RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.81 24.1893 0.885618
2 to 25 16.09 15.3912 0.432673
3 to 26 15.69 18.6068 0.648436
4 to 27 15.47 25.1388 0.908354
5 to 28 15.71 21.7381 0.804999
6 to 29 16.26 10.3407 0.111282
7 to 30 15.96 12.4282 0.226456
8 to 31 15.89 18.5901 0.647442
9 to 32 16.03 11.4986 0.170495
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.920747
Tough bday spacings test for dh-ranFile-2018-06-20_02:31: 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 10 44 76 84 103 81 49 22 19 8 4
(O-E)^2/E 0.1 1.5 0.1 1.9 0.3 0.1 0.2 2.0 1.1 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.613, p= 0.333
RESULTS OF GCD FOR dh-ranFile-2018-06-20_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.293696
p-value, dist. of gcd's: 0.243208
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.297 0.448 0.325 0.864 0.172 0.644 0.015 0.581
Bits 8 to 15---> 0.506 0.196 0.651 0.193 0.285 0.355 0.253 0.291
Bits 16 to 23---> 0.974 0.139 0.669 0.579 0.728 0.555 0.684 0.871
Bits 24 to 31---> 0.941 0.561 0.905 0.118 0.800 0.312 0.945 0.967
KS test for the above 32 p values: 0.161
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_02:31,
p-values for 5 runs: 0.3135, 0.5040, 0.6910, 0.3459, 0.3749
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 221 211.4 0.434 0.434
r= 29 5214 5134.0 1.246 1.681
r= 30 22934 23103.0 1.237 2.917
r= 31 11631 11551.5 0.547 3.464
chi-square = 3.464 with df = 3; p-value = 0.675
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 231 211.4 1.814 1.814
r= 30 5115 5134.0 0.070 1.884
r= 31 23150 23103.0 0.095 1.980
r= 32 11504 11551.5 0.196 2.175
chi-square = 2.175 with df = 3; p-value = 0.463
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_02:31
b-rank test for bits 1 to 8, p=0.50259
b-rank test for bits 2 to 9, p=0.06412
b-rank test for bits 3 to 10, p=0.89555
b-rank test for bits 4 to 11, p=0.14522
b-rank test for bits 5 to 12, p=0.91659
b-rank test for bits 6 to 13, p=0.69863
b-rank test for bits 7 to 14, p=0.51893
b-rank test for bits 8 to 15, p=0.82330
b-rank test for bits 9 to 16, p=0.80427
b-rank test for bits 10 to 17, p=0.46721
b-rank test for bits 11 to 18, p=0.57459
b-rank test for bits 12 to 19, p=0.71960
b-rank test for bits 13 to 20, p=0.06134
b-rank test for bits 14 to 21, p=0.23928
b-rank test for bits 15 to 22, p=0.92450
b-rank test for bits 16 to 23, p=0.69345
b-rank test for bits 17 to 24, p=0.66584
b-rank test for bits 18 to 25, p=0.36879
b-rank test for bits 19 to 26, p=0.79913
b-rank test for bits 20 to 27, p=0.88497
b-rank test for bits 21 to 28, p=0.52631
b-rank test for bits 22 to 29, p=0.65859
b-rank test for bits 23 to 30, p=0.35844
b-rank test for bits 24 to 31, p=0.01815
b-rank test for bits 25 to 32, p=0.96416
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 = 0.331017
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_02:31
(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 142336 1.00 0.840592
2 142185 0.64 0.740241
3 141386 -1.22 0.110715
4 141609 -0.70 0.241431
5 142608 1.63 0.948703
6 142062 0.36 0.639344
7 141981 0.17 0.566493
8 142166 0.60 0.725646
9 141125 -1.83 0.033435
10 141806 -0.24 0.404613
11 142151 0.56 0.713844
12 142060 0.35 0.637593
13 141501 -0.95 0.170031
14 142124 0.50 0.692013
15 141431 -1.12 0.131870
16 142044 0.31 0.623486
17 141577 -0.78 0.218735
18 141423 -1.14 0.127919
19 142926 2.38 0.991235
20 142044 0.31 0.623486
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_02:31
Bits used No. missing words z-score p-value
23 to 32 142089 0.6196 0.732224
22 to 31 141839 -0.2425 0.404190
21 to 30 142018 0.3747 0.646067
20 to 29 142210 1.0368 0.850084
19 to 28 142031 0.4196 0.662594
18 to 27 142019 0.3782 0.647349
17 to 26 141681 -0.7873 0.215540
16 to 25 141873 -0.1253 0.450153
15 to 24 141532 -1.3011 0.096606
14 to 23 141718 -0.6598 0.254704
13 to 22 141865 -0.1529 0.439254
12 to 21 141704 -0.7080 0.239462
11 to 20 142039 0.4471 0.672612
10 to 19 141827 -0.2839 0.388245
9 to 18 141991 0.2816 0.610883
8 to 17 141389 -1.7942 0.036387
7 to 16 142317 1.4058 0.920102
6 to 15 142491 2.0058 0.977559
5 to 14 142010 0.3471 0.635756
4 to 13 141605 -1.0494 0.146994
3 to 12 142128 0.7540 0.774586
2 to 11 141872 -0.1287 0.448788
1 to 10 141550 -1.2391 0.107660
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_02:31
Bits used No. missing words z-score p-value
28 to 32 142012 0.3480 0.636093
27 to 31 141798 -0.3774 0.352942
26 to 30 142263 1.1989 0.884713
25 to 29 142611 2.3785 0.991309
24 to 28 141597 -1.0587 0.144858
23 to 27 141937 0.0938 0.537365
22 to 26 142045 0.4599 0.677205
21 to 25 142216 1.0396 0.850728
20 to 24 141447 -1.5672 0.058532
19 to 23 142000 0.3074 0.620714
18 to 22 142375 1.5785 0.942779
17 to 21 142131 0.7514 0.773801
16 to 20 141770 -0.4723 0.318355
15 to 19 141737 -0.5842 0.279553
14 to 18 141844 -0.2215 0.412368
13 to 17 141888 -0.0723 0.471180
12 to 16 142105 0.6633 0.746427
11 to 15 141811 -0.3333 0.369446
10 to 14 141662 -0.8384 0.200901
9 to 13 141772 -0.4655 0.320778
8 to 12 141554 -1.2045 0.114197
7 to 11 142072 0.5514 0.709328
6 to 10 141960 0.1718 0.568188
5 to 9 142292 1.2972 0.902717
4 to 8 142151 0.8192 0.793670
3 to 7 141941 0.1074 0.542747
2 to 6 141642 -0.9062 0.182414
1 to 5 142116 0.7006 0.758216
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_02:31
Bits used No. missing words z-score p-value
31 to 32 141848 -0.1809 0.428217
30 to 31 141564 -1.0187 0.154179
29 to 30 142064 0.4563 0.675896
28 to 29 141825 -0.2488 0.401773
27 to 28 141940 0.0905 0.536044
26 to 27 141608 -0.8889 0.187034
25 to 26 141600 -0.9125 0.180759
24 to 25 142537 1.8515 0.967954
23 to 24 141776 -0.3933 0.347048
22 to 23 142018 0.3206 0.625728
21 to 22 142122 0.6273 0.734784
20 to 21 141818 -0.2694 0.393807
19 to 20 141913 0.0108 0.504319
18 to 19 142142 0.6863 0.753751
17 to 18 141872 -0.1101 0.456158
16 to 17 141745 -0.4847 0.313927
15 to 16 142163 0.7483 0.772857
14 to 15 141718 -0.5644 0.286243
13 to 14 142309 1.1790 0.880794
12 to 13 141713 -0.5791 0.281246
11 to 12 142224 0.9282 0.823356
10 to 11 142017 0.3176 0.624610
9 to 10 141877 -0.0954 0.462011
8 to 9 142109 0.5890 0.722068
7 to 8 140808 -3.2488 0.000580
6 to 7 141972 0.1849 0.573333
5 to 6 141310 -1.7679 0.038536
4 to 5 142318 1.2055 0.885998
3 to 4 140913 -2.9390 0.001646
2 to 3 142017 0.3176 0.624610
1 to 2 141744 -0.4877 0.312882
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2357.01 -2.022 0.021579
Test results for specific bytes for dh-ranFile-2018-06-20_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2364.29 -1.919 0.027478
2 to 9 2597.15 1.374 0.915258
3 to 10 2669.59 2.398 0.991765
4 to 11 2541.80 0.591 0.722766
5 to 12 2582.21 1.163 0.877501
6 to 13 2458.86 -0.582 0.280344
7 to 14 2477.83 -0.313 0.376959
8 to 15 2416.75 -1.177 0.119526
9 to 16 2578.16 1.105 0.865503
10 to 17 2474.42 -0.362 0.358792
11 to 18 2573.99 1.046 0.852321
12 to 19 2580.14 1.133 0.871470
13 to 20 2427.18 -1.030 0.151558
14 to 21 2449.96 -0.708 0.239591
15 to 22 2555.59 0.786 0.784106
16 to 23 2410.70 -1.263 0.103312
17 to 24 2543.97 0.622 0.732954
18 to 25 2590.90 1.286 0.900706
19 to 26 2476.16 -0.337 0.367987
20 to 27 2487.03 -0.183 0.427240
21 to 28 2297.71 -2.861 0.002113
22 to 29 2488.53 -0.162 0.435555
23 to 30 2391.99 -1.528 0.063313
24 to 31 2513.74 0.194 0.577014
25 to 32 2492.41 -0.107 0.457253
CDPARK for dh-ranFile-2018-06-20_02:31: 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
3551 1.2785 0.899470
3529 0.2740 0.607947
3542 0.8676 0.807188
3526 0.1370 0.554479
3539 0.7306 0.767486
3545 1.0046 0.842447
3516 -0.3196 0.374623
3529 0.2740 0.607947
3524 0.0457 0.518210
3502 -0.9589 0.168804
Square side=100, avg. no. parked=3530.30 sample std.=13.87
p-value of the KSTEST for those 10 p-values: 0.281514
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_02:31
0.5116,0.4982,0.5044,0.4835,0.1637,0.4895,0.1719,0.5524,0.1042,0.7261,
The KS test for those 10 p-values: 0.227557
The 3DSPHERES test for dh-ranFile-2018-06-20_02:31
sample no r^3 equiv. uni.
1 38.012 0.718348
2 9.659 0.275270
3 4.658 0.143825
4 98.019 0.961890
5 155.057 0.994307
6 50.328 0.813178
7 39.389 0.730975
8 40.829 0.743586
9 0.832 0.027353
10 84.217 0.939628
11 3.323 0.104864
12 76.354 0.921539
13 0.759 0.024982
14 5.295 0.161800
15 32.847 0.665425
16 21.357 0.509293
17 6.346 0.190665
18 29.582 0.626964
19 16.248 0.418181
20 28.245 0.609954
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.583221
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.5 -0.6 -0.8 1.7 0.3
-1.2 -0.4 -0.3 -0.3 -2.0 -0.3
0.7 -1.5 -0.7 1.9 1.0 0.1
-1.5 -0.2 1.4 0.4 0.3 -0.4
1.6 0.1 -1.7 0.6 -0.9 0.4
0.8 -0.3 1.1 0.7 0.3 -0.3
-0.5 0.2 1.3 -1.8 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:37.549659
z-score=-0.485572, p-value=0.333457
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_02:31
Test no p-value
1 0.643580
2 0.108158
3 0.390518
4 0.229531
5 0.082311
6 0.475021
7 0.941692
8 0.018228
9 0.893511
10 0.827257
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.754450
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_02:31:
(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 66493 0.45 66432 0.83
3 25000.00 24995 0.00 25155 0.96
4 6666.67 6819 3.48 6764 1.42
5 1388.89 1399 0.07 1353 0.93
6 238.10 246 0.26 256 1.35
7 34.72 40 0.80 35 0.00
8 4.96 7 0.84 4 0.19
p=0.56689 p=0.53884
Number of rngs required: 688412, p-value: 0.504
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_02:31
No. of wins: Observed Expected
98916 98585.9
z-score= 1.477, pvalue=0.93011
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66536 66666.7 0.256 0.256
2 37570 37654.3 0.189 0.445
3 27315 26954.7 4.815 5.260
4 19009 19313.5 4.800 10.060
5 13948 13851.4 0.673 10.733
6 10025 9943.5 0.667 11.400
7 7202 7145.0 0.454 11.855
8 5182 5139.1 0.359 12.213
9 3636 3699.9 1.102 13.316
10 2608 2666.3 1.275 14.590
11 1876 1923.3 1.165 15.755
12 1435 1388.7 1.541 17.296
13 992 1003.7 0.137 17.433
14 748 726.1 0.658 18.091
15 520 525.8 0.065 18.156
16 361 381.2 1.065 19.221
17 256 276.5 1.526 20.746
18 222 200.8 2.232 22.978
19 146 146.0 0.000 22.978
20 120 106.2 1.789 24.767
21 293 287.1 0.121 24.888
Chisq= 24.89 for 20 degrees of freedom, p= 0.79424
SUMMARY of craptest
p-value for no. of wins: 0.930107
p-value for throws/game: 0.794238
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_02:31
No. of wins: Observed Expected
98342 98585.9
z-score=-1.091, pvalue=0.13771
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66702 66666.7 0.019 0.019
2 37440 37654.3 1.220 1.239
3 26875 26954.7 0.236 1.474
4 19375 19313.5 0.196 1.671
5 13773 13851.4 0.444 2.115
6 9898 9943.5 0.209 2.323
7 7178 7145.0 0.152 2.475
8 5256 5139.1 2.660 5.136
9 3838 3699.9 5.157 10.293
10 2718 2666.3 1.003 11.296
11 1861 1923.3 2.020 13.315
12 1382 1388.7 0.033 13.348
13 1061 1003.7 3.269 16.618
14 750 726.1 0.784 17.402
15 554 525.8 1.508 18.910
16 397 381.2 0.659 19.569
17 252 276.5 2.178 21.747
18 193 200.8 0.305 22.052
19 144 146.0 0.027 22.079
20 109 106.2 0.073 22.152
21 244 287.1 6.474 28.626
Chisq= 28.63 for 20 degrees of freedom, p= 0.90461
SUMMARY of craptest
p-value for no. of wins: 0.137707
p-value for throws/game: 0.904613
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0016,0.0021,0.0145,0.0182,0.0182,0.0216,0.0250,0.0274,0.0275,
0.0334,0.0364,0.0385,0.0585,0.0613,0.0633,0.0641,0.0823,0.0966,0.1033,
0.1042,0.1049,0.1077,0.1082,0.1107,0.1113,0.1142,0.1180,0.1195,0.1279,
0.1319,0.1377,0.1390,0.1438,0.1449,0.1452,0.1470,0.1516,0.1542,0.1612,
0.1618,0.1637,0.1688,0.1700,0.1705,0.1719,0.1722,0.1808,0.1824,0.1870,
0.1907,0.1928,0.1957,0.2009,0.2155,0.2187,0.2265,0.2276,0.2295,0.2393,
0.2395,0.2396,0.2414,0.2432,0.2525,0.2547,0.2753,0.2796,0.2803,0.2812,
0.2815,0.2847,0.2862,0.2913,0.2937,0.2974,0.3116,0.3129,0.3135,0.3139,
0.3184,0.3208,0.3249,0.3310,0.3334,0.3335,0.3459,0.3470,0.3529,0.3552,
0.3584,0.3588,0.3680,0.3688,0.3694,0.3746,0.3749,0.3770,0.3882,0.3905,
0.3938,0.4018,0.4042,0.4046,0.4124,0.4182,0.4272,0.4282,0.4327,0.4356,
0.4393,0.4480,0.4488,0.4502,0.4562,0.4573,0.4620,0.4631,0.4672,0.4712,
0.4750,0.4835,0.4895,0.4982,0.5026,0.5040,0.5041,0.5043,0.5044,0.5060,
0.5093,0.5116,0.5182,0.5189,0.5263,0.5360,0.5374,0.5388,0.5427,0.5524,
0.5545,0.5548,0.5607,0.5665,0.5669,0.5682,0.5733,0.5746,0.5770,0.5787,
0.5811,0.5832,0.6079,0.6079,0.6100,0.6109,0.6207,0.6235,0.6235,0.6246,
0.6246,0.6257,0.6270,0.6358,0.6361,0.6376,0.6393,0.6436,0.6439,0.6461,
0.6473,0.6474,0.6484,0.6513,0.6586,0.6626,0.6654,0.6658,0.6693,0.6726,
0.6746,0.6759,0.6772,0.6839,0.6910,0.6920,0.6935,0.6986,0.7093,0.7138,
0.7183,0.7196,0.7221,0.7228,0.7256,0.7261,0.7279,0.7310,0.7322,0.7330,
0.7348,0.7402,0.7436,0.7464,0.7538,0.7544,0.7582,0.7675,0.7729,0.7738,
0.7746,0.7841,0.7937,0.7942,0.7991,0.7997,0.8043,0.8050,0.8072,0.8132,
0.8233,0.8234,0.8273,0.8406,0.8424,0.8501,0.8507,0.8523,0.8645,0.8655,
0.8710,0.8715,0.8775,0.8808,0.8847,0.8850,0.8856,0.8860,0.8935,0.8955,
0.8995,0.9007,0.9027,0.9045,0.9046,0.9084,0.9153,0.9166,0.9201,0.9207,
0.9215,0.9245,0.9301,0.9396,0.9408,0.9417,0.9428,0.9446,0.9487,0.9619,
0.9642,0.9665,0.9680,0.9745,0.9776,0.9912,0.9913,0.9918,0.9943,
Overall p-value after applying KStest on 269 p-values = 0.739832
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.