RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_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 15.69 11.9511 0.196909
2 to 25 15.79 16.1275 0.485188
3 to 26 15.54 19.8962 0.720427
4 to 27 15.75 30.1440 0.974675
5 to 28 15.63 27.3097 0.946321
6 to 29 15.85 22.6999 0.840722
7 to 30 15.92 14.6622 0.380202
8 to 31 15.84 16.7649 0.529600
9 to 32 15.92 26.4953 0.934103
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.108472
Tough bday spacings test for dh-ranFile-2018-07-12_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 8 39 68 89 99 85 64 23 14 5 6
(O-E)^2/E 0.1 0.2 0.4 0.8 0.0 0.6 2.7 1.5 0.1 0.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.694, p= 0.341
RESULTS OF GCD FOR dh-ranFile-2018-07-12_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.978535
p-value, dist. of gcd's: 0.365803
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.511 0.236 0.590 0.977 0.239 0.728 0.719 0.176
Bits 8 to 15---> 0.903 0.905 0.925 0.729 0.892 0.833 0.416 0.331
Bits 16 to 23---> 0.440 0.018 0.395 0.269 0.947 0.935 0.510 0.849
Bits 24 to 31---> 0.714 0.895 0.978 0.932 0.252 0.365 0.113 0.461
KS test for the above 32 p values: 0.953
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_16:31,
p-values for 5 runs: 0.6718, 0.8813, 0.1696, 0.0703, 0.2203
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5068 5134.0 0.849 1.044
r= 30 23165 23103.0 0.166 1.210
r= 31 11562 11551.5 0.010 1.219
chi-square = 1.219 with df = 3; p-value = 0.252
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5260 5134.0 3.092 5.064
r= 31 23076 23103.0 0.032 5.095
r= 32 11473 11551.5 0.534 5.629
chi-square = 5.629 with df = 3; p-value = 0.869
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_16:31
b-rank test for bits 1 to 8, p=0.86571
b-rank test for bits 2 to 9, p=0.32261
b-rank test for bits 3 to 10, p=0.91499
b-rank test for bits 4 to 11, p=0.59322
b-rank test for bits 5 to 12, p=0.96735
b-rank test for bits 6 to 13, p=0.68614
b-rank test for bits 7 to 14, p=0.42849
b-rank test for bits 8 to 15, p=0.37750
b-rank test for bits 9 to 16, p=0.80120
b-rank test for bits 10 to 17, p=0.91552
b-rank test for bits 11 to 18, p=0.36308
b-rank test for bits 12 to 19, p=0.49504
b-rank test for bits 13 to 20, p=0.77124
b-rank test for bits 14 to 21, p=0.45280
b-rank test for bits 15 to 22, p=0.30338
b-rank test for bits 16 to 23, p=0.52872
b-rank test for bits 17 to 24, p=0.28733
b-rank test for bits 18 to 25, p=0.86908
b-rank test for bits 19 to 26, p=0.66739
b-rank test for bits 20 to 27, p=0.82858
b-rank test for bits 21 to 28, p=0.71870
b-rank test for bits 22 to 29, p=0.20469
b-rank test for bits 23 to 30, p=0.41574
b-rank test for bits 24 to 31, p=0.13318
b-rank test for bits 25 to 32, p=0.30919
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 = 0.282332
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_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 142187 0.65 0.741754
2 141931 0.05 0.520190
3 141247 -1.55 0.060871
4 142575 1.56 0.940063
5 141304 -1.41 0.078634
6 142878 2.26 0.988190
7 142487 1.35 0.911443
8 142474 1.32 0.906469
9 140862 -2.45 0.007202
10 141903 -0.01 0.494100
11 141555 -0.83 0.203871
12 142127 0.51 0.694475
13 141389 -1.22 0.112045
14 142831 2.15 0.984358
15 142096 0.44 0.668634
16 142145 0.55 0.709057
17 141946 0.09 0.534139
18 142157 0.58 0.718594
19 141794 -0.27 0.393787
20 141167 -1.73 0.041422
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_16:31
Bits used No. missing words z-score p-value
23 to 32 141819 -0.3115 0.377717
22 to 31 141681 -0.7873 0.215540
21 to 30 142319 1.4127 0.921121
20 to 29 142108 0.6851 0.753350
19 to 28 141837 -0.2494 0.401520
18 to 27 142325 1.4333 0.924120
17 to 26 142148 0.8230 0.794746
16 to 25 141821 -0.3046 0.380341
15 to 24 142638 2.5127 0.994009
14 to 23 142341 1.4885 0.931693
13 to 22 141380 -1.8253 0.033980
12 to 21 141829 -0.2770 0.390890
11 to 20 142208 1.0299 0.848471
10 to 19 141953 0.1506 0.559849
9 to 18 142221 1.0747 0.858751
8 to 17 141268 -2.2115 0.013501
7 to 16 142293 1.3230 0.907082
6 to 15 141780 -0.4460 0.327811
5 to 14 141978 0.2368 0.593591
4 to 13 142236 1.1264 0.870012
3 to 12 141693 -0.7460 0.227844
2 to 11 142088 0.6161 0.731087
1 to 10 142371 1.5920 0.944304
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_16:31
Bits used No. missing words z-score p-value
28 to 32 141795 -0.3876 0.349171
27 to 31 142165 0.8667 0.806941
26 to 30 141568 -1.1571 0.123626
25 to 29 141688 -0.7503 0.226546
24 to 28 142381 1.5989 0.945077
23 to 27 142503 2.0124 0.977913
22 to 26 142267 1.2124 0.887328
21 to 25 141942 0.1107 0.544091
20 to 24 141524 -1.3062 0.095742
19 to 23 141719 -0.6452 0.259403
18 to 22 142050 0.4768 0.683265
17 to 21 141989 0.2701 0.606446
16 to 20 141969 0.2023 0.580148
15 to 19 141887 -0.0757 0.469831
14 to 18 141239 -2.2723 0.011534
13 to 17 141841 -0.2316 0.408414
12 to 16 141739 -0.5774 0.281838
11 to 15 141779 -0.4418 0.329318
10 to 14 142144 0.7955 0.786836
9 to 13 141582 -1.1096 0.133587
8 to 12 141559 -1.1876 0.117504
7 to 11 141747 -0.5503 0.291067
6 to 10 142585 2.2904 0.989001
5 to 9 141978 0.2328 0.592034
4 to 8 142129 0.7446 0.771757
3 to 7 141917 0.0260 0.510371
2 to 6 141634 -0.9333 0.175327
1 to 5 141734 -0.5943 0.276143
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_16:31
Bits used No. missing words z-score p-value
31 to 32 142526 1.8191 0.965551
30 to 31 141967 0.1701 0.567541
29 to 30 141950 0.1200 0.547747
28 to 29 141214 -2.0511 0.020128
27 to 28 142052 0.4209 0.663070
26 to 27 141910 0.0020 0.500789
25 to 26 142313 1.1908 0.883127
24 to 25 142005 0.2822 0.611110
23 to 24 142747 2.4710 0.993263
22 to 23 141961 0.1524 0.560572
21 to 22 141481 -1.2635 0.103203
20 to 21 142158 0.7335 0.768385
19 to 20 142246 0.9931 0.839676
18 to 19 142767 2.5300 0.994297
17 to 18 142491 1.7158 0.956904
16 to 17 141965 0.1642 0.565220
15 to 16 142122 0.6273 0.734784
14 to 15 141930 0.0610 0.524310
13 to 14 141483 -1.2576 0.104266
12 to 13 142199 0.8545 0.803582
11 to 12 141659 -0.7384 0.230125
10 to 11 141471 -1.2930 0.098004
9 to 10 141920 0.0315 0.512555
8 to 9 141575 -0.9862 0.162012
7 to 8 142007 0.2881 0.613370
6 to 7 141939 0.0875 0.534872
5 to 6 142305 1.1672 0.878429
4 to 5 141834 -0.2222 0.412074
3 to 4 141673 -0.6971 0.242858
2 to 3 142519 1.7984 0.963946
1 to 2 141866 -0.1278 0.449147
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2520.62 0.292 0.614688
Test results for specific bytes for dh-ranFile-2018-07-12_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2394.61 -1.490 0.068050
2 to 9 2414.12 -1.215 0.112264
3 to 10 2534.54 0.488 0.687394
4 to 11 2438.40 -0.871 0.191845
5 to 12 2549.03 0.693 0.755960
6 to 13 2577.62 1.098 0.863838
7 to 14 2527.33 0.387 0.650459
8 to 15 2479.37 -0.292 0.385247
9 to 16 2535.24 0.498 0.690873
10 to 17 2476.14 -0.337 0.367910
11 to 18 2534.89 0.493 0.689130
12 to 19 2454.49 -0.644 0.259899
13 to 20 2504.47 0.063 0.525189
14 to 21 2447.03 -0.749 0.226913
15 to 22 2540.77 0.577 0.717871
16 to 23 2479.34 -0.292 0.385091
17 to 24 2466.00 -0.481 0.315298
18 to 25 2462.16 -0.535 0.296300
19 to 26 2591.11 1.288 0.901211
20 to 27 2609.66 1.551 0.939530
21 to 28 2553.92 0.763 0.777127
22 to 29 2462.11 -0.536 0.296016
23 to 30 2268.59 -3.273 0.000533
24 to 31 2427.16 -1.030 0.151484
25 to 32 2422.00 -1.103 0.134986
CDPARK for dh-ranFile-2018-07-12_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
3521 -0.0913 0.463617
3516 -0.3196 0.374623
3553 1.3699 0.914635
3525 0.0913 0.536383
3582 2.6941 0.996471
3489 -1.5525 0.060270
3519 -0.1826 0.427537
3533 0.4566 0.676028
3540 0.7763 0.781201
3542 0.8676 0.807188
Square side=100, avg. no. parked=3532.00 sample std.=23.56
p-value of the KSTEST for those 10 p-values: 0.388781
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_16:31
0.5250,0.0542,0.6674,0.4551,0.5006,0.9902,0.0972,0.5964,0.4822,0.1803,
The KS test for those 10 p-values: 0.630702
The 3DSPHERES test for dh-ranFile-2018-07-12_16:31
sample no r^3 equiv. uni.
1 61.948 0.873172
2 156.292 0.994537
3 4.493 0.139102
4 14.545 0.384193
5 2.122 0.068278
6 5.097 0.156264
7 131.301 0.987433
8 28.295 0.610609
9 17.612 0.444037
10 58.194 0.856267
11 51.243 0.818790
12 67.646 0.895113
13 8.890 0.256459
14 24.591 0.559441
15 35.268 0.691366
16 2.146 0.069049
17 8.100 0.236619
18 23.631 0.545105
19 7.855 0.230350
20 25.260 0.569154
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.792975
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.9 -0.1 -0.1 0.0 1.2
0.7 -0.5 -0.1 -1.9 -1.1 0.7
0.7 -0.2 -0.3 -0.2 -0.0 -0.5
-0.5 0.2 -0.6 0.5 -0.1 1.2
1.3 0.4 0.5 -0.5 -0.9 1.5
-0.3 0.8 -0.3 -0.5 1.3 -0.3
-0.2 -1.3 2.1 -0.1 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:29.611093
z-score=-1.351741, p-value=0.075103
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_16:31
Test no p-value
1 0.186436
2 0.004231
3 0.143541
4 0.801538
5 0.801445
6 0.576172
7 0.287993
8 0.222559
9 0.744726
10 0.915324
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.689181
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_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 66626 0.02 66686 0.01
3 25000.00 25037 0.05 24933 0.18
4 6666.67 6641 0.10 6709 0.27
5 1388.89 1416 0.53 1415 0.49
6 238.10 247 0.33 222 1.09
7 34.72 27 1.72 33 0.09
8 4.96 5 0.00 1 3.16
p=0.16139 p=0.49152
Number of rngs required: 689642, p-value: 0.926
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_16:31
No. of wins: Observed Expected
98795 98585.9
z-score= 0.935, pvalue=0.82521
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66599 66666.7 0.069 0.069
2 37540 37654.3 0.347 0.416
3 26998 26954.7 0.069 0.485
4 19103 19313.5 2.293 2.779
5 14011 13851.4 1.838 4.617
6 9986 9943.5 0.181 4.798
7 7158 7145.0 0.024 4.822
8 5126 5139.1 0.033 4.855
9 3636 3699.9 1.102 5.958
10 2675 2666.3 0.028 5.986
11 1923 1923.3 0.000 5.986
12 1459 1388.7 3.555 9.541
13 1092 1003.7 7.765 17.306
14 702 726.1 0.803 18.109
15 555 525.8 1.618 19.726
16 393 381.2 0.368 20.095
17 301 276.5 2.164 22.258
18 198 200.8 0.040 22.298
19 130 146.0 1.750 24.048
20 105 106.2 0.014 24.062
21 310 287.1 1.824 25.886
Chisq= 25.89 for 20 degrees of freedom, p= 0.83040
SUMMARY of craptest
p-value for no. of wins: 0.825210
p-value for throws/game: 0.830402
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_16:31
No. of wins: Observed Expected
98553 98585.9
z-score=-0.147, pvalue=0.44158
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67123 66666.7 3.124 3.124
2 37723 37654.3 0.125 3.249
3 26369 26954.7 12.728 15.977
4 19319 19313.5 0.002 15.979
5 13809 13851.4 0.130 16.108
6 10025 9943.5 0.667 16.776
7 7038 7145.0 1.603 18.379
8 5146 5139.1 0.009 18.388
9 3735 3699.9 0.334 18.722
10 2680 2666.3 0.070 18.792
11 1986 1923.3 2.042 20.834
12 1388 1388.7 0.000 20.835
13 971 1003.7 1.066 21.901
14 771 726.1 2.771 24.672
15 522 525.8 0.028 24.700
16 398 381.2 0.745 25.445
17 269 276.5 0.206 25.651
18 211 200.8 0.515 26.166
19 137 146.0 0.553 26.719
20 103 106.2 0.097 26.816
21 277 287.1 0.356 27.172
Chisq= 27.17 for 20 degrees of freedom, p= 0.86952
SUMMARY of craptest
p-value for no. of wins: 0.441581
p-value for throws/game: 0.869517
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0042,0.0072,0.0115,0.0135,0.0182,0.0201,0.0340,0.0414,0.0542,
0.0603,0.0609,0.0681,0.0683,0.0690,0.0703,0.0751,0.0786,0.0957,0.0972,
0.0980,0.1032,0.1043,0.1085,0.1120,0.1123,0.1126,0.1175,0.1236,0.1332,
0.1336,0.1350,0.1391,0.1435,0.1515,0.1563,0.1614,0.1620,0.1696,0.1753,
0.1755,0.1803,0.1864,0.1918,0.1969,0.2039,0.2047,0.2155,0.2203,0.2226,
0.2265,0.2269,0.2278,0.2301,0.2303,0.2362,0.2366,0.2391,0.2429,0.2516,
0.2523,0.2565,0.2594,0.2599,0.2692,0.2761,0.2818,0.2823,0.2873,0.2880,
0.2911,0.2960,0.2963,0.3034,0.3092,0.3153,0.3226,0.3278,0.3293,0.3308,
0.3413,0.3492,0.3631,0.3651,0.3658,0.3679,0.3746,0.3775,0.3777,0.3802,
0.3803,0.3842,0.3851,0.3852,0.3888,0.3909,0.3938,0.3948,0.4015,0.4084,
0.4121,0.4157,0.4159,0.4275,0.4285,0.4403,0.4416,0.4440,0.4491,0.4528,
0.4551,0.4608,0.4636,0.4698,0.4822,0.4852,0.4915,0.4941,0.4950,0.5006,
0.5008,0.5101,0.5104,0.5105,0.5126,0.5202,0.5243,0.5250,0.5252,0.5287,
0.5296,0.5341,0.5349,0.5364,0.5441,0.5451,0.5477,0.5594,0.5598,0.5606,
0.5652,0.5675,0.5692,0.5762,0.5801,0.5897,0.5920,0.5932,0.5936,0.5964,
0.6064,0.6106,0.6111,0.6134,0.6147,0.6307,0.6505,0.6631,0.6674,0.6674,
0.6686,0.6718,0.6760,0.6833,0.6861,0.6874,0.6891,0.6892,0.6909,0.6914,
0.6945,0.7091,0.7141,0.7179,0.7186,0.7187,0.7189,0.7204,0.7276,0.7293,
0.7311,0.7348,0.7418,0.7447,0.7533,0.7560,0.7684,0.7712,0.7718,0.7771,
0.7812,0.7868,0.7930,0.7947,0.8012,0.8014,0.8015,0.8036,0.8069,0.8072,
0.8188,0.8252,0.8286,0.8304,0.8332,0.8397,0.8407,0.8485,0.8493,0.8563,
0.8588,0.8638,0.8657,0.8689,0.8691,0.8695,0.8700,0.8732,0.8784,0.8813,
0.8831,0.8873,0.8917,0.8946,0.8951,0.9012,0.9034,0.9051,0.9065,0.9071,
0.9114,0.9146,0.9150,0.9153,0.9155,0.9211,0.9241,0.9246,0.9259,0.9317,
0.9324,0.9341,0.9348,0.9395,0.9401,0.9443,0.9451,0.9463,0.9473,0.9526,
0.9569,0.9639,0.9656,0.9674,0.9747,0.9768,0.9779,0.9783,0.9785,0.9844,
0.9874,0.9882,0.9890,0.9902,0.9933,0.9940,0.9943,0.9945,0.9965,
Overall p-value after applying KStest on 269 p-values = 0.009720
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.