RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_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 15.90 15.3397 0.428971
2 to 25 15.85 22.6262 0.838181
3 to 26 16.05 14.9322 0.399637
4 to 27 15.93 8.7874 0.053303
5 to 28 15.90 18.8940 0.665347
6 to 29 15.97 7.5387 0.024557
7 to 30 16.04 21.7659 0.806109
8 to 31 16.12 13.0720 0.268644
9 to 32 15.83 19.7081 0.710566
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.821838
Tough bday spacings test for dh-ranFile-2018-07-06_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 12 39 73 98 93 74 49 35 20 2 5
(O-E)^2/E 0.9 0.2 0.0 0.0 0.2 0.2 0.2 0.9 1.8 3.2 0.2
Birthday Spacings: Sum(O-E)^2/E= 7.777, p= 0.349
RESULTS OF GCD FOR dh-ranFile-2018-07-06_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.931965
p-value, dist. of gcd's: 0.943745
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.945 0.353 0.307 0.126 0.896 0.343 0.357 0.941
Bits 8 to 15---> 0.527 0.673 0.459 0.265 0.313 0.218 0.433 0.392
Bits 16 to 23---> 0.732 0.545 0.095 0.001 0.073 0.783 0.941 0.449
Bits 24 to 31---> 0.765 0.154 0.654 0.163 0.904 0.093 0.814 0.889
KS test for the above 32 p values: 0.105
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_16:31,
p-values for 5 runs: 0.0240, 0.0561, 0.0279, 0.6558, 0.7660
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 223 211.4 0.634 0.634
r= 29 5143 5134.0 0.016 0.650
r= 30 23183 23103.0 0.277 0.927
r= 31 11451 11551.5 0.875 1.802
chi-square = 1.802 with df = 3; p-value = 0.385
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5240 5134.0 2.188 2.460
r= 31 23001 23103.0 0.451 2.911
r= 32 11540 11551.5 0.011 2.922
chi-square = 2.922 with df = 3; p-value = 0.596
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_16:31
b-rank test for bits 1 to 8, p=0.30707
b-rank test for bits 2 to 9, p=0.93745
b-rank test for bits 3 to 10, p=0.95729
b-rank test for bits 4 to 11, p=0.60423
b-rank test for bits 5 to 12, p=0.39207
b-rank test for bits 6 to 13, p=0.41846
b-rank test for bits 7 to 14, p=0.67047
b-rank test for bits 8 to 15, p=0.13384
b-rank test for bits 9 to 16, p=0.16393
b-rank test for bits 10 to 17, p=0.55019
b-rank test for bits 11 to 18, p=0.29776
b-rank test for bits 12 to 19, p=0.06350
b-rank test for bits 13 to 20, p=0.98182
b-rank test for bits 14 to 21, p=0.49408
b-rank test for bits 15 to 22, p=0.46621
b-rank test for bits 16 to 23, p=0.62860
b-rank test for bits 17 to 24, p=0.44084
b-rank test for bits 18 to 25, p=0.42825
b-rank test for bits 19 to 26, p=0.49703
b-rank test for bits 20 to 27, p=0.60922
b-rank test for bits 21 to 28, p=0.08832
b-rank test for bits 22 to 29, p=0.88789
b-rank test for bits 23 to 30, p=0.44564
b-rank test for bits 24 to 31, p=0.28946
b-rank test for bits 25 to 32, p=0.94078
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 = 0.593979
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_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 142048 0.32 0.627029
2 142049 0.33 0.627913
3 142170 0.61 0.728752
4 140974 -2.19 0.014432
5 140604 -3.05 0.001145
6 141402 -1.19 0.117939
7 141827 -0.19 0.423730
8 142496 1.37 0.914770
9 142163 0.59 0.723305
10 141161 -1.75 0.040194
11 141804 -0.25 0.402803
12 141405 -1.18 0.119330
13 141790 -0.28 0.390196
14 141756 -0.36 0.360079
15 142433 1.22 0.889435
16 141907 -0.01 0.497828
17 141689 -0.51 0.303350
18 141808 -0.24 0.406425
19 140695 -2.84 0.002275
20 141446 -1.08 0.139505
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_16:31
Bits used No. missing words z-score p-value
23 to 32 141471 -1.5115 0.065333
22 to 31 141741 -0.5804 0.280806
21 to 30 141504 -1.3977 0.081103
20 to 29 141759 -0.5184 0.302097
19 to 28 141592 -1.0942 0.136925
18 to 27 141921 0.0402 0.516050
17 to 26 142097 0.6471 0.741229
16 to 25 141761 -0.5115 0.304507
15 to 24 141779 -0.4494 0.326567
14 to 23 142534 2.1540 0.984381
13 to 22 142081 0.5920 0.723063
12 to 21 142452 1.8713 0.969347
11 to 20 141465 -1.5322 0.062740
10 to 19 141639 -0.9322 0.175624
9 to 18 141629 -0.9667 0.166858
8 to 17 141928 0.0644 0.525666
7 to 16 141737 -0.5942 0.276175
6 to 15 141923 0.0471 0.518798
5 to 14 141551 -1.2356 0.108300
4 to 13 141866 -0.1494 0.440614
3 to 12 141832 -0.2667 0.394867
2 to 11 142014 0.3609 0.640925
1 to 10 141818 -0.3149 0.376407
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_16:31
Bits used No. missing words z-score p-value
28 to 32 141763 -0.4960 0.309935
27 to 31 141417 -1.6689 0.047567
26 to 30 141819 -0.3062 0.379725
25 to 29 141658 -0.8520 0.197116
24 to 28 141949 0.1345 0.553486
23 to 27 141999 0.3040 0.619423
22 to 26 142303 1.3345 0.908976
21 to 25 141328 -1.9706 0.024384
20 to 24 142063 0.5209 0.698787
19 to 23 141944 0.1175 0.546778
18 to 22 141689 -0.7469 0.227568
17 to 21 142018 0.3684 0.643702
16 to 20 142088 0.6057 0.727630
15 to 19 142250 1.1548 0.875917
14 to 18 141364 -1.8486 0.032260
13 to 17 141637 -0.9232 0.177964
12 to 16 142459 1.8633 0.968789
11 to 15 142380 1.5955 0.944699
10 to 14 141338 -1.9367 0.026390
9 to 13 141787 -0.4147 0.339189
8 to 12 141544 -1.2384 0.107783
7 to 11 141777 -0.4486 0.326869
6 to 10 141907 -0.0079 0.496849
5 to 9 142004 0.3209 0.625863
4 to 8 141546 -1.2316 0.109044
3 to 7 142122 0.7209 0.764519
2 to 6 141569 -1.1537 0.124320
1 to 5 142527 2.0938 0.981861
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_16:31
Bits used No. missing words z-score p-value
31 to 32 141840 -0.2045 0.418976
30 to 31 142109 0.5890 0.722068
29 to 30 142138 0.6745 0.750017
28 to 29 141458 -1.3314 0.091536
27 to 28 142163 0.7483 0.772857
26 to 27 142314 1.1937 0.883706
25 to 26 142121 0.6244 0.733816
24 to 25 142350 1.2999 0.903184
23 to 24 142514 1.7837 0.962763
22 to 23 142251 1.0079 0.843243
21 to 22 141640 -0.7945 0.213457
20 to 21 141801 -0.3196 0.374652
19 to 20 141841 -0.2016 0.420129
18 to 19 141702 -0.6116 0.270404
17 to 18 142348 1.2940 0.902169
16 to 17 142049 0.4120 0.659832
15 to 16 141526 -1.1308 0.129077
14 to 15 142007 0.2881 0.613370
13 to 14 141821 -0.2606 0.397216
12 to 13 141911 0.0049 0.501965
11 to 12 141567 -1.0098 0.156290
10 to 11 142106 0.5801 0.719092
9 to 10 141437 -1.3933 0.081764
8 to 9 141902 -0.0216 0.491375
7 to 8 142111 0.5949 0.724044
6 to 7 141403 -1.4936 0.067640
5 to 6 141615 -0.8682 0.192634
4 to 5 141702 -0.6116 0.270404
3 to 4 141969 0.1760 0.569860
2 to 3 141984 0.2203 0.587168
1 to 2 142030 0.3560 0.639064
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2543.02 0.608 0.728543
Test results for specific bytes for dh-ranFile-2018-07-06_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2440.28 -0.845 0.199176
2 to 9 2520.19 0.286 0.612375
3 to 10 2563.56 0.899 0.815634
4 to 11 2501.09 0.015 0.506141
5 to 12 2587.83 1.242 0.892911
6 to 13 2625.02 1.768 0.961473
7 to 14 2503.88 0.055 0.521872
8 to 15 2592.77 1.312 0.905232
9 to 16 2454.34 -0.646 0.259235
10 to 17 2391.45 -1.535 0.062374
11 to 18 2469.50 -0.431 0.333135
12 to 19 2515.12 0.214 0.584674
13 to 20 2356.08 -2.035 0.020907
14 to 21 2546.47 0.657 0.744492
15 to 22 2366.19 -1.892 0.029221
16 to 23 2510.13 0.143 0.556971
17 to 24 2558.88 0.833 0.797507
18 to 25 2480.75 -0.272 0.392702
19 to 26 2479.86 -0.285 0.387903
20 to 27 2434.37 -0.928 0.176672
21 to 28 2439.34 -0.858 0.195482
22 to 29 2428.86 -1.006 0.157177
23 to 30 2529.06 0.411 0.659434
24 to 31 2445.64 -0.769 0.221033
25 to 32 2455.73 -0.626 0.265643
CDPARK for dh-ranFile-2018-07-06_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
3542 0.8676 0.807188
3500 -1.0502 0.146807
3558 1.5982 0.944998
3550 1.2329 0.891189
3505 -0.8219 0.205562
3502 -0.9589 0.168804
3475 -2.1918 0.014198
3565 1.9178 0.972432
3529 0.2740 0.607947
3545 1.0046 0.842447
Square side=100, avg. no. parked=3527.10 sample std.=28.34
p-value of the KSTEST for those 10 p-values: 0.251514
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_16:31
0.8239,0.0012,0.5869,0.4139,0.8939,0.5148,0.2417,0.5490,0.0266,0.7232,
The KS test for those 10 p-values: 0.523097
The 3DSPHERES test for dh-ranFile-2018-07-06_16:31
sample no r^3 equiv. uni.
1 17.119 0.434826
2 61.263 0.870242
3 12.019 0.330095
4 6.517 0.195247
5 31.570 0.650881
6 15.619 0.405865
7 35.950 0.698305
8 28.203 0.609406
9 27.700 0.602812
10 31.417 0.649092
11 35.201 0.690672
12 14.155 0.376151
13 26.413 0.585395
14 44.405 0.772403
15 11.626 0.321277
16 33.477 0.672376
17 10.147 0.286967
18 176.647 0.997228
19 15.708 0.407618
20 50.484 0.814145
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.164655
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.6 2.3 0.3 -0.6 0.1
1.0 1.6 -0.3 1.9 0.8 1.2
-1.3 0.2 -1.6 0.2 0.4 -0.1
1.4 0.3 -0.5 0.2 -0.2 -1.9
-0.1 -0.4 -0.8 -1.1 -1.1 -1.1
2.9 -0.4 0.7 0.9 0.6 -0.7
-0.2 -1.3 -0.8 -0.1 -1.3 0.0
-0.1
Chi-square with 42 degrees of freedom:47.282027
z-score=0.576316, p-value=0.734303
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_16:31
Test no p-value
1 0.452026
2 0.013144
3 0.784273
4 0.003027
5 0.572414
6 0.644109
7 0.378133
8 0.016319
9 0.166491
10 0.265899
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.030799
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_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 66935 1.08 66521 0.32
3 25000.00 24739 2.72 25041 0.07
4 6666.67 6668 0.00 6768 1.54
5 1388.89 1396 0.04 1404 0.16
6 238.10 223 0.96 225 0.72
7 34.72 29 0.94 35 0.00
8 4.96 9 3.29 5 0.00
p=0.82819 p=0.16806
Number of rngs required: 687472, p-value: 0.140
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_16:31
No. of wins: Observed Expected
98741 98585.9
z-score= 0.694, pvalue=0.75612
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66780 66666.7 0.193 0.193
2 37899 37654.3 1.590 1.783
3 26769 26954.7 1.280 3.062
4 19317 19313.5 0.001 3.063
5 13931 13851.4 0.457 3.520
6 9841 9943.5 1.057 4.578
7 7170 7145.0 0.087 4.665
8 5082 5139.1 0.634 5.299
9 3696 3699.9 0.004 5.303
10 2623 2666.3 0.703 6.006
11 1891 1923.3 0.543 6.549
12 1396 1388.7 0.038 6.587
13 958 1003.7 2.082 8.669
14 762 726.1 1.771 10.440
15 504 525.8 0.907 11.347
16 393 381.2 0.368 11.715
17 261 276.5 0.873 12.589
18 182 200.8 1.765 14.354
19 148 146.0 0.028 14.382
20 113 106.2 0.433 14.815
21 284 287.1 0.034 14.849
Chisq= 14.85 for 20 degrees of freedom, p= 0.21503
SUMMARY of craptest
p-value for no. of wins: 0.756122
p-value for throws/game: 0.215028
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_16:31
No. of wins: Observed Expected
98628 98585.9
z-score= 0.188, pvalue=0.57475
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66316 66666.7 1.845 1.845
2 37962 37654.3 2.514 4.359
3 26778 26954.7 1.159 5.517
4 19340 19313.5 0.036 5.554
5 14024 13851.4 2.150 7.704
6 9854 9943.5 0.806 8.510
7 7095 7145.0 0.350 8.861
8 5146 5139.1 0.009 8.870
9 3828 3699.9 4.438 13.308
10 2685 2666.3 0.131 13.439
11 1963 1923.3 0.818 14.257
12 1396 1388.7 0.038 14.295
13 993 1003.7 0.114 14.409
14 711 726.1 0.316 14.725
15 516 525.8 0.184 14.909
16 381 381.2 0.000 14.909
17 307 276.5 3.355 18.264
18 200 200.8 0.003 18.268
19 146 146.0 0.000 18.268
20 118 106.2 1.308 19.575
21 241 287.1 7.406 26.982
Chisq= 26.98 for 20 degrees of freedom, p= 0.86422
SUMMARY of craptest
p-value for no. of wins: 0.574750
p-value for throws/game: 0.864223
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0012,0.0014,0.0023,0.0030,0.0131,0.0142,0.0144,0.0163,0.0209,
0.0240,0.0244,0.0246,0.0264,0.0266,0.0279,0.0292,0.0308,0.0323,0.0402,
0.0476,0.0533,0.0561,0.0624,0.0627,0.0635,0.0653,0.0676,0.0725,0.0811,
0.0818,0.0883,0.0915,0.0927,0.0947,0.1046,0.1078,0.1083,0.1090,0.1179,
0.1193,0.1243,0.1261,0.1291,0.1338,0.1369,0.1395,0.1401,0.1468,0.1537,
0.1563,0.1572,0.1626,0.1639,0.1647,0.1665,0.1669,0.1681,0.1688,0.1756,
0.1767,0.1780,0.1926,0.1952,0.1955,0.1971,0.1992,0.2056,0.2135,0.2150,
0.2184,0.2210,0.2276,0.2417,0.2515,0.2592,0.2648,0.2656,0.2659,0.2686,
0.2704,0.2704,0.2762,0.2808,0.2870,0.2895,0.2978,0.3021,0.3034,0.3045,
0.3071,0.3075,0.3099,0.3129,0.3213,0.3266,0.3269,0.3301,0.3331,0.3392,
0.3429,0.3494,0.3532,0.3573,0.3601,0.3747,0.3762,0.3764,0.3781,0.3797,
0.3854,0.3879,0.3902,0.3921,0.3925,0.3927,0.3949,0.3972,0.3996,0.4028,
0.4059,0.4064,0.4076,0.4139,0.4185,0.4190,0.4201,0.4237,0.4283,0.4290,
0.4331,0.4348,0.4406,0.4408,0.4456,0.4486,0.4520,0.4593,0.4662,0.4914,
0.4941,0.4968,0.4970,0.4978,0.5020,0.5061,0.5148,0.5160,0.5188,0.5219,
0.5231,0.5257,0.5266,0.5449,0.5468,0.5490,0.5502,0.5535,0.5570,0.5699,
0.5724,0.5748,0.5847,0.5854,0.5869,0.5872,0.5940,0.5962,0.6028,0.6042,
0.6079,0.6092,0.6094,0.6124,0.6134,0.6194,0.6259,0.6270,0.6279,0.6286,
0.6391,0.6409,0.6437,0.6441,0.6491,0.6509,0.6544,0.6558,0.6594,0.6598,
0.6653,0.6705,0.6724,0.6726,0.6907,0.6983,0.6988,0.7106,0.7191,0.7221,
0.7231,0.7232,0.7233,0.7240,0.7276,0.7285,0.7288,0.7320,0.7338,0.7343,
0.7412,0.7445,0.7500,0.7561,0.7645,0.7653,0.7660,0.7724,0.7729,0.7834,
0.7843,0.7975,0.8061,0.8072,0.8141,0.8143,0.8156,0.8218,0.8239,0.8282,
0.8382,0.8424,0.8432,0.8642,0.8702,0.8759,0.8837,0.8879,0.8887,0.8894,
0.8912,0.8929,0.8939,0.8960,0.9022,0.9032,0.9043,0.9052,0.9090,0.9148,
0.9320,0.9375,0.9407,0.9408,0.9409,0.9437,0.9447,0.9450,0.9452,0.9573,
0.9615,0.9628,0.9688,0.9693,0.9724,0.9818,0.9819,0.9844,0.9972,
Overall p-value after applying KStest on 269 p-values = 0.114388
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.