RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 15.4065 0.433770
2 to 25 15.63 22.2656 0.825282
3 to 26 15.49 30.7791 0.978756
4 to 27 15.73 15.8993 0.469018
5 to 28 15.96 21.6187 0.800167
6 to 29 16.05 11.1192 0.149698
7 to 30 15.91 10.5300 0.120070
8 to 31 15.89 10.4347 0.115601
9 to 32 15.75 17.1911 0.558503
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.896143
Tough bday spacings test for dh-ranFile-2018-06-15_14:31: 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 10 38 80 95 103 73 38 41 12 6 4
(O-E)^2/E 0.1 0.1 0.6 0.1 0.3 0.3 3.8 4.2 0.6 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 10.119, p= 0.570
RESULTS OF GCD FOR dh-ranFile-2018-06-15_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.071876
p-value, dist. of gcd's: 0.670972
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.067 0.580 0.798 0.154 0.695 0.969 0.047 0.559
Bits 8 to 15---> 0.092 0.416 0.348 0.709 0.283 0.400 0.241 0.210
Bits 16 to 23---> 0.526 0.088 0.635 0.126 0.369 0.082 0.160 0.873
Bits 24 to 31---> 0.131 0.749 0.732 0.454 0.848 0.548 0.504 0.848
KS test for the above 32 p values: 0.532
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_14:31,
p-values for 5 runs: 0.5404, 0.1219, 0.7665, 0.3056, 0.6106
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5137 5134.0 0.002 0.515
r= 30 23166 23103.0 0.172 0.687
r= 31 11496 11551.5 0.267 0.954
chi-square = 0.954 with df = 3; p-value = 0.188
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5121 5134.0 0.033 1.016
r= 31 23134 23103.0 0.041 1.058
r= 32 11548 11551.5 0.001 1.059
chi-square = 1.059 with df = 3; p-value = 0.213
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_14:31
b-rank test for bits 1 to 8, p=0.48938
b-rank test for bits 2 to 9, p=0.89846
b-rank test for bits 3 to 10, p=0.20106
b-rank test for bits 4 to 11, p=0.07448
b-rank test for bits 5 to 12, p=0.08638
b-rank test for bits 6 to 13, p=0.69029
b-rank test for bits 7 to 14, p=0.91797
b-rank test for bits 8 to 15, p=0.41527
b-rank test for bits 9 to 16, p=0.40700
b-rank test for bits 10 to 17, p=0.04185
b-rank test for bits 11 to 18, p=0.69364
b-rank test for bits 12 to 19, p=0.81482
b-rank test for bits 13 to 20, p=0.22012
b-rank test for bits 14 to 21, p=0.15669
b-rank test for bits 15 to 22, p=0.28745
b-rank test for bits 16 to 23, p=0.40099
b-rank test for bits 17 to 24, p=0.88700
b-rank test for bits 18 to 25, p=0.71297
b-rank test for bits 19 to 26, p=0.46139
b-rank test for bits 20 to 27, p=0.83396
b-rank test for bits 21 to 28, p=0.26168
b-rank test for bits 22 to 29, p=0.83656
b-rank test for bits 23 to 30, p=0.64496
b-rank test for bits 24 to 31, p=0.45131
b-rank test for bits 25 to 32, p=0.98590
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 = 0.985431
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_14:31
(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 142317 0.95 0.829578
2 143103 2.79 0.997356
3 141776 -0.31 0.377703
4 141632 -0.65 0.258503
5 142325 0.97 0.834274
6 141643 -0.62 0.266883
7 142111 0.47 0.681248
8 141415 -1.15 0.124050
9 141699 -0.49 0.311563
10 142104 0.45 0.675387
11 141353 -1.30 0.096829
12 142669 1.77 0.962045
13 142138 0.53 0.703425
14 142011 0.24 0.593884
15 142209 0.70 0.758087
16 142111 0.47 0.681248
17 141504 -0.95 0.171811
18 142493 1.36 0.913671
19 141669 -0.56 0.287222
20 141735 -0.41 0.341889
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_14:31
Bits used No. missing words z-score p-value
23 to 32 141373 -1.8494 0.032199
22 to 31 141849 -0.2080 0.417601
21 to 30 141820 -0.3080 0.379028
20 to 29 141755 -0.5322 0.297303
19 to 28 142015 0.3644 0.642213
18 to 27 141803 -0.3667 0.356938
17 to 26 141523 -1.3322 0.091402
16 to 25 142157 0.8540 0.803457
15 to 24 141671 -0.8218 0.205588
14 to 23 141645 -0.9115 0.181021
13 to 22 141986 0.2644 0.604256
12 to 21 141275 -2.1873 0.014359
11 to 20 141720 -0.6529 0.256923
10 to 19 141871 -0.1322 0.447424
9 to 18 142499 2.0333 0.978991
8 to 17 141719 -0.6563 0.255812
7 to 16 142071 0.5575 0.711401
6 to 15 141457 -1.5598 0.059408
5 to 14 142237 1.1299 0.870740
4 to 13 142441 1.8333 0.966624
3 to 12 141632 -0.9563 0.169458
2 to 11 142141 0.7989 0.787815
1 to 10 141745 -0.5667 0.285474
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_14:31
Bits used No. missing words z-score p-value
28 to 32 141676 -0.7909 0.214487
27 to 31 141551 -1.2147 0.112244
26 to 30 141727 -0.6181 0.268265
25 to 29 141851 -0.1977 0.421629
24 to 28 141695 -0.7265 0.233753
23 to 27 141919 0.0328 0.513075
22 to 26 142236 1.1074 0.865930
21 to 25 141670 -0.8113 0.208600
20 to 24 141811 -0.3333 0.369446
19 to 23 142180 0.9175 0.820566
18 to 22 141658 -0.8520 0.197116
17 to 21 141503 -1.3774 0.084196
16 to 20 141490 -1.4215 0.077592
15 to 19 141766 -0.4859 0.313532
14 to 18 141627 -0.9571 0.169271
13 to 17 142111 0.6836 0.752895
12 to 16 142179 0.9141 0.819677
11 to 15 141835 -0.2520 0.400534
10 to 14 141789 -0.4079 0.341674
9 to 13 141469 -1.4926 0.067765
8 to 12 141389 -1.7638 0.038880
7 to 11 141791 -0.4011 0.344166
6 to 10 141852 -0.1943 0.422955
5 to 9 141338 -1.9367 0.026390
4 to 8 141674 -0.7977 0.212514
3 to 7 141298 -2.0723 0.019119
2 to 6 142065 0.5277 0.701145
1 to 5 141458 -1.5299 0.063017
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_14:31
Bits used No. missing words z-score p-value
31 to 32 141769 -0.4140 0.339454
30 to 31 142235 0.9607 0.831643
29 to 30 142520 1.8014 0.964179
28 to 29 142489 1.7099 0.956362
27 to 28 141631 -0.8210 0.205814
26 to 27 141712 -0.5821 0.280252
25 to 26 141654 -0.7532 0.225669
24 to 25 141504 -1.1957 0.115914
23 to 24 141903 -0.0187 0.492551
22 to 23 142261 1.0374 0.850219
21 to 22 142113 0.6008 0.726012
20 to 21 141983 0.2173 0.586019
19 to 20 141914 0.0138 0.505496
18 to 19 141406 -1.4847 0.068805
17 to 18 141528 -1.1249 0.130323
16 to 17 141917 0.0226 0.509025
15 to 16 141882 -0.0806 0.467872
14 to 15 141994 0.2498 0.598615
13 to 14 141573 -0.9921 0.160569
12 to 13 141997 0.2586 0.602033
11 to 12 141609 -0.8859 0.187828
10 to 11 142151 0.7129 0.762043
9 to 10 142279 1.0905 0.862247
8 to 9 141213 -2.0541 0.019984
7 to 8 141885 -0.0718 0.471393
6 to 7 142395 1.4327 0.924022
5 to 6 141688 -0.6529 0.256913
4 to 5 141775 -0.3963 0.345959
3 to 4 142220 0.9164 0.820280
2 to 3 141668 -0.7119 0.238267
1 to 2 142019 0.3235 0.626846
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2500.59 0.008 0.503346
Test results for specific bytes for dh-ranFile-2018-06-15_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2501.35 0.019 0.507644
2 to 9 2407.12 -1.314 0.094498
3 to 10 2546.27 0.654 0.743567
4 to 11 2372.36 -1.805 0.035530
5 to 12 2398.67 -1.433 0.075922
6 to 13 2488.36 -0.165 0.434610
7 to 14 2491.20 -0.124 0.450504
8 to 15 2450.59 -0.699 0.242336
9 to 16 2410.66 -1.263 0.103219
10 to 17 2362.97 -1.938 0.026319
11 to 18 2552.28 0.739 0.770154
12 to 19 2435.37 -0.914 0.180357
13 to 20 2471.22 -0.407 0.341999
14 to 21 2374.22 -1.779 0.037638
15 to 22 2486.75 -0.187 0.425683
16 to 23 2447.32 -0.745 0.228126
17 to 24 2406.45 -1.323 0.092919
18 to 25 2529.71 0.420 0.662819
19 to 26 2456.35 -0.617 0.268532
20 to 27 2530.37 0.429 0.666209
21 to 28 2385.25 -1.623 0.052312
22 to 29 2496.34 -0.052 0.479372
23 to 30 2631.17 1.855 0.968200
24 to 31 2514.79 0.209 0.582865
25 to 32 2412.31 -1.240 0.107455
CDPARK for dh-ranFile-2018-06-15_14:31: 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
3550 1.2329 0.891189
3542 0.8676 0.807188
3541 0.8219 0.794438
3537 0.6393 0.738676
3525 0.0913 0.536383
3569 2.1005 0.982156
3522 -0.0457 0.481790
3541 0.8219 0.794438
3533 0.4566 0.676028
3549 1.1872 0.882429
Square side=100, avg. no. parked=3540.90 sample std.=12.75
p-value of the KSTEST for those 10 p-values: 0.006447
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_14:31
0.7251,0.8679,0.0661,0.2445,0.9537,0.6025,0.5670,0.9017,0.9143,0.8818,
The KS test for those 10 p-values: 0.060119
The 3DSPHERES test for dh-ranFile-2018-06-15_14:31
sample no r^3 equiv. uni.
1 63.069 0.877824
2 19.662 0.480774
3 12.223 0.334645
4 6.680 0.199622
5 2.498 0.079895
6 15.381 0.401121
7 180.435 0.997557
8 89.085 0.948671
9 14.114 0.375299
10 2.204 0.070826
11 53.932 0.834324
12 28.129 0.608451
13 9.897 0.281015
14 8.304 0.241790
15 102.202 0.966851
16 12.623 0.343454
17 25.070 0.566417
18 28.784 0.616906
19 54.930 0.839746
20 2.174 0.069903
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.750938
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.6 1.3 0.5 -0.6 -1.2
-0.2 -0.2 -1.3 -0.3 0.6 -1.4
0.9 -0.1 0.7 -0.6 0.1 -0.7
1.4 -0.2 1.0 -0.6 1.3 2.2
-1.3 -1.7 -0.7 -1.4 0.3 1.5
-1.3 -0.3 -0.5 -0.2 0.5 -1.0
0.0 0.2 -0.4 -1.3 0.9 -1.0
1.8
Chi-square with 42 degrees of freedom:41.798032
z-score=-0.022037, p-value=0.520249
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_14:31
Test no p-value
1 0.701799
2 0.133827
3 0.079008
4 0.746455
5 0.862918
6 0.414141
7 0.227742
8 0.180042
9 0.254120
10 0.015692
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.186979
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_14:31:
(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 66752 0.11 66956 1.26
3 25000.00 24987 0.01 24753 2.44
4 6666.67 6635 0.15 6628 0.22
5 1388.89 1372 0.21 1387 0.00
6 238.10 222 1.09 248 0.41
7 34.72 27 1.72 23 3.96
8 4.96 4 0.19 4 0.19
p=0.25101 p=0.79480
Number of rngs required: 686799, p-value: 0.029
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_14:31
No. of wins: Observed Expected
98364 98585.9
z-score=-0.992, pvalue=0.16053
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66577 66666.7 0.121 0.121
2 37872 37654.3 1.258 1.379
3 27098 26954.7 0.761 2.140
4 19357 19313.5 0.098 2.239
5 13799 13851.4 0.198 2.437
6 10007 9943.5 0.405 2.842
7 7004 7145.0 2.784 5.625
8 5153 5139.1 0.038 5.663
9 3604 3699.9 2.484 8.147
10 2651 2666.3 0.088 8.235
11 1947 1923.3 0.291 8.526
12 1352 1388.7 0.972 9.498
13 989 1003.7 0.216 9.714
14 704 726.1 0.675 10.389
15 510 525.8 0.477 10.866
16 373 381.2 0.174 11.040
17 278 276.5 0.008 11.048
18 189 200.8 0.697 11.745
19 138 146.0 0.437 12.181
20 106 106.2 0.000 12.182
21 292 287.1 0.083 12.265
Chisq= 12.27 for 20 degrees of freedom, p= 0.09335
SUMMARY of craptest
p-value for no. of wins: 0.160530
p-value for throws/game: 0.093349
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_14:31
No. of wins: Observed Expected
98239 98585.9
z-score=-1.551, pvalue=0.06041
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66436 66666.7 0.798 0.798
2 37663 37654.3 0.002 0.800
3 27158 26954.7 1.533 2.333
4 19538 19313.5 2.610 4.943
5 13695 13851.4 1.766 6.710
6 9932 9943.5 0.013 6.723
7 7104 7145.0 0.236 6.959
8 5134 5139.1 0.005 6.964
9 3746 3699.9 0.575 7.539
10 2700 2666.3 0.426 7.965
11 1831 1923.3 4.432 12.397
12 1420 1388.7 0.704 13.101
13 955 1003.7 2.364 15.465
14 745 726.1 0.490 15.955
15 511 525.8 0.419 16.374
16 386 381.2 0.062 16.435
17 267 276.5 0.329 16.765
18 202 200.8 0.007 16.771
19 175 146.0 5.767 22.538
20 106 106.2 0.000 22.539
21 296 287.1 0.275 22.814
Chisq= 22.81 for 20 degrees of freedom, p= 0.70197
SUMMARY of craptest
p-value for no. of wins: 0.060408
p-value for throws/game: 0.701974
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0064,0.0144,0.0157,0.0191,0.0200,0.0263,0.0264,0.0295,0.0322,0.0355,
0.0376,0.0389,0.0418,0.0474,0.0523,0.0594,0.0601,0.0604,0.0630,0.0661,
0.0669,0.0678,0.0688,0.0699,0.0708,0.0719,0.0745,0.0759,0.0776,0.0790,
0.0799,0.0822,0.0842,0.0864,0.0884,0.0914,0.0924,0.0929,0.0933,0.0945,
0.0968,0.1032,0.1075,0.1122,0.1156,0.1159,0.1201,0.1219,0.1241,0.1265,
0.1303,0.1311,0.1338,0.1497,0.1537,0.1567,0.1601,0.1605,0.1606,0.1693,
0.1695,0.1718,0.1800,0.1804,0.1810,0.1870,0.1875,0.1878,0.1971,0.1996,
0.2011,0.2056,0.2058,0.2086,0.2103,0.2125,0.2130,0.2145,0.2201,0.2257,
0.2277,0.2281,0.2338,0.2383,0.2412,0.2418,0.2423,0.2445,0.2510,0.2541,
0.2558,0.2569,0.2569,0.2585,0.2617,0.2669,0.2683,0.2685,0.2803,0.2810,
0.2833,0.2855,0.2872,0.2874,0.2973,0.3056,0.3116,0.3135,0.3346,0.3395,
0.3417,0.3419,0.3420,0.3435,0.3442,0.3460,0.3481,0.3569,0.3686,0.3694,
0.3753,0.3777,0.3790,0.3999,0.4005,0.4010,0.4011,0.4070,0.4141,0.4153,
0.4156,0.4176,0.4216,0.4230,0.4257,0.4338,0.4346,0.4474,0.4505,0.4513,
0.4545,0.4614,0.4679,0.4690,0.4714,0.4794,0.4808,0.4818,0.4894,0.4926,
0.5033,0.5037,0.5055,0.5076,0.5090,0.5131,0.5202,0.5265,0.5318,0.5364,
0.5404,0.5478,0.5585,0.5586,0.5664,0.5670,0.5699,0.5800,0.5829,0.5860,
0.5939,0.5986,0.6020,0.6025,0.6043,0.6085,0.6106,0.6169,0.6268,0.6353,
0.6422,0.6450,0.6628,0.6662,0.6710,0.6754,0.6760,0.6812,0.6812,0.6903,
0.6936,0.6949,0.7011,0.7018,0.7020,0.7034,0.7092,0.7114,0.7130,0.7251,
0.7260,0.7319,0.7387,0.7436,0.7465,0.7495,0.7509,0.7529,0.7581,0.7620,
0.7665,0.7702,0.7878,0.7944,0.7944,0.7948,0.7984,0.8002,0.8035,0.8072,
0.8148,0.8197,0.8203,0.8206,0.8253,0.8296,0.8316,0.8340,0.8343,0.8343,
0.8366,0.8397,0.8476,0.8484,0.8502,0.8622,0.8629,0.8659,0.8679,0.8707,
0.8727,0.8778,0.8818,0.8824,0.8870,0.8912,0.8961,0.8985,0.9017,0.9137,
0.9143,0.9180,0.9240,0.9487,0.9537,0.9564,0.9620,0.9642,0.9666,0.9669,
0.9682,0.9692,0.9788,0.9790,0.9822,0.9854,0.9859,0.9974,0.9976,
Overall p-value after applying KStest on 269 p-values = 0.015609
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.