RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.62 11.4202 0.166095
2 to 25 15.69 20.3529 0.743423
3 to 26 15.59 25.3981 0.913852
4 to 27 15.59 13.5506 0.301382
5 to 28 15.76 12.9317 0.259257
6 to 29 16.02 25.2321 0.910366
7 to 30 15.76 16.9707 0.543650
8 to 31 15.64 28.4631 0.960190
9 to 32 15.58 26.9071 0.940556
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.130185
Tough bday spacings test for dh-ranFile-2018-06-18_08:31: 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 7 30 68 107 96 83 52 33 11 11 2
(O-E)^2/E 0.5 1.2 0.4 0.9 0.0 0.3 0.0 0.4 1.0 2.9 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.626, p= 0.432
RESULTS OF GCD FOR dh-ranFile-2018-06-18_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.476218
p-value, dist. of gcd's: 0.130327
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.772 0.349 0.957 0.833 0.711 0.688 0.910 0.416
Bits 8 to 15---> 0.766 0.552 0.434 0.228 0.362 0.194 0.328 0.567
Bits 16 to 23---> 0.495 0.547 0.083 0.145 0.375 0.007 0.007 0.544
Bits 24 to 31---> 0.419 0.936 0.403 0.382 0.179 0.026 0.538 0.762
KS test for the above 32 p values: 0.427
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_08:31,
p-values for 5 runs: 0.8353, 0.8333, 0.5565, 0.0421, 0.1471
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 193 211.4 1.605 1.605
r= 29 5160 5134.0 0.132 1.736
r= 30 23013 23103.0 0.351 2.087
r= 31 11634 11551.5 0.589 2.676
chi-square = 2.676 with df = 3; p-value = 0.556
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 246 211.4 5.657 5.657
r= 30 5204 5134.0 0.954 6.611
r= 31 22966 23103.0 0.813 7.424
r= 32 11584 11551.5 0.091 7.515
chi-square = 7.515 with df = 3; p-value = 0.943
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_08:31
b-rank test for bits 1 to 8, p=0.47648
b-rank test for bits 2 to 9, p=0.68981
b-rank test for bits 3 to 10, p=0.55519
b-rank test for bits 4 to 11, p=0.68923
b-rank test for bits 5 to 12, p=0.73399
b-rank test for bits 6 to 13, p=0.33772
b-rank test for bits 7 to 14, p=0.15356
b-rank test for bits 8 to 15, p=0.92584
b-rank test for bits 9 to 16, p=0.75111
b-rank test for bits 10 to 17, p=0.27893
b-rank test for bits 11 to 18, p=0.80501
b-rank test for bits 12 to 19, p=0.21428
b-rank test for bits 13 to 20, p=0.83556
b-rank test for bits 14 to 21, p=0.13774
b-rank test for bits 15 to 22, p=0.65432
b-rank test for bits 16 to 23, p=0.02294
b-rank test for bits 17 to 24, p=0.53277
b-rank test for bits 18 to 25, p=0.86286
b-rank test for bits 19 to 26, p=0.68403
b-rank test for bits 20 to 27, p=0.63079
b-rank test for bits 21 to 28, p=0.63568
b-rank test for bits 22 to 29, p=0.29692
b-rank test for bits 23 to 30, p=0.99120
b-rank test for bits 24 to 31, p=0.99227
b-rank test for bits 25 to 32, p=0.61645
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 = 0.224812
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_08:31
(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 141482 -1.00 0.159034
2 141698 -0.49 0.310737
3 141246 -1.55 0.060590
4 141859 -0.12 0.453195
5 142366 1.07 0.857011
6 141899 -0.02 0.490372
7 142235 0.76 0.776645
8 142542 1.48 0.930323
9 142704 1.86 0.968323
10 141884 -0.06 0.476404
11 142009 0.23 0.592070
12 141597 -0.73 0.232774
13 142840 2.17 0.985165
14 141408 -1.17 0.120733
15 141736 -0.40 0.342747
16 142318 0.95 0.830170
17 141778 -0.31 0.379480
18 142063 0.36 0.640218
19 142492 1.36 0.913303
20 141785 -0.29 0.385720
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_08:31
Bits used No. missing words z-score p-value
23 to 32 141567 -1.1804 0.118911
22 to 31 141520 -1.3425 0.089714
21 to 30 141503 -1.4011 0.080586
20 to 29 142158 0.8575 0.804411
19 to 28 141478 -1.4873 0.068462
18 to 27 142047 0.4747 0.682508
17 to 26 142226 1.0920 0.862576
16 to 25 141615 -1.0149 0.155069
15 to 24 141989 0.2747 0.608236
14 to 23 142107 0.6816 0.752261
13 to 22 141053 -2.9529 0.001574
12 to 21 141514 -1.3632 0.086409
11 to 20 141960 0.1747 0.569352
10 to 19 142143 0.8058 0.789809
9 to 18 143148 4.2713 0.999990
8 to 17 142290 1.3127 0.905350
7 to 16 142025 0.3989 0.655003
6 to 15 141639 -0.9322 0.175624
5 to 14 141764 -0.5011 0.308137
4 to 13 142552 2.2161 0.986658
3 to 12 142107 0.6816 0.752261
2 to 11 141875 -0.1184 0.452884
1 to 10 141459 -1.5529 0.060228
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_08:31
Bits used No. missing words z-score p-value
28 to 32 141646 -0.8926 0.186024
27 to 31 141798 -0.3774 0.352942
26 to 30 142073 0.5548 0.710489
25 to 29 141592 -1.0757 0.141032
24 to 28 141413 -1.6825 0.046238
23 to 27 141691 -0.7401 0.229619
22 to 26 142105 0.6633 0.746427
21 to 25 142107 0.6701 0.748593
20 to 24 141497 -1.3977 0.081097
19 to 23 141771 -0.4689 0.319565
18 to 22 141718 -0.6486 0.258306
17 to 21 141630 -0.9469 0.171850
16 to 20 142202 0.9921 0.839426
15 to 19 141840 -0.2350 0.407098
14 to 18 141824 -0.2893 0.386193
13 to 17 141662 -0.8384 0.200901
12 to 16 142460 1.8667 0.969027
11 to 15 141997 0.2972 0.616838
10 to 14 141987 0.2633 0.603836
9 to 13 142079 0.5752 0.717406
8 to 12 141942 0.1107 0.544091
7 to 11 142139 0.7785 0.781875
6 to 10 142148 0.8091 0.790757
5 to 9 142144 0.7955 0.786836
4 to 8 142113 0.6904 0.755031
3 to 7 141829 -0.2723 0.392694
2 to 6 141351 -1.8926 0.029203
1 to 5 141795 -0.3876 0.349171
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_08:31
Bits used No. missing words z-score p-value
31 to 32 141576 -0.9833 0.162736
30 to 31 141566 -1.0128 0.155584
29 to 30 142195 0.8427 0.800298
28 to 29 141829 -0.2370 0.406343
27 to 28 141729 -0.5319 0.297381
26 to 27 142082 0.5094 0.694747
25 to 26 142056 0.4327 0.667367
24 to 25 141809 -0.2960 0.383631
23 to 24 141740 -0.4995 0.308714
22 to 23 141849 -0.1780 0.429375
21 to 22 142244 0.9872 0.838234
20 to 21 141865 -0.1308 0.447980
19 to 20 141943 0.0993 0.539559
18 to 19 142100 0.5624 0.713095
17 to 18 141965 0.1642 0.565220
16 to 17 141851 -0.1721 0.431693
15 to 16 141948 0.1141 0.545409
14 to 15 141990 0.2380 0.594046
13 to 14 142363 1.3383 0.909594
12 to 13 142054 0.4268 0.665221
11 to 12 141985 0.2232 0.588316
10 to 11 141589 -0.9449 0.172348
9 to 10 141288 -1.8328 0.033414
8 to 9 142211 0.8899 0.813235
7 to 8 142454 1.6067 0.945939
6 to 7 141943 0.0993 0.539559
5 to 6 142087 0.5241 0.699896
4 to 5 142146 0.6981 0.757456
3 to 4 142342 1.2763 0.899078
2 to 3 141986 0.2262 0.589464
1 to 2 141395 -1.5172 0.064608
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2500.75 0.011 0.504243
Test results for specific bytes for dh-ranFile-2018-06-18_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2543.51 0.615 0.730850
2 to 9 2433.22 -0.944 0.172492
3 to 10 2585.88 1.215 0.887731
4 to 11 2449.97 -0.708 0.239625
5 to 12 2521.30 0.301 0.618401
6 to 13 2480.68 -0.273 0.392324
7 to 14 2439.44 -0.856 0.195892
8 to 15 2362.67 -1.942 0.026062
9 to 16 2474.34 -0.363 0.358354
10 to 17 2510.86 0.154 0.561005
11 to 18 2482.27 -0.251 0.401006
12 to 19 2413.86 -1.218 0.111564
13 to 20 2432.48 -0.955 0.169836
14 to 21 2474.17 -0.365 0.357425
15 to 22 2571.12 1.006 0.842739
16 to 23 2542.65 0.603 0.726798
17 to 24 2467.76 -0.456 0.324223
18 to 25 2490.04 -0.141 0.443996
19 to 26 2573.49 1.039 0.850657
20 to 27 2529.38 0.415 0.661086
21 to 28 2512.31 0.174 0.569123
22 to 29 2476.95 -0.326 0.372228
23 to 30 2491.96 -0.114 0.454710
24 to 31 2553.10 0.751 0.773645
25 to 32 2510.89 0.154 0.561172
CDPARK for dh-ranFile-2018-06-18_08:31: 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
3507 -0.7306 0.232514
3526 0.1370 0.554479
3525 0.0913 0.536383
3522 -0.0457 0.481790
3586 2.8767 0.997991
3504 -0.8676 0.192812
3554 1.4155 0.921543
3503 -0.9132 0.180558
3531 0.3653 0.642555
3491 -1.4612 0.071982
Square side=100, avg. no. parked=3524.90 sample std.=26.48
p-value of the KSTEST for those 10 p-values: 0.684864
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_08:31
0.2838,0.2360,0.5095,0.7614,0.6989,0.9122,0.6415,0.4874,0.2034,0.0670,
The KS test for those 10 p-values: 0.985222
The 3DSPHERES test for dh-ranFile-2018-06-18_08:31
sample no r^3 equiv. uni.
1 49.163 0.805782
2 94.602 0.957294
3 17.870 0.448806
4 36.597 0.704744
5 70.595 0.904931
6 25.724 0.575769
7 77.759 0.925126
8 19.437 0.476865
9 161.549 0.995415
10 189.333 0.998184
11 16.766 0.428153
12 19.956 0.485835
13 3.667 0.115067
14 109.039 0.973606
15 38.339 0.721394
16 7.766 0.228078
17 9.335 0.267399
18 11.761 0.324324
19 17.664 0.445001
20 12.840 0.348183
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.059279
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 1.3 0.3 -1.0 0.1
-0.2 -0.7 -0.4 -0.6 0.8 0.8
-0.5 0.5 -0.2 1.5 -0.5 0.7
0.4 0.1 -0.2 -0.9 -2.1 -0.3
-0.2 0.0 0.6 -0.7 0.5 1.5
0.5 -0.9 0.3 0.4 1.7 -0.8
0.0 -0.1 -0.4 0.4 0.9 -1.0
0.8
Chi-square with 42 degrees of freedom:25.724606
z-score=-1.775791, p-value=0.022669
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_08:31
Test no p-value
1 0.050432
2 0.606082
3 0.739793
4 0.005266
5 0.063331
6 0.109167
7 0.169975
8 0.039466
9 0.046293
10 0.406522
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000687
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_08:31:
(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 66799 0.26 66578 0.12
3 25000.00 24841 1.01 25050 0.10
4 6666.67 6686 0.06 6703 0.20
5 1388.89 1387 0.00 1378 0.09
6 238.10 248 0.41 251 0.70
7 34.72 33 0.09 32 0.21
8 4.96 5 0.00 7 0.84
p=0.06536 p=0.10496
Number of rngs required: 687949, p-value: 0.300
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_08:31
No. of wins: Observed Expected
98246 98585.9
z-score=-1.520, pvalue=0.06425
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66413 66666.7 0.965 0.965
2 37590 37654.3 0.110 1.075
3 27196 26954.7 2.160 3.235
4 19356 19313.5 0.094 3.328
5 13813 13851.4 0.107 3.435
6 9981 9943.5 0.141 3.576
7 7171 7145.0 0.094 3.670
8 5089 5139.1 0.488 4.158
9 3659 3699.9 0.451 4.610
10 2665 2666.3 0.001 4.610
11 1926 1923.3 0.004 4.614
12 1437 1388.7 1.677 6.291
13 942 1003.7 3.795 10.086
14 732 726.1 0.047 10.133
15 559 525.8 2.092 12.225
16 405 381.2 1.492 13.717
17 316 276.5 5.631 19.348
18 193 200.8 0.305 19.653
19 148 146.0 0.028 19.681
20 104 106.2 0.046 19.727
21 305 287.1 1.114 20.841
Chisq= 20.84 for 20 degrees of freedom, p= 0.59347
SUMMARY of craptest
p-value for no. of wins: 0.064250
p-value for throws/game: 0.593469
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_08:31
No. of wins: Observed Expected
98512 98585.9
z-score=-0.330, pvalue=0.37057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66800 66666.7 0.267 0.267
2 37709 37654.3 0.079 0.346
3 27015 26954.7 0.135 0.481
4 19402 19313.5 0.406 0.887
5 13900 13851.4 0.170 1.057
6 9915 9943.5 0.082 1.139
7 7109 7145.0 0.182 1.321
8 5048 5139.1 1.614 2.935
9 3699 3699.9 0.000 2.935
10 2616 2666.3 0.949 3.884
11 1877 1923.3 1.116 5.000
12 1385 1388.7 0.010 5.010
13 983 1003.7 0.428 5.437
14 722 726.1 0.024 5.461
15 489 525.8 2.580 8.041
16 352 381.2 2.229 10.271
17 264 276.5 0.569 10.839
18 184 200.8 1.410 12.250
19 140 146.0 0.245 12.495
20 106 106.2 0.000 12.495
21 285 287.1 0.016 12.511
Chisq= 12.51 for 20 degrees of freedom, p= 0.10263
SUMMARY of craptest
p-value for no. of wins: 0.370572
p-value for throws/game: 0.102632
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0016,0.0053,0.0068,0.0069,0.0227,0.0229,0.0258,0.0261,0.0292,
0.0334,0.0395,0.0421,0.0462,0.0463,0.0504,0.0593,0.0602,0.0606,0.0633,
0.0642,0.0646,0.0654,0.0670,0.0685,0.0720,0.0806,0.0811,0.0829,0.0864,
0.0897,0.1026,0.1050,0.1092,0.1116,0.1151,0.1189,0.1207,0.1302,0.1303,
0.1377,0.1410,0.1449,0.1471,0.1536,0.1551,0.1556,0.1590,0.1627,0.1661,
0.1698,0.1700,0.1718,0.1723,0.1725,0.1756,0.1791,0.1806,0.1860,0.1928,
0.1938,0.1959,0.2009,0.2034,0.2143,0.2248,0.2281,0.2285,0.2296,0.2325,
0.2328,0.2360,0.2396,0.2583,0.2593,0.2674,0.2789,0.2838,0.2969,0.2974,
0.3004,0.3014,0.3081,0.3087,0.3107,0.3196,0.3242,0.3243,0.3281,0.3377,
0.3427,0.3482,0.3492,0.3492,0.3529,0.3574,0.3584,0.3616,0.3706,0.3722,
0.3753,0.3795,0.3825,0.3836,0.3857,0.3862,0.3923,0.3927,0.4010,0.4035,
0.4063,0.4065,0.4071,0.4159,0.4192,0.4268,0.4282,0.4294,0.4317,0.4321,
0.4337,0.4440,0.4450,0.4480,0.4488,0.4529,0.4532,0.4547,0.4762,0.4764,
0.4765,0.4769,0.4818,0.4858,0.4874,0.4904,0.4946,0.5042,0.5095,0.5328,
0.5364,0.5383,0.5396,0.5396,0.5437,0.5441,0.5441,0.5454,0.5466,0.5515,
0.5545,0.5552,0.5557,0.5565,0.5610,0.5612,0.5652,0.5668,0.5691,0.5694,
0.5758,0.5883,0.5895,0.5921,0.5935,0.5940,0.6038,0.6061,0.6082,0.6165,
0.6168,0.6184,0.6308,0.6357,0.6402,0.6415,0.6426,0.6543,0.6550,0.6611,
0.6652,0.6674,0.6825,0.6840,0.6849,0.6876,0.6892,0.6898,0.6947,0.6989,
0.6999,0.7047,0.7105,0.7108,0.7131,0.7174,0.7214,0.7268,0.7308,0.7340,
0.7398,0.7434,0.7464,0.7486,0.7511,0.7523,0.7523,0.7550,0.7575,0.7614,
0.7624,0.7656,0.7720,0.7736,0.7766,0.7819,0.7868,0.7898,0.7908,0.8003,
0.8044,0.8050,0.8058,0.8132,0.8302,0.8327,0.8333,0.8353,0.8356,0.8382,
0.8394,0.8427,0.8507,0.8570,0.8626,0.8629,0.8877,0.8991,0.9049,0.9054,
0.9096,0.9104,0.9104,0.9122,0.9133,0.9139,0.9215,0.9251,0.9258,0.9303,
0.9358,0.9406,0.9428,0.9459,0.9571,0.9573,0.9602,0.9683,0.9690,0.9736,
0.9852,0.9852,0.9867,0.9912,0.9923,0.9954,0.9980,0.9982,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.765672
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.