RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.58 18.3431 0.632487
2 to 25 15.48 24.1082 0.883476
3 to 26 15.91 16.7495 0.528541
4 to 27 15.72 17.3190 0.567039
5 to 28 15.64 19.9044 0.720849
6 to 29 15.76 21.0212 0.774655
7 to 30 15.50 22.0565 0.817443
8 to 31 15.62 20.2537 0.738540
9 to 32 15.70 16.9503 0.542261
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.039394
Tough bday spacings test for dh-ranFile-2018-06-24_23:31: 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 12 39 71 99 91 65 64 27 20 9 3
(O-E)^2/E 0.9 0.2 0.1 0.0 0.5 2.2 2.7 0.3 1.8 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 9.665, p= 0.530
RESULTS OF GCD FOR dh-ranFile-2018-06-24_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.891383
p-value, dist. of gcd's: 0.216590
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.048 0.969 0.353 0.384 0.742 0.052 0.824 0.784
Bits 8 to 15---> 0.277 0.266 0.335 0.446 0.621 0.644 0.574 0.270
Bits 16 to 23---> 0.003 0.405 0.301 0.929 0.687 0.266 0.545 0.502
Bits 24 to 31---> 0.489 0.050 0.117 0.449 0.268 0.406 0.550 0.452
KS test for the above 32 p values: 0.788
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_23:31,
p-values for 5 runs: 0.2771, 0.7889, 0.7098, 0.9440, 0.6206
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 189 211.4 2.377 2.377
r= 29 5189 5134.0 0.589 2.966
r= 30 23133 23103.0 0.039 3.005
r= 31 11489 11551.5 0.338 3.343
chi-square = 3.343 with df = 3; p-value = 0.658
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 227 211.4 1.148 1.148
r= 30 5242 5134.0 2.271 3.420
r= 31 22840 23103.0 2.995 6.415
r= 32 11691 11551.5 1.684 8.099
chi-square = 8.099 with df = 3; p-value = 0.956
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_23:31
b-rank test for bits 1 to 8, p=0.73190
b-rank test for bits 2 to 9, p=0.75009
b-rank test for bits 3 to 10, p=0.63740
b-rank test for bits 4 to 11, p=0.39804
b-rank test for bits 5 to 12, p=0.72650
b-rank test for bits 6 to 13, p=0.01738
b-rank test for bits 7 to 14, p=0.50274
b-rank test for bits 8 to 15, p=0.41738
b-rank test for bits 9 to 16, p=0.28893
b-rank test for bits 10 to 17, p=0.47329
b-rank test for bits 11 to 18, p=0.79294
b-rank test for bits 12 to 19, p=0.67088
b-rank test for bits 13 to 20, p=0.53040
b-rank test for bits 14 to 21, p=0.56972
b-rank test for bits 15 to 22, p=0.09315
b-rank test for bits 16 to 23, p=0.17783
b-rank test for bits 17 to 24, p=0.53952
b-rank test for bits 18 to 25, p=0.04743
b-rank test for bits 19 to 26, p=0.61299
b-rank test for bits 20 to 27, p=0.26850
b-rank test for bits 21 to 28, p=0.01184
b-rank test for bits 22 to 29, p=0.10113
b-rank test for bits 23 to 30, p=0.55041
b-rank test for bits 24 to 31, p=0.47056
b-rank test for bits 25 to 32, p=0.77124
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 = 0.232855
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_23:31
(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 142299 0.91 0.818706
2 141348 -1.31 0.094841
3 142075 0.39 0.650651
4 141737 -0.40 0.343607
5 142173 0.62 0.731070
6 142279 0.86 0.806128
7 142280 0.87 0.806769
8 141714 -0.46 0.324059
9 142128 0.51 0.695293
10 141622 -0.67 0.251005
11 142808 2.10 0.982122
12 141659 -0.58 0.279313
13 142099 0.44 0.671173
14 141696 -0.50 0.309089
15 141383 -1.23 0.109397
16 141428 -1.12 0.130379
17 141513 -0.93 0.177222
18 142204 0.69 0.754425
19 142137 0.53 0.702616
20 141026 -2.06 0.019516
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_23:31
Bits used No. missing words z-score p-value
23 to 32 141814 -0.3287 0.371182
22 to 31 141821 -0.3046 0.380341
21 to 30 141797 -0.3873 0.349251
20 to 29 142363 1.5644 0.941136
19 to 28 141829 -0.2770 0.390890
18 to 27 141850 -0.2046 0.418948
17 to 26 142305 1.3644 0.913776
16 to 25 141207 -2.4218 0.007721
15 to 24 142349 1.5161 0.935253
14 to 23 142540 2.1747 0.985175
13 to 22 141922 0.0437 0.517424
12 to 21 141787 -0.4218 0.336575
11 to 20 141884 -0.0873 0.465199
10 to 19 142087 0.6127 0.729948
9 to 18 142208 1.0299 0.848471
8 to 17 142409 1.7230 0.957556
7 to 16 141989 0.2747 0.608236
6 to 15 141316 -2.0460 0.020380
5 to 14 142603 2.3920 0.991621
4 to 13 142125 0.7437 0.771468
3 to 12 141997 0.3023 0.618792
2 to 11 141557 -1.2149 0.112196
1 to 10 141620 -0.9977 0.159215
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_23:31
Bits used No. missing words z-score p-value
28 to 32 142540 2.1379 0.983736
27 to 31 141602 -1.0418 0.148753
26 to 30 142093 0.6226 0.733230
25 to 29 142361 1.5311 0.937126
24 to 28 141788 -0.4113 0.340431
23 to 27 141584 -1.1028 0.135054
22 to 26 141600 -1.0486 0.147187
21 to 25 141344 -1.9164 0.027659
20 to 24 141749 -0.5435 0.293396
19 to 23 142273 1.2328 0.891171
18 to 22 141786 -0.4181 0.337949
17 to 21 142148 0.8091 0.790757
16 to 20 141337 -1.9401 0.026184
15 to 19 141433 -1.6147 0.053190
14 to 18 141926 0.0565 0.522532
13 to 17 141571 -1.1469 0.125715
12 to 16 141918 0.0294 0.511723
11 to 15 141844 -0.2215 0.412368
10 to 14 142032 0.4158 0.661233
9 to 13 141845 -0.2181 0.413688
8 to 12 141763 -0.4960 0.309935
7 to 11 142340 1.4599 0.927841
6 to 10 142204 0.9989 0.841074
5 to 9 141407 -1.7028 0.044301
4 to 8 141688 -0.7503 0.226546
3 to 7 142020 0.3752 0.646227
2 to 6 141427 -1.6350 0.051023
1 to 5 141891 -0.0621 0.475227
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_23:31
Bits used No. missing words z-score p-value
31 to 32 141848 -0.1809 0.428217
30 to 31 141719 -0.5614 0.287247
29 to 30 142094 0.5447 0.707037
28 to 29 141682 -0.6706 0.251241
27 to 28 142048 0.4091 0.658751
26 to 27 141707 -0.5968 0.275306
25 to 26 141818 -0.2694 0.393807
24 to 25 141816 -0.2753 0.391539
23 to 24 141711 -0.5850 0.279259
22 to 23 141256 -1.9272 0.026976
21 to 22 141843 -0.1957 0.422437
20 to 21 141792 -0.3461 0.364632
19 to 20 141371 -1.5880 0.056144
18 to 19 142121 0.6244 0.733816
17 to 18 142073 0.4828 0.685382
16 to 17 142464 1.6362 0.949101
15 to 16 141837 -0.2134 0.415522
14 to 15 142188 0.8220 0.794472
13 to 14 141924 0.0433 0.517259
12 to 13 141577 -0.9803 0.163463
11 to 12 141743 -0.4906 0.311837
10 to 11 142413 1.4858 0.931328
9 to 10 141804 -0.3107 0.378011
8 to 9 141943 0.0993 0.539559
7 to 8 142023 0.3353 0.631304
6 to 7 141593 -0.9331 0.175377
5 to 6 141558 -1.0364 0.150014
4 to 5 141532 -1.1131 0.132840
3 to 4 141869 -0.1190 0.452651
2 to 3 141682 -0.6706 0.251241
1 to 2 141853 -0.1662 0.434014
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2415.76 -1.191 0.116765
Test results for specific bytes for dh-ranFile-2018-06-24_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2607.47 1.520 0.935721
2 to 9 2532.15 0.455 0.675344
3 to 10 2487.24 -0.180 0.428403
4 to 11 2543.07 0.609 0.728778
5 to 12 2488.32 -0.165 0.434403
6 to 13 2458.87 -0.582 0.280396
7 to 14 2403.86 -1.360 0.086985
8 to 15 2480.43 -0.277 0.391004
9 to 16 2527.17 0.384 0.649622
10 to 17 2453.31 -0.660 0.254512
11 to 18 2571.28 1.008 0.843293
12 to 19 2491.51 -0.120 0.452204
13 to 20 2522.68 0.321 0.625778
14 to 21 2501.45 0.020 0.508175
15 to 22 2392.25 -1.524 0.063775
16 to 23 2455.36 -0.631 0.263927
17 to 24 2305.44 -2.751 0.002967
18 to 25 2481.94 -0.255 0.399220
19 to 26 2583.73 1.184 0.881819
20 to 27 2447.44 -0.743 0.228660
21 to 28 2514.63 0.207 0.581948
22 to 29 2574.43 1.053 0.853743
23 to 30 2455.39 -0.631 0.264051
24 to 31 2477.74 -0.315 0.376438
25 to 32 2527.55 0.390 0.651614
CDPARK for dh-ranFile-2018-06-24_23:31: 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
3530 0.3196 0.625377
3530 0.3196 0.625377
3541 0.8219 0.794438
3557 1.5525 0.939730
3558 1.5982 0.944998
3525 0.0913 0.536383
3559 1.6438 0.949895
3528 0.2283 0.590298
3542 0.8676 0.807188
3522 -0.0457 0.481790
Square side=100, avg. no. parked=3539.20 sample std.=13.66
p-value of the KSTEST for those 10 p-values: 0.015469
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_23:31
0.5159,0.2191,0.3042,0.4857,0.0212,0.2587,0.0284,0.6005,0.3569,0.6501,
The KS test for those 10 p-values: 0.113141
The 3DSPHERES test for dh-ranFile-2018-06-24_23:31
sample no r^3 equiv. uni.
1 20.254 0.490913
2 58.539 0.857912
3 32.087 0.656841
4 55.040 0.840333
5 1.629 0.052837
6 21.804 0.516551
7 12.703 0.345210
8 82.285 0.935612
9 37.633 0.714763
10 26.910 0.592210
11 46.675 0.788989
12 0.639 0.021086
13 4.968 0.152619
14 30.216 0.634754
15 75.894 0.920325
16 12.187 0.333851
17 82.497 0.936065
18 45.531 0.780786
19 44.777 0.775204
20 60.237 0.865731
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.108468
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -0.4 0.6 0.3 0.0
-0.8 -0.9 -0.4 1.4 -0.1 -0.3
1.5 0.2 0.3 0.2 -0.7 -0.0
0.2 0.2 -1.3 1.2 0.4 -0.9
-0.3 -0.2 0.1 -0.3 -1.4 0.1
-1.8 -0.4 0.2 0.4 0.1 0.1
1.7 0.2 0.9 -0.7 1.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:27.486294
z-score=-1.583575, p-value=0.040961
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_23:31
Test no p-value
1 0.167808
2 0.769861
3 0.008939
4 0.889215
5 0.166690
6 0.146549
7 0.115475
8 0.304372
9 0.921373
10 0.032739
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.048166
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_23:31:
(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 66396 1.10 66711 0.03
3 25000.00 25256 2.62 24972 0.03
4 6666.67 6696 0.13 6668 0.00
5 1388.89 1361 0.56 1359 0.64
6 238.10 261 2.20 255 1.20
7 34.72 26 2.19 33 0.09
8 4.96 3 0.77 1 3.16
p=0.85639 p=0.47546
Number of rngs required: 687860, p-value: 0.266
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_23:31
No. of wins: Observed Expected
98550 98585.9
z-score=-0.160, pvalue=0.43629
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66563 66666.7 0.161 0.161
2 37534 37654.3 0.384 0.546
3 26872 26954.7 0.254 0.800
4 19378 19313.5 0.216 1.015
5 13780 13851.4 0.368 1.384
6 9812 9943.5 1.740 3.124
7 7279 7145.0 2.512 5.636
8 5220 5139.1 1.274 6.910
9 3797 3699.9 2.550 9.460
10 2672 2666.3 0.012 9.473
11 1979 1923.3 1.611 11.084
12 1416 1388.7 0.535 11.619
13 1034 1003.7 0.914 12.533
14 693 726.1 1.513 14.045
15 551 525.8 1.204 15.250
16 392 381.2 0.309 15.558
17 264 276.5 0.569 16.127
18 208 200.8 0.256 16.383
19 149 146.0 0.062 16.445
20 115 106.2 0.727 17.172
21 292 287.1 0.083 17.255
Chisq= 17.26 for 20 degrees of freedom, p= 0.36364
SUMMARY of craptest
p-value for no. of wins: 0.436291
p-value for throws/game: 0.363643
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_23:31
No. of wins: Observed Expected
98507 98585.9
z-score=-0.353, pvalue=0.36216
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66394 66666.7 1.115 1.115
2 37252 37654.3 4.299 5.414
3 27031 26954.7 0.216 5.630
4 19382 19313.5 0.243 5.873
5 14013 13851.4 1.885 7.758
6 10135 9943.5 3.686 11.444
7 7142 7145.0 0.001 11.445
8 5299 5139.1 4.977 16.422
9 3683 3699.9 0.077 16.499
10 2737 2666.3 1.875 18.374
11 1929 1923.3 0.017 18.391
12 1379 1388.7 0.068 18.459
13 1035 1003.7 0.975 19.434
14 721 726.1 0.036 19.471
15 497 525.8 1.581 21.052
16 377 381.2 0.045 21.097
17 289 276.5 0.561 21.659
18 194 200.8 0.232 21.891
19 143 146.0 0.061 21.952
20 87 106.2 3.476 25.428
21 281 287.1 0.130 25.558
Chisq= 25.56 for 20 degrees of freedom, p= 0.81910
SUMMARY of craptest
p-value for no. of wins: 0.362156
p-value for throws/game: 0.819098
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0030,0.0032,0.0077,0.0089,0.0118,0.0155,0.0174,0.0195,0.0204,0.0211,
0.0212,0.0262,0.0270,0.0277,0.0284,0.0327,0.0394,0.0410,0.0443,0.0474,
0.0476,0.0482,0.0499,0.0510,0.0519,0.0528,0.0532,0.0561,0.0638,0.0870,
0.0932,0.0948,0.1011,0.1085,0.1094,0.1122,0.1131,0.1155,0.1168,0.1173,
0.1257,0.1304,0.1328,0.1351,0.1465,0.1472,0.1488,0.1500,0.1526,0.1592,
0.1635,0.1667,0.1678,0.1754,0.1772,0.1778,0.2166,0.2191,0.2265,0.2287,
0.2329,0.2510,0.2512,0.2512,0.2545,0.2587,0.2639,0.2641,0.2655,0.2656,
0.2656,0.2680,0.2685,0.2698,0.2753,0.2765,0.2771,0.2793,0.2793,0.2804,
0.2872,0.2889,0.2934,0.3010,0.3042,0.3044,0.3091,0.3099,0.3118,0.3241,
0.3339,0.3349,0.3366,0.3379,0.3404,0.3436,0.3452,0.3493,0.3534,0.3569,
0.3622,0.3636,0.3646,0.3712,0.3764,0.3780,0.3803,0.3837,0.3909,0.3910,
0.3915,0.3938,0.3980,0.3992,0.4051,0.4058,0.4124,0.4137,0.4155,0.4174,
0.4189,0.4224,0.4282,0.4284,0.4340,0.4344,0.4363,0.4459,0.4494,0.4517,
0.4522,0.4527,0.4652,0.4706,0.4733,0.4752,0.4755,0.4818,0.4857,0.4886,
0.4909,0.5024,0.5027,0.5082,0.5117,0.5159,0.5166,0.5173,0.5174,0.5225,
0.5285,0.5297,0.5304,0.5364,0.5395,0.5396,0.5423,0.5446,0.5504,0.5504,
0.5670,0.5697,0.5740,0.5819,0.5903,0.5922,0.6005,0.6082,0.6130,0.6188,
0.6206,0.6214,0.6254,0.6254,0.6258,0.6313,0.6325,0.6348,0.6374,0.6438,
0.6462,0.6496,0.6501,0.6507,0.6516,0.6568,0.6583,0.6588,0.6612,0.6709,
0.6712,0.6753,0.6854,0.6869,0.6953,0.7026,0.7070,0.7098,0.7148,0.7208,
0.7265,0.7288,0.7299,0.7311,0.7319,0.7332,0.7338,0.7385,0.7418,0.7501,
0.7544,0.7699,0.7712,0.7715,0.7747,0.7752,0.7808,0.7839,0.7878,0.7889,
0.7890,0.7908,0.7929,0.7944,0.7945,0.8061,0.8068,0.8072,0.8174,0.8187,
0.8191,0.8240,0.8403,0.8411,0.8433,0.8485,0.8537,0.8564,0.8579,0.8657,
0.8818,0.8835,0.8892,0.8912,0.8914,0.9138,0.9203,0.9214,0.9278,0.9288,
0.9313,0.9353,0.9356,0.9357,0.9361,0.9371,0.9397,0.9411,0.9440,0.9450,
0.9491,0.9499,0.9560,0.9576,0.9685,0.9821,0.9837,0.9852,0.9916,
Overall p-value after applying KStest on 269 p-values = 0.268709
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.