= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = COMP-U-STAT = = = = = = = = STATISTICAL PATTERN GENERATOR AND MATHEMATICAL TREND ANALYZER = = = = = = = = (c) Copyright 2017 by James Ervin Glover, Ph.D. = = = = All Rights Reserved = = = = = = = = = = = = Part I(a) ( STAT 1 ----> STAT 70 ) = = = = = = = = = = = = 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 1 ---> 70 * * * ====================================================================== -- L 1 -- DETERMINES A SEQUENCE OF EVENTS WHICH INTERSECT EVERY EVENT OF A FIXED SEQUENCE OF PAST EVENTS, IN k SPECIFIC ELEMENTS, WHERE k IS IN THE INTERVAL (Xo,Yo), INCLUSIVE OF ENDPOINTS; INTERSECTS A SET OF K0-ELEMENT BLOCKS WITH m K0-ELEMENT EVENTS, WHERE m IS A POSITIVE INTEGER, AND FILTERS ONLY THOSE EVENTS HAVING k ELEMENTS IN COMMON WITH EACH EVENT OF THE FIXED (BASE) SET, FOR SOME INTEGER k VARYING IN THE RANGE (Xo,Yo), INCLUSIVE OF ENDPOINTS, WHERE Xo and Yo ARE NON-NEGATIVE INTEGERS, WITH Yo < K0+1 AND WITH, e.g., K0 = 6. ====================================================================== -- L 2 -- * * MONITOR MATRIX GENERATOR * * COMPARES A SET OF j-ELEMENT EVENTS WITH A SEQUENCE OF BASE SETS OF ELEMENTS, DETERMINES THE NUMBER OF ELEMENTS IN EACH EVENT IN COMMON WITH EACH BASE SET, DETERMINES THE RELATIVE FREQUENCIES AND SUM OF RELATIVE FREQUENCIES OF COMMON ELEMENTS FOR COMPARISON, AND GENERATES A MONITOR MATRIX, REFLECTING THE PATTERNS OF OCCURRENCES FROM THE ABOVE SEQUENCE OF BASE SETS WITH , e.g., j = 7 . GENERATES A FILE OF POSITIONAL CONFIGURATIONS FOR OCCURRENCE OF EACH ELEMENT OF THE FINAL TEST EVENT IN EACH PERMUTATION OR BASE SET OF THE SEQUENCE. ====================================================================== -- L 3 -- GENERATES, FOR A SEQUENCE OF k STAR EVENTS, THE SUM OF j ELEMENTS IN EACH EVENT, THE AVERAGE SUM OF ELEMENTS OVER k EVENTS, AND A CHART INDICATING WHETHER OR NOT EACH EVENT HAS A SUM OF ELEMENTS BELOW OR ABOVE A BALANCED SUM. ROUTINE ALSO DETERMINES WHETHER THE TREND FOR STAR EVENTS IS TOWARD SUMS OF ELEMENTS ABOVE OR BELOW THE AVERAGE SUM FOR A BALANCED EVENT WITH, e.g., j = 6. ====================================================================== -- L 4 -- DETERMINES THE PROJECTED SUM OF THE j ELEMENTS OF THE NEXT EVENT, BASED UPON THE COMPUTED AVERAGE SUM OF j ELEMENTS, OVER THE LAST k EVENTS. USED IN CONJUNCTION WITH PROGRAMS L 23 AND L 3, THIS ALLOWS PREDICTION OF THE MOST LIKELY RANGE OF THE ELEMENTS OF THE NEXT EVENT WITH, e.g., j = 6. ====================================================================== -- L 5 -- DETERMINES THE FREQUENCIES OF ELEMENTS FROM A SEQUENCE OF j-ELEMENT BLOCKS, THE SUM OF FREQUENCIES AND THE AVERAGE FREQUENCY OVER k EVENTS, SORTS THE FREEQUENCIES AND DETERMINES THE TOP t MOST FREQUENT ELEMENTS AND THE BOTTOM t LEAST FREQUENT ELEMENTS, AND DETERMINES SEQUENCES OF PROBABLE ELEMENTS BASED UPON ARBITRARY PRESCRIBED DISTANCES FROM THE AVERAGE FREQUENCY. STAT5 ALSO GENERATES A VERSION OF STAT1048.IN2. STAT5 GENERATES THE FILE STAT2522.IN2 FOR RANKING AND FILTERING TEST EVENTS IN DESCENDING ORDER OF ELEMENT FREQUENCY SUMS. STAT5 ALSO GENERATES THE HIGH-PROBABILITY FILE, PERM.INP. ====================================================================== -- L 6 -- FREQUENCY COUNTS FOR ELEMENTS IN A BASE SET (ADVANCED PREDICTING SYSTEM) COMPARES A SET OF k-ELEMENT BLOCKS WITH A SEQUENCE OF BASE SETS OF ELEMENTS AND DETERMINES THE NUMBER OF COMMON ELEMENTS. THE EVENTS ARE FILTERED FROM THE SEQUENCE OF k-ELEMENT BLOCKS FOR WHICH THE NUMBER OF ELEMENTS IN COMMON WITH A GIVEN BASE SET IS BETWEEN PRESCRIBED, INCLUSIVE BOUNDS, AND A PREDICTION IS MADE AS TO THE NEXT OCCURRENCE OF AN EVENT SATISFYING THIS CRITERION WITH, e.g., k = 7. ====================================================================== -- L 7 -- INTERSECTS A BLOCK OF j-ELEMENT EVENTS (STAR EVENTS) WITH A BLOCK OF m (j-1)-ELEMENT EVENTS (e.g., TEST EVENTS), WHERE m IS AN ARBITRARY POSITIVE INTEGER , AND DETERMINES CLASSES WITH INTERSECTIONS OF SIZES 3, 4, ... , j-1 WITH , e.g., j = 7. ====================================================================== -- L 8 -- GENERATES A SEQUENCE OF WHEELED EVENTS FROM A FIXED WHEEL OR SEQUENCE OF EVENTS BY THE ACTION OF AN ARBITRARILY CHOSEN PERMUTATION ON THE ELEMENTS IN THE FIXED WHEEL OF EVENTS. THE USER IS PROMPTED AT THE TERMINAL SCREEN FOR EACH EVENT OF THE FIXED WHEEL AND FOR ALL ELEMENTS IN EACH PERMUTATION ON THE ELEMENTS OF THE FIXED WHEEL. ====================================================================== -- L 9 -- DETERMINES AND TALLIES STAR ELEMENTS TO WITHIN THE LAST k EVENTS, WHERE k IS A POSITIVE INTEGER . ====================================================================== -- L 10 -- DETERMINES AND TALLIES STAR ELEMENTS TO WITHIN THE FIRST k EVENTS, WHERE k IS A POSITIVE INTEGER . ====================================================================== -- L 11 -- GENERATES A LEXICOGRAPHIC SEQUENCE OF k-SUBSETS OF AN n-SET, WHERE k AND n ARE POSITIVE INTEGERS , k < n < 81 . THE NUMBER OF DISTINCT k-SUBSETS GENERATED IS, AT MOST, nCk, ( n CHOOSE K) , (THE MAXIMUM NUMBER OF DISTINCT k-ELEMENT SUBSETS OF A SUPERSET OF SIZE n ). THE PROGRAM ALSO GENERATES THE NEXT K-SUBSET OF AN N-SET AND REPEATS THIS PROCEDURE FOR ANY DESIRED NUMBER OF K-SUBSETS. MOREOVER, THE ROUTINE FILTERS THE GENERATED EVENTS, BASED UPON A DESIRED PIVOTAL COLUMN NUMBER. AN EVENT OR PERMUTATION IS FILTERED IF ITS PIVOTAL COLUMN NUMBER IS DISTINCT FROM THAT OF THE PRECEDING EVENT. FILTERING IS FURTHER REFINED BY SELECTING ONLY THOSE EVENTS FROM THE SEQUENCE WITH INDICES CONGRUENT TO AN ELEMENT OF A DESIRED INTEGRAL VECTOR SELECTED BY THE ANALYST, I.E., < M1, M2, M3, M4, M5 > ( MOD T) , FOR SOME DESIRED INTEGER T AND SOME DESIRED INTEGERS M1, M2, M3, M4, and M5. ====================================================================== -- L 12 -- GENERATES RANDOM K-SUBSETS OF AN N-SET, WHERE K AND N ARE INTEGERS, ADAPTED FROM COMBINATORIAL ALGORITHMS (A. NIJENHUIS, H. WILF) , WHERE k AND n ARE ARBITRARY POSITIVE INTEGERS WITH k < n . STAT1492 MAY BE UTILIZED TO GENERATE INPUT PERMUTATIONS IN PERM.INP AS THE SYMMETRIC GROUP ON Q0 ELEMENTS. A CUMULATIVE FILE OF TEST EVENTS FOR STAT12 IS GENERATED IN STAT94.IN2 FOR FUTURE PROCESSING. AN EXPANDED SEQUENCE OF Q0 PERMUTATIONS IS GENERATED FROM EACH INPUT PERMUTATION OF PERM.INP AND RECORDED IN PERM2.OUT FOR FUTURE ANALYSIS. ====================================================================== -- L 13 -- DETERMINES THE NUMBER AND % OF PAST STAR EVENTS IN A SEQUENCE FOR WHICH THE MINIMUM AND MAXIMUM ELEMENTS LIE WITHIN A DESIRED SPECIFIED, INCLUSIVE RANGE, (Xo,Yo), AND PRINTS THOSE EVENTS WHICH WERE FILTERED FROM THE SEQUENCE, BACKING UP A DESIRED NUMBER OF EVENTS FROM THE FINAL EVENT. ====================================================================== -- L 14 -- GENERATES HIGH PROBABILITY DENSITY ELEMENTS FOR PROJECTED EVENTS FROM A SEQUENCE OF PAST STAR EVENTS, BASED UPON PAST FREQUENCY COUNTS OF ELEMENTS . (Version I) ====================================================================== -- L 15 -- GENERATES HIGH PROBABILITY DENSITY ELEMENTS FOR PROJECTED EVENTS FROM A SEQUENCE OF PAST STAR EVENTS, BASED UPON PAST FREQUENCY COUNTS OF ELEMENTS . (Version II) ====================================================================== -- L 16 -- GENERATES HIGH PROBABILITY DENSITY ELEMENTS FOR PROJECTED EVENTS FROM A SEQUENCE OF PAST STAR EVENTS, BASED UPON PAST FREQUENCY COUNTS OF ELEMENTS AND SUITABLE FOR A 6/4 BACK-UP PROCEDURE. (Version III) ====================================================================== -- L 17 -- READS A SEQUENCE OF STAR EVENTS ON THE ELEMENTS (1 ,..., n) AND AND GENERATES, FROM THIS SEQUENCE A SEQUENCE OF HIGH PROBABILITY ELEMENTS PROJECTED FOR THE NEXT k EVENTS WHERE k IS ARBITRARY WITH, e.g., n = 49. ====================================================================== -- L 18 -- GENERATES HIGH PROBABILITY DENSITY ELEMENTS FOR PROJECTED EVENTS FROM A SEQUENCE OF PAST STAR EVENTS, BASED UPON PAST FREQUENCY COUNTS OF ELEMENTS . (Version IV) ====================================================================== -- L 19 -- READS AND INTERSECTS A SEQUENCE OF STAR EVENTS OVER THE ELEMENTS (1 ,..., n) WITH A CORRESPONDING SEQUENCE OF BASE SETS GENERATED AS HIGHLY PROBABLE ELEMENTS TO DETERMINE AN EXPOSITORY SEQUENCE OF CARDINALITIES OF INTERSECTIONS. EACH EVENT IS INTERSECTED WITH A SET OF HIGHLY PROBABLE ELEMENTS GENERATED FROM THE PRECEDING 30 EVENTS WITH, e.g., n = 49. REQUIRED AS INPUT ARE THE MOST CURRENT VERSIONS OF THE OUTPUT FILES: L17.OT2 AND L17.OT3 ====================================================================== -- L 20 -- PARTITIONS THE ELEMENTS ( 1 ,..., n ) INTO 2 SETS: (1) ELEMENTS WITH NUMBER OF OCCURRENCES AFTER SKIPPING A SPECIFIED NUMBER OF EVENTS EXCEEDING THE AVERAGE NUMBER OF SUCH OCCURRENCES, OVER n ELEMENTS, AND (2) ELEMENTS WITH NUMBER OF OCCURRENCES AFTER SKIPPING A SPECIFIED NUMBER OF EVENTS LESS THAN OR EQUAL TO THE AVERAGE NUMBER OF SUCH OCCURRENCES, OVER n ELEMENTS. MOREOVER, ELEMENTS WITH NUMBER OF OCCURRENCES AFTER SKIPPING A SPECIFIED NUMBER OF OCCURRENCES WHICH ARE WITHIN AN ARBITRARY INTEGRAL DISTANCE OF THE AVERAGE NUMBER OF SUCH OCCURRENCES ARE ENUMERATED WITH , e.g., n = 49. INPUT REQUIRED FROM FILES: L55.OT4, L64.OUT (Most Current Versions) ====================================================================== -- L 21 -- GENERATES HIGH PROBABILITY DENSITY ELEMENTS FOR PROJECTED EVENTS FROM A SEQUENCE OF PAST STAR EVENTS, BASED UPON PAST FREQUENCY COUNTS OF ELEMENTS BY G. HOWARD'S % METHOD . ====================================================================== -- L 22 -- COLUMN-SORTS A GIVEN ARRAY OF INTEGERS IN ASCENDING ORDER AND ARRANGES A LIST OF EVENTS IN LEXICOGRAPHIC ORDER. ====================================================================== -- L 23 -- READS A BLOCK OR SEQUENCE OF EVENTS, DETERMINES THE SUM OF ELEMENTS IN EACH EVENT, AND PRINTS THE EVENTS FOR WHICH THE SUM OF ELEMENTS IS WITHIN AN ARBITRARY OR PREDETERMINED RANGE. ====================================================================== -- L 24 -- READS A BLOCK OF j-ELEMENT EVENTS, DETERMINES ALL PAIRINGS ELEMENTS IN EACH EVENT, AND PRINTS EACH BLOCK AS A SET OF SUCH PAIRINGS OF ELEMENTS, WITH CORRESPONDING DATES AND WITH , e.g., j = 6. ====================================================================== -- L 25 -- READS A SET OF 2-ELEMENT BLOCKS OR PAIRINGS OF ELEMENTS AND DETERMINES THE FREQUENCY OF OCCURRENCE OF EACH ELEMENT ( 1 ,..., n ) IN A PAIRING WITH , e.g., n = 49. ====================================================================== -- L 26 -- READS A SET OF j-ELEMENT EVENTS, DETERMINES ALL TRIPLES OF ELEMENTS PER EVENT IN THE BLOCK, AND PRINTS THE BLOCK AS A SET OF SUCH TRIPLETS, WITH CORRESPONDING DATES OF OCCURRENCE WITH , e.g., j = 7. ====================================================================== -- L 27 -- COMPARES A SEQUENCE OF j-ELEMENT EVENTS WITH A SEQUENCE OF FINITE BASE SETS OF ELEMENTS AND DETERMINES THE ELEMENTS WHICH ARE IN THE INTERSECTION OF EACH BASE SET WITH EACH EVENT OF THE SEQUENCE AND WHICH ARE BETWEEN PRESCRIBED, INCLUSIVE BOUNDS. FREQUENCIES AND RELATIVE FREQUENCIES OF COMMON ELEMENTS ARE COMPARED AND THOSE EVENTS WHICH SATISFY THE BOUNDARY CONDITIONS ARE FILTERED WITH, e.g., j = 6. ====================================================================== -- L 28 -- GENERATES A SEQUENCE OF WHEELED EVENTS FROM A FIXED WHEEL OR SEQUENCE OF EVENTS BY THE ACTION OF AN ARBITRARILY CHOSEN PERMUTATION ON THE ELEMENTS IN THE FIXED WHEEL OF EVENTS. THE EVENTS OF THE FIXED OR BASE WHEEL AND ALL ELEMENTS OF EACH PERMUTATION ON THE ELEMENTS OF THE FIXED WHEEL ARE READ FROM FILES PROVIDED BY THE USER. ====================================================================== -- L 29 -- DETERMINES THE ELEMENTS OCCURRING WITHIN THE LAST k EVENTS, WHERE k IS WITHIN ONE OF THE RANGES OR INTERVALS: (1,5), (6,10), (11,15), (16,20), (21,25) OR (25,IMAX), INCLUDING ENDPOINTS (WHERE EACH ELEMENT IS PRINTED AT EVERY OCCURRENCE WITHIN A GIVEN INTERVAL). ====================================================================== -- L 30 -- DETERMINES THE ELEMENTS OCCURRING WITHIN THE LAST k EVENTS, WHERE k IS WITHIN ONE OF THE RANGES OR INTERVALS: (1,5), (6,10), (11,15), (16,20), (21,25) OR (25,49), INCLUDING ENDPOINTS (WHERE EACH ELEMENT OCCURRING WITHIN A GIVEN INTERVAL IS PRINTED EXACTLY ONCE). ====================================================================== -- L 31 -- DETERMINES THE ELEMENTS OCCURRING WITHIN THE LAST k EVENTS, WHERE k IS WITHIN ONE OF THE RANGES OR INTERVALS: (1,2), (3, 4), ( 5, 6), ( 7, 8), ( 9,10) OR (11,49), INCLUDING ENDPOINTS (WHERE EACH ELEMENT OCCURRING WITHIN A GIVEN INTERVAL IS PRINTED EXACTLY ONCE). ====================================================================== -- L 32 -- DETERMINES THE FREQUENCIES OF ELEMENTS FROM A SEQUENCE OF j-ELEMENT BLOCKS, BACKS UP A FINITE NUMBER, k , OF EVENTS, DETERMINES AND PRINTS THE PROBABILITIES OF OCCURRENCE OF EACH OF THE ELEMENTS ( 1 ,..., n ), WITHIN THE LAST k EVENTS. (DETERMINED PROBABILITIES ARE BASED ONLY UPON THE LAST k EVENTS, WITH k ARBITRARY AND, e.g., j = 7 AND n = 49.) ====================================================================== -- L 33 -- DETERMINES THE FREQUENCIES OF ELEMENTS FROM A SEQUENCE OF j-ELEMENT BLOCKS, BACKS UP A FINITE NUMBER, k , OF EVENTS, FROM THE FINAL EVENT, DETERMINES AND PRINTS THE PROBABILITIES OF OCCURRENCE OF EACH OF THE ELEMENTS (1 ,..., 49), WITHIN THE LAST k EVENTS, AS WELL AS THE FREQUENCIES OF OCCURRENCE OF THE ELEMENTS (1 ,..., n). ONE SET OF DETERMINED PROBABILITIES IS BASED UPON THE LAST k EVENTS AND THE OTHER SET IS BASED UPON THE ENTIRE SEQUENCE OF EVENTS. (PROGRAM BACKS UP FROM THE FINAL EVENT AND TALLIES IT FOR REFERENCE) WITH k ARBITRARY AND, e.g., j = 7 AND n = 49. ====================================================================== -- L 34 -- DETERMINES A BASE SET AS A UNION OF FIXED BASE SETS AND PRINTS IT FOR WHEELING SYSTEMS AND FURTHER ANALYSIS (A FIXED OR VARIABLE BASE SET IS PERMUTED WITH 2 VARIABLE BASE SETS AND THE PROCESS IS REPEATED k TIMES) (INPUT: 3 BLOCKS OF BASE SETS). ====================================================================== -- L 35 -- DETERMINES A BASE SET AS A UNION OF FIXED BASE SETS AND PRINTS IT FOR WHEELING SYSTEMS AND FURTHER ANALYSIS (THREE FIXED OR VARIABLE BASE SETS ARE SYMMETRICALLY PERMUTED AND THE PROCESS IS REPEATED k TIMES). ====================================================================== -- L 36 -- DETERMINES A BASE SET AS A UNION OF FIXED BASE SETS AND PRINTS IT FOR WHEELING SYSTEMS AND FURTHER ANALYSIS (7 BASE SETS ARE SYMMETRICALLY UNITED BY VARIOUS COMBINATIONS OF ORDERS 2, 3, 4, 5, 6, AND 7, AND THE PROCESS IS REPEATED FINITELY MANY TIMES. INPUT: 7 BLOCKS OF BASE SETS OF SIZE j). (RESULT: nCk BLOCKS, with n BLOCKS TAKEN k AT A TIME, WHERE n = 7 and k = 1, 2, 3, 4, 5, 6, OR 7). ====================================================================== -- L 37 -- GENERATES A SEQUENCE OF WHEELED/PERMUTED EVENTS FROM A FIXED WHEEL AND A SEQUENCE OF PERMUTATIONS, EACH OF WHICH IS OF DEGREE k , THUS ALLOWING WHEELING OF k ELEMENTS WITH , e.g., k = 49. ====================================================================== -- L 38 -- DETERMINES THE FREQUENCIES OF ELEMENTS FROM A SEQUENCE OF j-ELEMENT BLOCKS OCCURRING WITHIN THE PREDETERMINED RANGES A: 1 ,..., 9; B: 10 ,..., 19; C: 20 ,..., 29; D: 30 ,..., 39; AND E: 40 ,..., 49 (A FREQUENCY TABLE OF RESULTS IS PRINTED) WITH, e.g., j = 7. ====================================================================== -- L 39 -- DETERMINES THE FREQUENCIES OF ELEMENTS FROM A SEQUENCE OF j-ELEMENT BLOCKS, BACKS UP A FINITE NUMBER, k , OF EVENTS FROM THE SEMI-FINAL EVENT, AND DETERMINES AND PRINTS OUT THE PROBABILITIES OF OCCURRENCE OF EACH OF THE ELEMENTS, (1 ,..., n) , WITHIN THE LAST k EVENTS. ONE SET OF PROBABILITIES IS BASED UPON THE LAST k EVENTS AND THE OTHER SET IS BASED UPON THE ENTIRE SEQUENCE OF EVENTS. THE PROGRAM BACKS UP FROM THE SEMI-FINAL EVENT, BUT TALLIES THE FINAL EVENT IN AN UNSORTED AND A SORTED LISTING OF FREQUENCIES AND PROBABILITIES WITH k ARBITRARY AND, e.g., j = 7 AND n =49. ====================================================================== -- L 40 -- DETERMINES THE FREQUENCIES OF ELEMENTS FROM A SEQUENCE OF 7-ELEMENT BLOCKS, BACKS UP A FINITE NUMBER k OF EVENTS, FROM THE FINAL EVENT, DETERMINES AND PRINTS THE PROBABILITIES OF OCCURRENCE OF EACH OF THE ELEMENTS (1 ,..., 49), WITHIN THE LAST k EVENTS, AND PRINTS A SUMMARY OF FREQUENCIES OF OCCURRENCE OF THE ELEMENTS (1 ,..., 49) . ONE SET OF PROBABILITIES IS BASED UPON THE LAST k EVENTS AND THE OTHER SET IS BASED UPON THE ENTIRE SEQUENCE OF EVENTS. THE PROGRAM BACKS UP FROM THE FINAL EVENT AND TALLIES IT IN AN UNSORTED AND A SORTED LISTING OF FREQUENCIES AND PROBABILITIES. ====================================================================== -- L 41 -- COMPUTES AND PRINTS A FREQUENCY CONFIGURATION MATRIX. (Version I) ====================================================================== -- L 42 -- DETERMINES THE FREQUENCIES OF ELEMENTS FROM A SEQUENCE OF j-ELEMENT BLOCKS AND DETERMINES THE NUMBER OF TIMES A GIVEN ELEMENT (1 ,..., n ) HAS OCCURRED IN k CONSECUTIVE EVENTS OUT OF A TOTAL OF IMAX EVENTS. (READS k CONSECUTIVE EVENTS FROM THE TOP DOWNWARD) WITH k ARBITRARY AND, e.g., j = 7 AND n = 51. ====================================================================== -- L 43 -- GENERATES SINGLE-TO-DOUBLE RATIOS AND DETERMINES THE ELEMENTS OF EACH TYPE (A,B,C,D,E,OR F) WHICH ALSO HAVE SD-Ratios LESS THAN OR EQUAL TO THE AVERAGE SD-Ratio. (RECEIVES OUTPUT FROM L 30 AS INPUT). ====================================================================== -- L 44 -- GENERATES SINGLE-TO-DOUBLE RATIOS AND DETERMINES THE ELEMENTS OF EACH TYPE (G,H,I,J,K,OR L) WHICH ALSO HAVE SD-Ratios LESS THAN OR EQUAL TO THE AVERAGE SD-Ratio. (RECEIVES OUTPUT FROM L 31 AS INPUT). ====================================================================== -- L 45 -- GENERATES DOUBLE-TO-SINGLE RATIOS AND DETERMINES THE ELEMENTS OF EACH TYPE (A,B,C,D,E,OR F) WHICH ALSO HAVE DS-Ratios GREATER THAN OR EQUAL TO THE AVERAGE DS-Ratio. (RECEIVES OUTPUT FROM L 30 AS INPUT). ====================================================================== -- L 46 -- GENERATES DOUBLE-TO-SINGLE-HIT RATIOS AND DETERMINES THE ELEMENTS OF EACH TYPE (G,H,I,J,K,OR L) WHICH ALSO HAVE DSH-Ratios GREATER THAN OR EQUAL TO THE AVERAGE DSH-Ratio. (RECEIVES OUTPUT FROM L 31 AS INPUT). ====================================================================== -- L 47 -- DETERMINES THE ELEMENTS OCCURRING WITHIN THE LAST k EVENTS, WHERE k IS WITHIN ONE OF THE RANGES OR INTERVALS: (1,5), (6,10), (11,15), (16,20), (21,25), OR (25,IMAX), INCLUDING ENDPOINTS, PRINTING EACH OF n ELEMENTS EXACTLY ONCE. ALSO PRINTS A SUMMARY OF FREQUENCIES OF TYPES (A, B, C, D, E, AND F) IN L30 OUTPUT3 FOR APPENDAGE TO THE FILE TYPE30 OUTPUT. (ENDPOINTS ARE INCLUDED) WITH , e.g., n = 49. ====================================================================== -- L 48 -- READS A SET OF j-ELEMENT BLOCKS, DETERMINES ALL QUADRUPLETS OF ELEMENTS IN EACH BLOCK, AND PRINTS EACH BLOCK AS A SET OF QUADRUPLETS WITH CORRESPONDING DATES OF OCCURRENCE WITH , e.g., j = 7. ====================================================================== -- L 49 -- READS A SET OF j-ELEMENT BLOCKS, DETERMINES ALL QUINTUPLETS OF ELEMENTS IN EACH BLOCK, AND PRINTS EACH BLOCK AS A SET OF QUINTUPLETS WITH CORRESPONDING DATES OF OCCURRENCE WITH , e.g., j = 7. ====================================================================== -- L 50 -- READS A SET OF j-ELEMENT BLOCKS, DETERMINES ALL SEXTUPLETS OF ELEMENTS IN EACH BLOCK, AND PRINTS EACH BLOCK AS A SET OF SEXTUPLETS WITH CORRESPONDING DATES OF OCCURRENCE WITH, e.g., j = 7. ====================================================================== -- L 51 -- DETERMINES AND PRINTS AN EVENTS-SINCE-LAST OCCURRENCE MATRIX FOR THE ELEMENTS ( 1 , ... , n ) WITH , e.g., n = 49. (Version II) ====================================================================== -- L 52 -- READS AND SORTS A SET OF 2-ELEMENT BLOCKS FROM L24 OUTPUT AND PRINTS EACH BLOCK AS A SET OF SORTED PAIRINGS OF ELEMENTS. ====================================================================== -- L 53 -- COMPUTES AND PRINTS A FREQUENCY CONFIGURATION MATRIX VIA STRINGS (CONTINUATION FOR L 51). ====================================================================== -- L 54 -- READS AND SORTS A SET OF 3-ELEMENT BLOCKS FROM L26 OUTPUT AND PRINTS EACH BLOCK AS A SET OF SORTED TRIPLETS OF ELEMENTS. ====================================================================== -- L 55 -- COMPUTES AND PRINTS A FREQUENCY CONFIGURATION MATRIX, INDICATING THE NUMBER OF EVENTS EACH ELEMENT ( 1 ,..., k ) "SKIPS" BEFORE OCCURRING AGAIN. DETERMINES HITS FOR ELEMENTS vs. NUMBER OF SKIPS SINCE THE LAST OCCURRENCE. DETERMINES THE NUMBER OF SINGLES SINCE THE LAST DOUBLE OVER THE LAST m EVENTS. DETERMINES FREQUENCIES OF LONGSHOT AND REPEAT ELEMENTS FOR A SEQUENCE OF EVENTS AND THEIR PERCENTAGES OF OCCURRENCE. PRINTS A TABLE OF SORTED SD-Ratios (Single-To-Double Ratios) AND GENERATES TABLES AND SEQUENCES OF HIGHLY PROBABLE ELEMENTS FROM BELOW-AVERAGE SD-Ratios, FROM SINGLES vs. DOUBLES, AND FROM SD-Ratios vs. # SINGLES OVER THE LAST m EVENTS. DETERMINES A MATRIX OF CONSECUTIVE HITS, WITH CORRESPONDING SD-Ratios, AVERAGES, AND RANKINGS WITH, e.g., k = 49 AND m = 100. ====================================================================== -- L 56 -- COMPUTES AND PRINTS A FREQUENCY CONFIGURATION MATRIX. (Version III) ====================================================================== -- L 57 -- COMPUTES AND PRINTS A FREQUENCY CONFIGURATION MATRIX (CONTINUATION PROGRAM FOR L 55). ====================================================================== -- L 58 -- COMPARES A SET OF k-ELEMENT BLOCKS WITH m j-ELEMENT BLOCKS, WHERE m IS A POSITIVE INTEGER (DESIGNED TO COMPARE PARTIAL EVENTS CONSISTING OF PAIRS, TRIPLETS, QUADRUPLETS, QUINTUPLETS, OR SEXTUPLETS TO PAST STAR EVENTS, WHERE k = 2, 3, ... , j-1) AND WITH , e.g., j = 6 . ====================================================================== -- L 59 -- DETERMINES AND PRINTS A FREQUENCY MATRIX OF OCCURRENCES FOR ELEMENTS vs. # "SKIPS" SINCE THE LAST OCCURRENCE FOR A FINAL OR GIVEN EVENT REQUESTED (INDICATING HOW MANY TIMES EACH ELEMENT ( 1 , ... , n ) "SKIPS" BEFORE IT OCCURS AGAIN) WITH, e.g., n = 49. ====================================================================== -- L 60 -- DETERMINES AND PRINTS : 1) A MATRIX OF LONGSHOT AND REPEAT ELEMENTS FOR A SEQUENCE OF EVENTS. 2) A FREQUENCY MATRIX FOR REPEATED ELEMENTS AND LONGSHOTS FOR A SEQUENCE OF EVENTS. 3) A FREQUENCY TABLE OF OCCURRENCES FOR ELEMENTS vs. # SKIPS SINCE THE LAST OCCURRENCE FOR A FINAL OR GIVEN EVENT REQUESTED. 4) A SKIP-AND-OCCURRENCE MATRIX , INDICATING THE RELATIVE NUMBER OF EVENTS IN WHICH EACH ELEMENT HAS SKIPPED OR OCCURRED ON A GIVEN DATE . ====================================================================== -- L 61 -- DETERMINES AND PRINTS THE INTERSECTIONS BETWEEN STAR EVENT k AND ELEMENTS OF TYPES ( A ,..., F ) GENERATED BY BACKING UP TO THE 1st EVENT FROM EVENT ( k-1 ). ALSO PRINTS THE 1st k EVENTS AND ALL ELEMENTS OF TYPES ( A ,..., F ) BACKING UP FROM EVENT ( k-1 ) AND PRINTS A FILE OF FREQUENCIES OF INTERSECTIONS BETWEEN STAR EVENT AND ELEMENTS OF EACH TYPE. ====================================================================== -- L 62 -- DETERMINES AND PRINTS THE INTERSECTIONS BETWEEN STAR EVENT k AND ELEMENTS OF TYPES ( G ,..., L ) GENERATED BY BACKING UP TO THE 1st EVENT FROM EVENT ( k-1 ). ALSO PRINTS THE 1st k EVENTS AND ALL ELEMENTS OF TYPES ( G ,..., L ) BACKING UP FROM EVENT ( k-1 ). ====================================================================== -- L 63 -- DETERMINES AND PRINTS THE DIFFERENCES BETWEEN CORRESPONDING ELEMENTS OF THE i-TH AND (i-1)-ST EVENTS AS WELL AS THE RESPECTIVE SUMS OF THE COMPUTED DIFFERENCES IN EACH EVENT. ====================================================================== -- L 64 -- SKIP AND HIT MATRIX II DETERMINES AND PRINTS OUT THE NUMBER OF TIMES EACH NUMBER ( 1 --> k ) HAS HIT AFTER SKIPPING ONE OR MORE DRAWINGS, i.e., RECORDS THE NUMBER OF TIMES EACH NUMBER ( 1 --> k ) HAS HIT AFTER SKIPPING ANY SPECIFIC NUMBER OF EVENTS BETWEEN OCCURRENCES. PRINTS A TABLE OF SORTED SDH Ratios (Single-To-Double-Hit Ratios) AND DSH Ratios (Double-To-Single-Hit Ratios) , AND GENERATES A SEQUENCE OF HIGH PROBABILITY ELEMENTS WITH SDH Ratios NOT EXCEEDING THE AVERAGE SDH Ratio , BACKING UP A SPECIFIED NUMBER OF EVENTS FROM THE FINAL EVENT WITH , e.g., k = 49. STAT64 ALSO GENERATES THE INPUT FILE STAT1048.IN2. CF. STAT1048. CF. ALSO STAT64 FOR GENERATION OF PERMUTATIONS FOR PERM.INP. STAT64 GENERATES THE INPUT FILE STAT1048.IN2. CF. STAT1048. STAT64 ALSO GENERATES THE INPUT FILE PERM.INP FOR STAT1824. CF. ALSO STAT543 AND STAT1401 FOR APPLICATIONS OF PERM.INP. PERM.INP IS GENERATED BY STAT64 FOR USAGE AS PERM.INP IN STAT1274 STAT1274 AND STAT1824. PERM.OUT IS GENERATED BY STAT64 FOR USAGE AS PERM.INP IN STAT1854. STAT64 IS A VARIANT OF STAT2903. CF. STAT2903. PERM.INP IS GENERATED FOR STAT3086. PERM2.INP IS GENERATED FOR STAT3058. STAT3407.TMP IS GENERATED FOR USE IN IN PERM.INP OF STAT3407. ====================================================================== -- L 65 -- READS A LIST OF n ELEMENTS, TRANSLATES, AND PRINTS THEM (mod t), READS A BLOCK OF STAR EVENTS AND PRINTS THE ELEMENTS BOTH AS INTEGERS AND AS INTEGERS (mod t) FOR AN ARBITRARY t AND WITH , e.g., n = 49. ====================================================================== -- L 66 -- DETERMINES THE FREQUENCIES OF OCCURRENCE OF EACH OF t ELEMENTS, BACKING UP A DESIRED NUMBER, n, OF EVENTS FROM EACH ELEMENT OF THE STAR EVENT (WHERE ELEMENTS ARE LISTED IN LEXICOGRAPHIC ORDER). IF THE FREQUENCY OF THE ELEMENT k EXCEEDS OR EQUALS n/d, FOR AN ARBITRARY SUITABLE DIVISOR, d, DETERMINED AT RANDOM, THEN THE ELEMENT k IS ADDED TO A BASE SET FOR WHEELING. THE ARITHMETIC MEAN m IS CALCULATED FOR EACH OF j COLUMNS (BACKING UP A FINITE NUMBER OF EVENTS) AND THE ELEMENTS m-1, m, AND m+1 ARE ADDED TO ANOTHER GENERATED BASE SET FOR WHEELING OR FURTHER ANALYSIS WITH, e.g., t = 49 AND j = 7. ====================================================================== -- L 67 -- DETERMINES THE ARITHMETIC MEAN OF THE LAST k STAR ELEMENTS, BACKING UP FROM EACH STAR ELEMENT (WHERE ELEMENTS ARE LISTED IN LEXICOGRAPHIC ORDER), CALCULATES THE RANGE OF ELEMENTS LIKELY TO BE GENERATED IN THE NEXT EVENT FROM THE DETERMINED MEAN DEVIATIONS FROM j COLUMNS OF ELEMENTS (BACKING UP FROM k EVENTS FROM THE FINAL EVENT) BASED UPON REGRESSION ANALYSIS. THE RESULTS ARE PRINTED AS A BLOCK OF HIGH PROBABILITY ELEMENTS FOR WHEELING OR FURTHER ANALYSIS WITH , e.g., j = 7. ====================================================================== -- L 68 -- DETERMINES THE ARITHMETIC MEAN, STANDARD DEVIATION, AND MEAN DEVIATION OF THE LAST k STAR ELEMENTS IN EACH COLUMN, BACKING UP FROM EACH STAR ELEMENT (WHERE THE j ELEMENTS ARE LISTED IN LEXICOGRAPHIC ORDER), FILTERS AND PRINTS THE EVENTS FROM A LIST OF EVENTS GENERATED OR WHEELED FROM ANOTHER SOURCE, THE ELEMENTS OF WHICH ARE WITHIN A DESIRED NUMBER OF STANDARD DEVIATIONS OR MEAN DEVIATIONS FROM THE CALCULATED MEAN FOR ELEMENTS IN EACH OF j COLUMNS WITH , e.g., j = 7. ====================================================================== -- L 69 -- DETERMINES THE ARITHMETIC MEAN OF THE LAST k STAR ELEMENTS, BACKING UP FROM EACH STAR ELEMENT (WHERE ELEMENTS ARE LISTED IN LEXICOGRAPHIC ORDER), CALCULATES THE RANGE OF ELEMENTS LIKELY TO BE GENERATED IN THE NEXT EVENT FROM THE DETERMINED ARITHMETIC MEANS (BASED UPON REGRESSION ANALYSIS), PRINTS THE RESULTS AS A BLOCK OF HIGH PROBABILITY ELEMENTS, DETERMINES AND PRINTS A MATRIX OF MEAN DEVIATIONS (BASED UPON, AND BACKING UP A DESIRED NUMBER OF EVENTS FROM, THE STAR EVENT), AND FILTERS A WHEEL OF EVENTS BASED UPON THE RANGES OF HIGHLY PROBABLE ELEMENTS (DETERMINED FROM THE MEAN DEVIATIONS OF CHOSEN ELEMENTS IN THE j COLUMNS, BACKING UP FROM THE STAR EVENT. FILTERING IS BASED UPON A MINIMUM OF NMAX POSITIONS IN EACH EVENT (WHERE NMAX = 1, 2, 3 ,..., j) SATISFYING INTERVAL CONSTRAINTS WITH , e.g., j = 7. ====================================================================== -- L 70 -- COMPUTES AND PRINTS, FOR EACH EVENT IN A SEQUENCE, CONSECUTIVE PAIRS OF ELEMENTS WITH THEIR CORRESPONDING FREQUENCIES AND THE AVERAGE NUMBER OF CONSECUTIVE PAIRINGS PER EVENT IN THE SEQUENCE. ======================================================================