RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_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 15.75 17.4856 0.578038
2 to 25 15.94 17.5069 0.579434
3 to 26 15.45 26.1560 0.928334
4 to 27 15.64 20.0555 0.728601
5 to 28 16.01 23.6162 0.869757
6 to 29 15.64 21.4361 0.792610
7 to 30 15.52 19.9708 0.724272
8 to 31 15.74 11.1787 0.152875
9 to 32 15.75 13.5888 0.304038
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.298098
Tough bday spacings test for dh-ranFile-2018-06-15_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 44 73 102 105 66 40 35 18 3 6
(O-E)^2/E 0.1 1.5 0.0 0.2 0.5 1.9 2.8 0.9 0.7 2.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 11.532, p= 0.682
RESULTS OF GCD FOR dh-ranFile-2018-06-15_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.650448
p-value, dist. of gcd's: 0.174883
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.497 0.137 0.845 0.793 0.107 0.073 0.665 0.279
Bits 8 to 15---> 0.473 0.564 0.923 0.732 0.080 0.949 0.148 0.673
Bits 16 to 23---> 0.879 0.023 0.284 0.203 0.215 0.308 0.117 0.673
Bits 24 to 31---> 0.810 0.797 0.331 0.713 0.831 0.375 0.878 0.028
KS test for the above 32 p values: 0.290
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_21:31,
p-values for 5 runs: 0.4471, 0.3178, 0.3640, 0.2648, 0.4502
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5127 5134.0 0.010 0.214
r= 30 23162 23103.0 0.150 0.365
r= 31 11493 11551.5 0.297 0.661
chi-square = 0.661 with df = 3; p-value = 0.118
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 221 211.4 0.434 0.434
r= 30 5101 5134.0 0.212 0.647
r= 31 23086 23103.0 0.013 0.659
r= 32 11592 11551.5 0.142 0.801
chi-square = 0.801 with df = 3; p-value = 0.151
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_21:31
b-rank test for bits 1 to 8, p=0.71085
b-rank test for bits 2 to 9, p=0.04512
b-rank test for bits 3 to 10, p=0.35870
b-rank test for bits 4 to 11, p=0.10671
b-rank test for bits 5 to 12, p=0.62211
b-rank test for bits 6 to 13, p=0.78914
b-rank test for bits 7 to 14, p=0.88270
b-rank test for bits 8 to 15, p=0.59369
b-rank test for bits 9 to 16, p=0.50965
b-rank test for bits 10 to 17, p=0.54574
b-rank test for bits 11 to 18, p=0.08103
b-rank test for bits 12 to 19, p=0.29873
b-rank test for bits 13 to 20, p=0.19861
b-rank test for bits 14 to 21, p=0.80727
b-rank test for bits 15 to 22, p=0.03465
b-rank test for bits 16 to 23, p=0.30138
b-rank test for bits 17 to 24, p=0.74524
b-rank test for bits 18 to 25, p=0.77334
b-rank test for bits 19 to 26, p=0.52697
b-rank test for bits 20 to 27, p=0.19930
b-rank test for bits 21 to 28, p=0.74037
b-rank test for bits 22 to 29, p=0.21691
b-rank test for bits 23 to 30, p=0.86377
b-rank test for bits 24 to 31, p=0.82115
b-rank test for bits 25 to 32, p=0.54824
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 = 0.810644
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_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 142598 1.61 0.946196
2 142182 0.64 0.737963
3 141877 -0.08 0.469894
4 141418 -1.15 0.125491
5 142516 1.42 0.921825
6 141437 -1.10 0.134889
7 141752 -0.37 0.356588
8 141800 -0.26 0.399190
9 142727 1.91 0.971962
10 141947 0.09 0.535067
11 141330 -1.35 0.087936
12 142276 0.86 0.804196
13 141546 -0.85 0.197968
14 141639 -0.63 0.263820
15 142767 2.00 0.977460
16 142035 0.29 0.615476
17 142044 0.31 0.623486
18 141443 -1.09 0.137954
19 141892 -0.04 0.483851
20 142592 1.60 0.944647
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_21:31
Bits used No. missing words z-score p-value
23 to 32 141922 0.0437 0.517424
22 to 31 141747 -0.5598 0.287822
21 to 30 141701 -0.7184 0.236262
20 to 29 141607 -1.0425 0.148586
19 to 28 141520 -1.3425 0.089714
18 to 27 141497 -1.4218 0.077538
17 to 26 141170 -2.5494 0.005395
16 to 25 141464 -1.5356 0.062316
15 to 24 141685 -0.7736 0.219598
14 to 23 141754 -0.5356 0.296110
13 to 22 141933 0.0816 0.532526
12 to 21 142458 1.8920 0.970752
11 to 20 141901 -0.0287 0.488542
10 to 19 142381 1.6264 0.948073
9 to 18 142130 0.7609 0.776651
8 to 17 142032 0.4230 0.663852
7 to 16 142037 0.4402 0.670119
6 to 15 141882 -0.0942 0.462459
5 to 14 141738 -0.5908 0.277330
4 to 13 141638 -0.9356 0.174734
3 to 12 142187 0.9575 0.830838
2 to 11 142213 1.0471 0.852482
1 to 10 141530 -1.3080 0.095431
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_21:31
Bits used No. missing words z-score p-value
28 to 32 142297 1.3141 0.905600
27 to 31 141717 -0.6520 0.257212
26 to 30 141777 -0.4486 0.326869
25 to 29 141905 -0.0147 0.494145
24 to 28 141136 -2.6215 0.004378
23 to 27 141548 -1.2248 0.110316
22 to 26 142177 0.9074 0.817891
21 to 25 142304 1.3379 0.909530
20 to 24 142066 0.5311 0.702320
19 to 23 141946 0.1243 0.549463
18 to 22 141571 -1.1469 0.125715
17 to 21 142251 1.1582 0.876610
16 to 20 142415 1.7141 0.956748
15 to 19 142386 1.6158 0.946935
14 to 18 142186 0.9379 0.825843
13 to 17 141878 -0.1062 0.457711
12 to 16 142107 0.6701 0.748593
11 to 15 141467 -1.4994 0.066882
10 to 14 141946 0.1243 0.549463
9 to 13 141710 -0.6757 0.249617
8 to 12 141895 -0.0486 0.480629
7 to 11 142170 0.8836 0.811551
6 to 10 142179 0.9141 0.819677
5 to 9 141373 -1.8181 0.034527
4 to 8 142580 2.2735 0.988501
3 to 7 141310 -2.0316 0.021096
2 to 6 141943 0.1141 0.545435
1 to 5 142035 0.4260 0.664946
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_21:31
Bits used No. missing words z-score p-value
31 to 32 141787 -0.3609 0.359104
30 to 31 142130 0.6509 0.742459
29 to 30 141571 -0.9980 0.159134
28 to 29 142024 0.3383 0.632416
27 to 28 141627 -0.8328 0.202470
26 to 27 142437 1.5565 0.940211
25 to 26 141770 -0.4110 0.340535
24 to 25 142162 0.7453 0.771967
23 to 24 141954 0.1318 0.552417
22 to 23 141448 -1.3609 0.086780
21 to 22 141501 -1.2045 0.114196
20 to 21 142077 0.4946 0.689559
19 to 20 142319 1.2085 0.886566
18 to 19 142271 1.0669 0.856985
17 to 18 142326 1.2291 0.890486
16 to 17 142324 1.2232 0.889376
15 to 16 141880 -0.0865 0.465527
14 to 15 142231 0.9489 0.828659
13 to 14 141775 -0.3963 0.345959
12 to 13 141722 -0.5526 0.290270
11 to 12 141885 -0.0718 0.471393
10 to 11 141434 -1.4022 0.080435
9 to 10 142255 1.0197 0.846059
8 to 9 141532 -1.1131 0.132840
7 to 8 142070 0.4740 0.682233
6 to 7 141491 -1.2340 0.108599
5 to 6 142133 0.6598 0.745307
4 to 5 142391 1.4209 0.922321
3 to 4 142274 1.0757 0.858974
2 to 3 141580 -0.9715 0.165656
1 to 2 142204 0.8692 0.807640
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2491.48 -0.120 0.452063
Test results for specific bytes for dh-ranFile-2018-06-15_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2501.82 0.026 0.510258
2 to 9 2399.29 -1.424 0.077182
3 to 10 2454.25 -0.647 0.258812
4 to 11 2640.17 1.982 0.976276
5 to 12 2405.05 -1.343 0.089671
6 to 13 2463.31 -0.519 0.301938
7 to 14 2536.03 0.509 0.694789
8 to 15 2445.60 -0.769 0.220854
9 to 16 2437.55 -0.883 0.188557
10 to 17 2468.29 -0.448 0.326923
11 to 18 2424.84 -1.063 0.143900
12 to 19 2434.88 -0.921 0.178538
13 to 20 2471.67 -0.401 0.344320
14 to 21 2464.61 -0.500 0.308364
15 to 22 2471.38 -0.405 0.342809
16 to 23 2360.58 -1.972 0.024325
17 to 24 2428.67 -1.009 0.156545
18 to 25 2548.67 0.688 0.754386
19 to 26 2450.69 -0.697 0.242775
20 to 27 2486.81 -0.187 0.426016
21 to 28 2447.02 -0.749 0.226840
22 to 29 2578.93 1.116 0.867839
23 to 30 2475.53 -0.346 0.364632
24 to 31 2442.88 -0.808 0.209613
25 to 32 2487.60 -0.175 0.430418
CDPARK for dh-ranFile-2018-06-15_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
3545 1.0046 0.842447
3543 0.9132 0.819442
3505 -0.8219 0.205562
3502 -0.9589 0.168804
3483 -1.8265 0.033889
3544 0.9589 0.831196
3515 -0.3653 0.357445
3490 -1.5068 0.065925
3498 -1.1416 0.126820
3533 0.4566 0.676028
Square side=100, avg. no. parked=3515.80 sample std.=22.47
p-value of the KSTEST for those 10 p-values: 0.320120
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_21:31
0.7303,0.7578,0.4301,0.7059,0.9826,0.7829,0.3431,0.6991,0.6328,0.0932,
The KS test for those 10 p-values: 0.253472
The 3DSPHERES test for dh-ranFile-2018-06-15_21:31
sample no r^3 equiv. uni.
1 26.776 0.590378
2 28.351 0.611339
3 21.389 0.509815
4 18.665 0.463223
5 60.908 0.868699
6 72.125 0.909659
7 17.167 0.435733
8 25.607 0.574105
9 35.134 0.689988
10 34.638 0.684821
11 16.866 0.430047
12 44.268 0.771357
13 53.041 0.829333
14 6.494 0.194646
15 26.803 0.590753
16 29.523 0.626227
17 10.580 0.297190
18 58.322 0.856879
19 11.205 0.311687
20 22.315 0.524714
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.096935
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.7 0.8 -0.3 0.5 -1.9
1.9 -1.4 1.0 0.5 -0.5 -1.7
-0.7 0.0 -1.1 -1.5 -0.0 0.8
0.3 0.2 1.5 -0.7 1.5 0.5
1.2 0.9 1.7 -0.5 -1.0 -0.6
-0.9 -1.3 -0.0 -1.2 -0.2 0.4
-0.7 -0.1 -0.4 -1.3 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:43.757719
z-score=0.191783, p-value=0.603240
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_21:31
Test no p-value
1 0.991565
2 0.489636
3 0.103467
4 0.138887
5 0.074857
6 0.070886
7 0.000368
8 0.214407
9 0.016774
10 0.008409
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000084
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_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 66454 0.68 66562 0.16
3 25000.00 25214 1.83 25136 0.74
4 6666.67 6699 0.16 6648 0.05
5 1388.89 1367 0.35 1370 0.26
6 238.10 228 0.43 247 0.33
7 34.72 30 0.64 32 0.21
8 4.96 7 0.84 4 0.19
p=0.44599 p=0.07534
Number of rngs required: 691354, p-value: 1.000
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_21:31
No. of wins: Observed Expected
98338 98585.9
z-score=-1.109, pvalue=0.13381
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66459 66666.7 0.647 0.647
2 38149 37654.3 6.499 7.146
3 26901 26954.7 0.107 7.253
4 19302 19313.5 0.007 7.260
5 13846 13851.4 0.002 7.262
6 9805 9943.5 1.930 9.192
7 7134 7145.0 0.017 9.209
8 5036 5139.1 2.067 11.276
9 3748 3699.9 0.626 11.903
10 2643 2666.3 0.204 12.106
11 1896 1923.3 0.388 12.494
12 1423 1388.7 0.845 13.340
13 993 1003.7 0.114 13.454
14 752 726.1 0.921 14.375
15 504 525.8 0.907 15.282
16 405 381.2 1.492 16.774
17 275 276.5 0.009 16.783
18 207 200.8 0.190 16.972
19 133 146.0 1.155 18.127
20 109 106.2 0.073 18.200
21 280 287.1 0.176 18.376
Chisq= 18.38 for 20 degrees of freedom, p= 0.43736
SUMMARY of craptest
p-value for no. of wins: 0.133808
p-value for throws/game: 0.437363
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_21:31
No. of wins: Observed Expected
98690 98585.9
z-score= 0.466, pvalue=0.67931
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66483 66666.7 0.506 0.506
2 37391 37654.3 1.841 2.347
3 27028 26954.7 0.199 2.547
4 19378 19313.5 0.216 2.762
5 13906 13851.4 0.215 2.977
6 9969 9943.5 0.065 3.042
7 7341 7145.0 5.375 8.418
8 5150 5139.1 0.023 8.441
9 3799 3699.9 2.656 11.097
10 2619 2666.3 0.839 11.936
11 1915 1923.3 0.036 11.972
12 1408 1388.7 0.267 12.239
13 985 1003.7 0.349 12.588
14 717 726.1 0.115 12.703
15 534 525.8 0.127 12.830
16 359 381.2 1.287 14.117
17 321 276.5 7.148 21.266
18 182 200.8 1.765 23.031
19 146 146.0 0.000 23.031
20 93 106.2 1.644 24.675
21 276 287.1 0.430 25.105
Chisq= 25.11 for 20 degrees of freedom, p= 0.80257
SUMMARY of craptest
p-value for no. of wins: 0.679314
p-value for throws/game: 0.802575
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0004,0.0044,0.0054,0.0084,0.0168,0.0211,0.0230,0.0243,0.0284,
0.0339,0.0345,0.0347,0.0451,0.0623,0.0659,0.0669,0.0709,0.0728,0.0749,
0.0753,0.0772,0.0775,0.0797,0.0804,0.0810,0.0868,0.0879,0.0897,0.0897,
0.0932,0.0954,0.0969,0.1035,0.1067,0.1073,0.1086,0.1103,0.1142,0.1167,
0.1178,0.1255,0.1257,0.1268,0.1328,0.1338,0.1349,0.1373,0.1380,0.1389,
0.1439,0.1484,0.1486,0.1508,0.1529,0.1565,0.1591,0.1657,0.1688,0.1747,
0.1749,0.1785,0.1886,0.1946,0.1980,0.1986,0.1993,0.2025,0.2031,0.2056,
0.2096,0.2144,0.2151,0.2169,0.2196,0.2209,0.2268,0.2363,0.2428,0.2496,
0.2535,0.2572,0.2588,0.2638,0.2648,0.2773,0.2788,0.2839,0.2878,0.2899,
0.2903,0.2961,0.2972,0.2981,0.2987,0.3014,0.3019,0.3040,0.3077,0.3084,
0.3117,0.3178,0.3201,0.3269,0.3269,0.3312,0.3405,0.3428,0.3431,0.3443,
0.3460,0.3566,0.3574,0.3587,0.3591,0.3640,0.3646,0.3749,0.3992,0.4260,
0.4300,0.4301,0.4304,0.4357,0.4374,0.4460,0.4471,0.4502,0.4521,0.4577,
0.4625,0.4632,0.4655,0.4699,0.4714,0.4727,0.4806,0.4839,0.4885,0.4896,
0.4941,0.4966,0.5096,0.5098,0.5103,0.5174,0.5247,0.5270,0.5325,0.5351,
0.5454,0.5457,0.5482,0.5495,0.5495,0.5524,0.5642,0.5741,0.5780,0.5794,
0.5904,0.5908,0.5937,0.6032,0.6113,0.6155,0.6221,0.6235,0.6262,0.6324,
0.6328,0.6504,0.6639,0.6648,0.6649,0.6701,0.6729,0.6732,0.6760,0.6793,
0.6822,0.6824,0.6848,0.6896,0.6900,0.6948,0.6991,0.7023,0.7059,0.7108,
0.7127,0.7243,0.7286,0.7303,0.7321,0.7380,0.7404,0.7425,0.7452,0.7453,
0.7486,0.7544,0.7578,0.7714,0.7720,0.7733,0.7767,0.7829,0.7891,0.7926,
0.7931,0.7967,0.8026,0.8042,0.8073,0.8076,0.8097,0.8106,0.8116,0.8179,
0.8194,0.8197,0.8212,0.8258,0.8287,0.8293,0.8307,0.8308,0.8312,0.8424,
0.8446,0.8461,0.8525,0.8569,0.8570,0.8590,0.8638,0.8678,0.8687,0.8698,
0.8766,0.8785,0.8789,0.8827,0.8866,0.8894,0.8905,0.9056,0.9095,0.9097,
0.9218,0.9223,0.9229,0.9283,0.9402,0.9446,0.9462,0.9469,0.9481,0.9486,
0.9567,0.9708,0.9720,0.9763,0.9775,0.9826,0.9885,0.9916,0.9998,
Overall p-value after applying KStest on 269 p-values = 0.184580
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.