10X$=SYS(CHR$(7)):R$=LEFT(X$,7):L$=RIGHT(X$,8) 13 REM ********************************************************************* 14 REM CMOD5 CMOD5 CMOD5 CMOD5 CMOD5 CMOD5 CMOD5 15 REM ********************************************************************* 20 REM 30 REM PRIOR FOR MEAN OF TWO PARAMETER NORMAL 40 REM 50 REM****************************************************************** 60 DIM #1,A1(111),A2(111),A3(111) 70 OPEN R$ AS FILE 1 110A1(0)=5 120 GOSUB 6054 130 S9=0 140 S6=0 150 DIM F(4,2) 160 X=0 170 N1=A2(0):L1=A2(1):Q=A2(2) 180 REM ********************************************************************* 190 REM NOTATION N1=DEGREES OF FREEDOM OF INVERSE CHI PRIOR ON ST> DEV> 200 REM L1=SCALE PARAMETER 210 REM G=HYPOTHETICAL SAMPLE SIZE 220 REM Q=MEDIAN 230 REM**************************************************************** 240 PRINT L$ 242 PRINT " PRIOR DISTRIBUTION ON THE MEAN" 243 PRINT 250 PRINT "THIS MODULE WILL ASSIST YOU IN SPECIFYING A PRIOR DISTRIBUTION" 260 PRINT "ON THE MEAN OF A NORMAL DISTRIBUTION." 270 PRINT 280 IF N1=0 THEN 310 290 G=N1+1 300 GOTO 510 310 PRINT "INPUT THE DEGREES OF FREEDOM OF YOUR PRIOR DISTRIBUTION ON" 320 PRINT "THE STANDARD DEVIATION."; 330 GOSUB 9000 340 N1=O1 350 G=N1+1 360 PRINT 370 IF N1>2 THEN 410 380 PRINT 390 PRINT "REENTER. DEGREEES OF FREEDOM MUST BE GREATER THAN 2." 400 GOTO 310 410 PRINT "INPUT THE SCALE PARAMETER."; 420 GOSUB 9000 430 L1=O1 440 G=O1+1 450 PRINT 460 IF L1>0 THEN 490 470 PRINT "REENTER. SCALE PARAMETER MUST BE POSITIVE." 480 GOTO 410 490 Q=L1/SQR(N1-2/3) 500 PRINT L$ 510REM 520A$="SUPPOSE THE POPULATION STANDARD DEVIATION IS ######.## ." 521 PRINT USING A$,Q 530 PRINT "SPECIFY THE 25TH, 50TH, AND 90TH PERCENTILES OF YOUR PRIOR" 540 PRINT "DISTRIBUTION ON THE POPULATION MEAN." 550 PRINT 560 PRINT "SPECIFY 25TH. YOUR BETTING ODDS ARE 3 TO 1 THAT THE MEAN IS MORE" 570 PRINT "THAN THIS VALUE."; 580 GOSUB 9000 590 Q1=O1 600 PRINT 610 PRINT "SPECIFY 50TH. YOUR ODDS ARE EVEN THAT THE MEAN IS LESS THAN THIS" 620 PRINT "VALUE."; 630 GOSUB 9000 640 IF O1 <= Q1 THEN 730 650 Q2=O1 660 PRINT 670 PRINT "SPECIFY 90TH. YOUR ODDS ARE 9 TO 1 THAT THE MEAN IS LESS THAN THIS" 680 PRINT "VALUE."; 690 GOSUB 9000 700 IF O1 <= Q2 THEN 730 710 Q3=O1 720 GOTO 780 730 PRINT "90TH MUST BE LARGER THAN 50TH AND 50TH LARGER THAN 25TH." 740 GOTO 550 750 REM************************************************************ 760 REM STANDARD DEVIATION IS ESTIMATED IN DIFFERENT WAYS 770 REM ********************************************************************** 780 K5=1 790 PRINT L$ 800 PRINT "HERE ARE THE PERCENTILES OF FOUR NORMAL DISTRIBUTIONS FITTED" 810 PRINT "TO YOUR PERCENTILE SPECIFICATIONS." 820 PRINT 830 A$=" 10TH 25TH 50TH 75TH 90TH" 831PRINT USING A$ 850 M=Q2 860 S=(Q2-Q1)/.6754 870 GOSUB 1220 880 S=(Q3-Q2)/1.282 890 K5=2 900 GOSUB 1220 910 S=(Q3-Q1)/1.957 920 M=Q3-1.282*S 930 K5=3 940 GOSUB 1220 950 M=.5*(M+Q2) 960 K5=4 970 GOSUB 1220 980 PRINT 990 PRINT "COMPARE THE PERCENTILES OF THESE DISTRIBUTIONS AND DECIDE " 1000 PRINT "WHICH DISTRIBUTION MOST CLOSELY CORRESPONDS TO YOUR PRIOR" 1010 PRINT "BELIEFS. YOU CAN EITHER TENTATIVELY ACCEPT ONE OF THESE" 1020 PRINT "DISTRIBUTIONS OR RESPECIFY THE PERCENTILES." 1030 PRINT 1040 PRINT "IF YOU WANT ONE OF THE DISTRIBUTIONS TYPE ITS NUMBER." 1050 PRINT "IF YOU WANT TO RESPECIFY THE PERCENTILES TYPE '0'." 1060 GOSUB 9000 1070 IF O1=0 THEN 1330 1080 IF O1=1 THEN 1150 1090 IF O1=2 THEN 1150 1100 IF O1=3 THEN 1150 1110 IF O1=4 THEN 1150 1120 PRINT "REENTER. INPUT MUST BE 0 OR NUMBER OF DISTRIBUTION."; 1130 GOSUB 9000 1140 GOTO 1070 1150 M=F(O1,1) 1160 S=F(O1,2) 1170 GOTO 1500 1180 PRINT 1190A$=" 10TH 25TH 50TH 75TH 90TH " 1191PRINT A$ 1200 RETURN 1210 GOTO 1240 1220 F1=M-1.282*S 1230 F2=M-.6754*S 1240 F3=M 1250 F4=M+.6754*S 1260 F5=M+1.282*S 1270A$="######## #######.## #######.## #######.## #######.## #######.##" 1271 PRINT USING A$ ,K5,F1,F2,F3,F4,F5 1300 F(K5,1)=M 1310 F(K5,2)=S 1320 RETURN 1330 PRINT 1340 PRINT "RESPECIFY YOUR PERCENTILES." 1350 PRINT "25TH."; 1360 GOSUB 9000 1380 Q1=O1 1390 PRINT "50TH."; 1400 GOSUB 9000 1420 Q2=O1 1430 PRINT "90TH."; 1440 GOSUB 9000 1450 Q3=O1 1460 IF Q1 >= Q2 THEN 1480 1470 IF Q3>Q2 THEN 780 1480 PRINT "REENTER. PERCENTILES MUST BE INCREASING." 1490 GOTO 1340 1500 REM **************************************************************** 1510 REM **** SWITCH FROM PERCENTILES TO HYPO SAMPLE SIZE ******** 1520 REM ****************************************************************** 1530 N2=(Q/S)*(Q/S) 1540 PRINT L$ 1550 IF S9=0 THEN 1590 1560 PRINT "HERE ARE SOME OF THE CHARACTERISTICS OF THE NORMAL" 1570 PRINT "DISTRIBUTION YOU ARE NOW CONSIDERING." 1580 GOTO 1640 1590 PRINT "HERE ARE SOME OF THE CHARACTERISTICS OF THE NORMAL" 1600 PRINT "DISTRIBUTION YOU ARE NOW CONSIDERING. THIS IS A" 1610 PRINT "CONDITIONAL DISTRIBUTION SINCE IT IS ASSUMED THAT" 1620A$="THE POPULATION STANDARD DEVIATION IS #####.##." 1621 PRINT USING A$ ,Q 1640 F2=M 1650 PRINT 1660A$="HYPOTHETICAL SAMPLE SIZE (M) #####.##." 1661 PRINT USING A$ ,N2 1680A$="MEAN=MODE=MEDIAN #########.##" 1681 PRINT USING A$ ,F2 1700 S=Q/SQR(N2) 1710A$="STANDARD DEVIATION #########.##" 1711 PRINT USING A$ ,S 1720 F4=F2+.6754*S 1730 F1=F2-.6754*S 1750 F5=F2+1.96*S 1760 F6=F2-1.96*S 1780A$="10TH PERCENTILE #########.##" 1781 PRINT USING A$ ,F6 1800A$="25TH PERCENTILE #########.##" 1801 PRINT USING A$ ,F1 1820A$="75TH PERCENTILE #########.##" 1821 PRINT USING A$ ,F4 1840A$="90TH PERCENTILE #########.##" 1841 PRINT USING A$ ,F5 1880 PRINT 1890 IF S9=1 THEN 2230 1900 S9=1 1910 PRINT "IF YOU DO NOT FEEL THAT THIS VALUE OF M REFLECTS YOUR" 1920 PRINT "PRIOR INFORMATION ABOUT THE MEAN YOU CAN SPECIFY A" 1930 PRINT "DIFFERENT M. A SMALLER M WILL GIVE LONGER INTERVALS" 1940 PRINT "AND A LARGER M SHORTER INTERVALS." 1950 PRINT 1960 PRINT "IF YOU WANT TO CHANGE M TYPE THE NEW VALUE ELSE '0'."; 1980 GOSUB 9000 1990 IF O1=0 THEN 2050 2000 IF O1>0 THEN 2030 2010 PRINT "REENTER. INPUT MUST BE 0 OR ACCEPTABLE M VALUE." 2020 GOTO 1980 2030 N2=O1 2040 GOTO 1540 2050 PRINT 2060 IF S6=1 THEN 2100 2070 PRINT "YOU CAN CHANGE THE CENTERING OF THE DISTRIBUTION BY" 2080 PRINT "SPECIFYING A DIFFERENT MEDIAN. THIS WILL NOT AFFECT" 2090 PRINT "THE HYPOTHETICAL SAMPLE SIZE." 2100 PRINT 2110 PRINT "IF YOU WANT TO SPECIFY A DIFFERENT MEDIAN TYPE '1'." 2120 PRINT "IF YOU DO NOT TYPE '0'." 2130 GOSUB 9000 2140 IF O1=1 THEN 2180 2150 IF O1=0 THEN 2320 2160 PRINT "REENTER. INPUT MUST BE 0 OR 1." 2170 GOTO 2130 2180 PRINT "SPECIFY DIFFERENT MEDIAN."; 2190 S6=1 2200 GOSUB 9000 2210 M=O1 2220 GOTO 1540 2230 PRINT "IF YOU WANT TO CHANGE M TYPE THE NEW VALUE ELSE '0'."; 2240A$="DEGREES OF FREEDOM #########.##" 2250 GOSUB 9000 2260 IF O1=0 THEN 2050 2270 IF O1<0 THEN 2300 2280 N2=O1 2290 GOTO 1540 2300 PRINT "REENTER. M MUST BE GREATER THAN 0." 2310 GOTO 2250 2320 PRINT L$ 2330 PRINT "HERE ARE SOME OF THE CHARACTERISTICS OF THE PRIOR MARGINAL" 2340 PRINT "DISTRIBUTION ON THE MEAN." 2350 PRINT 2360 PRINT " STUDENT'S T DISTRIBUTION" 2400 PRINT 2440A$="DEGREES OF FREEDOM #########.##" 2441 PRINT USING A$ ,N1 2450A$="SCALE PARAMETER #########.##" 2451 PRINT USING A$ ,L1*L1/N2 2460A$="MEAN=MEDIAN=MODE #########.##" 2461 PRINT USING A$ ,M 2470 S=L1/SQR(N2*(N1-2)) 2480A$="STANDARD DEVIATION #########.##" 2481 PRINT USING A$ ,S 2490 J5=.5 2500 GOSUB 7500 2510 GOSUB 2530 2520 GOTO 2570 2530 J2=J2*L1/SQR(N2*N1) 2540 J1=M-J2 2550 J2=M+J2 2560 RETURN 2570A$="50% HDR #########.## - ##########.##" 2571 PRINT USING A$ ,J1,J2 2580 J5=.75 2590 GOSUB 7500 2600 GOSUB 2530 2610A$="75% HDR #########.## - ##########.##" 2611 PRINT USING A$ ,J1,J2 2620 J5=.95 2630 GOSUB 7500 2640 GOSUB 2530 2650A$="95% HDR #########.## - ##########.##" 2651 PRINT USING A$ ,J1,J2 2660 PRINT 2670 PRINT "THIS COMPLETES THE SPECIFICATION OF A PRIOR ON THE MEAN." 2680 PRINT "IF YOU ARE NOT GOING DIRECTLY TO THE POSTERIOR ANALYSIS" 2690 PRINT "YOU SHOULD COPY DOWN THE DEGREES OF FREEDOM, MEAN, AND" 2700 PRINT "SCALE PARAMETER OF THE PRIOR MARGINAL DISTRIBUTION." 2705 PRINT "IF YOU WANT TO GO DIRECTLY TO POSTERIOR TYPE '1'." 2710 PRINT "IF YOU DO NOT TYPE '0'." 2720 GOSUB 9000 2730 I=O1 2740 IF I=1 THEN 2850 2750 IF I=0 THEN 2890 2760 PRINT "REENTER. INPUT MUST BE 0 OR 1." 2770 GOTO 2720 2780 REM ********************************************************* 2790 REM 2800 REM N1 DEGREES OF FREEDOM 2810 REM L1 SCALE FOR INV CHI 2820 REM F2 MEAN OF T DIST ON POPULKATION MEAN 2830 REM LAST SCALE FOR T ON MEAN 2840 REM 2850A2(0)=N1:A2(1)=L1:A2(2)=F2:A2(3)=L1*L1/N2:A2(4)=Q:A2(5)=0:A2(6)=N2 2860 CLOSE 1: CHAIN "CMOD6" 2870 REM 2880 REM ******************************************************* 2890 CLOSE 1: CHAIN "RSTRT" 2900 REM ******************************************************** 2910 REM APPENDED GOSUBS 2920 REM 2930 REM ********************************************************* 5850 REM **************************************************** 5852 REM LOG GAMMA ROUTINE 5853 REM INPUT G9 5854 REM OUTPUT G0 5860 G5=G9 5863 IF G9 <= 1.E+30 THEN 5872 5866 G0=1.E+38 5869 RETURN 5872 IF G9>1.E-09 THEN 5881 5875 G0=0 5878 RETURN 5881 IF G9<1.E+10 THEN 5890 5884 G0=G9*(LOG(G9)-1) 5887 RETURN 5890 G6=1 5893 IF 1880 THEN 6044 6043P=P+W(I1)*EXP(-D9) 6044 NEXT I1 6046 P=P*F0 6048 P=P*D0 6050 P=P+.5 6052 RETURN 6054 FOR I1=1 TO 16 6056 READ W(I1),O(I1) 6058 NEXT I1 6060 DATA 2.71525E-02,-.989401 6062 DATA 6.22535E-02,-.944575,9.51585E-02,-.865631 6064 DATA .124629,-.755404,.149596,-.617876 6066 DATA .169156,-.458017,.182603,-.281604,.189451,-9.50125E-02 6068 DATA .189451,9.50125E-02,.182603,.281604,.169156,.458017 6070 DATA .149596,.617876,.124629,.755404 6072 DATA 9.51585E-02,.865631,6.22535E-02,.944575,2.71525E-02 6074 DATA .989401 6076 RETURN 6078 G9=(N+1)/2 6080 GOSUB 5850 6082 F0=G0 6084 G9=N/2 6086 GOSUB 5850 6088 F0=EXP(F0-G0)/SQR(3.14159*N) 6090 RETURN 6092 REM FOLLOWING FOR NU=1 6094 P=.5+1/3.14159*ATN(Y3) 6096 RETURN 6097 REM END OF STUDENT'S T CDF ROUTINE 6098 REM************************************************************* 7500 REM ************************************************************ 7501 REM STUDENT'S T DISTRIBUTION HIGHEST DENSITY REGIONS 7502 REM INPUTS G J5 7503 REM J2 7504 REM 7505 Z8=.5 7506 N=G 7507 X9=1 7508 J1=0 7509 J2=X9 7510 GOSUB 6000 7511 P=2*P-1 7512 Z9=P 7513 IF P>J5 THEN 7517 7514 X9=X9+1 7515 Z8=Z9 7516 GOTO 7508 7517 X0=X9-1 7518 X2=X9 7519 X9=X0+(J5-Z8)*(X2-X0)/(Z9-Z8) 7520 J1=0 7521 J2=X9 7522 GOSUB 6000 7523 P=2*P-1 7524 IF ABS(P-J5)<.0001 THEN 7534 7525 IF P= 0 THEN 8070 8065 P=1-P 8070 X=X1 8075 RETURN 8076 REM 8077 REM END OF NORMAL CDF ROUTINE 8078 REM ********************************************************** 9000 REM--SUBROUTINE THAT DETERMINES IF RESTART HAS BEEN REQUESTED. 9005 INPUT O1 9015 IF O1=-9999 THEN 9025 9020 RETURN 9025 CLOSE 1: CHAIN "RSTRT" 9035 REM*************END ROUTINE 9999 END