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Luis A. Afonso
Posts:
4,743
From:
LIsbon (Portugal)
Registered:
2/16/05


“KNOTS”, check sample uniformity
Posted:
Dec 17, 2012 5:57 PM


?KNOTS?, check sample uniformity
___n= sample size
__________n=20_____40______60_____80_____100___ _fractile___ __0.005____0.109___0.114___0.114___0.115___0.116__ __0.010____0.118___0.122___0.123___0.123___0.124__ __0.025____0.132___0.136___0.137___0.137___0.138__ __0.050____0.147___0.150___0.151___0.152___0.152__ __0.175____0.158___0.161___0.161___0.162___0.163__ __0.100____0.167___0.170___0.171___0.171___0.171__ __0.200____0.197___0.199___0.200___0.200___0.201__ __0.300____0.223___0.225___0.226___0.226___0.226__ __0.400____0.250___0.252___0.252___0.252___0.253__ __0.500____0.279___0.280___0.281___0.281___0.281__ __0.600____0.312___0.313___0.314___0.314___0.314__ __0.700____0.353___0.354___0.355___0.355___0.355__ __0.800____0.408___0.409___0.409___0.409___0.410__ __0.900____0.497___0.498___0.499___0.499___0.499__ __0.925____0.532___0.532___0.534___0.534___0.534__ __0.950____0.579___0.580___0.580___0.581___0.581__ __0.975____0.655___0.655___0.657___0.657___0.658__ __0.990____0.745___0.747___0.750___0.751___0.750__ __0.995____0.805___0.813___0.814___0.814___0.814__
___Confidence Intervals
__Significance_ 5%___________ 1%_______
__n=20___[0.132, 0.655]___[0.109, 0.805] ____40___[0.136, 0.655]___[0.114, 0.813] ____60___[0.137, 0.657]___[0.114, 0.814] ____80___[0.137, 0.657]___[0.115, 0.814] ___100___[0.138, 0.658]___[0.116, 0.814]
Amazingly the CI bounds for different n are similar and seem to not grow without limit (asymptotic?).
Luis A. Afonso
REM "KNOTS" REM CLS PRINT "0_____...___1" PRINT " knots: 1/(2*n), 3/(2*n), ..."; PRINT ",(2*n3)/(2*n),(2*n1)/(2*n) " PRINT "Statistics>" PRINT "> SUM di (j=1, n) = SQR((y(j)  kn(j)) ^ 2 / n)" INPUT " n= "; n INPUT " all= "; ali DIM kn(n), X(n), XX(n), y(n) DIM w(8001) DIM u(30) REM FOR i = 1 TO n: kn(i) = (2 * i  1) / (n + n): NEXT i RANDOMIZE TIMER FOR rpt = 1 TO ali LOCATE 6, 50 PRINT USING "##########"; ali  rpt PRINT : PRINT FOR u = 1 TO n: X(u) = RND: XX(u) = X(u): NEXT u FOR u1 = 1 TO n w = X(u1): p = 1 FOR u2 = 1 TO n IF XX(u2) < w THEN p = p + 1 NEXT u2 y(p) = w NEXT u1 w = 0 FOR t = 1 TO n d = SQR((y(t)  kn(t)) ^ 2 / n) w = w + d NEXT t w = INT(w * 1000 + .5) w(w) = w(w) + 1 au = rpt / 10000: bu = INT(au) IF au <> bu THEN GOTO 20 u(1) = .005: u(2) = .01 u(3) = .025: u(4) = .05: u(5) = .075: u(6) = .1 u(7) = .2: u(8) = .3: u(9) = .4 u(10) = .5: u(11) = .6: u(12) = .7: u(13) = .8: u(14) = .9 u(15) = 1  u(5): u(16) = 1  u(4): u(17) = 1  u(3) u(18) = 1  u(2): u(19) = 1  u(1) REM FOR y = 1 TO 19 IF y = 1 THEN GOTO 7 IF y / 2 = INT(y / 2) THEN PRINT 7 su = 0: u = u(y) FOR tt = 0 TO 8000 su = su + w(tt) / rpt IF su > u THEN GOTO 17 NEXT tt 17 PRINT USING " #.### #.### "; u(y); tt / 1000; NEXT y 20 NEXT rpt END



