL=S RETURN KCAL=3 RETURN CSNTINUE DO 72 1=1,6 IFC.NOT.IFCRCI))GO TO 72 IFC.NOT.IFCRDCI))GO TO 72 IFCRDCI)=.FALSF. IFC.NOT.IFCWRCI))GO TO 72 IFC.NOT.IFCMRDCI))60 TO 72 IFCMRDCI)'.FALSE. CONTINUE DO 78 1x106 IFC.NOT.IlHCI))GO TC 78 IFC.NOT.ITHDCI))GO TO 78 ITHDCI)=.FALSE. COhTlNUE NCPT=O 00 147 1=1,6 To IF(ISLCI).AND.~FLCI))GC 1FCIFLCI))GO TC 147 I.CPTOI CO TO 146 C3NTINUE IFCHCPT.GT.O)tC TO 148 hCAL=S RETURN FAtNCPT)=l. IFCNCPT.EG.l)GO Tu 153 WNORM=CYT+CJJYCl)-YEl)/YSC) CALL NDNORCRNORM~PACl)) PAA=PACl)/Z. CALL NDNRISCPAA,YMCl)rIDUR) PFCl)=PACl) BPFCl)=PFCl) DO lb9 I=Z#NCPT IFCI.EQ.NCPT)GO TO 152 RNORM=CYl+CJJYCI)-YBl)/YSC) CALL MDNORCRNORNrPACI))

147

TO

65

395

3%

N. J. BRIDGES and R. B. MCCAMMON 89 90 91 92 93

94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 1lC 111 112 113 114 11s 116 117 118 119 120 121 122 123 124 125 126 127 128 129 13L 131 132 133 134 135 136 137 138 139 140 141 142 143 l&C 145 146 147 148 l&Y 15G 151 152 153 15c

152

PAA=PA~I-l~+~PA~I~-PA~I-l~~/2. CALL MDNRIS~PAA~YM~l~rIOUM~ PF(I)=PA(I)-PA(I-1) BPF (1)=PF(1) co TO 320 FF(NCPT)rPA(NCPT) BPf(NCPt)=PF(NCPT) CALL ~ONRIS(.S~YM(NCPT)rIDUM)

l&V

153

c c c 320

DETERMINE

HEAY

AND

STD

DEVS

OF

A AN0

B

D3 50 I=lrNCPT STD~I~=~JXC~I~-JX3~I~~~YSC/~~JY~~I~-JY3~I~~~XSC~ tiSTD(I)=STD(I) DO 45 J=l,NP IF~IYT~J~.LT.Y*~I~~GO TO 45 X~~~I~=IXT~J-l~*~YM~I~-IYl~J-l~~r(IXT(J~-IXl~J-l~~/~IYl~J~IYTtJ-1)) BX+lN(I)=XMN(I) G3 TO 50 C3NTINUE ClNTINUE 11h4=0 xSS(l)=O. xSS(2)-0. EYTRY GRAaSF

45 50

c c c

CALCULATE

THEORETICAL

DISTRIEUTION

DEL=XDIF/(YTOT-1) X(1)=X1 Y(l)d. DO 60 I=20NfOT X(X)=X(1-l)*DEL Y(I)=O. 00 70 J=lrNCPT 00 70 I=l,NTOT XC=(X(I)-X~N(J))/STD(J) CALL YDNOC(XC,ANORY) Y(I)=Y(I)tPF(J)~RkOR~ FiPLTIO D@ A0 I=l,NTOT CALL YDNRIS(Y(I)rTINOR~rIOUhl) ITY=Y~l*YSC'(TINORM-Yl) IF( ITY .LT.SOO)GO TO 80 NPLT=NPLTtl

cc

7P

c C c

CALCULATES

THE

CURVE

IY(NPLT)=ITY IX(NPLT)=(XBl+XSC+(XO-X1)) lF(IY(NPLT).LE.2400)GO NPLT=NPLT-1 GO TO 85 C3NTINUE CONTINUE IF(.NOT.CRVD)GO TO 94 CRUO=.FALSE. IF(.NOT.C~V)GO TO 96 CRV=.FALS:. CaNTINUE cFtv= .TRUE. CRVD=.TRUE. KCAL’.? RETURN EMD

80 85

91 96

TO

80

pr gosmoc

258 \cl \ca+03

.40000000e+02

\c463e+02 \c5oooooc+o1

.40540540~+02 .40000000~+03

.0b67258be+02

22 .38610038a+OO .17000000e+02 . .21233521e+02 .85000000e+02 .33590733e+02 .17500000*+03 .52895?52e+02 .25000oooe+03 .?1428571a+O2 .60000000~+03 .810a1080*+02

.17500000e+04

.95752895*+02

aa603087a+o

.40000000*+04

.12500000 .63320 .12