summaryrefslogtreecommitdiffstats
path: root/admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php
blob: 7d1359bed4f3784e39b07d2d2c836c5e194d0806 (plain) (blame)
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
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
<?php
//
// +----------------------------------------------------------------------+
// | PHP Version 4                                                        |
// +----------------------------------------------------------------------+
// | Copyright (c) 1997-2003 The PHP Group                                |
// +----------------------------------------------------------------------+
// | This source file is subject to version 2.0 of the PHP license,       |
// | that is bundled with this package in the file LICENSE, and is        |
// | available at through the world-wide-web at                           |
// | http://www.php.net/license/2_02.txt.                                 |
// | If you did not receive a copy of the PHP license and are unable to   |
// | obtain it through the world-wide-web, please send a note to          |
// | license@php.net so we can mail you a copy immediately.               |
// +----------------------------------------------------------------------+
// | Authors: Jesus M. Castagnetto <jmcastagnetto@php.net>                |
// +----------------------------------------------------------------------+
//
// $Id: Stats.php,v 1.15 2003/06/01 11:40:30 jmcastagnetto Exp $
//

include_once 'PEAR.php';

/**
* @package Math_Stats
*/

// Constants for defining the statistics to calculate /*{{{*/
/**
* STATS_BASIC to generate the basic descriptive statistics
*/
define('STATS_BASIC', 1);
/**
* STATS_FULL to generate also higher moments, mode, median, etc.
*/
define('STATS_FULL', 2);
/*}}}*/

// Constants describing the data set format /*{{{*/
/**
* STATS_DATA_SIMPLE for an array of numeric values. This is the default.
* e.g. $data = array(2,3,4,5,1,1,6);
*/
define('STATS_DATA_SIMPLE', 0);
/**
* STATS_DATA_CUMMULATIVE for an associative array of frequency values,
* where in each array entry, the index is the data point and the
* value the count (frequency):
* e.g. $data = array(3=>4, 2.3=>5, 1.25=>6, 0.5=>3)
*/
define('STATS_DATA_CUMMULATIVE', 1);
/*}}}*/

// Constants defining how to handle nulls /*{{{*/
/**
* STATS_REJECT_NULL, reject data sets with null values. This is the default.
* Any non-numeric value is considered a null in this context.
*/
define('STATS_REJECT_NULL', -1);
/**
* STATS_IGNORE_NULL, ignore null values and prune them from the data.
* Any non-numeric value is considered a null in this context.
*/
define('STATS_IGNORE_NULL', -2);
/**
* STATS_USE_NULL_AS_ZERO, assign the value of 0 (zero) to null values.
* Any non-numeric value is considered a null in this context.
*/
define('STATS_USE_NULL_AS_ZERO', -3);
/*}}}*/

/**
* A class to calculate descriptive statistics from a data set.
* Data sets can be simple arrays of data, or a cummulative hash.
* The second form is useful when passing large data set,
* for example the data set:
*
* <pre>
* $data1 = array (1,2,1,1,1,1,3,3,4.1,3,2,2,4.1,1,1,2,3,3,2,2,1,1,2,2);
* </pre>
*
* can be epxressed more compactly as:
*
* <pre>
* $data2 = array('1'=>9, '2'=>8, '3'=>5, '4.1'=>2);
* </pre>
*
* Example of use:
*
* <pre>
* include_once 'Math/Stats.php';
* $s = new Math_Stats();
* $s->setData($data1);
* // or
* // $s->setData($data2, STATS_DATA_CUMMULATIVE);
* $stats = $s->calcBasic();
* echo 'Mean: '.$stats['mean'].' StDev: '.$stats['stdev'].' <br />\n';
*
* // using data with nulls
* // first ignoring them:
* $data3 = array(1.2, 'foo', 2.4, 3.1, 4.2, 3.2, null, 5.1, 6.2);
* $s->setNullOption(STATS_IGNORE_NULL);
* $s->setData($data3);
* $stats3 = $s->calcFull();
*
* // and then assuming nulls == 0
* $s->setNullOption(STATS_USE_NULL_AS_ZERO);
* $s->setData($data3);
* $stats3 = $s->calcFull();
* </pre>
*
* Originally this class was part of NumPHP (Numeric PHP package)
*
* @author  Jesus M. Castagnetto <jmcastagnetto@php.net>
* @version 0.8
* @access  public
* @package Math_Stats
*/
class Base {/*{{{*/
    // properties /*{{{*/

    /**
     * The simple or cummulative data set.
     * Null by default.
     *
     * @access  private
     * @var array
     */
    public $_data = null;

    /**
     * Expanded data set. Only set when cummulative data
     * is being used. Null by default.
     *
     * @access  private
     * @var array
     */
    public $_dataExpanded = null;

    /**
     * Flag for data type, one of STATS_DATA_SIMPLE or
     * STATS_DATA_CUMMULATIVE. Null by default.
     *
     * @access  private
     * @var int
     */
    public $_dataOption = null;

    /**
     * Flag for null handling options. One of STATS_REJECT_NULL,
     * STATS_IGNORE_NULL or STATS_USE_NULL_AS_ZERO
     *
     * @access  private
     * @var int
     */
    public $_nullOption;

    /**
     * Array for caching result values, should be reset
     * when using setData()
     *
     * @access private
     * @var array
     */
    public $_calculatedValues = array();

    /*}}}*/

    /**
     * Constructor for the class
     *
     * @access  public
     * @param   optional    int $nullOption how to handle null values
     * @return  object  Math_Stats
     */
    function Math_Stats($nullOption=STATS_REJECT_NULL) {/*{{{*/
        $this->_nullOption = $nullOption;
    }/*}}}*/

    /**
     * Sets and verifies the data, checking for nulls and using
     * the current null handling option
     *
     * @access public
     * @param   array   $arr    the data set
     * @param   optional    int $opt    data format: STATS_DATA_CUMMULATIVE or STATS_DATA_SIMPLE (default)
     * @return  mixed   true on success, a PEAR_Error object otherwise
     */
    function setData($arr, $opt=STATS_DATA_SIMPLE) {/*{{{*/
        if (!is_array($arr)) {
            return PEAR::raiseError('invalid data, an array of numeric data was expected');
        }
        $this->_data = null;
        $this->_dataExpanded = null;
        $this->_dataOption = null;
        $this->_calculatedValues = array();
        if ($opt == STATS_DATA_SIMPLE) {
            $this->_dataOption = $opt;
            $this->_data = array_values($arr);
        } else if ($opt == STATS_DATA_CUMMULATIVE) {
            $this->_dataOption = $opt;
            $this->_data = $arr;
            $this->_dataExpanded = array();
        }
        return $this->_validate();
    }/*}}}*/

    /**
     * Returns the data which might have been modified
     * according to the current null handling options.
     *
     * @access  public
     * @param boolean $expanded whether to return a expanded list, default is false
     * @return  mixed   array of data on success, a PEAR_Error object otherwise
     * @see _validate()
     */
    function getData($expanded=false) {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if ($this->_dataOption == STATS_DATA_CUMMULATIVE && $expanded) {
            return $this->_dataExpanded;
        } else {
            return $this->_data;
        }
    }/*}}}*/

    /**
     * Sets the null handling option.
     * Must be called before assigning a new data set containing null values
     *
     * @access  public
     * @return  mixed   true on success, a PEAR_Error object otherwise
     * @see _validate()
     */
    function setNullOption($nullOption) {/*{{{*/
        if ($nullOption == STATS_REJECT_NULL
            || $nullOption == STATS_IGNORE_NULL
            || $nullOption == STATS_USE_NULL_AS_ZERO) {
            $this->_nullOption = $nullOption;
            return true;
        } else {
            return PEAR::raiseError('invalid null handling option expecting: '.
                        'STATS_REJECT_NULL, STATS_IGNORE_NULL or STATS_USE_NULL_AS_ZERO');
        }
    }/*}}}*/

    /**
     * Transforms the data by substracting each entry from the mean and
     * dividing by its standard deviation. This will reset all pre-calculated
     * values to their original (unset) defaults.
     *
     * @access public
     * @return mixed true on success, a PEAR_Error object otherwise
     * @see mean()
     * @see stDev()
     * @see setData()
     */
    function studentize() {/*{{{*/
        $mean = $this->mean();
        if (PEAR::isError($mean)) {
            return $mean;
        }
        $std = $this->stDev();
        if (PEAR::isError($std)) {
            return $std;
        }
        if ($std == 0) {
            return PEAR::raiseError('cannot studentize data, standard deviation is zero.');
        }
        $arr  = array();
        if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
            foreach ($this->_data as $val=>$freq) {
                $newval = ($val - $mean) / $std;
                $arr["$newval"] = $freq;
            }
        } else {
            foreach ($this->_data as $val) {
                $newval = ($val - $mean) / $std;
                $arr[] = $newval;
            }
        }
        return $this->setData($arr, $this->_dataOption);
    }/*}}}*/

    /**
     * Transforms the data by substracting each entry from the mean.
     * This will reset all pre-calculated values to their original (unset) defaults.
     *
     * @access public
     * @return mixed true on success, a PEAR_Error object otherwise
     * @see mean()
     * @see setData()
     */
    function center() {/*{{{*/
        $mean = $this->mean();
        if (PEAR::isError($mean)) {
            return $mean;
        }
        $arr  = array();
        if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
            foreach ($this->_data as $val=>$freq) {
                $newval = $val - $mean;
                $arr["$newval"] = $freq;
            }
        } else {
            foreach ($this->_data as $val) {
                $newval = $val - $mean;
                $arr[] = $newval;
            }
        }
        return $this->setData($arr, $this->_dataOption);
    }/*}}}*/

    /**
     * Calculates the basic or full statistics for the data set
     *
     * @access  public
     * @param   int $mode   one of STATS_BASIC or STATS_FULL
     * @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default),
     *                  or only the error message will be returned (when false), if an error happens.
     * @return  mixed   an associative array of statistics on success, a PEAR_Error object otherwise
     * @see calcBasic()
     * @see calcFull()
     */
    function calc($mode, $returnErrorObject=true) {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if ($mode == STATS_BASIC) {
            return $this->calcBasic($returnErrorObject);
        } elseif ($mode == STATS_FULL) {
            return $this->calcFull($returnErrorObject);
        } else {
            return PEAR::raiseError('incorrect mode, expected STATS_BASIC or STATS_FULL');
        }
    }/*}}}*/

    /**
     * Calculates a basic set of statistics
     *
     * @access  public
     * @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default),
     *                  or only the error message will be returned (when false), if an error happens.
     * @return  mixed   an associative array of statistics on success, a PEAR_Error object otherwise
     * @see calc()
     * @see calcFull()
     */
    function calcBasic($returnErrorObject=true) {/*{{{*/
            return array (
                'min' => $this->__format($this->min(), $returnErrorObject),
                'max' => $this->__format($this->max(), $returnErrorObject),
                'sum' => $this->__format($this->sum(), $returnErrorObject),
                'sum2' => $this->__format($this->sum2(), $returnErrorObject),
                'count' => $this->__format($this->count(), $returnErrorObject),
                'mean' => $this->__format($this->mean(), $returnErrorObject),
                'stdev' => $this->__format($this->stDev(), $returnErrorObject),
                'variance' => $this->__format($this->variance(), $returnErrorObject),
                'range' => $this->__format($this->range(), $returnErrorObject)
            );
    }/*}}}*/

    /**
     * Calculates a full set of statistics
     *
     * @access  public
     * @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default),
     *                  or only the error message will be returned (when false), if an error happens.
     * @return  mixed   an associative array of statistics on success, a PEAR_Error object otherwise
     * @see calc()
     * @see calcBasic()
     */
    function calcFull($returnErrorObject=true) {/*{{{*/
            return array (
                'min' => $this->__format($this->min(), $returnErrorObject),
                'max' => $this->__format($this->max(), $returnErrorObject),
                'sum' => $this->__format($this->sum(), $returnErrorObject),
                'sum2' => $this->__format($this->sum2(), $returnErrorObject),
                'count' => $this->__format($this->count(), $returnErrorObject),
                'mean' => $this->__format($this->mean(), $returnErrorObject),
                'median' => $this->__format($this->median(), $returnErrorObject),
                'mode' => $this->__format($this->mode(), $returnErrorObject),
                'midrange' => $this->__format($this->midrange(), $returnErrorObject),
                'geometric_mean' => $this->__format($this->geometricMean(), $returnErrorObject),
                'harmonic_mean' => $this->__format($this->harmonicMean(), $returnErrorObject),
                'stdev' => $this->__format($this->stDev(), $returnErrorObject),
                'absdev' => $this->__format($this->absDev(), $returnErrorObject),
                'variance' => $this->__format($this->variance(), $returnErrorObject),
                'range' => $this->__format($this->range(), $returnErrorObject),
                'std_error_of_mean' => $this->__format($this->stdErrorOfMean(), $returnErrorObject),
                'skewness' => $this->__format($this->skewness(), $returnErrorObject),
                'kurtosis' => $this->__format($this->kurtosis(), $returnErrorObject),
                'coeff_of_variation' => $this->__format($this->coeffOfVariation(), $returnErrorObject),
                'sample_central_moments' => array (
                            1 => $this->__format($this->sampleCentralMoment(1), $returnErrorObject),
                            2 => $this->__format($this->sampleCentralMoment(2), $returnErrorObject),
                            3 => $this->__format($this->sampleCentralMoment(3), $returnErrorObject),
                            4 => $this->__format($this->sampleCentralMoment(4), $returnErrorObject),
                            5 => $this->__format($this->sampleCentralMoment(5), $returnErrorObject)
                            ),
                'sample_raw_moments' => array (
                            1 => $this->__format($this->sampleRawMoment(1), $returnErrorObject),
                            2 => $this->__format($this->sampleRawMoment(2), $returnErrorObject),
                            3 => $this->__format($this->sampleRawMoment(3), $returnErrorObject),
                            4 => $this->__format($this->sampleRawMoment(4), $returnErrorObject),
                            5 => $this->__format($this->sampleRawMoment(5), $returnErrorObject)
                            ),
                'frequency' => $this->__format($this->frequency(), $returnErrorObject),
                'quartiles' => $this->__format($this->quartiles(), $returnErrorObject),
                'interquartile_range' => $this->__format($this->interquartileRange(), $returnErrorObject),
                'interquartile_mean' => $this->__format($this->interquartileMean(), $returnErrorObject),
                'quartile_deviation' => $this->__format($this->quartileDeviation(), $returnErrorObject),
                'quartile_variation_coefficient' => $this->__format($this->quartileVariationCoefficient(), $returnErrorObject),
                'quartile_skewness_coefficient' => $this->__format($this->quartileSkewnessCoefficient(), $returnErrorObject)
            );
    }/*}}}*/

    /**
     * Calculates the minimum of a data set.
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the minimum value on success, a PEAR_Error object otherwise
     * @see calc()
     * @see max()
     */
    function min() {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (!array_key_exists('min', $this->_calculatedValues)) {
            if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
                $min = min(array_keys($this->_data));
            } else {
                $min = min($this->_data);
            }
            $this->_calculatedValues['min'] = $min;
        }
        return $this->_calculatedValues['min'];
    }/*}}}*/

    /**
     * Calculates the maximum of a data set.
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the maximum value on success, a PEAR_Error object otherwise
     * @see calc()
     * @see min()
     */
    function max() {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (!array_key_exists('max', $this->_calculatedValues)) {
            if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
                $max = max(array_keys($this->_data));
            } else {
                $max = max($this->_data);
            }
            $this->_calculatedValues['max'] = $max;
        }
        return $this->_calculatedValues['max'];
    }/*}}}*/

    /**
     * Calculates SUM { xi }
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the sum on success, a PEAR_Error object otherwise
     * @see calc()
     * @see sum2()
     * @see sumN()
     */
    function sum() {/*{{{*/
        if (!array_key_exists('sum', $this->_calculatedValues)) {
            $sum = $this->sumN(1);
            if (PEAR::isError($sum)) {
                return $sum;
            } else {
                $this->_calculatedValues['sum'] = $sum;
            }
        }
        return $this->_calculatedValues['sum'];
    }/*}}}*/

    /**
     * Calculates SUM { (xi)^2 }
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the sum on success, a PEAR_Error object otherwise
     * @see calc()
     * @see sum()
     * @see sumN()
     */
    function sum2() {/*{{{*/
        if (!array_key_exists('sum2', $this->_calculatedValues)) {
            $sum2 = $this->sumN(2);
            if (PEAR::isError($sum2)) {
                return $sum2;
            } else {
                $this->_calculatedValues['sum2'] = $sum2;
            }
        }
        return $this->_calculatedValues['sum2'];
    }/*}}}*/

    /**
     * Calculates SUM { (xi)^n }
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @param   numeric $n  the exponent
     * @return  mixed   the sum on success, a PEAR_Error object otherwise
     * @see calc()
     * @see sum()
     * @see sum2()
     */
    function sumN($n) {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        $sumN = 0;
        if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
            foreach($this->_data as $val=>$freq) {
                $sumN += $freq * pow((double)$val, (double)$n);
            }
        } else {
            foreach($this->_data as $val) {
                $sumN += pow((double)$val, (double)$n);
            }
        }
        return $sumN;
    }/*}}}*/

    /**
     * Calculates PROD { (xi) }, (the product of all observations)
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the product on success, a PEAR_Error object otherwise
     * @see productN()
     */
    function product() {/*{{{*/
        if (!array_key_exists('product', $this->_calculatedValues)) {
            $product = $this->productN(1);
            if (PEAR::isError($product)) {
                return $product;
            } else {
                $this->_calculatedValues['product'] = $product;
            }
        }
        return $this->_calculatedValues['product'];
    }/*}}}*/

    /**
     * Calculates PROD { (xi)^n }, which is the product of all observations
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @param   numeric $n  the exponent
     * @return  mixed   the product on success, a PEAR_Error object otherwise
     * @see product()
     */
    function productN($n) {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        $prodN = 1.0;
        if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
            foreach($this->_data as $val=>$freq) {
                if ($val == 0) {
                    return 0.0;
                }
                $prodN *= $freq * pow((double)$val, (double)$n);
            }
        } else {
            foreach($this->_data as $val) {
                if ($val == 0) {
                    return 0.0;
                }
                $prodN *= pow((double)$val, (double)$n);
            }
        }
        return $prodN;

    }/*}}}*/

    /**
     * Calculates the number of data points in the set
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the count on success, a PEAR_Error object otherwise
     * @see calc()
     */
    function count() {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (!array_key_exists('count', $this->_calculatedValues)) {
            if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
                $count = count($this->_dataExpanded);
            } else {
                $count = count($this->_data);
            }
            $this->_calculatedValues['count'] = $count;
        }
        return $this->_calculatedValues['count'];
    }/*}}}*/

    /**
     * Calculates the mean (average) of the data points in the set
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the mean value on success, a PEAR_Error object otherwise
     * @see calc()
     * @see sum()
     * @see count()
     */
    function mean() {/*{{{*/
        if (!array_key_exists('mean', $this->_calculatedValues)) {
            $sum = $this->sum();
            if (PEAR::isError($sum)) {
                return $sum;
            }
            $count = $this->count();
            if (PEAR::isError($count)) {
                return $count;
            }
            $this->_calculatedValues['mean'] = $sum / $count;
        }
        return $this->_calculatedValues['mean'];
    }/*}}}*/

    /**
     * Calculates the range of the data set = max - min
     *
     * @access public
     * @return mixed the value of the range on success, a PEAR_Error object otherwise.
     */
    function range() {/*{{{*/
        if (!array_key_exists('range', $this->_calculatedValues)) {
            $min = $this->min();
            if (PEAR::isError($min)) {
                return $min;
            }
            $max = $this->max();
            if (PEAR::isError($max)) {
                return $max;
            }
            $this->_calculatedValues['range'] = $max - $min;
        }
        return $this->_calculatedValues['range'];

    }/*}}}*/

    /**
     * Calculates the variance (unbiased) of the data points in the set
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the variance value on success, a PEAR_Error object otherwise
     * @see calc()
     * @see __sumdiff()
     * @see count()
     */
    function variance() {/*{{{*/
        if (!array_key_exists('variance', $this->_calculatedValues)) {
            $variance = $this->__calcVariance();
            if (PEAR::isError($variance)) {
                return $variance;
            }
            $this->_calculatedValues['variance'] = $variance;
        }
        return $this->_calculatedValues['variance'];
    }/*}}}*/

    /**
     * Calculates the standard deviation (unbiased) of the data points in the set
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the standard deviation on success, a PEAR_Error object otherwise
     * @see calc()
     * @see variance()
     */
    function stDev() {/*{{{*/
        if (!array_key_exists('stDev', $this->_calculatedValues)) {
            $variance = $this->variance();
            if (PEAR::isError($variance)) {
                return $variance;
            }
            $this->_calculatedValues['stDev'] = sqrt($variance);
        }
        return $this->_calculatedValues['stDev'];
    }/*}}}*/

    /**
     * Calculates the variance (unbiased) of the data points in the set
     * given a fixed mean (average) value. Not used in calcBasic(), calcFull()
     * or calc().
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @param   numeric $mean   the fixed mean value
     * @return  mixed   the variance on success, a PEAR_Error object otherwise
     * @see __sumdiff()
     * @see count()
     * @see variance()
     */
    function varianceWithMean($mean) {/*{{{*/
        return $this->__calcVariance($mean);
    }/*}}}*/

    /**
     * Calculates the standard deviation (unbiased) of the data points in the set
     * given a fixed mean (average) value. Not used in calcBasic(), calcFull()
     * or calc().
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @param   numeric $mean   the fixed mean value
     * @return  mixed   the standard deviation on success, a PEAR_Error object otherwise
     * @see varianceWithMean()
     * @see stDev()
     */
    function stDevWithMean($mean) {/*{{{*/
        $varianceWM = $this->varianceWithMean($mean);
        if (PEAR::isError($varianceWM)) {
            return $varianceWM;
        }
        return sqrt($varianceWM);
    }/*}}}*/

    /**
     * Calculates the absolute deviation of the data points in the set
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the absolute deviation on success, a PEAR_Error object otherwise
     * @see calc()
     * @see __sumabsdev()
     * @see count()
     * @see absDevWithMean()
     */
    function absDev() {/*{{{*/
        if (!array_key_exists('absDev', $this->_calculatedValues)) {
            $absDev = $this->__calcAbsoluteDeviation();
            if (PEAR::isError($absdev)) {
                return $absdev;
            }
            $this->_calculatedValues['absDev'] = $absDev;
        }
        return $this->_calculatedValues['absDev'];
    }/*}}}*/

    /**
     * Calculates the absolute deviation of the data points in the set
     * given a fixed mean (average) value. Not used in calcBasic(), calcFull()
     * or calc().
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @param   numeric $mean   the fixed mean value
     * @return  mixed   the absolute deviation on success, a PEAR_Error object otherwise
     * @see __sumabsdev()
     * @see absDev()
     */
    function absDevWithMean($mean) {/*{{{*/
        return $this->__calcAbsoluteDeviation($mean);
    }/*}}}*/

    /**
     * Calculates the skewness of the data distribution in the set
     * The skewness measures the degree of asymmetry of a distribution,
     * and is related to the third central moment of a distribution.
     * A normal distribution has a skewness = 0
     * A distribution with a tail off towards the high end of the scale
     * (positive skew) has a skewness > 0
     * A distribution with a tail off towards the low end of the scale
     * (negative skew) has a skewness < 0
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the skewness value on success, a PEAR_Error object otherwise
     * @see __sumdiff()
     * @see count()
     * @see stDev()
     * @see calc()
     */
    function skewness() {/*{{{*/
        if (!array_key_exists('skewness', $this->_calculatedValues)) {
            $count = $this->count();
            if (PEAR::isError($count)) {
                return $count;
            }
            $stDev = $this->stDev();
            if (PEAR::isError($stDev)) {
                return $stDev;
            }
            $sumdiff3 = $this->__sumdiff(3);
            if (PEAR::isError($sumdiff3)) {
                return $sumdiff3;
            }
            $this->_calculatedValues['skewness'] = ($sumdiff3 / ($count * pow($stDev, 3)));
        }
        return $this->_calculatedValues['skewness'];
    }/*}}}*/

    /**
     * Calculates the kurtosis of the data distribution in the set
     * The kurtosis measures the degrees of peakedness of a distribution.
     * It is also called the "excess" or "excess coefficient", and is
     * a normalized form of the fourth central moment of a distribution.
     * A normal distributions has kurtosis = 0
     * A narrow and peaked (leptokurtic) distribution has a
     * kurtosis > 0
     * A flat and wide (platykurtic) distribution has a kurtosis < 0
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the kurtosis value on success, a PEAR_Error object otherwise
     * @see __sumdiff()
     * @see count()
     * @see stDev()
     * @see calc()
     */
    function kurtosis() {/*{{{*/
        if (!array_key_exists('kurtosis', $this->_calculatedValues)) {
            $count = $this->count();
            if (PEAR::isError($count)) {
                return $count;
            }
            $stDev = $this->stDev();
            if (PEAR::isError($stDev)) {
                return $stDev;
            }
            $sumdiff4 = $this->__sumdiff(4);
            if (PEAR::isError($sumdiff4)) {
                return $sumdiff4;
            }
            $this->_calculatedValues['kurtosis'] = ($sumdiff4 / ($count * pow($stDev, 4))) - 3;
        }
        return $this->_calculatedValues['kurtosis'];
    }/*}}}*/

    /**
     * Calculates the median of a data set.
     * The median is the value such that half of the points are below it
     * in a sorted data set.
     * If the number of values is odd, it is the middle item.
     * If the number of values is even, is the average of the two middle items.
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the median value on success, a PEAR_Error object otherwise
     * @see count()
     * @see calc()
     */
    function median() {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (!array_key_exists('median', $this->_calculatedValues)) {
            if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
                $arr =& $this->_dataExpanded;
            } else {
                $arr =& $this->_data;
            }
            $n = $this->count();
            if (PEAR::isError($n)) {
                return $n;
            }
            $h = intval($n / 2);
            if ($n % 2 == 0) {
                $median = ($arr[$h] + $arr[$h - 1]) / 2;
            } else {
                $median = $arr[$h + 1];
            }
            $this->_calculatedValues['median'] = $median;
        }
        return $this->_calculatedValues['median'];
    }/*}}}*/

    /**
     * Calculates the mode of a data set.
     * The mode is the value with the highest frequency in the data set.
     * There can be more than one mode.
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   an array of mode value on success, a PEAR_Error object otherwise
     * @see frequency()
     * @see calc()
     */
    function mode() {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (!array_key_exists('mode', $this->_calculatedValues)) {
            if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
                $arr = $this->_data;
            } else {
                $arr = $this->frequency();
            }
            arsort($arr);
            $mcount = 1;
            foreach ($arr as $val=>$freq) {
                if ($mcount == 1) {
                    $mode = array($val);
                    $mfreq = $freq;
                    ++$mcount;
                    continue;
                }
                if ($mfreq == $freq)
                    $mode[] = $val;
                if ($mfreq > $freq)
                    break;
            }
            $this->_calculatedValues['mode'] = $mode;
        }
        return $this->_calculatedValues['mode'];
    }/*}}}*/

    /**
     * Calculates the midrange of a data set.
     * The midrange is the average of the minimum and maximum of the data set.
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the midrange value on success, a PEAR_Error object otherwise
     * @see min()
     * @see max()
     * @see calc()
     */
    function midrange() {/*{{{*/
        if (!array_key_exists('midrange', $this->_calculatedValues)) {
            $min = $this->min();
            if (PEAR::isError($min)) {
                return $min;
            }
            $max = $this->max();
            if (PEAR::isError($max)) {
                return $max;
            }
            $this->_calculatedValues['midrange'] = (($max + $min) / 2);
        }
        return $this->_calculatedValues['midrange'];
    }/*}}}*/

    /**
     * Calculates the geometrical mean of the data points in the set
     * Handles cummulative data sets correctly
     *
     * @access public
     * @return mixed the geometrical mean value on success, a PEAR_Error object otherwise
     * @see calc()
     * @see product()
     * @see count()
     */
    function geometricMean() {/*{{{*/
        if (!array_key_exists('geometricMean', $this->_calculatedValues)) {
            $count = $this->count();
            if (PEAR::isError($count)) {
                return $count;
            }
            $prod = $this->product();
            if (PEAR::isError($prod)) {
                return $prod;
            }
            if ($prod == 0.0) {
                return 0.0;
            }
            if ($prod < 0) {
                return PEAR::raiseError('The product of the data set is negative, geometric mean undefined.');
            }
            $this->_calculatedValues['geometricMean'] = pow($prod , 1 / $count);
        }
        return $this->_calculatedValues['geometricMean'];
    }/*}}}*/

    /**
     * Calculates the harmonic mean of the data points in the set
     * Handles cummulative data sets correctly
     *
     * @access public
     * @return mixed the harmonic mean value on success, a PEAR_Error object otherwise
     * @see calc()
     * @see count()
     */
    function harmonicMean() {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (!array_key_exists('harmonicMean', $this->_calculatedValues)) {
            $count = $this->count();
            if (PEAR::isError($count)) {
                return $count;
            }
            $invsum = 0.0;
            if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
                foreach($this->_data as $val=>$freq) {
                    if ($val == 0) {
                        return PEAR::raiseError('cannot calculate a '.
                                'harmonic mean with data values of zero.');
                    }
                    $invsum += $freq / $val;
                }
            } else {
                foreach($this->_data as $val) {
                    if ($val == 0) {
                        return PEAR::raiseError('cannot calculate a '.
                                'harmonic mean with data values of zero.');
                    }
                    $invsum += 1 / $val;
                }
            }
            $this->_calculatedValues['harmonicMean'] = $count / $invsum;
        }
        return $this->_calculatedValues['harmonicMean'];
    }/*}}}*/

    /**
     * Calculates the nth central moment (m{n}) of a data set.
     *
     * The definition of a sample central moment is:
     *
     *     m{n} = 1/N * SUM { (xi - avg)^n }
     *
     * where: N = sample size, avg = sample mean.
     *
     * @access public
     * @param integer $n moment to calculate
     * @return mixed the numeric value of the moment on success, PEAR_Error otherwise
     */
    function sampleCentralMoment($n) {/*{{{*/
        if (!is_int($n) || $n < 1) {
            return PEAR::isError('moment must be a positive integer >= 1.');
        }

        if ($n == 1) {
            return 0;
        }
        $count = $this->count();
        if (PEAR::isError($count)) {
            return $count;
        }
        if ($count == 0) {
            return PEAR::raiseError("Cannot calculate {$n}th sample moment, ".
                    'there are zero data entries');
        }
        $sum = $this->__sumdiff($n);
        if (PEAR::isError($sum)) {
            return $sum;
        }
        return ($sum / $count);
    }/*}}}*/

    /**
     * Calculates the nth raw moment (m{n}) of a data set.
     *
     * The definition of a sample central moment is:
     *
     *     m{n} = 1/N * SUM { xi^n }
     *
     * where: N = sample size, avg = sample mean.
     *
     * @access public
     * @param integer $n moment to calculate
     * @return mixed the numeric value of the moment on success, PEAR_Error otherwise
     */
    function sampleRawMoment($n) {/*{{{*/
        if (!is_int($n) || $n < 1) {
            return PEAR::isError('moment must be a positive integer >= 1.');
        }

        $count = $this->count();
        if (PEAR::isError($count)) {
            return $count;
        }
        if ($count == 0) {
            return PEAR::raiseError("Cannot calculate {$n}th raw moment, ".
                    'there are zero data entries.');
        }
        $sum = $this->sumN($n);
        if (PEAR::isError($sum)) {
            return $sum;
        }
        return ($sum / $count);
    }/*}}}*/


    /**
     * Calculates the coefficient of variation of a data set.
     * The coefficient of variation measures the spread of a set of data
     * as a proportion of its mean. It is often expressed as a percentage.
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   the coefficient of variation on success, a PEAR_Error object otherwise
     * @see stDev()
     * @see mean()
     * @see calc()
     */
    function coeffOfVariation() {/*{{{*/
        if (!array_key_exists('coeffOfVariation', $this->_calculatedValues)) {
            $mean = $this->mean();
            if (PEAR::isError($mean)) {
                return $mean;
            }
            if ($mean == 0.0) {
                return PEAR::raiseError('cannot calculate the coefficient '.
                        'of variation, mean of sample is zero');
            }
            $stDev = $this->stDev();
            if (PEAR::isError($stDev)) {
                return $stDev;
            }

            $this->_calculatedValues['coeffOfVariation'] = $stDev / $mean;
        }
        return $this->_calculatedValues['coeffOfVariation'];
    }/*}}}*/

    /**
     * Calculates the standard error of the mean.
     * It is the standard deviation of the sampling distribution of
     * the mean. The formula is:
     *
     * S.E. Mean = SD / (N)^(1/2)
     *
     * This formula does not assume a normal distribution, and shows
     * that the size of the standard error of the mean is inversely
     * proportional to the square root of the sample size.
     *
     * @access  public
     * @return  mixed   the standard error of the mean on success, a PEAR_Error object otherwise
     * @see stDev()
     * @see count()
     * @see calc()
     */
    function stdErrorOfMean() {/*{{{*/
        if (!array_key_exists('stdErrorOfMean', $this->_calculatedValues)) {
            $count = $this->count();
            if (PEAR::isError($count)) {
                return $count;
            }
            $stDev = $this->stDev();
            if (PEAR::isError($stDev)) {
                return $stDev;
            }
            $this->_calculatedValues['stdErrorOfMean'] = $stDev / sqrt($count);
        }
        return $this->_calculatedValues['stdErrorOfMean'];
    }/*}}}*/

    /**
     * Calculates the value frequency table of a data set.
     * Handles cummulative data sets correctly
     *
     * @access  public
     * @return  mixed   an associative array of value=>frequency items on success, a PEAR_Error object otherwise
     * @see min()
     * @see max()
     * @see calc()
     */
    function frequency() {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (!array_key_exists('frequency', $this->_calculatedValues)) {
            if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
                $freq = $this->_data;
            } else {
                $freq = array();
                foreach ($this->_data as $val) {
                    $freq["$val"]++;
                }
                ksort($freq);
            }
            $this->_calculatedValues['frequency'] = $freq;
        }
        return $this->_calculatedValues['frequency'];
    }/*}}}*/

    /**
     * The quartiles are defined as the values that divide a sorted
     * data set into four equal-sized subsets, and correspond to the
     * 25th, 50th, and 75th percentiles.
     *
     * @access public
     * @return mixed an associative array of quartiles on success, a PEAR_Error otherwise
     * @see percentile()
     */
    function quartiles() {/*{{{*/
        if (!array_key_exists('quartiles', $this->_calculatedValues)) {
            $q1 = $this->percentile(25);
            if (PEAR::isError($q1)) {
                return $q1;
            }
            $q2 = $this->percentile(50);
            if (PEAR::isError($q2)) {
                return $q2;
            }
            $q3 = $this->percentile(75);
            if (PEAR::isError($q3)) {
                return $q3;
            }
            $this->_calculatedValues['quartiles'] = array (
                                        '25' => $q1,
                                        '50' => $q2,
                                        '75' => $q3
                                        );
        }
        return $this->_calculatedValues['quartiles'];
    }/*}}}*/

    /**
     * The interquartile mean is defined as the mean of the values left
     * after discarding the lower 25% and top 25% ranked values, i.e.:
     *
     *  interquart mean = mean(<P(25),P(75)>)
     *
     *  where: P = percentile
     *
     * @todo need to double check the equation
     * @access public
     * @return mixed a numeric value on success, a PEAR_Error otherwise
     * @see quartiles()
     */
    function interquartileMean() {/*{{{*/
        if (!array_key_exists('interquartileMean', $this->_calculatedValues)) {
            $quart = $this->quartiles();
            if (PEAR::isError($quart)) {
                return $quart;
            }
            $q3 = $quart['75'];
            $q1 = $quart['25'];
            $sum = 0;
            $n = 0;
            foreach ($this->getData(true) as $val) {
                if ($val >= $q1 && $val <= $q3) {
                    $sum += $val;
                    ++$n;
                }
            }
            if ($n == 0) {
                return PEAR::raiseError('error calculating interquartile mean, '.
                                        'empty interquartile range of values.');
            }
            $this->_calculatedValues['interquartileMean'] = $sum / $n;
        }
        return $this->_calculatedValues['interquartileMean'];
    }/*}}}*/

    /**
     * The interquartile range is the distance between the 75th and 25th
     * percentiles. Basically the range of the middle 50% of the data set,
     * and thus is not affected by outliers or extreme values.
     *
     *  interquart range = P(75) - P(25)
     *
     *  where: P = percentile
     *
     * @access public
     * @return mixed a numeric value on success, a PEAR_Error otherwise
     * @see quartiles()
     */
    function interquartileRange() {/*{{{*/
        if (!array_key_exists('interquartileRange', $this->_calculatedValues)) {
            $quart = $this->quartiles();
            if (PEAR::isError($quart)) {
                return $quart;
            }
            $q3 = $quart['75'];
            $q1 = $quart['25'];
            $this->_calculatedValues['interquartileRange'] = $q3 - $q1;
        }
        return $this->_calculatedValues['interquartileRange'];
    }/*}}}*/

    /**
     * The quartile deviation is half of the interquartile range value
     *
     *  quart dev = (P(75) - P(25)) / 2
     *
     *  where: P = percentile
     *
     * @access public
     * @return mixed a numeric value on success, a PEAR_Error otherwise
     * @see quartiles()
     * @see interquartileRange()
     */
    function quartileDeviation() {/*{{{*/
        if (!array_key_exists('quartileDeviation', $this->_calculatedValues)) {
            $iqr = $this->interquartileRange();
            if (PEAR::isError($iqr)) {
                return $iqr;
            }
            $this->_calculatedValues['quartileDeviation'] = $iqr / 2;
        }
        return $this->_calculatedValues['quartileDeviation'];
    }/*}}}*/

    /**
     * The quartile variation coefficient is defines as follows:
     *
     *  quart var coeff = 100 * (P(75) - P(25)) / (P(75) + P(25))
     *
     *  where: P = percentile
     *
     * @todo need to double check the equation
     * @access public
     * @return mixed a numeric value on success, a PEAR_Error otherwise
     * @see quartiles()
     */
    function quartileVariationCoefficient() {/*{{{*/
        if (!array_key_exists('quartileVariationCoefficient', $this->_calculatedValues)) {
            $quart = $this->quartiles();
            if (PEAR::isError($quart)) {
                return $quart;
            }
            $q3 = $quart['75'];
            $q1 = $quart['25'];
            $d = $q3 - $q1;
            $s = $q3 + $q1;
            $this->_calculatedValues['quartileVariationCoefficient'] = 100 * $d / $s;
        }
        return $this->_calculatedValues['quartileVariationCoefficient'];
    }/*}}}*/

    /**
     * The quartile skewness coefficient (also known as Bowley Skewness),
     * is defined as follows:
     *
     *  quart skewness coeff = (P(25) - 2*P(50) + P(75)) / (P(75) - P(25))
     *
     *  where: P = percentile
     *
     * @todo need to double check the equation
     * @access public
     * @return mixed a numeric value on success, a PEAR_Error otherwise
     * @see quartiles()
     */
    function quartileSkewnessCoefficient() {/*{{{*/
        if (!array_key_exists('quartileSkewnessCoefficient', $this->_calculatedValues)) {
            $quart = $this->quartiles();
            if (PEAR::isError($quart)) {
                return $quart;
            }
            $q3 = $quart['75'];
            $q2 = $quart['50'];
            $q1 = $quart['25'];
            $d = $q3 - 2*$q2 + $q1;
            $s = $q3 - $q1;
            $this->_calculatedValues['quartileSkewnessCoefficient'] = $d / $s;
        }
        return $this->_calculatedValues['quartileSkewnessCoefficient'];
    }/*}}}*/

    /**
     * The pth percentile is the value such that p% of the a sorted data set
     * is smaller than it, and (100 - p)% of the data is larger.
     *
     * A quick algorithm to pick the appropriate value from a sorted data
     * set is as follows:
     *
     * - Count the number of values: n
     * - Calculate the position of the value in the data list: i = p * (n + 1)
     * - if i is an integer, return the data at that position
     * - if i < 1, return the minimum of the data set
     * - if i > n, return the maximum of the data set
     * - otherwise, average the entries at adjacent positions to i
     *
     * The median is the 50th percentile value.
     *
     * @todo need to double check generality of the algorithm
     *
     * @access public
     * @param numeric $p the percentile to estimate, e.g. 25 for 25th percentile
     * @return mixed a numeric value on success, a PEAR_Error otherwise
     * @see quartiles()
     * @see median()
     */
    function percentile($p) {/*{{{*/
        $count = $this->count();
        if (PEAR::isError($count)) {
            return $count;
        }
        if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
            $data =& $this->_dataExpanded;
        } else {
            $data =& $this->_data;
        }
        $obsidx = $p * ($count + 1) / 100;
        if (intval($obsidx) == $obsidx) {
            return $data[($obsidx - 1)];
        } elseif ($obsidx < 1) {
            return $data[0];
        } elseif ($obsidx > $count) {
            return $data[($count - 1)];
        } else {
            $left = floor($obsidx - 1);
            $right = ceil($obsidx - 1);
            return ($data[$left] + $data[$right]) / 2;
        }
    }/*}}}*/

    // private methods

    /**
     * Utility function to calculate: SUM { (xi - mean)^n }
     *
     * @access private
     * @param   numeric $power  the exponent
     * @param   optional    double   $mean   the data set mean value
     * @return  mixed   the sum on success, a PEAR_Error object otherwise
     *
     * @see stDev()
     * @see variaceWithMean();
     * @see skewness();
     * @see kurtosis();
     */
    function __sumdiff($power, $mean=null) {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (is_null($mean)) {
            $mean = $this->mean();
            if (PEAR::isError($mean)) {
                return $mean;
            }
        }
        $sdiff = 0;
        if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
            foreach ($this->_data as $val=>$freq) {
                $sdiff += $freq * pow((double)($val - $mean), (double)$power);
            }
        } else {
            foreach ($this->_data as $val)
                $sdiff += pow((double)($val - $mean), (double)$power);
        }
        return $sdiff;
    }/*}}}*/

    /**
     * Utility function to calculate the variance with or without
     * a fixed mean
     *
     * @access private
     * @param $mean the fixed mean to use, null as default
     * @return mixed a numeric value on success, a PEAR_Error otherwise
     * @see variance()
     * @see varianceWithMean()
     */
    function __calcVariance($mean = null) {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        $sumdiff2 = $this->__sumdiff(2, $mean);
        if (PEAR::isError($sumdiff2)) {
            return $sumdiff2;
        }
        $count = $this->count();
        if (PEAR::isError($count)) {
            return $count;
        }
        if ($count == 1) {
            return PEAR::raiseError('cannot calculate variance of a singe data point');
        }
        return  ($sumdiff2 / ($count - 1));
    }/*}}}*/

    /**
     * Utility function to calculate the absolute deviation with or without
     * a fixed mean
     *
     * @access private
     * @param $mean the fixed mean to use, null as default
     * @return mixed a numeric value on success, a PEAR_Error otherwise
     * @see absDev()
     * @see absDevWithMean()
     */
    function __calcAbsoluteDeviation($mean = null) {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        $count = $this->count();
        if (PEAR::isError($count)) {
            return $count;
        }
        $sumabsdev = $this->__sumabsdev($mean);
        if (PEAR::isError($sumabsdev)) {
            return $sumabsdev;
        }
        return $sumabsdev / $count;
    }/*}}}*/

    /**
     * Utility function to calculate: SUM { | xi - mean | }
     *
     * @access  private
     * @param   optional    double   $mean   the mean value for the set or population
     * @return  mixed   the sum on success, a PEAR_Error object otherwise
     *
     * @see absDev()
     * @see absDevWithMean()
     */
    function __sumabsdev($mean=null) {/*{{{*/
        if ($this->_data == null) {
            return PEAR::raiseError('data has not been set');
        }
        if (is_null($mean)) {
            $mean = $this->mean();
        }
        $sdev = 0;
        if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
            foreach ($this->_data as $val=>$freq) {
                $sdev += $freq * abs($val - $mean);
            }
        } else {
            foreach ($this->_data as $val) {
                $sdev += abs($val - $mean);
            }
        }
        return $sdev;
    }/*}}}*/

    /**
     * Utility function to format a PEAR_Error to be used by calc(),
     * calcBasic() and calcFull()
     *
     * @access private
     * @param mixed $v value to be formatted
     * @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default),
     *                  or only the error message will be returned (when false)
     * @return mixed if the value is a PEAR_Error object, and $useErrorObject
     *              is false, then a string with the error message will be returned,
     *              otherwise the value will not be modified and returned as passed.
     */
    function __format($v, $useErrorObject=true) {/*{{{*/
        if (PEAR::isError($v) && $useErrorObject == false) {
            return $v->getMessage();
        } else {
            return $v;
        }
    }/*}}}*/

    /**
     * Utility function to validate the data and modify it
     * according to the current null handling option
     *
     * @access  private
     * @return  mixed true on success, a PEAR_Error object otherwise
     *
     * @see setData()
     */
    function _validate() {/*{{{*/
        $flag = ($this->_dataOption == STATS_DATA_CUMMULATIVE);
        foreach ($this->_data as $key=>$value) {
            $d = ($flag) ? $key : $value;
            $v = ($flag) ? $value : $key;
            if (!is_numeric($d)) {
                switch ($this->_nullOption) {
                    case STATS_IGNORE_NULL :
                        unset($this->_data["$key"]);
                        break;
                    case STATS_USE_NULL_AS_ZERO:
                        if ($flag) {
                            unset($this->_data["$key"]);
                            $this->_data[0] += $v;
                        } else {
                            $this->_data[$key] = 0;
                        }
                        break;
                    case STATS_REJECT_NULL :
                    default:
                        return PEAR::raiseError('data rejected, contains NULL values');
                        break;
                }
            }
        }
        if ($flag) {
            ksort($this->_data);
            $this->_dataExpanded = array();
            foreach ($this->_data as $val=>$freq) {
                $this->_dataExpanded = array_pad($this->_dataExpanded, count($this->_dataExpanded) + $freq, $val);
            }
            sort($this->_dataExpanded);
        } else {
            sort($this->_data);
        }
        return true;
    }/*}}}*/

}/*}}}*/

// vim: ts=4:sw=4:et:
// vim6: fdl=1: fdm=marker:

?>