RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.54 27.3585 0.946985
2 to 25 15.96 36.6770 0.996279
3 to 26 15.93 11.6693 0.180263
4 to 27 15.87 8.7502 0.052227
5 to 28 16.03 13.5818 0.303551
6 to 29 15.93 19.5388 0.701505
7 to 30 15.82 17.5127 0.579811
8 to 31 15.64 11.1093 0.149172
9 to 32 15.69 15.9663 0.473776
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.693467
Tough bday spacings test for dh-ranFile-2018-06-30_21:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 8 34 64 109 112 74 48 33 9 7 2
(O-E)^2/E 0.1 0.2 1.2 1.3 2.1 0.2 0.3 0.4 2.3 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 9.207, p= 0.487
RESULTS OF GCD FOR dh-ranFile-2018-06-30_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.534390
p-value, dist. of gcd's: 0.221189
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.981 0.686 0.427 0.653 0.172 0.451 0.850 0.826
Bits 8 to 15---> 0.830 0.610 0.674 0.828 0.678 0.934 0.991 0.476
Bits 16 to 23---> 0.844 0.932 0.002 0.548 0.935 0.015 0.066 0.821
Bits 24 to 31---> 0.220 0.010 0.257 0.724 0.462 0.979 0.714 0.974
KS test for the above 32 p values: 0.986
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_21:31,
p-values for 5 runs: 0.9111, 0.1853, 0.4543, 0.3345, 0.0691
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 188 211.4 2.594 2.594
r= 29 5107 5134.0 0.142 2.736
r= 30 23226 23103.0 0.654 3.390
r= 31 11479 11551.5 0.455 3.846
chi-square = 3.846 with df = 3; p-value = 0.721
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 5138 5134.0 0.003 0.263
r= 31 23042 23103.0 0.161 0.425
r= 32 11616 11551.5 0.360 0.785
chi-square = 0.785 with df = 3; p-value = 0.147
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_21:31
b-rank test for bits 1 to 8, p=0.46064
b-rank test for bits 2 to 9, p=0.75371
b-rank test for bits 3 to 10, p=0.02017
b-rank test for bits 4 to 11, p=0.75562
b-rank test for bits 5 to 12, p=0.64956
b-rank test for bits 6 to 13, p=0.44381
b-rank test for bits 7 to 14, p=0.14343
b-rank test for bits 8 to 15, p=0.37595
b-rank test for bits 9 to 16, p=0.41948
b-rank test for bits 10 to 17, p=0.62366
b-rank test for bits 11 to 18, p=0.87800
b-rank test for bits 12 to 19, p=0.77152
b-rank test for bits 13 to 20, p=0.34257
b-rank test for bits 14 to 21, p=0.83419
b-rank test for bits 15 to 22, p=0.84353
b-rank test for bits 16 to 23, p=0.22503
b-rank test for bits 17 to 24, p=0.72095
b-rank test for bits 18 to 25, p=0.93381
b-rank test for bits 19 to 26, p=0.15051
b-rank test for bits 20 to 27, p=0.76255
b-rank test for bits 21 to 28, p=0.30120
b-rank test for bits 22 to 29, p=0.65699
b-rank test for bits 23 to 30, p=0.05515
b-rank test for bits 24 to 31, p=0.34935
b-rank test for bits 25 to 32, p=0.29915
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.895813
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_21:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 141929 0.05 0.518328
2 141763 -0.34 0.366216
3 142065 0.36 0.641965
4 142342 1.01 0.843971
5 142374 1.09 0.861189
6 141779 -0.30 0.380370
7 141450 -1.07 0.141591
8 141691 -0.51 0.304985
9 141955 0.11 0.542489
10 142006 0.23 0.589347
11 142519 1.42 0.922844
12 141303 -1.42 0.078291
13 142268 0.84 0.798989
14 142430 1.22 0.888106
15 141058 -1.99 0.023346
16 141513 -0.93 0.177222
17 141950 0.10 0.537852
18 142542 1.48 0.930323
19 141354 -1.30 0.097230
20 141702 -0.48 0.314045
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_21:31
Bits used No. missing words z-score p-value
23 to 32 141615 -1.0149 0.155069
22 to 31 141582 -1.1287 0.129507
21 to 30 142084 0.6023 0.726516
20 to 29 142304 1.3609 0.913232
19 to 28 141835 -0.2563 0.398856
18 to 27 141792 -0.4046 0.342891
17 to 26 142120 0.7264 0.766218
16 to 25 142360 1.5540 0.939912
15 to 24 141652 -0.8873 0.187447
14 to 23 142030 0.4161 0.661333
13 to 22 142031 0.4196 0.662594
12 to 21 142481 1.9713 0.975654
11 to 20 142435 1.8127 0.965058
10 to 19 142123 0.7368 0.769376
9 to 18 141836 -0.2529 0.400187
8 to 17 141988 0.2713 0.606911
7 to 16 141774 -0.4667 0.320373
6 to 15 141750 -0.5494 0.291361
5 to 14 141955 0.1575 0.562568
4 to 13 141342 -1.9563 0.025214
3 to 12 141903 -0.0218 0.491293
2 to 11 141449 -1.5873 0.056217
1 to 10 141424 -1.6736 0.047109
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_21:31
Bits used No. missing words z-score p-value
28 to 32 141961 0.1752 0.569520
27 to 31 141411 -1.6893 0.045585
26 to 30 141923 0.0463 0.518480
25 to 29 142429 1.7616 0.960931
24 to 28 141852 -0.1943 0.422955
23 to 27 142210 1.0192 0.845951
22 to 26 142109 0.6768 0.750749
21 to 25 141579 -1.1198 0.131407
20 to 24 142218 1.0463 0.852298
19 to 23 142605 2.3582 0.990818
18 to 22 141743 -0.5638 0.286435
17 to 21 142216 1.0396 0.850728
16 to 20 141717 -0.6520 0.257212
15 to 19 141483 -1.4452 0.074203
14 to 18 142100 0.6463 0.740970
13 to 17 141926 0.0565 0.522532
12 to 16 141420 -1.6587 0.048584
11 to 15 141824 -0.2893 0.386193
10 to 14 141140 -2.6079 0.004555
9 to 13 142069 0.5413 0.705834
8 to 12 141667 -0.8215 0.205693
7 to 11 142067 0.5345 0.703493
6 to 10 141519 -1.3232 0.092892
5 to 9 142091 0.6158 0.730997
4 to 8 141918 0.0294 0.511723
3 to 7 141736 -0.5876 0.278414
2 to 6 141570 -1.1503 0.125016
1 to 5 141866 -0.1469 0.441613
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_21:31
Bits used No. missing words z-score p-value
31 to 32 142238 0.9695 0.833859
30 to 31 141717 -0.5673 0.285240
29 to 30 141732 -0.5231 0.300453
28 to 29 142036 0.3737 0.645671
27 to 28 141950 0.1200 0.547747
26 to 27 141664 -0.7237 0.234629
25 to 26 142008 0.2911 0.614498
24 to 25 142213 0.8958 0.814815
23 to 24 142158 0.7335 0.768385
22 to 23 141612 -0.8771 0.190222
21 to 22 142146 0.6981 0.757456
20 to 21 141615 -0.8682 0.192634
19 to 20 141864 -0.1337 0.446813
18 to 19 141776 -0.3933 0.347048
17 to 18 141659 -0.7384 0.230125
16 to 17 142278 1.0875 0.861597
15 to 16 142416 1.4946 0.932491
14 to 15 142222 0.9223 0.821822
13 to 14 141618 -0.8594 0.195065
12 to 13 141744 -0.4877 0.312882
11 to 12 141505 -1.1927 0.116491
10 to 11 141780 -0.3815 0.351415
9 to 10 141576 -0.9833 0.162736
8 to 9 141762 -0.4346 0.331926
7 to 8 141850 -0.1750 0.430534
6 to 7 142300 1.1524 0.875426
5 to 6 141578 -0.9774 0.164192
4 to 5 142270 1.0639 0.856318
3 to 4 142103 0.5713 0.716101
2 to 3 142276 1.0816 0.860290
1 to 2 141989 0.2350 0.592901
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2599.42 1.406 0.920148
Test results for specific bytes for dh-ranFile-2018-06-30_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2484.31 -0.222 0.412197
2 to 9 2608.38 1.533 0.937335
3 to 10 2422.19 -1.100 0.135580
4 to 11 2473.96 -0.368 0.356365
5 to 12 2521.39 0.302 0.618862
6 to 13 2488.10 -0.168 0.433181
7 to 14 2332.71 -2.366 0.008996
8 to 15 2509.99 0.141 0.556168
9 to 16 2692.85 2.727 0.996808
10 to 17 2538.27 0.541 0.705811
11 to 18 2482.70 -0.245 0.403378
12 to 19 2549.50 0.700 0.758043
13 to 20 2561.20 0.866 0.806623
14 to 21 2573.90 1.045 0.852017
15 to 22 2424.66 -1.065 0.143331
16 to 23 2416.22 -1.185 0.118040
17 to 24 2528.23 0.399 0.655153
18 to 25 2352.28 -2.089 0.018348
19 to 26 2537.25 0.527 0.700808
20 to 27 2451.93 -0.680 0.248298
21 to 28 2524.42 0.345 0.635084
22 to 29 2503.93 0.056 0.522153
23 to 30 2506.73 0.095 0.537937
24 to 31 2649.07 2.108 0.982492
25 to 32 2473.38 -0.377 0.353270
CDPARK for dh-ranFile-2018-06-30_21:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3557 1.5525 0.939730
3534 0.5023 0.692266
3549 1.1872 0.882429
3508 -0.6849 0.246694
3526 0.1370 0.554479
3499 -1.0959 0.136563
3540 0.7763 0.781201
3504 -0.8676 0.192812
3550 1.2329 0.891189
3505 -0.8219 0.205562
Square side=100, avg. no. parked=3527.20 sample std.=20.71
p-value of the KSTEST for those 10 p-values: 0.639907
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_21:31
0.4577,0.8005,0.1765,0.6142,0.5610,0.4726,0.5761,0.5538,0.4948,0.8195,
The KS test for those 10 p-values: 0.244114
The 3DSPHERES test for dh-ranFile-2018-06-30_21:31
sample no r^3 equiv. uni.
1 2.881 0.091557
2 4.535 0.140291
3 37.147 0.710105
4 41.538 0.749575
5 39.037 0.727805
6 11.411 0.316397
7 33.736 0.675193
8 6.529 0.195580
9 0.933 0.030610
10 11.825 0.325766
11 2.472 0.079097
12 2.145 0.069004
13 12.813 0.347597
14 19.568 0.479143
15 17.211 0.436571
16 16.605 0.425063
17 18.456 0.459472
18 21.787 0.516277
19 24.816 0.562727
20 65.174 0.886102
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.257693
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 -0.1 1.1 0.2 -0.1
1.1 -0.1 0.2 1.1 -0.5 -0.9
-0.1 -0.1 0.7 0.5 1.0 -1.6
-0.4 -0.3 0.2 0.3 -0.8 0.4
0.8 -0.1 -2.0 0.8 -0.2 0.5
-1.0 0.2 0.8 1.0 1.5 1.5
1.7 -1.3 -0.4 1.0 -1.3 0.0
0.8
Chi-square with 42 degrees of freedom:31.329555
z-score=-1.164241, p-value=0.113876
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_21:31
Test no p-value
1 0.098893
2 0.051316
3 0.439781
4 0.820149
5 0.023632
6 0.337415
7 0.048115
8 0.011978
9 0.196575
10 0.828608
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.007296
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_21:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66580 0.11 66566 0.15
3 25000.00 25103 0.42 25142 0.81
4 6666.67 6686 0.06 6621 0.31
5 1388.89 1365 0.41 1365 0.41
6 238.10 239 0.00 267 3.51
7 34.72 23 3.96 29 0.94
8 4.96 3 0.77 9 3.29
p=0.54685 p=0.84892
Number of rngs required: 690436, p-value: 0.992
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_21:31
No. of wins: Observed Expected
98694 98585.9
z-score= 0.484, pvalue=0.68569
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66891 66666.7 0.755 0.755
2 37564 37654.3 0.217 0.972
3 26944 26954.7 0.004 0.976
4 19359 19313.5 0.107 1.083
5 13774 13851.4 0.433 1.516
6 9941 9943.5 0.001 1.517
7 7118 7145.0 0.102 1.619
8 5054 5139.1 1.408 3.027
9 3720 3699.9 0.110 3.137
10 2611 2666.3 1.147 4.283
11 1967 1923.3 0.992 5.275
12 1340 1388.7 1.711 6.986
13 1095 1003.7 8.302 15.288
14 689 726.1 1.900 17.187
15 520 525.8 0.065 17.252
16 397 381.2 0.659 17.911
17 274 276.5 0.023 17.935
18 211 200.8 0.515 18.450
19 152 146.0 0.248 18.698
20 107 106.2 0.006 18.703
21 272 287.1 0.796 19.499
Chisq= 19.50 for 20 degrees of freedom, p= 0.51036
SUMMARY of craptest
p-value for no. of wins: 0.685690
p-value for throws/game: 0.510360
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_21:31
No. of wins: Observed Expected
98189 98585.9
z-score=-1.775, pvalue=0.03795
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66416 66666.7 0.943 0.943
2 37531 37654.3 0.404 1.346
3 27241 26954.7 3.040 4.387
4 19434 19313.5 0.752 5.139
5 13778 13851.4 0.389 5.528
6 10014 9943.5 0.499 6.027
7 7090 7145.0 0.424 6.451
8 5052 5139.1 1.475 7.926
9 3806 3699.9 3.045 10.971
10 2742 2666.3 2.149 13.120
11 1932 1923.3 0.039 13.159
12 1342 1388.7 1.573 14.733
13 979 1003.7 0.609 15.341
14 741 726.1 0.304 15.645
15 525 525.8 0.001 15.647
16 349 381.2 2.712 18.359
17 285 276.5 0.259 18.617
18 200 200.8 0.003 18.621
19 142 146.0 0.109 18.730
20 129 106.2 4.888 23.617
21 272 287.1 0.796 24.413
Chisq= 24.41 for 20 degrees of freedom, p= 0.77518
SUMMARY of craptest
p-value for no. of wins: 0.037950
p-value for throws/game: 0.775176
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0021,0.0046,0.0073,0.0090,0.0102,0.0120,0.0146,0.0183,0.0202,0.0233,
0.0236,0.0252,0.0306,0.0380,0.0456,0.0471,0.0481,0.0486,0.0513,0.0522,
0.0551,0.0562,0.0655,0.0690,0.0691,0.0742,0.0783,0.0791,0.0916,0.0929,
0.0972,0.0989,0.1139,0.1165,0.1180,0.1250,0.1295,0.1314,0.1356,0.1366,
0.1403,0.1416,0.1433,0.1434,0.1468,0.1492,0.1505,0.1551,0.1627,0.1642,
0.1715,0.1765,0.1772,0.1803,0.1853,0.1874,0.1902,0.1926,0.1928,0.1951,
0.1956,0.1966,0.2056,0.2057,0.2197,0.2212,0.2250,0.2301,0.2346,0.2441,
0.2467,0.2483,0.2570,0.2572,0.2577,0.2784,0.2852,0.2864,0.2914,0.2992,
0.3005,0.3012,0.3036,0.3050,0.3129,0.3140,0.3164,0.3204,0.3258,0.3319,
0.3345,0.3374,0.3426,0.3429,0.3470,0.3476,0.3494,0.3514,0.3533,0.3564,
0.3662,0.3759,0.3804,0.3862,0.3989,0.4002,0.4034,0.4122,0.4195,0.4230,
0.4251,0.4270,0.4305,0.4332,0.4366,0.4398,0.4416,0.4438,0.4468,0.4511,
0.4543,0.4577,0.4595,0.4606,0.4616,0.4726,0.4738,0.4761,0.4791,0.4875,
0.4913,0.4948,0.5104,0.5117,0.5163,0.5183,0.5185,0.5222,0.5225,0.5344,
0.5379,0.5379,0.5425,0.5468,0.5477,0.5477,0.5538,0.5545,0.5562,0.5610,
0.5626,0.5627,0.5695,0.5761,0.5798,0.5893,0.5929,0.6069,0.6100,0.6142,
0.6145,0.6189,0.6237,0.6351,0.6399,0.6420,0.6457,0.6496,0.6534,0.6552,
0.6570,0.6613,0.6626,0.6741,0.6752,0.6776,0.6857,0.6863,0.6923,0.6935,
0.7008,0.7015,0.7035,0.7058,0.7058,0.7101,0.7135,0.7161,0.7210,0.7214,
0.7241,0.7265,0.7278,0.7310,0.7410,0.7496,0.7507,0.7537,0.7556,0.7575,
0.7580,0.7626,0.7662,0.7684,0.7694,0.7715,0.7752,0.7812,0.7990,0.8005,
0.8066,0.8148,0.8195,0.8201,0.8214,0.8218,0.8260,0.8276,0.8286,0.8301,
0.8339,0.8342,0.8435,0.8440,0.8441,0.8460,0.8489,0.8498,0.8507,0.8520,
0.8523,0.8563,0.8603,0.8612,0.8616,0.8754,0.8780,0.8824,0.8861,0.8881,
0.8912,0.8958,0.9111,0.9132,0.9201,0.9228,0.9303,0.9319,0.9325,0.9338,
0.9339,0.9354,0.9373,0.9397,0.9399,0.9470,0.9609,0.9651,0.9743,0.9757,
0.9787,0.9814,0.9825,0.9864,0.9908,0.9913,0.9922,0.9963,0.9968,
Overall p-value after applying KStest on 269 p-values = 0.763833
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.