RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_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 15.77 26.5037 0.934240
2 to 25 15.93 17.9072 0.605283
3 to 26 15.57 14.9785 0.402969
4 to 27 15.75 17.9090 0.605397
5 to 28 15.69 16.2511 0.493889
6 to 29 15.46 27.8585 0.953381
7 to 30 15.87 17.5746 0.583861
8 to 31 15.88 25.6550 0.919020
9 to 32 15.84 16.3199 0.498716
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.085416
Tough bday spacings test for dh-ranFile-2018-07-06_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 33 92 93 85 78 63 32 11 3 2
(O-E)^2/E 0.1 0.4 4.8 0.2 1.6 0.0 2.3 0.2 1.0 2.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 13.659, p= 0.811
RESULTS OF GCD FOR dh-ranFile-2018-07-06_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.919321
p-value, dist. of gcd's: 0.138114
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.632 0.771 0.259 0.200 0.401 0.773 0.775 0.113
Bits 8 to 15---> 0.976 0.294 0.887 0.010 0.135 0.318 0.517 0.198
Bits 16 to 23---> 0.690 0.774 0.143 0.906 0.375 0.176 0.165 0.541
Bits 24 to 31---> 0.058 0.421 0.098 0.563 0.272 0.903 0.832 0.208
KS test for the above 32 p values: 0.530
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_21:31,
p-values for 5 runs: 0.7778, 0.6892, 0.8505, 0.9925, 0.6117
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 217 211.4 0.147 0.147
r= 29 5164 5134.0 0.175 0.323
r= 30 23002 23103.0 0.442 0.765
r= 31 11617 11551.5 0.371 1.136
chi-square = 1.136 with df = 3; p-value = 0.232
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5032 5134.0 2.027 2.232
r= 31 23128 23103.0 0.027 2.259
r= 32 11622 11551.5 0.430 2.689
chi-square = 2.689 with df = 3; p-value = 0.558
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_21:31
b-rank test for bits 1 to 8, p=0.58806
b-rank test for bits 2 to 9, p=0.20400
b-rank test for bits 3 to 10, p=0.30699
b-rank test for bits 4 to 11, p=0.01188
b-rank test for bits 5 to 12, p=0.51048
b-rank test for bits 6 to 13, p=0.52499
b-rank test for bits 7 to 14, p=0.28219
b-rank test for bits 8 to 15, p=0.88151
b-rank test for bits 9 to 16, p=0.45189
b-rank test for bits 10 to 17, p=0.97599
b-rank test for bits 11 to 18, p=0.63812
b-rank test for bits 12 to 19, p=0.79432
b-rank test for bits 13 to 20, p=0.27989
b-rank test for bits 14 to 21, p=0.86954
b-rank test for bits 15 to 22, p=0.84725
b-rank test for bits 16 to 23, p=0.57275
b-rank test for bits 17 to 24, p=0.20038
b-rank test for bits 18 to 25, p=0.47976
b-rank test for bits 19 to 26, p=0.57209
b-rank test for bits 20 to 27, p=0.03067
b-rank test for bits 21 to 28, p=0.68992
b-rank test for bits 22 to 29, p=0.22333
b-rank test for bits 23 to 30, p=0.65040
b-rank test for bits 24 to 31, p=0.70779
b-rank test for bits 25 to 32, p=0.96380
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 = 0.850059
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_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 142051 0.33 0.629680
2 142167 0.60 0.726424
3 143498 3.71 0.999897
4 142405 1.16 0.876590
5 142031 0.28 0.611900
6 142302 0.92 0.820547
7 141638 -0.63 0.263057
8 142001 0.21 0.584798
9 142074 0.38 0.649786
10 142451 1.27 0.897169
11 141873 -0.08 0.466177
12 141442 -1.09 0.137440
13 141911 0.00 0.501557
14 141606 -0.71 0.239251
15 141206 -1.64 0.050161
16 141505 -0.94 0.172407
17 142165 0.60 0.724866
18 141467 -1.03 0.150689
19 141661 -0.58 0.280886
20 142177 0.63 0.734145
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_21:31
Bits used No. missing words z-score p-value
23 to 32 141581 -1.1322 0.128781
22 to 31 141661 -0.8563 0.195913
21 to 30 141837 -0.2494 0.401520
20 to 29 142074 0.5678 0.714924
19 to 28 141290 -2.1356 0.016355
18 to 27 141992 0.2851 0.612204
17 to 26 141834 -0.2598 0.397525
16 to 25 142413 1.7368 0.958788
15 to 24 141861 -0.1667 0.433821
14 to 23 141537 -1.2839 0.099589
13 to 22 141883 -0.0908 0.463829
12 to 21 141826 -0.2873 0.386924
11 to 20 142120 0.7264 0.766218
10 to 19 142175 0.9161 0.820194
9 to 18 142189 0.9644 0.832572
8 to 17 141958 0.1678 0.566641
7 to 16 142118 0.7196 0.764100
6 to 15 141789 -0.4149 0.339096
5 to 14 141779 -0.4494 0.326567
4 to 13 141857 -0.1804 0.428400
3 to 12 141402 -1.7494 0.040110
2 to 11 142047 0.4747 0.682508
1 to 10 141780 -0.4460 0.327811
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_21:31
Bits used No. missing words z-score p-value
28 to 32 142352 1.5006 0.933267
27 to 31 142120 0.7141 0.762428
26 to 30 142139 0.7785 0.781875
25 to 29 142218 1.0463 0.852298
24 to 28 142153 0.8260 0.795598
23 to 27 141884 -0.0859 0.465787
22 to 26 141815 -0.3198 0.374574
21 to 25 142121 0.7175 0.763475
20 to 24 141655 -0.8621 0.194306
19 to 23 141752 -0.5333 0.296905
18 to 22 142050 0.4768 0.683265
17 to 21 142418 1.7243 0.957674
16 to 20 142115 0.6972 0.757157
15 to 19 142092 0.6192 0.732114
14 to 18 141762 -0.4994 0.308741
13 to 17 141901 -0.0282 0.488737
12 to 16 142074 0.5582 0.711647
11 to 15 142135 0.7650 0.777859
10 to 14 141801 -0.3672 0.356727
9 to 13 141872 -0.1265 0.449651
8 to 12 141680 -0.7774 0.218464
7 to 11 141865 -0.1503 0.440275
6 to 10 141927 0.0599 0.523882
5 to 9 142244 1.1345 0.871702
4 to 8 142081 0.5819 0.719694
3 to 7 142239 1.1175 0.868115
2 to 6 141643 -0.9028 0.183312
1 to 5 141939 0.1006 0.540057
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_21:31
Bits used No. missing words z-score p-value
31 to 32 141856 -0.1573 0.437498
30 to 31 142224 0.9282 0.823356
29 to 30 141437 -1.3933 0.081764
28 to 29 141863 -0.1367 0.445647
27 to 28 141722 -0.5526 0.290270
26 to 27 141784 -0.3697 0.355801
25 to 26 141709 -0.5909 0.277279
24 to 25 141985 0.2232 0.588316
23 to 24 141961 0.1524 0.560572
22 to 23 141427 -1.4228 0.077397
21 to 22 142245 0.9902 0.838956
20 to 21 142076 0.4917 0.688517
19 to 20 141849 -0.1780 0.429375
18 to 19 141690 -0.6470 0.258819
17 to 18 142212 0.8928 0.814026
16 to 17 141683 -0.6676 0.252182
15 to 16 142054 0.4268 0.665221
14 to 15 141851 -0.1721 0.431693
13 to 14 141787 -0.3609 0.359104
12 to 13 141814 -0.2812 0.389275
11 to 12 142266 1.0521 0.853629
10 to 11 141247 -1.9538 0.025364
9 to 10 141454 -1.3432 0.089611
8 to 9 141767 -0.4199 0.337297
7 to 8 141792 -0.3461 0.364632
6 to 7 142185 0.8132 0.791944
5 to 6 141919 0.0285 0.511378
4 to 5 141202 -2.0865 0.018466
3 to 4 141880 -0.0865 0.465527
2 to 3 142292 1.1288 0.870513
1 to 2 142096 0.5506 0.709063
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2547.83 0.676 0.750622
Test results for specific bytes for dh-ranFile-2018-07-06_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2448.47 -0.729 0.233088
2 to 9 2594.97 1.343 0.910371
3 to 10 2533.94 0.480 0.684390
4 to 11 2402.62 -1.377 0.084238
5 to 12 2457.63 -0.599 0.274517
6 to 13 2403.94 -1.359 0.087150
7 to 14 2350.49 -2.114 0.017241
8 to 15 2503.93 0.056 0.522149
9 to 16 2537.34 0.528 0.701273
10 to 17 2503.60 0.051 0.520302
11 to 18 2527.78 0.393 0.652778
12 to 19 2604.91 1.484 0.931053
13 to 20 2529.08 0.411 0.659558
14 to 21 2475.04 -0.353 0.362073
15 to 22 2505.90 0.083 0.533226
16 to 23 2391.11 -1.540 0.061794
17 to 24 2493.06 -0.098 0.460935
18 to 25 2417.27 -1.170 0.121004
19 to 26 2570.64 0.999 0.841111
20 to 27 2529.76 0.421 0.663057
21 to 28 2403.49 -1.365 0.086158
22 to 29 2468.30 -0.448 0.326969
23 to 30 2441.71 -0.824 0.204886
24 to 31 2409.64 -1.278 0.100634
25 to 32 2544.92 0.635 0.737375
CDPARK for dh-ranFile-2018-07-06_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
3534 0.5023 0.692266
3495 -1.2785 0.100530
3515 -0.3653 0.357445
3516 -0.3196 0.374623
3566 1.9635 0.975204
3511 -0.5479 0.291865
3517 -0.2740 0.392053
3483 -1.8265 0.033889
3512 -0.5023 0.307734
3539 0.7306 0.767486
Square side=100, avg. no. parked=3518.80 sample std.=22.02
p-value of the KSTEST for those 10 p-values: 0.614391
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_21:31
0.8659,0.8460,0.9065,0.3851,0.4499,0.1348,0.4668,0.5389,0.8948,0.3239,
The KS test for those 10 p-values: 0.472789
The 3DSPHERES test for dh-ranFile-2018-07-06_21:31
sample no r^3 equiv. uni.
1 7.922 0.232087
2 28.843 0.617651
3 10.012 0.283761
4 12.609 0.343145
5 67.547 0.894767
6 68.283 0.897317
7 10.015 0.283817
8 4.835 0.148838
9 1.742 0.056417
10 33.647 0.674230
11 13.926 0.371354
12 34.060 0.678680
13 135.425 0.989047
14 2.482 0.079416
15 21.277 0.507978
16 41.042 0.745400
17 43.927 0.768746
18 34.800 0.686512
19 10.316 0.290970
20 105.331 0.970134
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.902638
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 -0.8 -1.3 2.1 -0.4
-0.4 1.1 -0.8 -0.3 -0.8 -2.1
-0.9 0.6 1.2 -1.1 0.3 -0.5
0.6 -0.8 0.3 0.1 1.0 0.3
-0.0 2.1 -1.2 -0.2 -1.0 1.2
2.2 1.8 -0.3 1.8 0.3 -1.0
-0.5 0.5 -0.4 0.4 -1.3 1.0
-0.1
Chi-square with 42 degrees of freedom:45.389024
z-score=0.369773, p-value=0.667353
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_21:31
Test no p-value
1 0.687674
2 0.015270
3 0.921287
4 0.036932
5 0.029860
6 0.841846
7 0.818688
8 0.038815
9 0.039005
10 0.452817
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.012620
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_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 66614 0.04 66305 1.96
3 25000.00 25066 0.17 25214 1.83
4 6666.67 6610 0.48 6839 4.45
5 1388.89 1445 2.27 1361 0.56
6 238.10 222 1.09 242 0.06
7 34.72 36 0.05 36 0.05
8 4.96 6 0.22 2 1.77
p=0.36623 p=0.90143
Number of rngs required: 688828, p-value: 0.688
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_21:31
No. of wins: Observed Expected
98796 98585.9
z-score= 0.940, pvalue=0.82636
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66212 66666.7 3.101 3.101
2 37712 37654.3 0.088 3.189
3 26974 26954.7 0.014 3.203
4 19510 19313.5 2.000 5.203
5 13945 13851.4 0.632 5.835
6 9928 9943.5 0.024 5.859
7 7259 7145.0 1.818 7.678
8 5158 5139.1 0.070 7.747
9 3656 3699.9 0.520 8.267
10 2716 2666.3 0.927 9.194
11 1969 1923.3 1.084 10.278
12 1369 1388.7 0.281 10.559
13 981 1003.7 0.514 11.073
14 708 726.1 0.453 11.526
15 518 525.8 0.117 11.643
16 341 381.2 4.229 15.872
17 280 276.5 0.043 15.916
18 203 200.8 0.023 15.939
19 150 146.0 0.110 16.050
20 125 106.2 3.322 19.372
21 286 287.1 0.004 19.376
Chisq= 19.38 for 20 degrees of freedom, p= 0.50249
SUMMARY of craptest
p-value for no. of wins: 0.826359
p-value for throws/game: 0.502490
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_21:31
No. of wins: Observed Expected
98758 98585.9
z-score= 0.770, pvalue=0.77933
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66657 66666.7 0.001 0.001
2 37802 37654.3 0.579 0.581
3 26793 26954.7 0.970 1.551
4 19445 19313.5 0.896 2.447
5 13866 13851.4 0.015 2.462
6 9990 9943.5 0.217 2.679
7 7076 7145.0 0.667 3.346
8 5084 5139.1 0.590 3.936
9 3642 3699.9 0.905 4.841
10 2719 2666.3 1.042 5.883
11 1909 1923.3 0.107 5.990
12 1339 1388.7 1.782 7.771
13 1023 1003.7 0.371 8.142
14 701 726.1 0.870 9.012
15 526 525.8 0.000 9.012
16 377 381.2 0.045 9.058
17 299 276.5 1.824 10.882
18 211 200.8 0.515 11.397
19 145 146.0 0.007 11.403
20 109 106.2 0.073 11.476
21 287 287.1 0.000 11.476
Chisq= 11.48 for 20 degrees of freedom, p= 0.06708
SUMMARY of craptest
p-value for no. of wins: 0.779325
p-value for throws/game: 0.067081
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0101,0.0119,0.0126,0.0153,0.0164,0.0172,0.0185,0.0254,0.0299,0.0307,
0.0339,0.0369,0.0388,0.0390,0.0401,0.0502,0.0564,0.0580,0.0618,0.0671,
0.0774,0.0794,0.0818,0.0842,0.0854,0.0862,0.0872,0.0896,0.0978,0.0996,
0.1005,0.1006,0.1132,0.1210,0.1288,0.1348,0.1350,0.1374,0.1381,0.1432,
0.1488,0.1507,0.1647,0.1724,0.1757,0.1833,0.1943,0.1959,0.1980,0.1999,
0.2004,0.2040,0.2049,0.2076,0.2185,0.2233,0.2315,0.2321,0.2331,0.2393,
0.2522,0.2588,0.2592,0.2631,0.2716,0.2745,0.2773,0.2799,0.2809,0.2822,
0.2838,0.2838,0.2903,0.2910,0.2919,0.2938,0.2969,0.3070,0.3077,0.3087,
0.3176,0.3239,0.3266,0.3270,0.3278,0.3373,0.3391,0.3431,0.3558,0.3567,
0.3574,0.3591,0.3621,0.3646,0.3662,0.3714,0.3746,0.3746,0.3747,0.3851,
0.3869,0.3893,0.3921,0.3975,0.4005,0.4015,0.4030,0.4205,0.4284,0.4294,
0.4317,0.4338,0.4375,0.4403,0.4456,0.4497,0.4499,0.4519,0.4528,0.4609,
0.4638,0.4655,0.4658,0.4662,0.4668,0.4728,0.4798,0.4887,0.4939,0.4987,
0.5016,0.5025,0.5080,0.5105,0.5114,0.5173,0.5203,0.5221,0.5239,0.5250,
0.5300,0.5332,0.5389,0.5401,0.5413,0.5579,0.5606,0.5630,0.5666,0.5721,
0.5727,0.5839,0.5848,0.5881,0.5883,0.6053,0.6054,0.6117,0.6119,0.6122,
0.6144,0.6177,0.6297,0.6323,0.6381,0.6498,0.6504,0.6528,0.6596,0.6631,
0.6652,0.6674,0.6742,0.6787,0.6825,0.6833,0.6844,0.6865,0.6877,0.6878,
0.6885,0.6892,0.6899,0.6900,0.6923,0.7013,0.7078,0.7091,0.7116,0.7149,
0.7197,0.7249,0.7264,0.7321,0.7341,0.7374,0.7454,0.7506,0.7572,0.7624,
0.7635,0.7641,0.7662,0.7675,0.7687,0.7711,0.7731,0.7741,0.7753,0.7778,
0.7779,0.7793,0.7819,0.7919,0.7943,0.7956,0.8109,0.8140,0.8187,0.8202,
0.8205,0.8234,0.8264,0.8320,0.8326,0.8390,0.8411,0.8418,0.8460,0.8472,
0.8501,0.8505,0.8523,0.8536,0.8659,0.8681,0.8695,0.8705,0.8717,0.8766,
0.8815,0.8874,0.8948,0.8948,0.8972,0.8973,0.9014,0.9026,0.9034,0.9057,
0.9065,0.9104,0.9190,0.9193,0.9213,0.9311,0.9333,0.9342,0.9534,0.9577,
0.9588,0.9638,0.9701,0.9752,0.9755,0.9760,0.9890,0.9925,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.801057
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.