RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_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 19.6498 0.707469
2 to 25 15.70 13.2488 0.280621
3 to 26 15.84 18.2583 0.627279
4 to 27 15.94 17.1715 0.557195
5 to 28 16.00 22.2630 0.825185
6 to 29 15.88 20.9099 0.769652
7 to 30 15.59 22.7623 0.842849
8 to 31 15.97 21.5582 0.797688
9 to 32 15.77 21.5311 0.796571
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.040737
Tough bday spacings test for dh-ranFile-2018-06-27_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 14 36 73 97 106 71 53 19 12 13 6
(O-E)^2/E 2.6 0.0 0.0 0.0 0.7 0.7 0.0 3.9 0.6 6.2 0.9
Birthday Spacings: Sum(O-E)^2/E= 15.491, p= 0.885
RESULTS OF GCD FOR dh-ranFile-2018-06-27_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.572511
p-value, dist. of gcd's: 0.462839
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.653 0.994 0.530 0.881 0.746 0.570 0.471 0.989
Bits 8 to 15---> 0.221 0.918 0.911 0.015 0.861 0.856 0.007 0.583
Bits 16 to 23---> 0.473 0.164 0.873 0.764 0.740 0.067 0.265 0.818
Bits 24 to 31---> 0.574 0.586 0.389 0.926 0.032 0.565 0.072 0.302
KS test for the above 32 p values: 0.769
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_02:31,
p-values for 5 runs: 0.6474, 0.7508, 0.4632, 0.9237, 0.7168
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5079 5134.0 0.589 1.441
r= 30 23054 23103.0 0.104 1.545
r= 31 11669 11551.5 1.195 2.740
chi-square = 2.740 with df = 3; p-value = 0.567
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5163 5134.0 0.164 0.195
r= 31 23106 23103.0 0.000 0.196
r= 32 11517 11551.5 0.103 0.299
chi-square = 0.299 with df = 3; p-value = 0.040
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_02:31
b-rank test for bits 1 to 8, p=0.01487
b-rank test for bits 2 to 9, p=0.83830
b-rank test for bits 3 to 10, p=0.32137
b-rank test for bits 4 to 11, p=0.10601
b-rank test for bits 5 to 12, p=0.70764
b-rank test for bits 6 to 13, p=0.37395
b-rank test for bits 7 to 14, p=0.11999
b-rank test for bits 8 to 15, p=0.90129
b-rank test for bits 9 to 16, p=0.02814
b-rank test for bits 10 to 17, p=0.48968
b-rank test for bits 11 to 18, p=0.43014
b-rank test for bits 12 to 19, p=0.10270
b-rank test for bits 13 to 20, p=0.25546
b-rank test for bits 14 to 21, p=0.38353
b-rank test for bits 15 to 22, p=0.73717
b-rank test for bits 16 to 23, p=0.16233
b-rank test for bits 17 to 24, p=0.15036
b-rank test for bits 18 to 25, p=0.52794
b-rank test for bits 19 to 26, p=0.84178
b-rank test for bits 20 to 27, p=0.20168
b-rank test for bits 21 to 28, p=0.73037
b-rank test for bits 22 to 29, p=0.58129
b-rank test for bits 23 to 30, p=0.34112
b-rank test for bits 24 to 31, p=0.93582
b-rank test for bits 25 to 32, p=0.67244
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 = 0.543016
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_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 141853 -0.13 0.447646
2 141797 -0.26 0.396486
3 141655 -0.59 0.276180
4 142077 0.39 0.652379
5 142526 1.44 0.925182
6 142673 1.78 0.962811
7 141643 -0.62 0.266883
8 142275 0.85 0.803550
9 141333 -1.35 0.089060
10 142736 1.93 0.973288
11 141992 0.19 0.576581
12 141856 -0.12 0.450419
13 142115 0.48 0.684577
14 141955 0.11 0.542489
15 143206 3.03 0.998776
16 141551 -0.84 0.201235
17 142544 1.48 0.930946
18 141389 -1.22 0.112045
19 141402 -1.19 0.117939
20 142149 0.56 0.712252
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_02:31
Bits used No. missing words z-score p-value
23 to 32 141736 -0.5977 0.275024
22 to 31 142102 0.6644 0.746776
21 to 30 141612 -1.0253 0.152617
20 to 29 141513 -1.3667 0.085867
19 to 28 141929 0.0678 0.527039
18 to 27 142056 0.5058 0.693487
17 to 26 142199 0.9989 0.841069
16 to 25 141628 -0.9701 0.165998
15 to 24 141803 -0.3667 0.356938
14 to 23 141790 -0.4115 0.340359
13 to 22 142008 0.3402 0.633163
12 to 21 142073 0.5644 0.713752
11 to 20 141856 -0.1839 0.427047
10 to 19 141784 -0.4322 0.332808
9 to 18 142234 1.1196 0.868548
8 to 17 142085 0.6058 0.727663
7 to 16 142223 1.0816 0.860289
6 to 15 142003 0.3230 0.626652
5 to 14 141944 0.1196 0.547581
4 to 13 142055 0.5023 0.692275
3 to 12 141765 -0.4977 0.309351
2 to 11 141715 -0.6701 0.251396
1 to 10 141780 -0.4460 0.327811
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_02:31
Bits used No. missing words z-score p-value
28 to 32 142283 1.2667 0.897365
27 to 31 142363 1.5379 0.937959
26 to 30 141979 0.2362 0.593349
25 to 29 141644 -0.8994 0.184214
24 to 28 141701 -0.7062 0.240031
23 to 27 142087 0.6023 0.726503
22 to 26 142016 0.3616 0.641172
21 to 25 142149 0.8124 0.791731
20 to 24 141781 -0.4350 0.331775
19 to 23 141849 -0.2045 0.418978
18 to 22 142249 1.1514 0.875221
17 to 21 141582 -1.1096 0.133587
16 to 20 141916 0.0226 0.509019
15 to 19 141412 -1.6859 0.045911
14 to 18 141878 -0.1062 0.457711
13 to 17 142204 0.9989 0.841074
12 to 16 141878 -0.1062 0.457711
11 to 15 142308 1.3514 0.911720
10 to 14 142265 1.2057 0.886026
9 to 13 142089 0.6091 0.728755
8 to 12 141916 0.0226 0.509019
7 to 11 141851 -0.1977 0.421629
6 to 10 141940 0.1040 0.541402
5 to 9 142092 0.6192 0.732114
4 to 8 141877 -0.1096 0.456366
3 to 7 142144 0.7955 0.786836
2 to 6 142416 1.7175 0.957058
1 to 5 141723 -0.6316 0.263815
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_02:31
Bits used No. missing words z-score p-value
31 to 32 142193 0.8368 0.798643
30 to 31 141256 -1.9272 0.026976
29 to 30 141246 -1.9567 0.025190
28 to 29 141898 -0.0334 0.486669
27 to 28 141521 -1.1455 0.125998
26 to 27 141722 -0.5526 0.290270
25 to 26 141782 -0.3756 0.353605
24 to 25 141950 0.1200 0.547747
23 to 24 142119 0.6185 0.731876
22 to 23 142294 1.1347 0.871754
21 to 22 141315 -1.7532 0.039785
20 to 21 141758 -0.4464 0.327654
19 to 20 141915 0.0167 0.506672
18 to 19 142015 0.3117 0.622370
17 to 18 142429 1.5329 0.937356
16 to 17 142582 1.9843 0.976388
15 to 16 142004 0.2793 0.609978
14 to 15 141705 -0.6027 0.273340
13 to 14 142522 1.8073 0.964641
12 to 13 141595 -0.9272 0.176904
11 to 12 141847 -0.1839 0.427060
10 to 11 141920 0.0315 0.512555
9 to 10 141821 -0.2606 0.397216
8 to 9 142190 0.8279 0.796146
7 to 8 142114 0.6037 0.726994
6 to 7 141786 -0.3638 0.358002
5 to 6 141726 -0.5408 0.294324
4 to 5 141360 -1.6204 0.052569
3 to 4 141936 0.0787 0.531354
2 to 3 141841 -0.2016 0.420129
1 to 2 142760 2.5094 0.993952
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2498.18 -0.026 0.489730
Test results for specific bytes for dh-ranFile-2018-06-27_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2541.63 0.589 0.721982
2 to 9 2472.64 -0.387 0.349395
3 to 10 2451.63 -0.684 0.246961
4 to 11 2408.74 -1.291 0.098421
5 to 12 2572.33 1.023 0.846830
6 to 13 2610.86 1.568 0.941531
7 to 14 2525.38 0.359 0.640155
8 to 15 2571.68 1.014 0.844646
9 to 16 2466.44 -0.475 0.317510
10 to 17 2528.08 0.397 0.654365
11 to 18 2490.87 -0.129 0.448613
12 to 19 2611.81 1.581 0.943088
13 to 20 2397.85 -1.445 0.074277
14 to 21 2447.53 -0.742 0.229020
15 to 22 2582.15 1.162 0.877333
16 to 23 2481.99 -0.255 0.399464
17 to 24 2391.73 -1.531 0.062869
18 to 25 2511.78 0.167 0.566145
19 to 26 2512.21 0.173 0.568548
20 to 27 2417.40 -1.168 0.121363
21 to 28 2392.02 -1.527 0.063374
22 to 29 2496.40 -0.051 0.479716
23 to 30 2505.34 0.075 0.530083
24 to 31 2509.36 0.132 0.552674
25 to 32 2565.52 0.927 0.822923
CDPARK for dh-ranFile-2018-06-27_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
3501 -1.0046 0.157553
3529 0.2740 0.607947
3520 -0.1370 0.445521
3532 0.4110 0.659449
3551 1.2785 0.899470
3493 -1.3699 0.085365
3540 0.7763 0.781201
3498 -1.1416 0.126820
3522 -0.0457 0.481790
3542 0.8676 0.807188
Square side=100, avg. no. parked=3522.80 sample std.=18.89
p-value of the KSTEST for those 10 p-values: 0.962288
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_02:31
0.4730,0.2143,0.4591,0.7466,0.4573,0.3147,0.1315,0.7172,0.0924,0.5207,
The KS test for those 10 p-values: 0.417983
The 3DSPHERES test for dh-ranFile-2018-06-27_02:31
sample no r^3 equiv. uni.
1 10.738 0.300888
2 17.053 0.433584
3 3.151 0.099711
4 13.398 0.360210
5 58.037 0.855515
6 9.350 0.267774
7 2.676 0.085324
8 93.116 0.955125
9 4.245 0.131959
10 0.043 0.001431
11 45.746 0.782346
12 63.958 0.881391
13 3.523 0.110810
14 0.357 0.011824
15 39.660 0.733401
16 52.462 0.826009
17 108.019 0.972693
18 70.988 0.906168
19 36.707 0.705824
20 20.468 0.494531
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.335611
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.9 -0.4 0.6 -0.5 0.7
0.9 1.2 0.2 -0.1 0.5 -3.1
-0.1 0.1 -0.1 -0.3 0.7 1.7
-0.2 -0.5 -1.1 -0.2 1.8 -0.6
0.7 0.2 -1.3 -0.3 0.1 -0.4
1.2 -0.7 -1.1 0.4 0.9 0.8
0.7 0.8 -0.4 -0.7 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:33.917088
z-score=-0.881918, p-value=0.191663
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_02:31
Test no p-value
1 0.424413
2 0.870054
3 0.513380
4 0.681189
5 0.868061
6 0.043845
7 0.072401
8 0.337560
9 0.776642
10 0.068323
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.696795
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_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 66686 0.01 66459 0.65
3 25000.00 24872 0.66 25309 3.82
4 6666.67 6757 1.22 6597 0.73
5 1388.89 1405 0.19 1338 1.86
6 238.10 235 0.04 251 0.70
7 34.72 38 0.31 38 0.31
8 4.96 6 0.22 7 0.84
p=0.14751 p=0.82114
Number of rngs required: 687918, p-value: 0.288
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_02:31
No. of wins: Observed Expected
98998 98585.9
z-score= 1.843, pvalue=0.96736
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66652 66666.7 0.003 0.003
2 37685 37654.3 0.025 0.028
3 27020 26954.7 0.158 0.186
4 19198 19313.5 0.690 0.877
5 13836 13851.4 0.017 0.894
6 9972 9943.5 0.081 0.975
7 7088 7145.0 0.455 1.430
8 5233 5139.1 1.717 3.147
9 3577 3699.9 4.080 7.227
10 2771 2666.3 4.112 11.339
11 1941 1923.3 0.162 11.501
12 1393 1388.7 0.013 11.514
13 1019 1003.7 0.233 11.747
14 730 726.1 0.021 11.767
15 535 525.8 0.160 11.927
16 393 381.2 0.368 12.295
17 273 276.5 0.045 12.341
18 183 200.8 1.583 13.924
19 132 146.0 1.340 15.263
20 87 106.2 3.476 18.740
21 282 287.1 0.091 18.831
Chisq= 18.83 for 20 degrees of freedom, p= 0.46714
SUMMARY of craptest
p-value for no. of wins: 0.967360
p-value for throws/game: 0.467140
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_02:31
No. of wins: Observed Expected
98699 98585.9
z-score= 0.506, pvalue=0.69358
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66873 66666.7 0.639 0.639
2 37629 37654.3 0.017 0.656
3 26960 26954.7 0.001 0.657
4 19472 19313.5 1.301 1.958
5 13783 13851.4 0.338 2.296
6 9960 9943.5 0.027 2.323
7 6934 7145.0 6.233 8.556
8 5051 5139.1 1.509 10.065
9 3711 3699.9 0.034 10.099
10 2653 2666.3 0.066 10.165
11 1943 1923.3 0.201 10.366
12 1434 1388.7 1.475 11.841
13 964 1003.7 1.571 13.413
14 710 726.1 0.359 13.771
15 535 525.8 0.160 13.931
16 379 381.2 0.012 13.943
17 273 276.5 0.045 13.989
18 205 200.8 0.087 14.075
19 155 146.0 0.557 14.632
20 102 106.2 0.167 14.799
21 274 287.1 0.599 15.398
Chisq= 15.40 for 20 degrees of freedom, p= 0.24681
SUMMARY of craptest
p-value for no. of wins: 0.693584
p-value for throws/game: 0.246814
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0066,0.0118,0.0148,0.0149,0.0252,0.0270,0.0281,0.0318,0.0397,
0.0398,0.0407,0.0438,0.0459,0.0526,0.0629,0.0634,0.0675,0.0683,0.0717,
0.0724,0.0743,0.0853,0.0854,0.0859,0.0891,0.0924,0.0984,0.0997,0.1027,
0.1060,0.1108,0.1120,0.1179,0.1200,0.1214,0.1260,0.1268,0.1315,0.1320,
0.1336,0.1475,0.1504,0.1526,0.1576,0.1623,0.1639,0.1660,0.1769,0.1842,
0.1917,0.2012,0.2017,0.2143,0.2208,0.2290,0.2400,0.2468,0.2470,0.2514,
0.2555,0.2638,0.2653,0.2669,0.2678,0.2733,0.2750,0.2762,0.2806,0.2880,
0.2903,0.2943,0.3009,0.3016,0.3094,0.3147,0.3175,0.3214,0.3277,0.3278,
0.3318,0.3328,0.3356,0.3376,0.3404,0.3411,0.3494,0.3536,0.3569,0.3580,
0.3602,0.3740,0.3835,0.3885,0.3965,0.3972,0.3995,0.4180,0.4190,0.4201,
0.4216,0.4244,0.4270,0.4271,0.4301,0.4336,0.4455,0.4476,0.4486,0.4504,
0.4564,0.4573,0.4577,0.4577,0.4591,0.4628,0.4632,0.4671,0.4713,0.4728,
0.4730,0.4797,0.4818,0.4867,0.4897,0.4897,0.4945,0.5067,0.5090,0.5090,
0.5126,0.5134,0.5207,0.5270,0.5279,0.5297,0.5301,0.5314,0.5414,0.5425,
0.5430,0.5476,0.5477,0.5527,0.5572,0.5651,0.5661,0.5665,0.5685,0.5700,
0.5725,0.5743,0.5766,0.5813,0.5829,0.5858,0.5933,0.6079,0.6100,0.6224,
0.6267,0.6273,0.6332,0.6402,0.6412,0.6474,0.6524,0.6527,0.6544,0.6594,
0.6724,0.6812,0.6846,0.6923,0.6935,0.6936,0.6968,0.7058,0.7075,0.7076,
0.7123,0.7138,0.7168,0.7172,0.7220,0.7265,0.7270,0.7277,0.7288,0.7304,
0.7319,0.7321,0.7334,0.7372,0.7400,0.7457,0.7466,0.7468,0.7508,0.7641,
0.7685,0.7697,0.7766,0.7812,0.7823,0.7868,0.7917,0.7961,0.7966,0.7977,
0.7986,0.8035,0.8072,0.8178,0.8211,0.8229,0.8252,0.8260,0.8383,0.8411,
0.8411,0.8418,0.8428,0.8446,0.8468,0.8555,0.8558,0.8603,0.8610,0.8681,
0.8685,0.8701,0.8718,0.8726,0.8752,0.8773,0.8813,0.8814,0.8848,0.8860,
0.8974,0.8995,0.9013,0.9062,0.9109,0.9117,0.9177,0.9237,0.9252,0.9264,
0.9309,0.9358,0.9374,0.9380,0.9415,0.9431,0.9551,0.9571,0.9623,0.9628,
0.9646,0.9674,0.9727,0.9733,0.9764,0.9886,0.9937,0.9940,0.9988,
Overall p-value after applying KStest on 269 p-values = 0.499353
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.