RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.99 16.8797 0.537454
2 to 25 15.83 10.8836 0.137452
3 to 26 15.77 25.4734 0.915396
4 to 27 15.96 13.5193 0.299211
5 to 28 15.94 21.9233 0.812314
6 to 29 15.88 19.3343 0.690315
7 to 30 15.60 24.6856 0.898029
8 to 31 15.96 14.9545 0.401240
9 to 32 15.63 18.3048 0.630138
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.647453
Tough bday spacings test for dh-ranFile-2018-06-28_16:31: 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 4 36 84 99 88 89 54 27 11 5 3
(O-E)^2/E 2.9 0.0 1.6 0.0 1.0 1.5 0.1 0.3 1.0 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 8.990, p= 0.467
RESULTS OF GCD FOR dh-ranFile-2018-06-28_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.797601
p-value, dist. of gcd's: 0.633564
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.381 0.904 0.853 0.422 0.884 0.952 0.580 0.060
Bits 8 to 15---> 0.859 0.528 0.267 0.718 0.515 0.410 0.718 0.098
Bits 16 to 23---> 0.881 0.291 0.199 0.497 0.339 0.993 0.021 0.756
Bits 24 to 31---> 0.193 0.355 0.153 0.653 0.611 0.882 0.106 0.206
KS test for the above 32 p values: 0.008
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_16:31,
p-values for 5 runs: 0.0758, 0.6263, 0.7486, 0.7888, 0.0114
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5043 5134.0 1.613 1.614
r= 30 23233 23103.0 0.731 2.345
r= 31 11513 11551.5 0.128 2.474
chi-square = 2.474 with df = 3; p-value = 0.520
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5037 5134.0 1.833 2.816
r= 31 23201 23103.0 0.415 3.232
r= 32 11565 11551.5 0.016 3.247
chi-square = 3.247 with df = 3; p-value = 0.645
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_16:31
b-rank test for bits 1 to 8, p=0.71266
b-rank test for bits 2 to 9, p=0.80514
b-rank test for bits 3 to 10, p=0.34177
b-rank test for bits 4 to 11, p=0.82989
b-rank test for bits 5 to 12, p=0.36478
b-rank test for bits 6 to 13, p=0.74887
b-rank test for bits 7 to 14, p=0.00838
b-rank test for bits 8 to 15, p=0.51703
b-rank test for bits 9 to 16, p=0.27918
b-rank test for bits 10 to 17, p=0.17086
b-rank test for bits 11 to 18, p=0.92960
b-rank test for bits 12 to 19, p=0.14015
b-rank test for bits 13 to 20, p=0.32768
b-rank test for bits 14 to 21, p=0.27918
b-rank test for bits 15 to 22, p=0.49712
b-rank test for bits 16 to 23, p=0.70085
b-rank test for bits 17 to 24, p=0.33061
b-rank test for bits 18 to 25, p=0.10520
b-rank test for bits 19 to 26, p=0.44857
b-rank test for bits 20 to 27, p=0.80055
b-rank test for bits 21 to 28, p=0.53891
b-rank test for bits 22 to 29, p=0.16961
b-rank test for bits 23 to 30, p=0.67295
b-rank test for bits 24 to 31, p=0.38529
b-rank test for bits 25 to 32, p=0.65008
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 = 0.706555
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_16:31
(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 141155 -1.76 0.038996
2 142148 0.56 0.711455
3 141583 -0.76 0.222895
4 142128 0.51 0.695293
5 141821 -0.21 0.418248
6 141433 -1.11 0.132871
7 142721 1.90 0.971048
8 142037 0.30 0.617261
9 142547 1.49 0.931873
10 141876 -0.08 0.468964
11 141726 -0.43 0.334201
12 141717 -0.45 0.326583
13 141710 -0.47 0.320706
14 142066 0.37 0.642837
15 142162 0.59 0.722522
16 141790 -0.28 0.390196
17 142427 1.21 0.886766
18 141917 0.02 0.507149
19 141875 -0.08 0.468035
20 141992 0.19 0.576581
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_16:31
Bits used No. missing words z-score p-value
23 to 32 141931 0.0747 0.529783
22 to 31 141987 0.2678 0.605584
21 to 30 141545 -1.2563 0.104502
20 to 29 142084 0.6023 0.726516
19 to 28 141793 -0.4011 0.344159
18 to 27 141559 -1.2080 0.113517
17 to 26 142171 0.9023 0.816554
16 to 25 141776 -0.4598 0.322845
15 to 24 141956 0.1609 0.563926
14 to 23 142130 0.7609 0.776651
13 to 22 142509 2.0678 0.980672
12 to 21 142367 1.5782 0.942737
11 to 20 142351 1.5230 0.936121
10 to 19 141648 -0.9011 0.183758
9 to 18 142017 0.3713 0.644784
8 to 17 142020 0.3816 0.648629
7 to 16 141498 -1.4184 0.078040
6 to 15 141419 -1.6908 0.045438
5 to 14 142018 0.3747 0.646067
4 to 13 141946 0.1264 0.550312
3 to 12 142095 0.6402 0.738992
2 to 11 142067 0.5437 0.706673
1 to 10 141823 -0.2977 0.382970
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_16:31
Bits used No. missing words z-score p-value
28 to 32 142096 0.6328 0.736561
27 to 31 142063 0.5209 0.698787
26 to 30 142137 0.7718 0.779873
25 to 29 142278 1.2497 0.894301
24 to 28 142493 1.9785 0.976066
23 to 27 141942 0.1107 0.544091
22 to 26 142320 1.3921 0.918054
21 to 25 142244 1.1345 0.871702
20 to 24 141424 -1.6452 0.049966
19 to 23 141652 -0.8723 0.191521
18 to 22 142242 1.1277 0.870276
17 to 21 141671 -0.8079 0.209575
16 to 20 141874 -0.1198 0.452336
15 to 19 142155 0.8328 0.797516
14 to 18 141500 -1.3876 0.082636
13 to 17 141686 -0.7571 0.224510
12 to 16 142251 1.1582 0.876610
11 to 15 141976 0.2260 0.589399
10 to 14 141977 0.2294 0.590717
9 to 13 141561 -1.1808 0.118845
8 to 12 141989 0.2701 0.606446
7 to 11 141864 -0.1537 0.438939
6 to 10 142182 0.9243 0.822336
5 to 9 142147 0.8057 0.789781
4 to 8 142466 1.8870 0.970421
3 to 7 142020 0.3752 0.646227
2 to 6 141985 0.2565 0.601221
1 to 5 141729 -0.6113 0.270504
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_16:31
Bits used No. missing words z-score p-value
31 to 32 141932 0.0669 0.526659
30 to 31 141992 0.2439 0.596332
29 to 30 141797 -0.3314 0.370187
28 to 29 141880 -0.0865 0.465527
27 to 28 142269 1.0610 0.855649
26 to 27 142014 0.3088 0.621248
25 to 26 141644 -0.7827 0.216906
24 to 25 141640 -0.7945 0.213457
23 to 24 142409 1.4740 0.929753
22 to 23 142063 0.4533 0.674835
21 to 22 142105 0.5772 0.718097
20 to 21 141704 -0.6057 0.272359
19 to 20 142023 0.3353 0.631304
18 to 19 141458 -1.3314 0.091536
17 to 18 142117 0.6126 0.729928
16 to 17 142318 1.2055 0.885998
15 to 16 141834 -0.2222 0.412074
14 to 15 142217 0.9076 0.817950
13 to 14 141716 -0.5703 0.284239
12 to 13 141751 -0.4671 0.320232
11 to 12 141243 -1.9656 0.024674
10 to 11 141582 -0.9656 0.167128
9 to 10 142507 1.7630 0.961053
8 to 9 141984 0.2203 0.587168
7 to 8 141544 -1.0777 0.140591
6 to 7 142055 0.4297 0.666295
5 to 6 141474 -1.2842 0.099543
4 to 5 142212 0.8928 0.814026
3 to 4 142038 0.3796 0.647863
2 to 3 141997 0.2586 0.602033
1 to 2 142033 0.3648 0.642373
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2517.15 0.243 0.595819
Test results for specific bytes for dh-ranFile-2018-06-28_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2517.46 0.247 0.597536
2 to 9 2565.93 0.932 0.824430
3 to 10 2331.80 -2.379 0.008687
4 to 11 2513.43 0.190 0.575319
5 to 12 2560.79 0.860 0.805024
6 to 13 2489.75 -0.145 0.442355
7 to 14 2427.87 -1.020 0.153846
8 to 15 2428.73 -1.008 0.156741
9 to 16 2508.16 0.115 0.545950
10 to 17 2580.30 1.136 0.871954
11 to 18 2454.50 -0.643 0.259952
12 to 19 2611.98 1.584 0.943369
13 to 20 2380.82 -1.685 0.045955
14 to 21 2293.56 -2.920 0.001753
15 to 22 2458.70 -0.584 0.279587
16 to 23 2575.82 1.072 0.858189
17 to 24 2409.12 -1.285 0.099347
18 to 25 2513.89 0.196 0.577840
19 to 26 2426.32 -1.042 0.148704
20 to 27 2386.34 -1.607 0.053986
21 to 28 2623.58 1.748 0.959736
22 to 29 2477.60 -0.317 0.375722
23 to 30 2561.87 0.875 0.809213
24 to 31 2397.42 -1.451 0.073439
25 to 32 2619.34 1.688 0.954269
CDPARK for dh-ranFile-2018-06-28_16:31: 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
3513 -0.4566 0.323972
3553 1.3699 0.914635
3508 -0.6849 0.246694
3503 -0.9132 0.180558
3504 -0.8676 0.192812
3537 0.6393 0.738676
3555 1.4612 0.928018
3498 -1.1416 0.126820
3523 0.0000 0.500000
3517 -0.2740 0.392053
Square side=100, avg. no. parked=3521.10 sample std.=19.57
p-value of the KSTEST for those 10 p-values: 0.708234
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_16:31
0.4399,0.6671,0.6408,0.8645,0.8025,0.2112,0.5713,0.1916,0.6581,0.3935,
The KS test for those 10 p-values: 0.629181
The 3DSPHERES test for dh-ranFile-2018-06-28_16:31
sample no r^3 equiv. uni.
1 131.974 0.987712
2 5.575 0.169576
3 14.510 0.383473
4 1.272 0.041508
5 40.253 0.738614
6 24.488 0.557919
7 18.811 0.465828
8 78.922 0.927974
9 15.804 0.409507
10 4.106 0.127927
11 20.242 0.490704
12 27.945 0.606035
13 8.509 0.246956
14 43.639 0.766516
15 19.766 0.482560
16 4.858 0.149489
17 41.081 0.745734
18 20.624 0.497147
19 44.661 0.774334
20 16.840 0.429549
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.886354
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.9 1.3 -1.7 0.1 1.6
-0.8 -0.6 1.2 -2.2 -0.5 0.0
0.1 -1.1 -1.2 0.5 -0.0 -0.8
0.4 1.8 -0.4 0.3 -0.5 1.2
0.3 2.5 -0.1 -0.7 -0.8 -0.3
0.8 -1.0 1.2 -0.6 0.2 1.5
-1.2 0.5 -0.4 -1.3 -0.6 0.0
1.8
Chi-square with 42 degrees of freedom:45.260045
z-score=0.355700, p-value=0.662485
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_16:31
Test no p-value
1 0.198049
2 0.004797
3 0.005504
4 0.068162
5 0.772051
6 0.019388
7 0.194553
8 0.219916
9 0.537551
10 0.504930
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002253
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_16:31:
(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 66531 0.28 66744 0.09
3 25000.00 25024 0.02 25045 0.08
4 6666.67 6739 0.78 6585 1.00
5 1388.89 1401 0.11 1356 0.78
6 238.10 254 1.06 227 0.52
7 34.72 44 2.48 34 0.01
8 4.96 6 0.22 8 1.86
p=0.44980 p=0.36994
Number of rngs required: 688175, p-value: 0.397
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_16:31
No. of wins: Observed Expected
98661 98585.9
z-score= 0.336, pvalue=0.63159
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66484 66666.7 0.501 0.501
2 37626 37654.3 0.021 0.522
3 26883 26954.7 0.191 0.713
4 19353 19313.5 0.081 0.794
5 13881 13851.4 0.063 0.857
6 9951 9943.5 0.006 0.862
7 7146 7145.0 0.000 0.863
8 5157 5139.1 0.063 0.925
9 3684 3699.9 0.068 0.993
10 2718 2666.3 1.003 1.996
11 2059 1923.3 9.570 11.566
12 1450 1388.7 2.702 14.268
13 1010 1003.7 0.039 14.307
14 718 726.1 0.091 14.399
15 494 525.8 1.927 16.326
16 381 381.2 0.000 16.326
17 265 276.5 0.482 16.808
18 206 200.8 0.133 16.941
19 147 146.0 0.007 16.948
20 93 106.2 1.644 18.592
21 294 287.1 0.165 18.757
Chisq= 18.76 for 20 degrees of freedom, p= 0.46235
SUMMARY of craptest
p-value for no. of wins: 0.631593
p-value for throws/game: 0.462353
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_16:31
No. of wins: Observed Expected
98651 98585.9
z-score= 0.291, pvalue=0.61461
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66501 66666.7 0.412 0.412
2 37843 37654.3 0.945 1.357
3 26946 26954.7 0.003 1.360
4 19396 19313.5 0.353 1.713
5 13852 13851.4 0.000 1.713
6 10016 9943.5 0.528 2.241
7 7080 7145.0 0.592 2.832
8 5155 5139.1 0.049 2.882
9 3648 3699.9 0.727 3.609
10 2655 2666.3 0.048 3.657
11 1951 1923.3 0.398 4.055
12 1326 1388.7 2.834 6.889
13 977 1003.7 0.711 7.600
14 718 726.1 0.091 7.692
15 542 525.8 0.497 8.189
16 373 381.2 0.174 8.363
17 300 276.5 1.990 10.353
18 193 200.8 0.305 10.658
19 123 146.0 3.619 14.277
20 105 106.2 0.014 14.291
21 300 287.1 0.578 14.869
Chisq= 14.87 for 20 degrees of freedom, p= 0.21617
SUMMARY of craptest
p-value for no. of wins: 0.614608
p-value for throws/game: 0.216168
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0023,0.0048,0.0055,0.0079,0.0084,0.0087,0.0114,0.0194,0.0215,
0.0247,0.0390,0.0415,0.0454,0.0460,0.0500,0.0540,0.0603,0.0682,0.0734,
0.0758,0.0780,0.0826,0.0915,0.0980,0.0993,0.0995,0.1045,0.1052,0.1061,
0.1135,0.1188,0.1268,0.1279,0.1329,0.1375,0.1401,0.1406,0.1487,0.1495,
0.1527,0.1538,0.1567,0.1671,0.1696,0.1696,0.1709,0.1806,0.1838,0.1915,
0.1916,0.1928,0.1931,0.1946,0.1980,0.1986,0.2059,0.2096,0.2112,0.2135,
0.2162,0.2169,0.2199,0.2229,0.2245,0.2467,0.2470,0.2600,0.2673,0.2705,
0.2724,0.2792,0.2792,0.2796,0.2842,0.2906,0.2992,0.3202,0.3207,0.3228,
0.3240,0.3266,0.3277,0.3306,0.3342,0.3388,0.3418,0.3442,0.3547,0.3648,
0.3699,0.3702,0.3757,0.3812,0.3830,0.3835,0.3853,0.3902,0.3921,0.3935,
0.3965,0.4012,0.4095,0.4104,0.4121,0.4182,0.4220,0.4295,0.4389,0.4399,
0.4424,0.4486,0.4498,0.4523,0.4624,0.4655,0.4658,0.4669,0.4680,0.4690,
0.4826,0.4907,0.4970,0.4971,0.4971,0.5000,0.5049,0.5071,0.5153,0.5170,
0.5199,0.5267,0.5278,0.5298,0.5375,0.5376,0.5389,0.5441,0.5459,0.5503,
0.5579,0.5639,0.5713,0.5753,0.5766,0.5778,0.5800,0.5872,0.5894,0.5907,
0.5958,0.5963,0.5975,0.6012,0.6020,0.6056,0.6060,0.6064,0.6109,0.6146,
0.6173,0.6212,0.6263,0.6292,0.6301,0.6313,0.6316,0.6336,0.6408,0.6424,
0.6428,0.6448,0.6450,0.6461,0.6462,0.6475,0.6479,0.6486,0.6501,0.6528,
0.6581,0.6625,0.6663,0.6671,0.6729,0.6748,0.6903,0.6953,0.6988,0.7009,
0.7066,0.7067,0.7082,0.7115,0.7127,0.7178,0.7181,0.7185,0.7225,0.7265,
0.7299,0.7366,0.7386,0.7387,0.7390,0.7457,0.7486,0.7489,0.7559,0.7665,
0.7721,0.7743,0.7767,0.7799,0.7888,0.7898,0.7975,0.7976,0.8005,0.8025,
0.8050,0.8051,0.8092,0.8123,0.8140,0.8166,0.8180,0.8223,0.8244,0.8299,
0.8528,0.8556,0.8582,0.8593,0.8645,0.8703,0.8717,0.8720,0.8766,0.8806,
0.8817,0.8841,0.8860,0.8864,0.8868,0.8943,0.8980,0.9038,0.9146,0.9154,
0.9181,0.9280,0.9280,0.9296,0.9298,0.9319,0.9361,0.9427,0.9434,0.9517,
0.9543,0.9597,0.9611,0.9704,0.9710,0.9761,0.9807,0.9877,0.9930,
Overall p-value after applying KStest on 269 p-values = 0.595484
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.