= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = COMP-U-STAT = = = = = = = = STATISTICAL PATTERN GENERATOR AND MATHEMATICAL TREND ANALYZER = = = = = = = = (c) Copyright 2017 by James Ervin Glover, Ph.D. = = = = All Rights Reserved = = = = = = = = = = = = Part III(c) ( STAT 370 ----> STAT 399 ) = = = = = = = = = = = = The COMP-U-STAT System consists of a cluster of more than 3706 = = = = modular programs, providing the analyst with a clear and distinct = = = = scientific and mathematical edge in generating novel and useful = = = = statistical patterns for analyzing trends from random variables. = = = = The following is a glossary describing the functions of all = = = = routines in the sequence. There are many statistical applications = = = = of the COMP-U-STAT cluster. Please see available DEMO Diskettes, = = = = provided upon request, for numerous examples of output files. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ====================================================================== * * * GLOSSARY OF COMP-U-STAT PROGRAMS 370 ---> 399 * * * ====================================================================== -- L 370 -- READS A SEQUENCE OF IMAX STAR EVENTS AND A SEQUENCE OF K0 TEST EVENTS, CONSISTING OF A SET OF HIGH-PROBABILITY ELEMENTS GENERATED FROM ANOTHER SOURCE, SUCH AS STAT363 TO GENERATE A 3 x 3 MATRIX OF HIGH-PROBABILITY ELEMENTS. A SEQUENCE OF 30 NEW TEST EVENTS IS GENERATED FROM THE 3 x 3 MATRIX DETERMINED BY SELECTING 3 ROWS AND 3 COLUMNS FROM THE INITIAL K0 TEST EVENTS. THIS PROCESS IS CYCLICALLY REPEATED FOR ANY DESIRED COMBINATION OF 3 ROWS AND 3 COLUMNS, YIELDING A HOMOGENEOUS SEQUENCE OF HIGH-PROBABILITY NEW EVENTS. A DESIRED FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR (IF ANY) IS INTERSECTED WITH EACH OF THE NEW TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT. THE FIRST INPUT FILE CONSISTS OF K0 GENERATED EVENTS, E.G., FROM STAT363, AND THE SECOND CONSISTS OF THE SEQUENCE OF 6-TUPLES (3 SELECTED ROW NUMBERS AND 3 SELECTED COLUMN NUMBERS). THE MAXIMUM NUMBER OF NEW CYCLICALLY GENERATED TEST EVENTS IS 600. ============================================================================== -- L 371 -- READS A SEQUENCE OF IMAX STAR EVENTS AND A SEQUENCE OF K0 TEST EVENTS, CONSISTING OF A SET OF HIGH-PROBABILITY ELEMENTS GENERATED FROM ANOTHER SOURCE, SUCH AS STAT363 TO GENERATE A K0 x 3 MATRIX OF HIGH-PROBABILITY ELEMENTS. A SEQUENCE OF 45 NEW TEST EVENTS IS GENERATED FROM THE K0 x 3 MATRIX DETERMINED BY SELECTING K0 ROWS AND 3 COLUMNS FROM THE INITIAL K0 TEST EVENTS. THIS PROCESS IS CYCLICALLY REPEATED FOR ANY DESIRED COMBINATION OF K0 ROWS AND 3 COLUMNS, YIELDING A HOMOGENEOUS SEQUENCE OF HIGH-PROBABILITY NEW EVENTS. A DESIRED FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR (IF ANY) IS INTERSECTED WITH EACH OF THE NEW TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT. THE FIRST INPUT FILE CONSISTS OF SEQUENCES OF K0 GENERATED EVENTS, E.G., FROM STAT363, AND THE SECOND CONSISTS OF THE SEQUENCE OF 3-TUPLES (3 SELECTED COLUMN NUMBERS FOR EACH CYCLE). COLUMN NUMBERS). THE MAXIMUM NUMBER OF NEW CYCLICALLY GENERATED TEST EVENTS IS 600. ============================================================================== -- L 372 -- READS A SEQUENCE OF IMAX STAR EVENTS AND A SEQUENCE OF ALPHA BLOCKS, CONSISTING OF 6 ROWS AND HEADERS OF 3-ELEMENT EVENTS DETERMINED FROM ANOTHER SOURCE, SUCH AS STAT368, AS A SET OF HIGH-PROBABILITY ELEMENTS. THROUGH A CYCLICAL PROCESS, A SEQUENCE OF 50 NEW TEST EVENTS IS GENERATED FROM THE K0 x 3 MATRIX DETERMINED BY SELECTING K0 ROWS AND 3 COLUMNS FROM KO OF THE INITIAL 6 EVENTS PER BLOCK. THIS PROCESS IS CYCLICALLY REPEATED FOR ANY DESIRED COMBINATION OF K0 ROWS AND 3 COLUMNS, YIELDING A HOMOGENEOUS SEQUENCE OF HIGH-PROBABILITY NEW EVENTS. A DESIRED FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR (IF ANY) IS INTERSECTED WITH EACH OF THE NEW TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT. THE FIRST INPUT FILE CONSISTS OF SEQUENCES OF K0 GENERATED EVENTS, E.G., FROM STAT363, AND THE SECOND CONSISTS OF THE SEQUENCE OF 3-TUPLES (3 SELECTED COLUMN NUMBERS FOR EACH CYCLE). COLUMN NUMBERS). THE MAXIMUM NUMBER OF NEW CYCLICALLY GENERATED TEST EVENTS IS 600. ============================================================================== -- L 373 -- READS A SEQUENCE OF LMAX K0-ELEMENT TEST EVENTS ON L0 ELEMENTS AND FILTERS THOSE EVENTS FROM THE SEQUENCE WITH INDEXES CONGRUENT (MOD M) TO A DESIRED VECTOR OF 5 (NOT NECESSARILY DISTINCT) ELEMENTS, FOR A DESIRED INTEGER, M. THE ANALYST IS QUERIED FOR A DESIRED VALUE OF M AND A DESIRED VECTOR, < D1, D2, ... , D5 >, OF POSITIVE INTEGERS. THE FILTERED EVENTS ARE DISPLAYED FOR FURTHER ANALYSIS. ============================================================================== -- L 374 -- READS A (K0 x 3)-DIMENSIONAL BLOCK, , ON ELEMENTS < 1, ... , L0 > WITH A HEADER FOR EACH ROW INDICATING THE NUMBER OF ELEMENTS IN THAT ROW AND A SEQUENCE, , OF KMAX 3-ELEMENT TEST EVENTS, IN GROUPS OF 6 ROWS PER BLOCK, ADDING THE ELEMENTS OF EACH EVENT IN TO THE CORRESPONDING ELEMENTS IN EACH ROW OF , GENERATING A NEW SEQUENCE, , OF KMAX NEW (K0 x 3)-DIMENSIONAL BLOCKS. THE EXECUTION PROCESSES UP TO 200 EVENTS FROM INPUT SEQUENCE, . A SEQUENCE OF IMAX STAR EVENTS IS ALSO READ AND THE ANALYST IS QUERIED FOR A DESIRED EVENT NUMBER WHOSE SUCCESSOR IS INTERSECTED WITH EACH GENERATED TEST EVENT FOR WHICH COMMON ELEMENTS AND THEIR CARDINALITIES ARE IDENTIFIED. STAT374 IS A VARIANT OF STAT368. ============================================================================== -- L 375 -- LIMIT MATRICES I READS A SEQUENCE OF STAR EVENTS ON THE ELEMENTS < 1, ... , L0 > AND A (K0 x 3)-DIMENSIONAL BLOCK, , ON REAL-VALUED ELEMENTS FROM STAT176 OR ANOTHER SOURCE, WHERE EACH ROW CONTAINS THE MEAN OF A (COLUMN) SEQUENCE AND TWO ELEMENTS WHICH ARE k STANDARD DEVIATIONS AWAY FROM THE MEAN FOR A DESIRED INTEGRAL VALUE OF K. A SEQUENCE OF (K0 x 3)-DIMENSIONAL ARRAYS IS GENERATED, ITERATIVELY, FROM THE INITIAL SEQUENCE AND PAIRWISE AVERAGES OF ELEMENTS IN EACH OF THE K0 ROWS. THE ANALYST IS QUERIED FOR A DESIRED MAXIMUM NUMBER OF ITERATIONS, TO GENERATE A LIMIT MATRIX FOR THE SEQUENCE OF PAIRWISE AVERAGES. THE LIMIT MATRIX IS INTERSECTED WITH THE SUCCESSOR (IF ANY) OF A DESIRED STAR EVENT AND COMMON ELEMENTS ARE IDENTIFIED. ============================================================================== -- L 376 -- LIMIT MATRICES II READS A SEQUENCE OF STAR EVENTS ON THE ELEMENTS < 1, ... , L0 > AND A (K0 x 3)-DIMENSIONAL BLOCK, , ON REAL-VALUED ELEMENTS FROM STAT176 OR ANOTHER SOURCE, WHERE EACH ROW CONTAINS THE MEAN OF A (COLUMN) SEQUENCE AND TWO ELEMENTS WHICH ARE k STANDARD DEVIATIONS AWAY FROM THE MEAN FOR A DESIRED INTEGRAL VALUE OF K. A SEQUENCE OF (K0 x 3)-DIMENSIONAL ARRAYS IS GENERATED, ITERATIVELY, FROM THE INITIAL SEQUENCE AND PAIRWISE AVERAGES OF ELEMENTS IN EACH OF THE K0 ROWS. THE ANALYST IS QUERIED FOR A DESIRED MAXIMUM NUMBER OF ITERATIONS, TO GENERATE A LIMIT MATRIX FOR THE SEQUENCE OF PAIRWISE AVERAGES. THE LIMIT MATRIX IS INTERSECTED WITH THE SUCCESSOR (IF ANY) OF A DESIRED STAR EVENT AND COMMON ELEMENTS ARE IDENTIFIED. STAT376 IS A VARIANT OF STAT375 IN THAT A SERIES OF DESIRED REAL-VALUED DIVISORS OF PAIRS OF ELEMENTS IS USED, RATHER THAN 2.0, WITH THIS PROCESS BEING CYCLICALLY REPEATED ANY DESIRED NUMBER OF TIMES. ============================================================================== -- L 377 -- READS A SEQUENCE OF IMAX STAR EVENTS AND A SEQUENCE OF ALPHA BLOCKS, CONSISTING OF KMAX 3-ELEMENT ROWS OF ELEMENTS, EACH BLOCK CONSTRUCTED FROM A PARALLEL CLASS OF EITHER A RESOLVABLE OR ALMOST RESOLVABLE MENDELSOHN TRIPLE SYSTEM GENERATED FROM ANOTHER SOURCE, AS A SET OF HIGH-PROBABILITY ELEMENTS. A SEQUENCE OF LMAX NEW TEST EVENTS IS GENERATED FROM THE SEQUENCE OF KMAX x 3 MATRICES OR PARALLEL CLASSES. THIS PROCESS IS CYCLICALLY REPEATED FOR ANY DESIRED NUMBER OF ROWS, YIELDING A HOMOGENEOUS SEQUENCE OF HIGH-PROBABILITY NEW EVENTS. A DESIRED FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR (IF ANY) IS INTERSECTED WITH EACH OF THE NEW TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT. THE MAXIMUM NUMBER OF NEW CYCLICALLY GENERATED TEST EVENTS IS 1000. ============================================================================== -- L 378 -- READS A SEQUENCE OF IMAX STAR EVENTS AND A SEQUENCE OF LMAX TEST EVENTS, CONSISTING OF A SET OF HIGH-PROBABILITY ELEMENTS GENERATED FROM ANOTHER SOURCE, SUCH AS STAT258, STAT280, STAT346 OR STAT347. A SEQUENCE OF 30 x ( n C 2 ) NEW TEST EVENTS IS GENERATED BY THE SELECTION OF K0 = 5 SPECIFIC ELEMENTS FROM EVERY POSSIBLE PAIR OF EVENTS FROM THE SEQUENCE OF LMAX EVENTS. ON THE OTHER HAND, A SEQUENCE OF 80 x ( n C 2 ) NEW TEST EVENTS IS GENERATED BY THE SELECTION OF K0 = 6 SPECIFIC ELEMENTS FROM EVERY POSSIBLE PAIR OF EVENTS FROM THE SEQUENCE OF LMAX EVENTS. A DESIRED FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR (IF ANY) IS INTERSECTED WITH EACH OF THE LMAX TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT. NOTE THAT THERE MUST EXIST AT LEAST 2 EVENTS IN THE INITIAL SEQUENCE OF INPUT TEST EVENTS. (STAT378 IS A VARIANT OF STAT351, ALLOWING FOR THE SELECTION OF MULTIPLE ELEMENTS PER ROW OF THE PAIRS OF EVENTS. THE SEQUENCE OF EVENTS CAN BE REVERSED FOR FULL COVERAGE.) ============================================================================== -- L 379 -- READS A SEQUENCE OF IMAX STAR EVENTS AND A SEQUENCE OF LMAX 2-ELEMENT EVENTS, CONSISTING OF A SET OF HIGH-PROBABILITY ELEMENTS GENERATED FROM ANOTHER SOURCE, SUCH AS STAT256, STAT301, STAT280 OR STAT346. A SEQUENCE OF 12 x ( n C 4 ) NEW TEST EVENTS IS GENERATED BY THE SELECTION OF K0 = 5 SPECIFIC ELEMENTS FROM EVERY POSSIBLE QUADRUPLE OF EVENTS FROM THE SEQUENCE OF LMAX EVENTS. ON THE OTHER HAND, A SEQUENCE OF 16 x ( n C 5 ) NEW TEST EVENTS IS GENERATED BY THE SELECTION OF K0 = 6 SPECIFIC ELEMENTS FROM EVERY POSSIBLE QUINTUPLE OF EVENTS FROM THE SEQUENCE OF LMAX EVENTS. A DESIRED FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR (IF ANY) IS INTERSECTED WITH EACH OF THE LMAX TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT. NOTE THAT THERE MUST EXIST AT LEAST 5 EVENTS IN THE INITIAL SEQUENCE OF INPUT TEST EVENTS. (STAT379 IS A VARIANT OF STAT359). ============================================================================== -- L 380 -- SKIP AND HIT MATRIX IX DETERMINES AND PRINTS THE NUMBER OF TIMES EACH ELEMENT ( 1, ... , L0) HAS OCCURRED AFTER SKIPPING ONE OR MORE EVENTS, i.e., RECORDS THE NUMBER OF TIMES EACH ELEMENT ( 1, ..., L0 ) HAS OCCURRED AFTER SKIPPING ANY SPECIFIC NUMBER OF EVENTS BETWEEN OCCURRENCES. THE ELEMENTS ( 1, ... , L0 ) ARE THEN RANKED IN DESCENDING ORDER, BASED UPON THE NUMBER OF TIMES EACH ELEMENT HAS OCCURRED AFTER SKIPPING ITS CURRENT NUMBER OF ELAPSED EVENTS. THE ANALYST IS QUERIED FOR A DESIRED MAXIMUM NUMBER OF HIGH-PROBABILITY ELEMENTS TO BE GENERATED AND A DESIRED FINAL EVENT, JMAX, THE SUCCESSOR OF WHICH IS TO BE INTERSECTED WITH THE SEQUENCE OF HIGH-PROBABILITY ELEMENTS. ELEMENTS ARE IDENTIFIED WHICH ARE COMMON TO EVENT JMAX+1 AND THE SEQUENCE OF GENERATED HIGH-PROBABILITY ELEMENTS. STAT380 IS A VARIANT OF STAT354 IN THAT THE ORDER OF PRINTING THE ELEMENTS FOR STAT350.INP IS ARRANGED IN A BALANCED WAY, ACCORDING TO CONGRUENCE OF ELEMENTS TO PRESCRIBED VECTOR VALUES (MOD JJ), RATHER THAN CONSECUTIVELY BY ROW NUMBER (AS IS THE CASE FOR STAT381). HOWEVER, HIGH-PROBABILITY ELEMENTS ARE PRINTED AS TRIPLETS, RATHER THAN AS PAIRS. THIS PROCESS IS CYCLICALLY REPEATED, AS DESIRED. ============================================================================== -- L 381 -- SKIP AND HIT MATRIX X DETERMINES AND PRINTS THE NUMBER OF TIMES EACH ELEMENT ( 1, ... , L0) HAS OCCURRED AFTER SKIPPING ONE OR MORE EVENTS, i.e., RECORDS THE NUMBER OF TIMES EACH ELEMENT ( 1, ..., L0 ) HAS OCCURRED AFTER SKIPPING ANY SPECIFIC NUMBER OF EVENTS BETWEEN OCCURRENCES. THE ELEMENTS ( 1, ... , L0 ) ARE THEN RANKED IN DESCENDING ORDER, BASED UPON THE NUMBER OF TIMES EACH ELEMENT HAS OCCURRED AFTER SKIPPING ITS CURRENT NUMBER OF ELAPSED EVENTS. THE ANALYST IS QUERIED FOR A DESIRED MAXIMUM NUMBER OF HIGH-PROBABILITY ELEMENTS TO BE GENERATED AND A DESIRED FINAL EVENT, JMAX, THE SUCCESSOR OF WHICH IS TO BE INTERSECTED WITH THE SEQUENCE OF HIGH-PROBABILITY ELEMENTS. ELEMENTS ARE IDENTIFIED WHICH ARE COMMON TO EVENT JMAX+1 AND THE SEQUENCE OF GENERATED HIGH-PROBABILITY ELEMENTS. STAT381 IS A VARIANT OF STAT353 IN THAT THE ORDER OF PRINTING THE ELEMENTS FOR STAT350.INP IS ARRANGED CONSECUTIVELY, BY ROW NUMBER, RATHER THAN ACCORDING TO CONGRUENCE OF ELEMENTS TO PRESCRIBED VECTOR (MOD JJ), AS IS THE CASE FOR STAT 354. HOWEVER, HIGH-PROBABILITY ELEMENTS ARE PRINTED AS TRIPLETS FOR STAT361, RATHER THAN AS PAIRS. ============================================================================== -- L 382 -- SKIP AND HIT MATRIX XI DETERMINES AND PRINTS THE NUMBER OF TIMES EACH ELEMENT ( 1, ... , L0) HAS OCCURRED AFTER SKIPPING ONE OR MORE EVENTS, i.e., RECORDS THE NUMBER OF TIMES EACH ELEMENT ( 1, ..., L0 ) HAS OCCURRED AFTER SKIPPING ANY SPECIFIC NUMBER OF EVENTS BETWEEN OCCURRENCES. THE ELEMENTS ( 1, ... , L0 ) ARE THEN RANKED IN DESCENDING ORDER, BASED UPON THE NUMBER OF TIMES EACH ELEMENT HAS OCCURRED AFTER SKIPPING ITS CURRENT NUMBER OF ELAPSED EVENTS. THE ANALYST IS QUERIED FOR A DESIRED MAXIMUM NUMBER OF HIGH-PROBABILITY ELEMENTS TO BE GENERATED AND A DESIRED FINAL EVENT, JMAX, THE SUCCESSOR OF WHICH IS TO BE INTERSECTED WITH THE SEQUENCE OF HIGH-PROBABILITY ELEMENTS. ELEMENTS ARE IDENTIFIED WHICH ARE COMMON TO EVENT JMAX+1 AND THE SEQUENCE OF GENERATED HIGH-PROBABILITY ELEMENTS. STAT382 IS A VARIANT OF STAT380 IN THAT THE ORDER OF PRINTING THE ELEMENTS FOR STAT350.INP IS ARRANGED IN A BALANCED WAY, ACCORDING TO EQUALITY OF ELEMENTS TO RANDOMLY SELECTED INTEGRAL VECTOR VALUES, RATHER THAN VECTOR VALUES (MOD JJ ), AS IS THE CASE FOR STAT380. HOWEVER, HIGH-PROBABILITY ELEMENTS ARE PRINTED AS PAIRS, RATHER THAN AS TRIPLETS. THIS PROCESS IS CYCLICALLY REPEATED, AS DESIRED. ============================================================================== -- L 383 -- SKIP AND HIT MATRIX XII DETERMINES AND PRINTS THE NUMBER OF TIMES EACH ELEMENT ( 1, ... , L0) HAS OCCURRED AFTER SKIPPING ONE OR MORE EVENTS, i.e., RECORDS THE NUMBER OF TIMES EACH ELEMENT ( 1, ..., L0 ) HAS OCCURRED AFTER SKIPPING ANY SPECIFIC NUMBER OF EVENTS BETWEEN OCCURRENCES. THE ELEMENTS ( 1, ... , L0 ) ARE THEN RANKED IN DESCENDING ORDER, BASED UPON THE NUMBER OF TIMES EACH ELEMENT HAS OCCURRED AFTER SKIPPING ITS CURRENT NUMBER OF ELAPSED EVENTS. THE ANALYST IS QUERIED FOR A DESIRED MAXIMUM NUMBER OF HIGH-PROBABILITY ELEMENTS TO BE GENERATED AND A DESIRED FINAL EVENT, JMAX, THE SUCCESSOR OF WHICH IS TO BE INTERSECTED WITH THE SEQUENCE OF HIGH-PROBABILITY ELEMENTS. ELEMENTS ARE IDENTIFIED WHICH ARE COMMON TO EVENT JMAX+1 AND THE SEQUENCE OF GENERATED HIGH-PROBABILITY ELEMENTS. STAT383 IS A VARIANT OF STAT380 IN THAT THE ORDER OF PRINTING THE ELEMENTS FOR STAT350.INP IS ARRANGED IN A BALANCED WAY, ACCORDING TO EQUALITY OF ELEMENTS TO RANDOMLY SELECTED INTEGRAL VECTOR VALUES, RATHER THAN VECTOR VALUES (MOD JJ ), AS IS THE CASE FOR STAT380. HOWEVER, HIGH-PROBABILITY ELEMENTS ARE PRINTED AS TRIPLETS, RATHER THAN AS PAIRS. THIS PROCESS IS CYCLICALLY REPEATED, AS DESIRED. ============================================================================== -- L 384 -- READS A SEQUENCE OF IMAX STAR EVENTS AND A SEQUENCE OF ALPHA BLOCKS, CONSISTING OF 6 ROWS OF 2-ELEMENT EVENTS PER BLOCK DETERMINED FROM ANOTHER SOURCE, SUCH AS STAT382, AS A SET OF HIGH-PROBABILITY ELEMENTS. THROUGH A CYCLICAL PROCESS, A SEQUENCE OF 30 NEW TEST EVENTS PER BLOCK IS GENERATED FROM THE K0 x 2 MATRIX DETERMINED BY SELECTING K0 ROWS AND 2 COLUMNS FROM K0 OF THE INITIAL 6 EVENTS PER BLOCK. THIS PROCESS IS CYCLICALLY REPEATED FOR EACH OF THE ALPHA BLOCKS OF K0 ROWS AND 2 COLUMNS, YIELDING A HOMOGENEOUS SEQUENCE OF NEW HIGH-PROBABILITY EVENTS. A DESIRED FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR (IF IT EXISTS) IS INTERSECTED WITH EACH OF THE NEW TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT. THE INPUT FILE CONSISTS OF SEQUENCES OF K0 GENERATED EVENTS, E.G., FROM STAT382, AND THE SECOND CONSISTS OF THE SEQUENCE OF IMAX STAR EVENTS. THE MAXIMUM NUMBER OF NEW CYCLICALLY GENERATED TEST EVENTS IS 600. ============================================================================== -- L 385 -- READS A SEQUENCE OF IMAX STAR EVENTS ON K0 ELEMENTS AND DETERMINES FOR A DESIRED FINAL CHOSEN EVENT, JMAX, OVER THE IMAX STAR EVENTS, A NEW SEQUENCE OF JMAX+2 TEST EVENTS, FOR i = 1 , ... , IMAX AND j = 1, ... , K0 , WHERE B(i,j) IS THE j-th ELEMENT OF THE i-th ROW OF THE GENERATED TEST SEQUENCE, REPRESENTING THE PREDICTED ELEMENT OF COLUMN j WHICH WILL PRESERVE THE MEAN OF COLUMN j, OVER IMAX EVENTS, FOR UP TO 300 STAR EVENTS. THE NUMBER OF ELEMENTS IN COMMON BETWEEN A FINAL CHOSEN EVENT FROM THE STAR SEQUENCE AND EACH EVENT OF THE GENERATED SEQUENCE OF TEST EVENTS IS ALSO DETERMINED. THOSE TEST EVENTS ARE IDENTIFIED WHICH HAVE A # OF ELEMENTS IN COMMON WITH THE FINAL EVENT EXCEEDING SOME DESIRED MINIMUM THRESHOLD. NOTE: CORRESPONDING ELEMENT DIFFERENCES D(i,j) = B(i,j) - A(i,j) , WHERE B(i,j) <===> PREDICTED ELEMENTS AND A(i,j) <===> ACTUAL STAR ELEMENTS , FOR i = 1 , ... , JMAX+2 AND j = 1 , ... , K0 ARE ALSO GENERATED. STAT385 IS A VARIANT OF STAT272, WITH A HOMOGENEOUS SEQUENCE OF EVENTS BEING GENERATED FROM A SEED SET OF 5 EVENTS, EACH CONSISTING OF K0 MOVING AVERAGES. ============================================================================== -- L 386 -- GENERATES HIGH-PROBABILITY DENSITY ELEMENTS FOR A SEQUENCE OF IMAX STAR EVENTS ON THE ELEMENTS OF < 1, 2, ... , L0 >, BY EXAMINING THE NUMBER OF OCCURRENCES OF EACH ELEMENT WITHIN THE LAST 5 EVENTS AND WITHIN THE LAST 6 TO 10 EVENTS, BACKING UP A CHOSEN DISTANCE FROM A DESIRED FINAL EVENT. THIS PROCESS IS CYCLICALLY REPEATED A DESIRED NUMBER OF TIMES FOR SELECTED FINAL STAR EVENTS AND SELECTED BACKING-UP DISTANCES. THE GENERATED PERMUTATION SEQUENCE OF HIGH- PROBABILITY ELEMENTS IS INTERSECTED WITH THE THE EVENT SUCCEEDING THE FINAL SELECTED STAR EVENT (IF ANY) AND COMMON ELEMENTS ARE IDENTIFIED. THE GENERATED SEQUENCE OF HIGH-PROBABILITY ELEMENTS IS ALSO PRINTED AS STAT368.INP FOR FURTHER ANALYSIS AND USE. STAT386 IS AN EMBELLISHMENT OF STAT21 AND HAS DEMONSTRATED SUBSTANTIAL INTERSECTION NUMBERS WITH SUCCEEDING STAR EVENTS. ============================================================================== -- L 387 -- READS A SEQUENCE OF IMAX STAR EVENTS ON ELEMENTS < 1, ... , L0 > AND DETERMINES AVERAGES OF EACH OF K0 COLUMNS FOR BLOCKS OF EVENTS HAVING LEXICOGRAPHIC LEADING ELEMENT, J0, FOR J0 = 1 , 2, ... AS SELECTED BY THE ANALYST, WHERE THE IMAX STAR EVENTS ARE LISTED IN LEXICOGRAPHIC ORDER. THIS ALLOWS FOR GENERATION OF A NEW HOMOGENEOUS SEQUENCE OF EVENTS, CONSISTING OF HIGHLY-PROBABLE ELEMENTS. ============================================================================== -- L 388 -- READS A SEQUENCE OF STAR EVENTS ON THE ELEMENTS ( 1 , ... , L0 ) AND PRINTS THE ELEMENTS OF EACH OF j COLUMNS ( j = 1 , ... , K0 ), AS j SEPARATE BLOCKS FOR STAT176.INP, BACKING-UP AND INCLUDING A DESIRED NUMBER, Q0, OF EVENTS (WITH, e.g., L0 = 51, K0 = 6 , AND Q0 = 10 ). THE ROUTINE ALSO PERFORMS A COLUMN-WISE SORT OF EACH OF THE K0 SEPARATE COLUMNS AND PRINTS AS BEFORE. STAT388 IS A VARIANT OF STAT193, EXCEPT THAT HOMOGENEOUS HIGH-PROBABILITY EVENTS ARE GENERATED FROM EVENTS IN STAT388.OT2, INSTEAD OF STAT388.OUT. ============================================================================== -- L 389 -- READS A SEQUENCE OF IMAX STAR EVENTS, A SEQUENCE OF LMAX TEST EVENTS AND PNUM PERMUTATION SEQUENCES ON MMAX ELEMENTS GENERATED FROM ANOTHER SOURCE, SUCH AS STAT375, AND FILTERS THOSE TEST EVENTS HAVING A PRESCRIBED NUMBER OF ELEMENTS WITHIN EPSILON = 1 UNIT OF AT LEAST ONE ELEMENT OF EACH SEQUENCE OF MMAX ELEMENTS. THE FILTERED SEQUENCE IS AN INDUCED HOMOGENEOUS SEQUENCE OF HIGH-PROBABILITY EVENTS. A FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR IS INTERSECTED WITH EACH OF THE LMAX TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT (IF IT EXISTS), FOR UP TO 400 STAR OR TEST EVENTS AND UP TO 10 PERMUTATIONS. ============================================================================== -- L 390 -- READS A SEQUENCE OF IMAX STAR EVENTS, A SEQUENCE OF LMAX TEST EVENTS AND PNUM PERMUTATION SEQUENCES ON MMAX ELEMENTS GENERATED FROM ANOTHER SOURCE, SUCH AS STAT375 OR S, AND FILTERS THOSE TEST EVENTS HAVING A PRESCRIBED NUMBER OF ELEMENTS WITHIN EPSILON UNITS, WHERE EPSILON IS AN ARBITRARILY SMALL POSITIVE INTEGER, OF A DESIRED NUMBER OF ELEMENTS OF EACH SEQUENCE OF MMAX ELEMENTS. THE FILTERED SEQUENCE IS AN INDUCED HOMOGENEOUS SEQUENCE OF HIGH-PROBABILITY EVENTS. A FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR IS INTERSECTED WITH EACH OF THE LMAX TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT (IF IT EXISTS), FOR UP TO 400 STAR OR TEST EVENTS AND UP TO 10 PERMUTATIONS. STAT390 IS A VARIANT OF STAT389, WITH FLEXIBILITY OF EPSILON. ============================================================================== -- L 391 -- READS A SEQUENCE OF IMAX STAR EVENTS, A SEQUENCE OF LMAX TEST EVENTS AND PNUM PERMUTATION SEQUENCES ON MMAX ELEMENTS GENERATED FROM ANOTHER SOURCE, SUCH AS STAT375, AND FILTERS THOSE TEST EVENTS HAVING A PRESCRIBED NUMBER OF ELEMENTS INTERSECTING EACH PERMUTATION SEQUENCE. A MATRIX OF SUCH EVENTS IS THEN GENERATED. THE FILTERED SEQUENCE IS AN INDUCED HOMOGENEOUS SEQUENCE OF HIGH-PROBABILITY EVENTS. A FINAL EVENT IS CHOSEN FROM THE IMAX STAR EVENTS AND ITS SUCCESSOR IS INTERSECTED WITH EACH OF THE LMAX TEST EVENTS. SUBSEQUENTLY, A CONFIGURATION MATRIX IS GENERATED TO REFLECT ELEMENTS IN COMMON BETWEEN NEW TEST EVENTS AND THE FINAL SUCCESSOR STAR EVENT (IF IT EXISTS), FOR UP TO 400 STAR OR TEST EVENTS AND UP TO 10 PERMUTATIONS. STAT391 IS A VARIANT OF STAT390. ============================================================================== -- L 392 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS ON THE ELEMENTS < 1 , ... , L0 > AND A SEQUENCE OF LMAX K0-ELEMENT TEST EVENTS AND GENERATES TWO HOMOGENEOUS SEQUENCES OF ILMAX = (LMAX * LMAX * LMAX)+6 NEW TEST EVENTS BY TAKING TRIPLES OF ELEMENTS FROM THE LAST THREE COLUMNS OF EACH EVENT WITH K0 - 3 ELEMENTS FROM THE REMAINING THREE COLUMNS OF THREE OTHER TEST EVENTS SELECTED ALGORITHMICALLY. STAT392 IS A VARIANT OF STAT193. HOWEVER, A FIXED SET OF LMAX INPUT EVENTS IS READ, RATHER THAN A GENERATED SET, FOR UP TO 800 EVENTS. ============================================================================== -- L 393 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS ON THE ELEMENTS < 1 , ... , L0 > AND A BLOCK OF LMAX K0-ELEMENT TEST EVENTS, INTERSECTING THE SUCCESSOR (IF IT EXITS) OF EACH EVENT IN A DESIRED RANGE OF STAR EVENTS WITH EACH TEST EVENT. A SEQUENCE OF CONFIGURA- TION MATRICES IS GENERATED, INDICATING THE OCCURRENCE AND POSITIONS OF STAR ELEMENTS COMMON TO THE BLOCK AND EACH STAR EVENT IN THE SELECTED RANGE, FOR UP TO 800 STAR EVENTS. ============================================================================== -- L 394 -- READS A SEQUENCE OF IMAX STAR EVENTS AND A SEQUENCE OF LMAX TEST EVENTS AND DETERMINES THE NUMBER OF ELEMENTS IN COMMON BETWEEN THE EVENT SUCCEEDING A SELECTED STAR EVENT (IF IT EXISTS) AND EACH OF THE LMAX TEST EVENTS. MOREOVER, THE NUMBER AND PERCENTAGE OF 0's , 1's, 2's, ... , K0's ARE COMPUTED AS CARDINALITIES OF INTERSECTION NUMBERS BETWEEN TEST EVENTS AND THE SUCCESSIVE EVENT TO THE SELECTED STAR EVENT FOR UP TO 600 STAR EVENTS AND 600 TEST EVENTS. A CONFIGURATION MATRIX IS GENERATED WHICH INDICATES THE ELEMENTS IN COMMON BETWEEN TEST EVENTS AND THE SUCCESSIVE STAR EVENT. ============================================================================== -- L 395 -- READS, ANALYZES, AND SORTS A SEQUENCE OF FUNCTIONAL VALUES (e.g., SAMPLE POINTS FROM SOME POPULATION), DETERMINES THE MEAN, MEDIAN, VARIANCE, STANDARD DEVIATION, MEAN DEVIATION, PEARSONIAN COEFFICIENT OF SKEWEDNESS, ANALYZES THE INPUT DISTRIBUTION WITH RESPECT TO INTERVALS CONTAINING SPECIFIED PERCENTAGES OF THE VALUES, ACCORDING TO CHEBYSHEV'S THEOREM, AND COMPUTES A PROBABILITY DISTRIBUTION FOR RANDOM VARIABLE X. (REAL INPUT VALUES OF THE SAMPLE POINTS OR REAL FUNCTIONAL VALUES ARE READ FROM THE FILE STAT395.INP, WHICH IS EITHER PROVIDED BY THE ANALYST OR GENERATED FROM AN EXTERNAL PROGRAM. FILE STAT395.INP: (LINES 1 - 13 , HEADER DATA ; REMAINING LINES: SEQUENCE OF N RECORDS CONSISTING OF' NAME : COLS. 1 - 27 ; SS# : COLS. 28 - 38 ; BLANKS : COLS. 39 - 44 ; SCORE 1 : COLS. 45 - 46 ; BLANKS : COLS. 47 - 52; SCORE 2 : COLS. 53 - 54 ; BLANKS : COLS. 55 - 59 ; SCORE 3 : COLS. 60 - 63. FORMAT FOR EACH OF THE N RECORDS : FORMAT FOR EACH OF THE N RECORDS (WHERE THE MAX. VALUE OF N=500) A27,I3,1X,I2,1X,I4,6X,I2,6X,I2,5X,F4.1 ============================================================================== -- L 396 -- READS AN INPUT FILE OF NAMES AND SCORES OR FUNCTIONAL VALUES, FILTERING THE RECORDS ACCORDING TO THE GENDER SELECTED BY THE ANALYST. THE OUTPUT FILE OF FILTERED RECORDS IS PRINTED AS AN INPUT FILE FOR STAT395. THE FOLLOWING ARE SPECFIED FILE NAMES: OUTPUT1 = STAT396.OUT AND OUTPUT2 = STAT395.INP , INPUT = STAT396.INP: (LINES 1 - 13 , HEADER DATA ; REMAINING LINES: SEQUENCE OF N RECORDS CONSISTING OF NAME : COLS. 1 - 27 ; SS# : COLS. 28 - 38 ; BLANKS : COLS. 39 - 44 ; SCORE 1 : COLS. 45 - 46 ; BLANKS : COLS. 47 - 52; SCORE 2 : COLS. 53 - 54 ; BLANKS : COLS. 55 - 59 ; SCORE 3 : COLS. 60 - 63 ; BLANKS : COLS. 64 - 69 ; GENDER : COL 70. FORMAT FOR EACH OF THE N RECORDS (WHERE THE MAX. VALUE OF N=500) A27,I3,1X,I2,1X,I4,6X,I2,6X,I2,5X,F4.1,6X,A1 ============================================================================== -- L 397 -- READS, ANALYZES, AND SORTS A SEQUENCE OF FUNCTIONAL VALUES (e.g., SAMPLE POINTS FROM SOME POPULATION), DETERMINES THE MEAN, MEDIAN, VARIANCE, STANDARD DEVIATION, MEAN DEVIATION, PEARSONIAN COEFFICIENT OF SKEWEDNESS, ANALYZES THE INPUT DISTRIBUTION WITH RESPECT TO INTERVALS CONTAINING SPECIFIED PERCENTAGES OF THE VALUES, ACCORDING TO CHEBYSHEV'S THEOREM, AND COMPUTES A PROBABILITY DISTRIBUTION FOR RANDOM VARIABLE X. (REAL INPUT VALUES OF THE SAMPLE POINTS OR REAL FUNCTIONAL VALUES ARE READ FROM THE FILE STAT397.INP, WHICH IS EITHER PROVIDED BY THE ANALYST OR GENERATED FROM AN EXTERNAL PROGRAM. FILE STAT397.INP: (LINES 1 - 13 , HEADER DATA ; REMAINING LINES: SEQUENCE OF N RECORDS CONSISTING OF' NAME : COLS. 1 - 27 ; SS# : COLS. 28 - 38 ; BLANKS : COLS. 39 - 44 ; SCORE 1 : COLS. 45 - 46 ; BLANKS : COLS. 47 - 52; SCORE 2 : COLS. 53 - 54 ; BLANKS : COLS. 55 - 59 ; SCORE 3 : COLS. 60 - 63 ; BLANKS : COLS. 64 - 69 ; GENDER : COL. 70 . FORMAT FOR EACH OF THE N RECORDS : ( WHERE THE MAXIMUM VALUE OF N = 500 ) A27,I3,1X,I2,1X,I4,6X,I2,6X,I2,5X,F4.1,6X,A1 ============================================================================== -- L 398 -- READS A SEQUENCE OF IMAX BASE EVENTS AND DETERMINES, FOR A SELECTED EVENT NUMBER, JMAX, AND A DESIRED NUMBER OF ELEMENTS IN THE RANGE IN THAT EVENT, A SUBSEQUENCE OF SUCCESSORS OF BASE EVENTS WHICH CONTAIN BETWEEN q1 > 0 AND q2 < K0 ELEMENTS FALLING WITHIN A SELECTED RANGE OF VALUES FOR EACH OF THE K0 COLUMNS PER EVENT. THE RANGE < A(JMAX,J) - EPSILON , A(JMAX,J) + EPSILON > FOR EACH COLUMN INDEX J = 1 , ... , K0 , AS WELL AS, A DESIRED NON-NEGATIVE INTEGRAL VALUE OF EPSILON FOR A GIVEN ELEMENT A(I,J) SERVE AS THE FILTERING CRITERIA FOR BASE EVENTS. THE SUCCESSIVE EVENT FOR EACH FAVORABLE EVENT IS FILTERED, BACKING UP A DESIRED NUMBER OF EVENTS FROM THE FINAL EVENT. THE RESULTING MATRIX IS DESIGNED TO INDICATE WHICH ELEMENTS ARE MOST LIKELY TO OCCUR FOLLOWING EACH OF THE K0 ELEMENTS OF THE DESIRED FINAL EVENT. THE ROUTINE ALSO DETERMINES THE SET OF ELEMENTS IN COMMON BETWEEN THE SET OF SUCCESSORS AND THE SET OF ELEMENTS OF THE EVENT FOLLOWING THE DESIRED FINAL EVENT, FOR UP TO 500 EVENTS. ============================================================================== -- L 399 -- READS A SEQUENCE OF IMAX BASE EVENTS AND DETERMINES, FOR A SELECTED EVENT NUMBER, JMAX, AND A DESIRED NUMBER OF ELEMENTS IN THE RANGE IN THAT EVENT, A SUBSEQUENCE OF BASE EVENTS WHICH CONTAIN BETWEEN q1 > 0 AND q2 < K0 ELEMENTS FALLING WITHIN A SELECTED RANGE OF VALUES FOR EACH OF THE K0 COLUMNS PER EVENT. THE RANGE < A(JMAX,J) - EPSILON , A(JMAX,J) + EPSILON > FOR EACH COLUMN INDEX J = 1 , ... , K0 , AS WELL AS, A DESIRED NON-NEGATIVE INTEGRAL VALUE OF EPSILON FOR A GIVEN ELEMENT A(I,J) SERVE AS THE FILTERING CRITERIA FOR BASE EVENTS. EACH FAVORABLE BASE EVENT IS FILTERED BASED UPON THESE CRITERIA, BACKING UP A DESIRED NUMBER OF EVENTS FROM THE FINAL EVENT. THE RESULTING MATRIX IS DESIGNED TO INDICATE WHICH ELEMENTS ARE MOST LIKELY TO OCCUR FOLLOWING EACH OF THE K0 ELEMENTS OF THE DESIRED FINAL EVENT. THE ROUTINE ALSO DETERMINES THE SET OF ELEMENTS IN COMMON BETWEEN THE SET OF BASE EVENTS AND THE SET OF ELEMENTS OF THE EVENT FOLLOWING THE DESIRED FINAL EVENT, FOR UP TO 500 EVENTS. ==============================================================================