RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_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 15.76 19.4731 0.697937
2 to 25 15.62 21.1913 0.782150
3 to 26 15.81 7.7861 0.029091
4 to 27 15.81 15.7176 0.456061
5 to 28 15.86 21.0982 0.778070
6 to 29 15.85 21.3905 0.790693
7 to 30 15.90 8.8266 0.054454
8 to 31 15.95 11.1129 0.149363
9 to 32 16.04 17.7348 0.594249
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.572351
Tough bday spacings test for dh-ranFile-2018-06-18_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 6 35 75 99 103 70 49 36 15 7 5
(O-E)^2/E 1.1 0.1 0.0 0.0 0.3 0.8 0.2 1.3 0.0 0.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 4.085, p= 0.057
RESULTS OF GCD FOR dh-ranFile-2018-06-18_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.723333
p-value, dist. of gcd's: 0.820274
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.963 0.842 0.665 0.786 0.106 0.836 0.791 0.405
Bits 8 to 15---> 0.862 0.013 0.767 0.410 0.956 0.412 0.892 0.067
Bits 16 to 23---> 0.861 0.764 0.480 0.850 0.084 0.911 0.027 0.890
Bits 24 to 31---> 0.456 0.386 0.869 0.024 0.170 0.617 0.544 0.363
KS test for the above 32 p values: 0.891
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_02:31,
p-values for 5 runs: 0.7755, 0.4944, 0.1860, 0.4285, 0.8902
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 235 211.4 2.630 2.630
r= 29 5141 5134.0 0.010 2.640
r= 30 23155 23103.0 0.117 2.757
r= 31 11469 11551.5 0.590 3.346
chi-square = 3.346 with df = 3; p-value = 0.659
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 233 211.4 2.203 2.203
r= 30 5125 5134.0 0.016 2.219
r= 31 23102 23103.0 0.000 2.219
r= 32 11540 11551.5 0.011 2.230
chi-square = 2.230 with df = 3; p-value = 0.474
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_02:31
b-rank test for bits 1 to 8, p=0.57021
b-rank test for bits 2 to 9, p=0.40982
b-rank test for bits 3 to 10, p=0.02126
b-rank test for bits 4 to 11, p=0.22770
b-rank test for bits 5 to 12, p=0.83403
b-rank test for bits 6 to 13, p=0.40245
b-rank test for bits 7 to 14, p=0.14032
b-rank test for bits 8 to 15, p=0.02528
b-rank test for bits 9 to 16, p=0.37082
b-rank test for bits 10 to 17, p=0.34050
b-rank test for bits 11 to 18, p=0.77830
b-rank test for bits 12 to 19, p=0.61768
b-rank test for bits 13 to 20, p=0.43212
b-rank test for bits 14 to 21, p=0.82864
b-rank test for bits 15 to 22, p=0.83101
b-rank test for bits 16 to 23, p=0.15581
b-rank test for bits 17 to 24, p=0.28478
b-rank test for bits 18 to 25, p=0.17765
b-rank test for bits 19 to 26, p=0.40277
b-rank test for bits 20 to 27, p=0.60986
b-rank test for bits 21 to 28, p=0.23259
b-rank test for bits 22 to 29, p=0.75844
b-rank test for bits 23 to 30, p=0.91488
b-rank test for bits 24 to 31, p=0.61894
b-rank test for bits 25 to 32, p=0.00032
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 = 0.365596
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_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 140588 -3.09 0.001010
2 141361 -1.28 0.100071
3 142070 0.38 0.646317
4 141910 0.00 0.500625
5 141570 -0.79 0.213939
6 141861 -0.11 0.455047
7 141305 -1.41 0.078977
8 142703 1.85 0.968157
9 142166 0.60 0.725646
10 142446 1.25 0.895061
11 142087 0.42 0.660972
12 141729 -0.42 0.336756
13 141992 0.19 0.576581
14 142222 0.73 0.767469
15 141527 -0.89 0.185850
16 141654 -0.60 0.275399
17 141566 -0.80 0.211227
18 142266 0.83 0.797674
19 142262 0.82 0.795029
20 142469 1.31 0.904502
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_02:31
Bits used No. missing words z-score p-value
23 to 32 141980 0.2437 0.596264
22 to 31 141594 -1.0873 0.138442
21 to 30 142066 0.5402 0.705485
20 to 29 141838 -0.2460 0.402855
19 to 28 142056 0.5058 0.693487
18 to 27 141876 -0.1149 0.454250
17 to 26 142255 1.1920 0.883363
16 to 25 141795 -0.3942 0.346701
15 to 24 141625 -0.9804 0.163432
14 to 23 142503 2.0471 0.979678
13 to 22 141863 -0.1598 0.436536
12 to 21 142146 0.8161 0.792780
11 to 20 141609 -1.0356 0.150190
10 to 19 142594 2.3609 0.990885
9 to 18 141673 -0.8149 0.207556
8 to 17 141749 -0.5529 0.290179
7 to 16 141850 -0.2046 0.418948
6 to 15 142004 0.3264 0.627957
5 to 14 142123 0.7368 0.769376
4 to 13 142115 0.7092 0.760902
3 to 12 142431 1.7989 0.963980
2 to 11 141217 -2.3873 0.008485
1 to 10 141561 -1.2011 0.114849
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_02:31
Bits used No. missing words z-score p-value
28 to 32 141492 -1.4147 0.078581
27 to 31 141792 -0.3977 0.345415
26 to 30 141626 -0.9604 0.168417
25 to 29 141943 0.1141 0.545435
24 to 28 141845 -0.2181 0.413688
23 to 27 141964 0.1853 0.573512
22 to 26 141967 0.1955 0.577496
21 to 25 142132 0.7548 0.774820
20 to 24 141922 0.0429 0.517129
19 to 23 141629 -0.9503 0.170987
18 to 22 142099 0.6429 0.739872
17 to 21 142093 0.6226 0.733230
16 to 20 142088 0.6057 0.727630
15 to 19 141962 0.1785 0.570852
14 to 18 141642 -0.9062 0.182414
13 to 17 142590 2.3074 0.989483
12 to 16 142622 2.4158 0.992150
11 to 15 142215 1.0362 0.849938
10 to 14 141674 -0.7977 0.212514
9 to 13 142121 0.7175 0.763475
8 to 12 141947 0.1277 0.550805
7 to 11 141865 -0.1503 0.440275
6 to 10 141936 0.0904 0.536018
5 to 9 141351 -1.8926 0.029203
4 to 8 141819 -0.3062 0.379725
3 to 7 141702 -0.7028 0.241086
2 to 6 142027 0.3989 0.655010
1 to 5 141921 0.0396 0.515778
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_02:31
Bits used No. missing words z-score p-value
31 to 32 141908 -0.0039 0.498435
30 to 31 141554 -1.0482 0.147280
29 to 30 140938 -2.8653 0.002083
28 to 29 141886 -0.0688 0.472566
27 to 28 141992 0.2439 0.596332
26 to 27 141690 -0.6470 0.258819
25 to 26 141814 -0.2812 0.389275
24 to 25 141828 -0.2399 0.405199
23 to 24 142318 1.2055 0.885998
22 to 23 141677 -0.6853 0.246565
21 to 22 141727 -0.5378 0.295342
20 to 21 142237 0.9666 0.833123
19 to 20 141505 -1.1927 0.116491
18 to 19 141870 -0.1160 0.453819
17 to 18 142083 0.5123 0.695780
16 to 17 141292 -1.8210 0.034301
15 to 16 142056 0.4327 0.667367
14 to 15 142296 1.1406 0.872986
13 to 14 142198 0.8515 0.802764
12 to 13 142090 0.5329 0.702966
11 to 12 141579 -0.9744 0.164923
10 to 11 141653 -0.7561 0.224784
9 to 10 142105 0.5772 0.718097
8 to 9 141999 0.2645 0.604308
7 to 8 143080 3.4533 0.999723
6 to 7 141598 -0.9184 0.179211
5 to 6 141560 -1.0305 0.151394
4 to 5 141947 0.1111 0.544240
3 to 4 141876 -0.0983 0.460840
2 to 3 141890 -0.0570 0.477264
1 to 2 141519 -1.1514 0.124781
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2478.97 -0.297 0.383066
Test results for specific bytes for dh-ranFile-2018-06-18_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2483.01 -0.240 0.405040
2 to 9 2470.65 -0.415 0.339062
3 to 10 2512.76 0.180 0.571581
4 to 11 2486.17 -0.196 0.422453
5 to 12 2582.37 1.165 0.877978
6 to 13 2415.48 -1.195 0.115981
7 to 14 2542.50 0.601 0.726081
8 to 15 2456.84 -0.610 0.270797
9 to 16 2564.87 0.917 0.820544
10 to 17 2580.71 1.141 0.873137
11 to 18 2510.74 0.152 0.560385
12 to 19 2556.35 0.797 0.787229
13 to 20 2453.24 -0.661 0.254199
14 to 21 2470.88 -0.412 0.340251
15 to 22 2442.18 -0.818 0.206748
16 to 23 2493.19 -0.096 0.461620
17 to 24 2576.69 1.085 0.860944
18 to 25 2580.46 1.138 0.872425
19 to 26 2553.99 0.763 0.777410
20 to 27 2333.05 -2.361 0.009113
21 to 28 2282.65 -3.074 0.001057
22 to 29 2582.63 1.169 0.878710
23 to 30 2486.83 -0.186 0.426140
24 to 31 2492.68 -0.104 0.458780
25 to 32 2476.49 -0.332 0.369776
CDPARK for dh-ranFile-2018-06-18_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
3508 -0.6849 0.246694
3526 0.1370 0.554479
3531 0.3653 0.642555
3521 -0.0913 0.463617
3536 0.5936 0.723613
3530 0.3196 0.625377
3516 -0.3196 0.374623
3542 0.8676 0.807188
3512 -0.5023 0.307734
3486 -1.6895 0.045562
Square side=100, avg. no. parked=3520.80 sample std.=15.40
p-value of the KSTEST for those 10 p-values: 0.774006
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_02:31
0.8377,0.7168,0.5677,0.4456,0.3782,0.5176,0.3707,0.2685,0.8217,0.2333,
The KS test for those 10 p-values: 0.606355
The 3DSPHERES test for dh-ranFile-2018-06-18_02:31
sample no r^3 equiv. uni.
1 0.509 0.016814
2 30.921 0.643241
3 3.737 0.117110
4 1.088 0.035615
5 13.230 0.356605
6 0.048 0.001612
7 30.901 0.643006
8 64.637 0.884047
9 7.567 0.222942
10 55.797 0.844311
11 65.176 0.886110
12 42.376 0.756476
13 64.198 0.882339
14 40.811 0.743435
15 84.087 0.939366
16 36.473 0.703513
17 56.062 0.845680
18 8.944 0.257791
19 0.650 0.021433
20 17.311 0.438443
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.182627
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.3 -2.8 -2.2 0.3 0.3
-0.9 2.1 -1.4 -0.1 1.3 1.4
0.7 -0.5 1.0 -1.0 -0.4 1.9
-0.6 0.7 -2.8 -1.1 0.6 -2.0
0.3 2.0 -0.7 0.6 -0.1 0.3
-0.6 -0.5 1.8 -0.5 -0.5 1.3
0.3 -0.7 0.5 2.1 1.6 0.0
-1.1
Chi-square with 42 degrees of freedom:67.439267
z-score=2.775652, p-value=0.992357
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_02:31
Test no p-value
1 0.293312
2 0.102524
3 0.348710
4 0.452469
5 0.725198
6 0.015424
7 0.098100
8 0.685143
9 0.559857
10 0.939301
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.676274
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_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 66571 0.14 66440 0.77
3 25000.00 25100 0.40 25079 0.25
4 6666.67 6686 0.06 6752 1.09
5 1388.89 1373 0.18 1408 0.26
6 238.10 233 0.11 273 5.12
7 34.72 32 0.21 40 0.80
8 4.96 4 0.19 7 0.84
p=0.02742 p=0.83384
Number of rngs required: 689399, p-value: 0.876
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_02:31
No. of wins: Observed Expected
98549 98585.9
z-score=-0.165, pvalue=0.43453
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66274 66666.7 2.313 2.313
2 37736 37654.3 0.177 2.490
3 27021 26954.7 0.163 2.653
4 19435 19313.5 0.765 3.418
5 13920 13851.4 0.340 3.757
6 10017 9943.5 0.543 4.300
7 7069 7145.0 0.809 5.109
8 5078 5139.1 0.726 5.835
9 3650 3699.9 0.672 6.507
10 2630 2666.3 0.494 7.001
11 1958 1923.3 0.625 7.626
12 1372 1388.7 0.202 7.828
13 1047 1003.7 1.867 9.694
14 771 726.1 2.771 12.466
15 567 525.8 3.222 15.688
16 436 381.2 7.893 23.581
17 284 276.5 0.201 23.782
18 199 200.8 0.017 23.799
19 154 146.0 0.440 24.239
20 110 106.2 0.135 24.374
21 272 287.1 0.796 25.170
Chisq= 25.17 for 20 degrees of freedom, p= 0.80498
SUMMARY of craptest
p-value for no. of wins: 0.434530
p-value for throws/game: 0.804983
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_02:31
No. of wins: Observed Expected
98336 98585.9
z-score=-1.118, pvalue=0.13189
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66405 66666.7 1.027 1.027
2 37565 37654.3 0.212 1.239
3 27153 26954.7 1.458 2.697
4 19247 19313.5 0.229 2.926
5 13825 13851.4 0.050 2.976
6 9866 9943.5 0.605 3.581
7 7205 7145.0 0.503 4.085
8 5246 5139.1 2.225 6.309
9 3786 3699.9 2.005 8.315
10 2700 2666.3 0.426 8.741
11 1937 1923.3 0.097 8.838
12 1412 1388.7 0.390 9.227
13 1109 1003.7 11.044 20.271
14 719 726.1 0.070 20.341
15 523 525.8 0.015 20.357
16 379 381.2 0.012 20.369
17 249 276.5 2.743 23.111
18 192 200.8 0.388 23.500
19 127 146.0 2.469 25.968
20 102 106.2 0.167 26.136
21 253 287.1 4.053 30.189
Chisq= 30.19 for 20 degrees of freedom, p= 0.93315
SUMMARY of craptest
p-value for no. of wins: 0.131887
p-value for throws/game: 0.933153
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0010,0.0011,0.0016,0.0021,0.0085,0.0091,0.0129,0.0154,0.0168,
0.0213,0.0214,0.0245,0.0253,0.0267,0.0274,0.0291,0.0292,0.0343,0.0356,
0.0456,0.0545,0.0566,0.0671,0.0786,0.0790,0.0844,0.0981,0.1001,0.1025,
0.1057,0.1148,0.1160,0.1165,0.1171,0.1248,0.1319,0.1384,0.1403,0.1473,
0.1494,0.1502,0.1514,0.1558,0.1634,0.1649,0.1684,0.1695,0.1710,0.1777,
0.1792,0.1824,0.1826,0.1858,0.1860,0.2067,0.2076,0.2112,0.2125,0.2139,
0.2229,0.2248,0.2277,0.2326,0.2333,0.2411,0.2466,0.2467,0.2542,0.2578,
0.2588,0.2685,0.2708,0.2754,0.2848,0.2902,0.2933,0.2953,0.3077,0.3368,
0.3391,0.3403,0.3405,0.3454,0.3467,0.3487,0.3566,0.3626,0.3656,0.3698,
0.3707,0.3708,0.3746,0.3782,0.3797,0.3831,0.3858,0.3893,0.4025,0.4028,
0.4029,0.4050,0.4051,0.4052,0.4098,0.4098,0.4116,0.4137,0.4189,0.4225,
0.4261,0.4285,0.4321,0.4345,0.4365,0.4384,0.4403,0.4456,0.4525,0.4538,
0.4542,0.4550,0.4561,0.4563,0.4588,0.4608,0.4616,0.4636,0.4726,0.4740,
0.4773,0.4800,0.4944,0.4984,0.5006,0.5158,0.5171,0.5176,0.5360,0.5441,
0.5442,0.5454,0.5508,0.5545,0.5599,0.5604,0.5677,0.5702,0.5709,0.5716,
0.5724,0.5735,0.5766,0.5775,0.5942,0.5963,0.5963,0.6043,0.6064,0.6099,
0.6166,0.6177,0.6189,0.6254,0.6280,0.6426,0.6430,0.6432,0.6463,0.6550,
0.6587,0.6610,0.6652,0.6674,0.6763,0.6851,0.6935,0.6958,0.6979,0.7030,
0.7035,0.7055,0.7168,0.7181,0.7233,0.7236,0.7252,0.7256,0.7261,0.7276,
0.7332,0.7399,0.7434,0.7565,0.7584,0.7609,0.7635,0.7641,0.7672,0.7675,
0.7694,0.7740,0.7748,0.7755,0.7774,0.7781,0.7783,0.7822,0.7856,0.7872,
0.7906,0.7907,0.7928,0.7950,0.7977,0.8028,0.8050,0.8072,0.8203,0.8205,
0.8217,0.8286,0.8310,0.8331,0.8338,0.8340,0.8357,0.8377,0.8423,0.8443,
0.8457,0.8499,0.8500,0.8605,0.8609,0.8617,0.8693,0.8724,0.8730,0.8731,
0.8763,0.8780,0.8787,0.8823,0.8834,0.8840,0.8860,0.8861,0.8898,0.8902,
0.8910,0.8920,0.8951,0.9045,0.9109,0.9149,0.9332,0.9393,0.9394,0.9561,
0.9635,0.9640,0.9682,0.9797,0.9895,0.9909,0.9922,0.9924,0.9997,
Overall p-value after applying KStest on 269 p-values = 0.313482
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.