/usr/share/tcltk/tcllib1.16/math/statistics.tcl is in tcllib 1.16-dfsg-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 | # statistics.tcl --
#
# Package for basic statistical analysis
#
# version 0.1: initial implementation, january 2003
# version 0.1.1: added linear regres
# version 0.1.2: border case in stdev taken care of
# version 0.1.3: moved initialisation of CDF to first call, november 2004
# version 0.3: added test for normality (as implemented by Torsten Reincke), march 2006
# (also fixed an error in the export list)
# version 0.4: added the multivariate linear regression procedures by
# Eric Kemp-Benedict, february 2007
# version 0.5: added the population standard deviation and variance,
# as suggested by Dimitrios Zachariadis
# version 0.6: added pdf and cdf procedures for various distributions
# (provided by Eric Kemp-Benedict)
# version 0.7: added Kruskal-Wallis test (by Torsten Berg)
# version 0.8: added Wilcoxon test and Spearman rank correlation
# version 0.9: added kernel density estimation
package require Tcl 8.4
package provide math::statistics 0.9
package require math
if {![llength [info commands ::lrepeat]]} {
# Forward portability, emulate lrepeat
proc ::lrepeat {n args} {
if {$n < 1} {
return -code error "must have a count of at least 1"
}
set res {}
while {$n} {
foreach x $args { lappend res $x }
incr n -1
}
return $res
}
}
# ::math::statistics --
# Namespace holding the procedures and variables
#
namespace eval ::math::statistics {
#
# Safer: change to short procedures
#
namespace export mean min max number var stdev pvar pstdev basic-stats corr \
histogram interval-mean-stdev t-test-mean quantiles \
test-normal lillieforsFit \
autocorr crosscorr filter map samplescount median \
test-2x2 print-2x2 control-xbar test_xbar \
control-Rchart test-Rchart \
test-Kruskal-Wallis analyse-Kruskal-Wallis group-rank \
test-Wilcoxon spearman-rank spearman-rank-extended
#
# Error messages
#
variable NEGSTDEV {Zero or negative standard deviation}
variable TOOFEWDATA {Too few or invalid data}
variable OUTOFRANGE {Argument out of range}
#
# Coefficients involved
#
variable factorNormalPdf
set factorNormalPdf [expr {sqrt(8.0*atan(1.0))}]
# xbar/R-charts:
# Data from:
# Peter W.M. John:
# Statistical methods in engineering and quality assurance
# Wiley and Sons, 1990
#
variable control_factors {
A2 {1.880 1.093 0.729 0.577 0.483 0.419 0.419}
D3 {0.0 0.0 0.0 0.0 0.0 0.076 0.076}
D4 {3.267 2.574 2.282 2.114 2.004 1.924 1.924}
}
}
# mean, min, max, number, var, stdev, pvar, pstdev --
# Return the mean (minimum, maximum) value of a list of numbers
# or number of non-missing values
#
# Arguments:
# type Type of value to be returned
# values List of values to be examined
#
# Results:
# Value that was required
#
#
namespace eval ::math::statistics {
foreach type {mean min max number stdev var pstdev pvar} {
proc $type { values } "BasicStats $type \$values"
}
proc basic-stats { values } "BasicStats all \$values"
}
# BasicStats --
# Return the one or all of the basic statistical properties
#
# Arguments:
# type Type of value to be returned
# values List of values to be examined
#
# Results:
# Value that was required
#
proc ::math::statistics::BasicStats { type values } {
variable TOOFEWDATA
if { [lsearch {all mean min max number stdev var pstdev pvar} $type] < 0 } {
return -code error \
-errorcode ARG -errorinfo [list unknown type of statistic -- $type] \
[list unknown type of statistic -- $type]
}
set min {}
set max {}
set mean {}
set stdev {}
set var {}
set sum 0.0
set sumsq 0.0
set number 0
set first {}
foreach value $values {
if { $value == {} } {
continue
}
set value [expr {double($value)}]
if { $first == {} } {
set first $value
}
incr number
set sum [expr {$sum+$value}]
set sumsq [expr {$sumsq+($value-$first)*($value-$first)}]
if { $min == {} || $value < $min } {
set min $value
}
if { $max == {} || $value > $max } {
set max $value
}
}
if { $number > 0 } {
set mean [expr {$sum/$number}]
} else {
return -code error -errorcode DATA -errorinfo $TOOFEWDATA $TOOFEWDATA
}
if { $number > 1 } {
set var [expr {($sumsq-($mean-$first)*($sum-$number*$first))/double($number-1)}]
#
# Take care of a rare situation: uniform data might
# cause a tiny negative difference
#
if { $var < 0.0 } {
set var 0.0
}
set stdev [expr {sqrt($var)}]
}
set pvar [expr {($sumsq-($mean-$first)*($sum-$number*$first))/double($number)}]
#
# Take care of a rare situation: uniform data might
# cause a tiny negative difference
#
if { $pvar < 0.0 } {
set pvar 0.0
}
set pstdev [expr {sqrt($pvar)}]
set all [list $mean $min $max $number $stdev $var $pstdev $pvar]
#
# Return the appropriate value
#
set $type
}
# histogram --
# Return histogram information from a list of numbers
#
# Arguments:
# limits Upper limits for the buckets (in increasing order)
# values List of values to be examined
# weights List of weights, one per value (optional)
#
# Results:
# List of number of values in each bucket (length is one more than
# the number of limits)
#
#
proc ::math::statistics::histogram { limits values {weights {}} } {
if { [llength $limits] < 1 } {
return -code error -errorcode ARG -errorinfo {No limits given} {No limits given}
}
if { [llength $weights] > 0 && [llength $values] != [llength $weights] } {
return -code error -errorcode ARG -errorinfo {Number of weights be equal to number of values} {Weights and values differ in length}
}
set limits [lsort -real -increasing $limits]
for { set index 0 } { $index <= [llength $limits] } { incr index } {
set buckets($index) 0
}
set last [llength $limits]
# Will do integer arithmetic if unset
if {$weights eq ""} {
set weights [lrepeat [llength $values] 1]
}
foreach value $values weight $weights {
if { $value == {} } {
continue
}
set index 0
set found 0
foreach limit $limits {
if { $value <= $limit } {
set found 1
set buckets($index) [expr $buckets($index)+$weight]
break
}
incr index
}
if { $found == 0 } {
set buckets($last) [expr $buckets($last)+$weight]
}
}
set result {}
for { set index 0 } { $index <= $last } { incr index } {
lappend result $buckets($index)
}
return $result
}
# corr --
# Return the correlation coefficient of two sets of data
#
# Arguments:
# data1 List with the first set of data
# data2 List with the second set of data
#
# Result:
# Correlation coefficient of the two
#
proc ::math::statistics::corr { data1 data2 } {
variable TOOFEWDATA
set number 0
set sum1 0.0
set sum2 0.0
set sumsq1 0.0
set sumsq2 0.0
set sumprod 0.0
foreach value1 $data1 value2 $data2 {
if { $value1 == {} || $value2 == {} } {
continue
}
set value1 [expr {double($value1)}]
set value2 [expr {double($value2)}]
set sum1 [expr {$sum1+$value1}]
set sum2 [expr {$sum2+$value2}]
set sumsq1 [expr {$sumsq1+$value1*$value1}]
set sumsq2 [expr {$sumsq2+$value2*$value2}]
set sumprod [expr {$sumprod+$value1*$value2}]
incr number
}
if { $number > 0 } {
set numerator [expr {$number*$sumprod-$sum1*$sum2}]
set denom1 [expr {sqrt($number*$sumsq1-$sum1*$sum1)}]
set denom2 [expr {sqrt($number*$sumsq2-$sum2*$sum2)}]
if { $denom1 != 0.0 && $denom2 != 0.0 } {
set corr_coeff [expr {$numerator/$denom1/$denom2}]
} elseif { $denom1 != 0.0 || $denom2 != 0.0 } {
set corr_coeff 0.0 ;# Uniform against non-uniform
} else {
set corr_coeff 1.0 ;# Both uniform
}
} else {
return -code error -errorcode DATA -errorinfo $TOOFEWDATA $TOOFEWDATA
}
return $corr_coeff
}
# lillieforsFit --
# Calculate the goodness of fit according to Lilliefors
# (goodness of fit to a normal distribution)
#
# Arguments:
# values List of values to be tested for normality
#
# Result:
# Value of the statistic D
#
proc ::math::statistics::lillieforsFit {values} {
#
# calculate the goodness of fit according to Lilliefors
# (goodness of fit to a normal distribution)
#
# values -> list of values to be tested for normality
# (these values are sampled counts)
#
# calculate standard deviation and mean of the sample:
set n [llength $values]
if { $n < 5 } {
return -code error "Insufficient number of data (at least five required)"
}
set sd [stdev $values]
set mean [mean $values]
# sort the sample for further processing:
set values [lsort -real $values]
# standardize the sample data (Z-scores):
foreach x $values {
lappend stdData [expr {($x - $mean)/double($sd)}]
}
# compute the value of the distribution function at every sampled point:
foreach x $stdData {
lappend expData [pnorm $x]
}
# compute D+:
set i 0
foreach x $expData {
incr i
lappend dplus [expr {$i/double($n)-$x}]
}
set dplus [lindex [lsort -real $dplus] end]
# compute D-:
set i 0
foreach x $expData {
incr i
lappend dminus [expr {$x-($i-1)/double($n)}]
}
set dminus [lindex [lsort -real $dminus] end]
# Calculate the test statistic D
# by finding the maximal vertical difference
# between the sample and the expectation:
#
set D [expr {$dplus > $dminus ? $dplus : $dminus}]
# We now use the modified statistic Z,
# because D is only reliable
# if the p-value is smaller than 0.1
return [expr {$D * (sqrt($n) - 0.01 + 0.831/sqrt($n))}]
}
# pnorm --
# Calculate the cumulative distribution function (cdf)
# for the standard normal distribution like in the statistical
# software 'R' (mean=0 and sd=1)
#
# Arguments:
# x Value fro which the cdf should be calculated
#
# Result:
# Value of the statistic D
#
proc ::math::statistics::pnorm {x} {
#
# cumulative distribution function (cdf)
# for the standard normal distribution like in the statistical software 'R'
# (mean=0 and sd=1)
#
# x -> value for which the cdf should be calculated
#
set sum [expr {double($x)}]
set oldSum 0.0
set i 1
set denom 1.0
while {$sum != $oldSum} {
set oldSum $sum
incr i 2
set denom [expr {$denom*$i}]
#puts "$i - $denom"
set sum [expr {$oldSum + pow($x,$i)/$denom}]
}
return [expr {0.5 + $sum * exp(-0.5 * $x*$x - 0.91893853320467274178)}]
}
# pnorm_quicker --
# Calculate the cumulative distribution function (cdf)
# for the standard normal distribution - quicker alternative
# (less accurate)
#
# Arguments:
# x Value for which the cdf should be calculated
#
# Result:
# Value of the statistic D
#
proc ::math::statistics::pnorm_quicker {x} {
set n [expr {abs($x)}]
set n [expr {1.0 + $n*(0.04986735 + $n*(0.02114101 + $n*(0.00327763 \
+ $n*(0.0000380036 + $n*(0.0000488906 + $n*0.000005383)))))}]
set n [expr {1.0/pow($n,16)}]
#
if {$x >= 0} {
return [expr {1 - $n/2.0}]
} else {
return [expr {$n/2.0}]
}
}
# test-normal --
# Test for normality (using method Lilliefors)
#
# Arguments:
# data Values that need to be tested
# confidence ...
#
# Result:
# 1 if of the statistic D
#
proc ::math::statistics::test-normal {data confidence} {
set D [lillieforsFit $data]
set Dcrit --
if { abs($confidence-0.80) < 0.0001 } {
set Dcrit 0.741
}
if { abs($confidence-0.85) < 0.0001 } {
set Dcrit 0.775
}
if { abs($confidence-0.90) < 0.0001 } {
set Dcrit 0.819
}
if { abs($confidence-0.95) < 0.0001 } {
set Dcrit 0.895
}
if { abs($confidence-0.99) < 0.0001 } {
set Dcrit 1.035
}
if { $Dcrit != "--" } {
return [expr {$D > $Dcrit ? 1 : 0 }]
} else {
return -code error "Confidence level must be one of: 0.80, 0.85, 0.90, 0.95 or 0.99"
}
}
# t-test-mean --
# Test whether the mean value of a sample is in accordance with the
# estimated normal distribution with a certain level of confidence
# (Student's t test)
#
# Arguments:
# data List of raw data values (small sample)
# est_mean Estimated mean of the distribution
# est_stdev Estimated stdev of the distribution
# confidence Confidence level (0.95 or 0.99 for instance)
#
# Result:
# 1 if the test is positive, 0 otherwise. If there are too few data,
# returns an empty string
#
proc ::math::statistics::t-test-mean { data est_mean est_stdev confidence } {
variable NEGSTDEV
variable TOOFEWDATA
if { $est_stdev <= 0.0 } {
return -code error -errorcode ARG -errorinfo $NEGSTDEV $NEGSTDEV
}
set allstats [BasicStats all $data]
set conf2 [expr {(1.0+$confidence)/2.0}]
set sample_mean [lindex $allstats 0]
set sample_number [lindex $allstats 3]
if { $sample_number > 1 } {
set tzero [expr {abs($sample_mean-$est_mean)/$est_stdev * \
sqrt($sample_number-1)}]
set degrees [expr {$sample_number-1}]
set prob [cdf-students-t $degrees $tzero]
return [expr {$prob<$conf2}]
} else {
return -code error -errorcode DATA -errorinfo $TOOFEWDATA $TOOFEWDATA
}
}
# interval-mean-stdev --
# Return the interval containing the mean value and one
# containing the standard deviation with a certain
# level of confidence (assuming a normal distribution)
#
# Arguments:
# data List of raw data values
# confidence Confidence level (0.95 or 0.99 for instance)
#
# Result:
# List having the following elements: lower and upper bounds of
# mean, lower and upper bounds of stdev
#
#
proc ::math::statistics::interval-mean-stdev { data confidence } {
variable TOOFEWDATA
set allstats [BasicStats all $data]
set conf2 [expr {(1.0+$confidence)/2.0}]
set mean [lindex $allstats 0]
set number [lindex $allstats 3]
set stdev [lindex $allstats 4]
if { $number > 1 } {
set degrees [expr {$number-1}]
set student_t [expr {sqrt([Inverse-cdf-toms322 1 $degrees $conf2])}]
set mean_lower [expr {$mean-$student_t*$stdev/sqrt($number)}]
set mean_upper [expr {$mean+$student_t*$stdev/sqrt($number)}]
set stdev_lower {}
set stdev_upper {}
return [list $mean_lower $mean_upper $stdev_lower $stdev_upper]
} else {
return -code error -errorcode DATA -errorinfo $TOOFEWDATA $TOOFEWDATA
}
}
# quantiles --
# Return the quantiles for a given set of data or histogram
#
# Arguments:
# (two arguments)
# data List of raw data values
# confidence Confidence level (0.95 or 0.99 for instance)
# (three arguments)
# limits List of upper limits from histogram
# counts List of counts for for each interval in histogram
# confidence Confidence level (0.95 or 0.99 for instance)
#
# Result:
# List of quantiles
#
proc ::math::statistics::quantiles { arg1 arg2 {arg3 {}} } {
variable TOOFEWDATA
if { [catch {
if { $arg3 == {} } {
set result \
[::math::statistics::QuantilesRawData $arg1 $arg2]
} else {
set result \
[::math::statistics::QuantilesHistogram $arg1 $arg2 $arg3]
}
} msg] } {
return -code error -errorcode $msg $msg
}
return $result
}
# QuantilesRawData --
# Return the quantiles based on raw data
#
# Arguments:
# data List of raw data values
# confidence Confidence level (0.95 or 0.99 for instance)
#
# Result:
# List of quantiles
#
proc ::math::statistics::QuantilesRawData { data confidence } {
variable TOOFEWDATA
variable OUTOFRANGE
if { [llength $confidence] <= 0 } {
return -code error -errorcode ARG "$TOOFEWDATA - quantiles"
}
if { [llength $data] <= 0 } {
return -code error -errorcode ARG "$TOOFEWDATA - raw data"
}
foreach cond $confidence {
if { $cond <= 0.0 || $cond >= 1.0 } {
return -code error -errorcode ARG "$OUTOFRANGE - quantiles"
}
}
#
# Sort the data first
#
set sorted_data [lsort -real -increasing $data]
#
# Determine the list element lower or equal to the quantile
# and return the corresponding value
#
set result {}
set number_data [llength $sorted_data]
foreach cond $confidence {
set elem [expr {round($number_data*$cond)-1}]
if { $elem < 0 } {
set elem 0
}
lappend result [lindex $sorted_data $elem]
}
return $result
}
# QuantilesHistogram --
# Return the quantiles based on histogram information only
#
# Arguments:
# limits Upper limits for histogram intervals
# counts Counts for each interval
# confidence Confidence level (0.95 or 0.99 for instance)
#
# Result:
# List of quantiles
#
proc ::math::statistics::QuantilesHistogram { limits counts confidence } {
variable TOOFEWDATA
variable OUTOFRANGE
if { [llength $confidence] <= 0 } {
return -code error -errorcode ARG "$TOOFEWDATA - quantiles"
}
if { [llength $confidence] <= 0 } {
return -code error -errorcode ARG "$TOOFEWDATA - histogram limits"
}
if { [llength $counts] <= [llength $limits] } {
return -code error -errorcode ARG "$TOOFEWDATA - histogram counts"
}
foreach cond $confidence {
if { $cond <= 0.0 || $cond >= 1.0 } {
return -code error -errorcode ARG "$OUTOFRANGE - quantiles"
}
}
#
# Accumulate the histogram counts first
#
set sum 0
set accumulated_counts {}
foreach count $counts {
set sum [expr {$sum+$count}]
lappend accumulated_counts $sum
}
set total_counts $sum
#
# Determine the list element lower or equal to the quantile
# and return the corresponding value (use interpolation if
# possible)
#
set result {}
foreach cond $confidence {
set found 0
set bound [expr {round($total_counts*$cond)}]
set lower_limit {}
set lower_count 0
foreach acc_count $accumulated_counts limit $limits {
if { $acc_count >= $bound } {
set found 1
break
}
set lower_limit $limit
set lower_count $acc_count
}
if { $lower_limit == {} || $limit == {} || $found == 0 } {
set quant $limit
if { $limit == {} } {
set quant $lower_limit
}
} else {
set quant [expr {$limit+($lower_limit-$limit) *
($acc_count-$bound)/($acc_count-$lower_count)}]
}
lappend result $quant
}
return $result
}
# autocorr --
# Return the autocorrelation function (assuming equidistance between
# samples)
#
# Arguments:
# data Raw data for which the autocorrelation must be determined
#
# Result:
# List of autocorrelation values (about 1/2 the number of raw data)
#
proc ::math::statistics::autocorr { data } {
variable TOOFEWDATA
if { [llength $data] <= 1 } {
return -code error -errorcode ARG "$TOOFEWDATA"
}
return [crosscorr $data $data]
}
# crosscorr --
# Return the cross-correlation function (assuming equidistance
# between samples)
#
# Arguments:
# data1 First set of raw data
# data2 Second set of raw data
#
# Result:
# List of cross-correlation values (about 1/2 the number of raw data)
#
# Note:
# The number of data pairs is not kept constant - because tests
# showed rather awkward results when it was kept constant.
#
proc ::math::statistics::crosscorr { data1 data2 } {
variable TOOFEWDATA
if { [llength $data1] <= 1 || [llength $data2] <= 1 } {
return -code error -errorcode ARG "$TOOFEWDATA"
}
#
# First determine the number of data pairs
#
set number1 [llength $data1]
set number2 [llength $data2]
set basic_stat1 [basic-stats $data1]
set basic_stat2 [basic-stats $data2]
set vmean1 [lindex $basic_stat1 0]
set vmean2 [lindex $basic_stat2 0]
set vvar1 [lindex $basic_stat1 end]
set vvar2 [lindex $basic_stat2 end]
set number_pairs $number1
if { $number1 > $number2 } {
set number_pairs $number2
}
set number_values $number_pairs
set number_delays [expr {$number_values/2.0}]
set scale [expr {sqrt($vvar1*$vvar2)}]
set result {}
for { set delay 0 } { $delay < $number_delays } { incr delay } {
set sumcross 0.0
set no_cross 0
for { set idx 0 } { $idx < $number_values } { incr idx } {
set value1 [lindex $data1 $idx]
set value2 [lindex $data2 [expr {$idx+$delay}]]
if { $value1 != {} && $value2 != {} } {
set sumcross \
[expr {$sumcross+($value1-$vmean1)*($value2-$vmean2)}]
incr no_cross
}
}
lappend result [expr {$sumcross/($no_cross*$scale)}]
incr number_values -1
}
return $result
}
# mean-histogram-limits
# Determine reasonable limits based on mean and standard deviation
# for a histogram
#
# Arguments:
# mean Mean of the data
# stdev Standard deviation
# number Number of limits to generate (defaults to 8)
#
# Result:
# List of limits
#
proc ::math::statistics::mean-histogram-limits { mean stdev {number 8} } {
variable NEGSTDEV
if { $stdev <= 0.0 } {
return -code error -errorcode ARG "$NEGSTDEV"
}
if { $number < 1 } {
return -code error -errorcode ARG "Number of limits must be positive"
}
#
# Always: between mean-3.0*stdev and mean+3.0*stdev
# number = 2: -0.25, 0.25
# number = 3: -0.25, 0, 0.25
# number = 4: -1, -0.25, 0.25, 1
# number = 5: -1, -0.25, 0, 0.25, 1
# number = 6: -2, -1, -0.25, 0.25, 1, 2
# number = 7: -2, -1, -0.25, 0, 0.25, 1, 2
# number = 8: -3, -2, -1, -0.25, 0.25, 1, 2, 3
#
switch -- $number {
"1" { set limits {0.0} }
"2" { set limits {-0.25 0.25} }
"3" { set limits {-0.25 0.0 0.25} }
"4" { set limits {-1.0 -0.25 0.25 1.0} }
"5" { set limits {-1.0 -0.25 0.0 0.25 1.0} }
"6" { set limits {-2.0 -1.0 -0.25 0.25 1.0 2.0} }
"7" { set limits {-2.0 -1.0 -0.25 0.0 0.25 1.0 2.0} }
"8" { set limits {-3.0 -2.0 -1.0 -0.25 0.25 1.0 2.0 3.0} }
"9" { set limits {-3.0 -2.0 -1.0 -0.25 0.0 0.25 1.0 2.0 3.0} }
default {
set dlim [expr {6.0/double($number-1)}]
for {set i 0} {$i <$number} {incr i} {
lappend limits [expr {$dlim*($i-($number-1)/2.0)}]
}
}
}
set result {}
foreach limit $limits {
lappend result [expr {$mean+$limit*$stdev}]
}
return $result
}
# minmax-histogram-limits
# Determine reasonable limits based on minimum and maximum bounds
# for a histogram
#
# Arguments:
# min Estimated minimum
# max Estimated maximum
# number Number of limits to generate (defaults to 8)
#
# Result:
# List of limits
#
proc ::math::statistics::minmax-histogram-limits { min max {number 8} } {
variable NEGSTDEV
if { $number < 1 } {
return -code error -errorcode ARG "Number of limits must be positive"
}
if { $min >= $max } {
return -code error -errorcode ARG "Minimum must be lower than maximum"
}
set result {}
set dlim [expr {($max-$min)/double($number-1)}]
for {set i 0} {$i <$number} {incr i} {
lappend result [expr {$min+$dlim*$i}]
}
return $result
}
# linear-model
# Determine the coefficients for a linear regression between
# two series of data (the model: Y = A + B*X)
#
# Arguments:
# xdata Series of independent (X) data
# ydata Series of dependent (Y) data
# intercept Whether to use an intercept or not (optional)
#
# Result:
# List of the following items:
# - (Estimate of) Intercept A
# - (Estimate of) Slope B
# - Standard deviation of Y relative to fit
# - Correlation coefficient R2
# - Number of degrees of freedom df
# - Standard error of the intercept A
# - Significance level of A
# - Standard error of the slope B
# - Significance level of B
#
#
proc ::math::statistics::linear-model { xdata ydata {intercept 1} } {
variable TOOFEWDATA
if { [llength $xdata] < 3 } {
return -code error -errorcode ARG "$TOOFEWDATA: not enough independent data"
}
if { [llength $ydata] < 3 } {
return -code error -errorcode ARG "$TOOFEWDATA: not enough dependent data"
}
if { [llength $xdata] != [llength $ydata] } {
return -code error -errorcode ARG "$TOOFEWDATA: number of dependent data differs from number of independent data"
}
set sumx 0.0
set sumy 0.0
set sumx2 0.0
set sumy2 0.0
set sumxy 0.0
set df 0
foreach x $xdata y $ydata {
if { $x != "" && $y != "" } {
set sumx [expr {$sumx+$x}]
set sumy [expr {$sumy+$y}]
set sumx2 [expr {$sumx2+$x*$x}]
set sumy2 [expr {$sumy2+$y*$y}]
set sumxy [expr {$sumxy+$x*$y}]
incr df
}
}
if { $df <= 2 } {
return -code error -errorcode ARG "$TOOFEWDATA: too few valid data"
}
if { $sumx2 == 0.0 } {
return -code error -errorcode ARG "$TOOFEWDATA: independent values are all the same"
}
#
# Calculate the intermediate quantities
#
set sx [expr {$sumx2-$sumx*$sumx/$df}]
set sy [expr {$sumy2-$sumy*$sumy/$df}]
set sxy [expr {$sumxy-$sumx*$sumy/$df}]
#
# Calculate the coefficients
#
if { $intercept } {
set B [expr {$sxy/$sx}]
set A [expr {($sumy-$B*$sumx)/$df}]
} else {
set B [expr {$sumxy/$sumx2}]
set A 0.0
}
#
# Calculate the error estimates
#
set stdevY 0.0
set varY 0.0
if { $intercept } {
set ve [expr {$sy-$B*$sxy}]
if { $ve >= 0.0 } {
set varY [expr {$ve/($df-2)}]
}
} else {
set ve [expr {$sumy2-$B*$sumxy}]
if { $ve >= 0.0 } {
set varY [expr {$ve/($df-1)}]
}
}
set seY [expr {sqrt($varY)}]
if { $intercept } {
set R2 [expr {$sxy*$sxy/($sx*$sy)}]
set seA [expr {$seY*sqrt(1.0/$df+$sumx*$sumx/($sx*$df*$df))}]
set seB [expr {sqrt($varY/$sx)}]
set tA {}
set tB {}
if { $seA != 0.0 } {
set tA [expr {$A/$seA*sqrt($df-2)}]
}
if { $seB != 0.0 } {
set tB [expr {$B/$seB*sqrt($df-2)}]
}
} else {
set R2 [expr {$sumxy*$sumxy/($sumx2*$sumy2)}]
set seA {}
set tA {}
set tB {}
set seB [expr {sqrt($varY/$sumx2)}]
if { $seB != 0.0 } {
set tB [expr {$B/$seB*sqrt($df-1)}]
}
}
#
# Return the list of parameters
#
return [list $A $B $seY $R2 $df $seA $tA $seB $tB]
}
# linear-residuals
# Determine the difference between actual data and predicted from
# the linear model
#
# Arguments:
# xdata Series of independent (X) data
# ydata Series of dependent (Y) data
# intercept Whether to use an intercept or not (optional)
#
# Result:
# List of differences
#
proc ::math::statistics::linear-residuals { xdata ydata {intercept 1} } {
variable TOOFEWDATA
if { [llength $xdata] < 3 } {
return -code error -errorcode ARG "$TOOFEWDATA: no independent data"
}
if { [llength $ydata] < 3 } {
return -code error -errorcode ARG "$TOOFEWDATA: no dependent data"
}
if { [llength $xdata] != [llength $ydata] } {
return -code error -errorcode ARG "$TOOFEWDATA: number of dependent data differs from number of independent data"
}
foreach {A B} [linear-model $xdata $ydata $intercept] {break}
set result {}
foreach x $xdata y $ydata {
set residue [expr {$y-$A-$B*$x}]
lappend result $residue
}
return $result
}
# median
# Determine the median from a list of data
#
# Arguments:
# data (Unsorted) list of data
#
# Result:
# Median (either the middle value or the mean of two values in the
# middle)
#
# Note:
# Adapted from the Wiki page "Stats", code provided by JPS
#
proc ::math::statistics::median { data } {
set org_data $data
set data {}
foreach value $org_data {
if { $value != {} } {
lappend data $value
}
}
set len [llength $data]
set data [lsort -real $data]
if { $len % 2 } {
lindex $data [expr {($len-1)/2}]
} else {
expr {([lindex $data [expr {($len / 2) - 1}]] \
+ [lindex $data [expr {$len / 2}]]) / 2.0}
}
}
# test-2x2 --
# Compute the chi-square statistic for a 2x2 table
#
# Arguments:
# a Element upper-left
# b Element upper-right
# c Element lower-left
# d Element lower-right
# Return value:
# Chi-square
# Note:
# There is only one degree of freedom - this is important
# when comparing the value to the tabulated values
# of chi-square
#
proc ::math::statistics::test-2x2 { a b c d } {
set ab [expr {$a+$b}]
set ac [expr {$a+$c}]
set bd [expr {$b+$d}]
set cd [expr {$c+$d}]
set N [expr {$a+$b+$c+$d}]
set det [expr {$a*$d-$b*$c}]
set result [expr {double($N*$det*$det)/double($ab*$cd*$ac*$bd)}]
}
# print-2x2 --
# Print a 2x2 table
#
# Arguments:
# a Element upper-left
# b Element upper-right
# c Element lower-left
# d Element lower-right
# Return value:
# Printed version with marginals
#
proc ::math::statistics::print-2x2 { a b c d } {
set ab [expr {$a+$b}]
set ac [expr {$a+$c}]
set bd [expr {$b+$d}]
set cd [expr {$c+$d}]
set N [expr {$a+$b+$c+$d}]
set chisq [test-2x2 $a $b $c $d]
set line [string repeat - 10]
set result [format "%10d%10d | %10d\n" $a $b $ab]
append result [format "%10d%10d | %10d\n" $c $d $cd]
append result [format "%10s%10s + %10s\n" $line $line $line]
append result [format "%10d%10d | %10d\n" $ac $bd $N]
append result "Chisquare = $chisq\n"
append result "Difference is significant?\n"
append result " at 95%: [expr {$chisq<3.84146? "no":"yes"}]\n"
append result " at 99%: [expr {$chisq<6.63490? "no":"yes"}]"
}
# control-xbar --
# Determine the control lines for an x-bar chart
#
# Arguments:
# data List of observed values (at least 20*nsamples)
# nsamples Number of data per subsamples (default: 4)
# Return value:
# List of: mean, lower limit, upper limit, number of data per
# subsample. Can be used in the test-xbar procedure
#
proc ::math::statistics::control-xbar { data {nsamples 4} } {
variable TOOFEWDATA
variable control_factors
#
# Check the number of data
#
if { $nsamples <= 1 } {
return -code error -errorcode DATA -errorinfo $OUTOFRANGE \
"Number of data per subsample must be at least 2"
}
if { [llength $data] < 20*$nsamples } {
return -code error -errorcode DATA -errorinfo $TOOFEWDATA $TOOFEWDATA
}
set nogroups [expr {[llength $data]/$nsamples}]
set mrange 0.0
set xmeans 0.0
for { set i 0 } { $i < $nogroups } { incr i } {
set subsample [lrange $data [expr {$i*$nsamples}] [expr {$i*$nsamples+$nsamples-1}]]
set xmean 0.0
set xmin [lindex $subsample 0]
set xmax $xmin
foreach d $subsample {
set xmean [expr {$xmean+$d}]
set xmin [expr {$xmin<$d? $xmin : $d}]
set xmax [expr {$xmax>$d? $xmax : $d}]
}
set xmean [expr {$xmean/double($nsamples)}]
set xmeans [expr {$xmeans+$xmean}]
set mrange [expr {$mrange+($xmax-$xmin)}]
}
#
# Determine the control lines
#
set xmeans [expr {$xmeans/double($nogroups)}]
set mrange [expr {$mrange/double($nogroups)}]
set A2 [lindex [lindex $control_factors 1] $nsamples]
if { $A2 == "" } { set A2 [lindex [lindex $control_factors 1] end] }
return [list $xmeans [expr {$xmeans-$A2*$mrange}] \
[expr {$xmeans+$A2*$mrange}] $nsamples]
}
# test-xbar --
# Determine if any data points lie outside the x-bar control limits
#
# Arguments:
# control List returned by control-xbar with control data
# data List of observed values
# Return value:
# Indices of any subsamples that violate the control limits
#
proc ::math::statistics::test-xbar { control data } {
foreach {xmean xlower xupper nsamples} $control {break}
if { [llength $data] < 1 } {
return -code error -errorcode DATA -errorinfo $TOOFEWDATA $TOOFEWDATA
}
set nogroups [expr {[llength $data]/$nsamples}]
if { $nogroups <= 0 } {
set nogroup 1
set nsamples [llength $data]
}
set result {}
for { set i 0 } { $i < $nogroups } { incr i } {
set subsample [lrange $data [expr {$i*$nsamples}] [expr {$i*$nsamples+$nsamples-1}]]
set xmean 0.0
foreach d $subsample {
set xmean [expr {$xmean+$d}]
}
set xmean [expr {$xmean/double($nsamples)}]
if { $xmean < $xlower } { lappend result $i }
if { $xmean > $xupper } { lappend result $i }
}
return $result
}
# control-Rchart --
# Determine the control lines for an R chart
#
# Arguments:
# data List of observed values (at least 20*nsamples)
# nsamples Number of data per subsamples (default: 4)
# Return value:
# List of: mean range, lower limit, upper limit, number of data per
# subsample. Can be used in the test-Rchart procedure
#
proc ::math::statistics::control-Rchart { data {nsamples 4} } {
variable TOOFEWDATA
variable control_factors
#
# Check the number of data
#
if { $nsamples <= 1 } {
return -code error -errorcode DATA -errorinfo $OUTOFRANGE \
"Number of data per subsample must be at least 2"
}
if { [llength $data] < 20*$nsamples } {
return -code error -errorcode DATA -errorinfo $TOOFEWDATA $TOOFEWDATA
}
set nogroups [expr {[llength $data]/$nsamples}]
set mrange 0.0
for { set i 0 } { $i < $nogroups } { incr i } {
set subsample [lrange $data [expr {$i*$nsamples}] [expr {$i*$nsamples+$nsamples-1}]]
set xmin [lindex $subsample 0]
set xmax $xmin
foreach d $subsample {
set xmin [expr {$xmin<$d? $xmin : $d}]
set xmax [expr {$xmax>$d? $xmax : $d}]
}
set mrange [expr {$mrange+($xmax-$xmin)}]
}
#
# Determine the control lines
#
set mrange [expr {$mrange/double($nogroups)}]
set D3 [lindex [lindex $control_factors 3] $nsamples]
set D4 [lindex [lindex $control_factors 5] $nsamples]
if { $D3 == "" } { set D3 [lindex [lindex $control_factors 3] end] }
if { $D4 == "" } { set D4 [lindex [lindex $control_factors 5] end] }
return [list $mrange [expr {$D3*$mrange}] \
[expr {$D4*$mrange}] $nsamples]
}
# test-Rchart --
# Determine if any data points lie outside the R-chart control limits
#
# Arguments:
# control List returned by control-xbar with control data
# data List of observed values
# Return value:
# Indices of any subsamples that violate the control limits
#
proc ::math::statistics::test-Rchart { control data } {
foreach {rmean rlower rupper nsamples} $control {break}
#
# Check the number of data
#
if { [llength $data] < 1 } {
return -code error -errorcode DATA -errorinfo $TOOFEWDATA $TOOFEWDATA
}
set nogroups [expr {[llength $data]/$nsamples}]
set result {}
for { set i 0 } { $i < $nogroups } { incr i } {
set subsample [lrange $data [expr {$i*$nsamples}] [expr {$i*$nsamples+$nsamples-1}]]
set xmin [lindex $subsample 0]
set xmax $xmin
foreach d $subsample {
set xmin [expr {$xmin<$d? $xmin : $d}]
set xmax [expr {$xmax>$d? $xmax : $d}]
}
set range [expr {$xmax-$xmin}]
if { $range < $rlower } { lappend result $i }
if { $range > $rupper } { lappend result $i }
}
return $result
}
#
# Load the auxiliary scripts
#
source [file join [file dirname [info script]] pdf_stat.tcl]
source [file join [file dirname [info script]] plotstat.tcl]
source [file join [file dirname [info script]] liststat.tcl]
source [file join [file dirname [info script]] mvlinreg.tcl]
source [file join [file dirname [info script]] kruskal.tcl]
source [file join [file dirname [info script]] wilcoxon.tcl]
source [file join [file dirname [info script]] stat_kernel.tcl]
#
# Define the tables
#
namespace eval ::math::statistics {
variable student_t_table
# set student_t_table [::math::interpolation::defineTable student_t
# {X 80% 90% 95% 98% 99%}
# {X 0.80 0.90 0.95 0.98 0.99
# 1 3.078 6.314 12.706 31.821 63.657
# 2 1.886 2.920 4.303 6.965 9.925
# 3 1.638 2.353 3.182 4.541 5.841
# 5 1.476 2.015 2.571 3.365 4.032
# 10 1.372 1.812 2.228 2.764 3.169
# 15 1.341 1.753 2.131 2.602 2.947
# 20 1.325 1.725 2.086 2.528 2.845
# 30 1.310 1.697 2.042 2.457 2.750
# 60 1.296 1.671 2.000 2.390 2.660
# 1.0e9 1.282 1.645 1.960 2.326 2.576 }]
# PM
#set chi_squared_table [::math::interpolation::defineTable chi_square
# ...
}
#
# Simple test code
#
if { [info exists ::argv0] && ([file tail [info script]] == [file tail $::argv0]) } {
console show
puts [interp aliases]
set values {1 1 1 1 {}}
puts [::math::statistics::basic-stats $values]
set values {1 2 3 4}
puts [::math::statistics::basic-stats $values]
set values {1 -1 1 -2}
puts [::math::statistics::basic-stats $values]
puts [::math::statistics::mean $values]
puts [::math::statistics::min $values]
puts [::math::statistics::max $values]
puts [::math::statistics::number $values]
puts [::math::statistics::stdev $values]
puts [::math::statistics::var $values]
set novals 100
#set maxvals 100001
set maxvals 1001
while { $novals < $maxvals } {
set values {}
for { set i 0 } { $i < $novals } { incr i } {
lappend values [expr {rand()}]
}
puts [::math::statistics::basic-stats $values]
puts [::math::statistics::histogram {0.0 0.2 0.4 0.6 0.8 1.0} $values]
set novals [expr {$novals*10}]
}
puts "Normal distribution:"
puts "X=0: [::math::statistics::pdf-normal 0.0 1.0 0.0]"
puts "X=1: [::math::statistics::pdf-normal 0.0 1.0 1.0]"
puts "X=-1: [::math::statistics::pdf-normal 0.0 1.0 -1.0]"
set data1 {0.0 1.0 3.0 4.0 100.0 -23.0}
set data2 {1.0 2.0 4.0 5.0 101.0 -22.0}
set data3 {0.0 2.0 6.0 8.0 200.0 -46.0}
set data4 {2.0 6.0 8.0 200.0 -46.0 1.0}
set data5 {100.0 99.0 90.0 93.0 5.0 123.0}
puts "Correlation data1 and data1: [::math::statistics::corr $data1 $data1]"
puts "Correlation data1 and data2: [::math::statistics::corr $data1 $data2]"
puts "Correlation data1 and data3: [::math::statistics::corr $data1 $data3]"
puts "Correlation data1 and data4: [::math::statistics::corr $data1 $data4]"
puts "Correlation data1 and data5: [::math::statistics::corr $data1 $data5]"
# set data {1.0 2.0 2.3 4.0 3.4 1.2 0.6 5.6}
# puts [::math::statistics::basicStats $data]
# puts [::math::statistics::interval-mean-stdev $data 0.90]
# puts [::math::statistics::interval-mean-stdev $data 0.95]
# puts [::math::statistics::interval-mean-stdev $data 0.99]
# puts "\nTest mean values:"
# puts [::math::statistics::test-mean $data 2.0 0.1 0.90]
# puts [::math::statistics::test-mean $data 2.0 0.5 0.90]
# puts [::math::statistics::test-mean $data 2.0 1.0 0.90]
# puts [::math::statistics::test-mean $data 2.0 2.0 0.90]
set rc [catch {
set m [::math::statistics::mean {}]
} msg ] ; # {}
puts "Result: $rc $msg"
puts "\nTest quantiles:"
set data {1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0}
set quantiles {0.11 0.21 0.51 0.91 0.99}
set limits {2.1 4.1 6.1 8.1}
puts [::math::statistics::quantiles $data $quantiles]
set histogram [::math::statistics::histogram $limits $data]
puts [::math::statistics::quantiles $limits $histogram $quantiles]
puts "\nTest autocorrelation:"
set data {1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0}
puts [::math::statistics::autocorr $data]
set data {1.0 -1.1 2.0 -0.6 3.0 -4.0 0.5 0.9 -1.0}
puts [::math::statistics::autocorr $data]
puts "\nTest histogram limits:"
puts [::math::statistics::mean-histogram-limits 1.0 1.0]
puts [::math::statistics::mean-histogram-limits 1.0 1.0 4]
puts [::math::statistics::minmax-histogram-limits 1.0 10.0 10]
}
#
# Test xbar/R-chart procedures
#
if { 0 } {
set data {}
for { set i 0 } { $i < 500 } { incr i } {
lappend data [expr {rand()}]
}
set limits [::math::statistics::control-xbar $data]
puts $limits
puts "Outliers? [::math::statistics::test-xbar $limits $data]"
set newdata {1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 10.0 10.0 10.0 10.0}
puts "Outliers? [::math::statistics::test-xbar $limits $newdata] -- 0 2"
set limits [::math::statistics::control-Rchart $data]
puts $limits
puts "Outliers? [::math::statistics::test-Rchart $limits $data]"
set newdata {0.0 1.0 2.0 1.0 0.4 0.5 0.6 0.5 10.0 0.0 10.0 10.0}
puts "Outliers? [::math::statistics::test-Rchart $limits $newdata] -- 0 2"
}
|