RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_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 15.90 12.6303 0.239437
2 to 25 15.69 14.8898 0.396581
3 to 26 15.96 30.6881 0.978211
4 to 27 15.55 22.1224 0.819944
5 to 28 16.12 19.5178 0.700365
6 to 29 16.05 28.1382 0.956650
7 to 30 16.25 27.1260 0.943754
8 to 31 15.94 19.9464 0.723021
9 to 32 15.45 27.7085 0.951538
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.007382
Tough bday spacings test for dh-ranFile-2018-06-29_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 9 31 79 91 94 79 56 35 13 7 6
(O-E)^2/E 0.0 0.9 0.4 0.5 0.1 0.0 0.3 0.9 0.2 0.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 4.315, p= 0.068
RESULTS OF GCD FOR dh-ranFile-2018-06-29_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.504054
p-value, dist. of gcd's: 0.137477
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.986 0.640 0.853 0.635 0.965 0.532 0.323 0.726
Bits 8 to 15---> 0.821 0.875 0.108 0.202 0.130 0.175 0.611 0.406
Bits 16 to 23---> 0.661 0.518 0.435 0.763 0.815 0.234 0.766 0.688
Bits 24 to 31---> 0.275 0.878 0.191 0.830 0.335 0.707 0.224 0.846
KS test for the above 32 p values: 0.741
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_21:31,
p-values for 5 runs: 0.3309, 0.4623, 0.2839, 0.4957, 0.8477
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 235 211.4 2.630 2.630
r= 29 5120 5134.0 0.038 2.669
r= 30 23124 23103.0 0.019 2.688
r= 31 11521 11551.5 0.081 2.768
chi-square = 2.768 with df = 3; p-value = 0.571
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 195 211.4 1.275 1.275
r= 30 5042 5134.0 1.649 2.924
r= 31 22946 23103.0 1.068 3.992
r= 32 11817 11551.5 6.101 10.093
chi-square = 10.093 with df = 3; p-value = 0.982
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_21:31
b-rank test for bits 1 to 8, p=0.40449
b-rank test for bits 2 to 9, p=0.89788
b-rank test for bits 3 to 10, p=0.82070
b-rank test for bits 4 to 11, p=0.31912
b-rank test for bits 5 to 12, p=0.48811
b-rank test for bits 6 to 13, p=0.93026
b-rank test for bits 7 to 14, p=0.16177
b-rank test for bits 8 to 15, p=0.07180
b-rank test for bits 9 to 16, p=0.69135
b-rank test for bits 10 to 17, p=0.76081
b-rank test for bits 11 to 18, p=0.96943
b-rank test for bits 12 to 19, p=0.62557
b-rank test for bits 13 to 20, p=0.86757
b-rank test for bits 14 to 21, p=0.64061
b-rank test for bits 15 to 22, p=0.83389
b-rank test for bits 16 to 23, p=0.77989
b-rank test for bits 17 to 24, p=0.60057
b-rank test for bits 18 to 25, p=0.32142
b-rank test for bits 19 to 26, p=0.91489
b-rank test for bits 20 to 27, p=0.57405
b-rank test for bits 21 to 28, p=0.29365
b-rank test for bits 22 to 29, p=0.39067
b-rank test for bits 23 to 30, p=0.19961
b-rank test for bits 24 to 31, p=0.53359
b-rank test for bits 25 to 32, p=0.37675
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 = 0.306726
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_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 141466 -1.04 0.150144
2 141842 -0.16 0.437499
3 141387 -1.22 0.111157
4 140990 -2.15 0.015858
5 142151 0.56 0.713844
6 141169 -1.73 0.041838
7 142379 1.10 0.863758
8 141654 -0.60 0.275399
9 142098 0.44 0.670328
10 141422 -1.14 0.127431
11 142568 1.54 0.938092
12 141599 -0.73 0.234205
13 142436 1.23 0.890752
14 142237 0.77 0.778038
15 142231 0.75 0.773844
16 141171 -1.73 0.042257
17 141478 -1.01 0.156780
18 142778 2.03 0.978802
19 141162 -1.75 0.040397
20 142360 1.05 0.853822
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_21:31
Bits used No. missing words z-score p-value
23 to 32 142720 2.7954 0.997408
22 to 31 141788 -0.4184 0.337835
21 to 30 142029 0.4127 0.660070
20 to 29 142176 0.9196 0.821097
19 to 28 141916 0.0230 0.509175
18 to 27 141945 0.1230 0.548947
17 to 26 141858 -0.1770 0.429754
16 to 25 142194 0.9816 0.836857
15 to 24 141813 -0.3322 0.369880
14 to 23 142047 0.4747 0.682508
13 to 22 141328 -2.0046 0.022504
12 to 21 141617 -1.0080 0.156719
11 to 20 142198 0.9954 0.840233
10 to 19 141356 -1.9080 0.028193
9 to 18 141963 0.1851 0.573413
8 to 17 141449 -1.5873 0.056217
7 to 16 141054 -2.9494 0.001592
6 to 15 142209 1.0333 0.849279
5 to 14 142215 1.0540 0.854066
4 to 13 141913 0.0127 0.505049
3 to 12 142123 0.7368 0.769376
2 to 11 141899 -0.0356 0.485792
1 to 10 141095 -2.8080 0.002492
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_21:31
Bits used No. missing words z-score p-value
28 to 32 142008 0.3345 0.630989
27 to 31 142095 0.6294 0.735453
26 to 30 142216 1.0396 0.850728
25 to 29 141980 0.2396 0.594664
24 to 28 141752 -0.5333 0.296905
23 to 27 142041 0.4463 0.672324
22 to 26 141877 -0.1096 0.456366
21 to 25 142364 1.5413 0.938373
20 to 24 142471 1.9040 0.971543
19 to 23 141920 0.0362 0.514426
18 to 22 142214 1.0328 0.849147
17 to 21 142028 0.4023 0.656258
16 to 20 142393 1.6396 0.949452
15 to 19 142362 1.5345 0.937544
14 to 18 142115 0.6972 0.757157
13 to 17 142259 1.1853 0.882055
12 to 16 142066 0.5311 0.702320
11 to 15 142050 0.4768 0.683265
10 to 14 142309 1.3548 0.912262
9 to 13 142094 0.6260 0.734343
8 to 12 142357 1.5175 0.935433
7 to 11 142295 1.3074 0.904454
6 to 10 141373 -1.8181 0.034527
5 to 9 141842 -0.2282 0.409731
4 to 8 142066 0.5311 0.702320
3 to 7 142289 1.2870 0.900956
2 to 6 142004 0.3209 0.625863
1 to 5 141966 0.1921 0.576169
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_21:31
Bits used No. missing words z-score p-value
31 to 32 141688 -0.6529 0.256913
30 to 31 141612 -0.8771 0.190222
29 to 30 141707 -0.5968 0.275306
28 to 29 141404 -1.4906 0.068027
27 to 28 142120 0.6214 0.732847
26 to 27 141901 -0.0246 0.490198
25 to 26 142849 2.7719 0.997213
24 to 25 141994 0.2498 0.598615
23 to 24 142204 0.8692 0.807640
22 to 23 142599 2.0344 0.979046
21 to 22 141722 -0.5526 0.290270
20 to 21 141441 -1.3815 0.083562
19 to 20 142007 0.2881 0.613370
18 to 19 141660 -0.7355 0.231022
17 to 18 141398 -1.5083 0.065733
16 to 17 141540 -1.0895 0.137974
15 to 16 142026 0.3442 0.634637
14 to 15 142182 0.8043 0.789399
13 to 14 142142 0.6863 0.753751
12 to 13 141998 0.2616 0.603171
11 to 12 141508 -1.1839 0.118233
10 to 11 141950 0.1200 0.547747
9 to 10 142180 0.7984 0.787691
8 to 9 142244 0.9872 0.838234
7 to 8 141359 -1.6234 0.052253
6 to 7 141505 -1.1927 0.116491
5 to 6 141795 -0.3373 0.367962
4 to 5 141850 -0.1750 0.430534
3 to 4 141448 -1.3609 0.086780
2 to 3 142101 0.5654 0.714099
1 to 2 141803 -0.3137 0.376891
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2446.41 -0.758 0.224248
Test results for specific bytes for dh-ranFile-2018-06-29_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2439.75 -0.852 0.197081
2 to 9 2471.67 -0.401 0.344351
3 to 10 2506.07 0.086 0.534217
4 to 11 2557.82 0.818 0.793235
5 to 12 2454.51 -0.643 0.260022
6 to 13 2575.88 1.073 0.858378
7 to 14 2452.28 -0.675 0.249887
8 to 15 2431.25 -0.972 0.165461
9 to 16 2520.02 0.283 0.611480
10 to 17 2518.43 0.261 0.602813
11 to 18 2674.48 2.467 0.993197
12 to 19 2567.36 0.953 0.829590
13 to 20 2566.66 0.943 0.827084
14 to 21 2628.13 1.812 0.965013
15 to 22 2531.45 0.445 0.671768
16 to 23 2498.30 -0.024 0.490403
17 to 24 2517.14 0.242 0.595768
18 to 25 2602.97 1.456 0.927341
19 to 26 2373.97 -1.782 0.037348
20 to 27 2475.07 -0.353 0.362214
21 to 28 2565.82 0.931 0.824039
22 to 29 2545.49 0.643 0.739978
23 to 30 2485.83 -0.200 0.420584
24 to 31 2517.54 0.248 0.597980
25 to 32 2472.45 -0.390 0.348411
CDPARK for dh-ranFile-2018-06-29_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
3531 0.3653 0.642555
3504 -0.8676 0.192812
3519 -0.1826 0.427537
3529 0.2740 0.607947
3574 2.3288 0.990064
3505 -0.8219 0.205562
3516 -0.3196 0.374623
3516 -0.3196 0.374623
3534 0.5023 0.692266
3530 0.3196 0.625377
Square side=100, avg. no. parked=3525.80 sample std.=18.95
p-value of the KSTEST for those 10 p-values: 0.617591
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_21:31
0.4261,0.0216,0.7138,0.6188,0.6081,0.6810,0.5781,0.3627,0.6988,0.6613,
The KS test for those 10 p-values: 0.228401
The 3DSPHERES test for dh-ranFile-2018-06-29_21:31
sample no r^3 equiv. uni.
1 11.416 0.316503
2 5.818 0.176300
3 8.396 0.244115
4 35.857 0.697364
5 5.345 0.163195
6 19.241 0.473428
7 3.035 0.096232
8 18.479 0.459888
9 4.842 0.149046
10 51.538 0.820561
11 30.190 0.634443
12 45.653 0.781677
13 54.206 0.835832
14 16.544 0.423896
15 59.076 0.860433
16 6.458 0.193674
17 28.545 0.613843
18 20.061 0.487625
19 3.202 0.101229
20 54.090 0.835198
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.711003
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 1.3 -0.6 -1.1 -0.5 -0.4
0.5 -1.2 -1.8 0.3 0.7 0.7
0.9 2.6 1.0 0.5 -1.8 -0.8
-0.3 -0.3 -0.8 0.1 -0.6 -0.4
1.0 -0.1 -0.8 0.7 -0.2 0.2
-1.2 0.8 -0.1 0.7 -0.1 -1.4
0.0 0.5 -0.4 0.4 0.9 -1.0
-0.1
Chi-square with 42 degrees of freedom:36.977143
z-score=-0.548039, p-value=0.309249
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_21:31
Test no p-value
1 0.099652
2 0.018001
3 0.289326
4 0.010799
5 0.512992
6 0.106669
7 0.412493
8 0.342056
9 0.664218
10 0.620726
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.041155
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_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 66694 0.01 66825 0.38
3 25000.00 24964 0.05 24939 0.15
4 6666.67 6647 0.06 6590 0.88
5 1388.89 1414 0.45 1370 0.26
6 238.10 239 0.00 243 0.10
7 34.72 35 0.00 29 0.94
8 4.96 6 0.22 3 0.77
p=0.00789 p=0.25356
Number of rngs required: 688427, p-value: 0.511
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_21:31
No. of wins: Observed Expected
98485 98585.9
z-score=-0.451, pvalue=0.32596
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66541 66666.7 0.237 0.237
2 37688 37654.3 0.030 0.267
3 27023 26954.7 0.173 0.440
4 19224 19313.5 0.414 0.854
5 13807 13851.4 0.142 0.997
6 10048 9943.5 1.097 2.094
7 7101 7145.0 0.271 2.365
8 5105 5139.1 0.226 2.591
9 3751 3699.9 0.707 3.298
10 2699 2666.3 0.401 3.699
11 1995 1923.3 2.671 6.370
12 1369 1388.7 0.281 6.650
13 1008 1003.7 0.018 6.669
14 687 726.1 2.110 8.778
15 539 525.8 0.330 9.108
16 372 381.2 0.220 9.328
17 316 276.5 5.631 14.959
18 210 200.8 0.419 15.377
19 130 146.0 1.750 17.127
20 108 106.2 0.030 17.157
21 279 287.1 0.229 17.387
Chisq= 17.39 for 20 degrees of freedom, p= 0.37226
SUMMARY of craptest
p-value for no. of wins: 0.325959
p-value for throws/game: 0.372261
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_21:31
No. of wins: Observed Expected
98575 98585.9
z-score=-0.049, pvalue=0.48063
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66300 66666.7 2.017 2.017
2 37990 37654.3 2.992 5.009
3 27038 26954.7 0.257 5.266
4 19272 19313.5 0.089 5.355
5 13836 13851.4 0.017 5.373
6 9961 9943.5 0.031 5.403
7 7065 7145.0 0.896 6.300
8 5177 5139.1 0.280 6.579
9 3647 3699.9 0.755 7.335
10 2690 2666.3 0.211 7.545
11 1920 1923.3 0.006 7.551
12 1392 1388.7 0.008 7.559
13 1038 1003.7 1.171 8.730
14 735 726.1 0.108 8.838
15 559 525.8 2.092 10.930
16 355 381.2 1.794 12.724
17 292 276.5 0.864 13.588
18 193 200.8 0.305 13.894
19 161 146.0 1.544 15.438
20 100 106.2 0.364 15.802
21 279 287.1 0.229 16.031
Chisq= 16.03 for 20 degrees of freedom, p= 0.28530
SUMMARY of craptest
p-value for no. of wins: 0.480633
p-value for throws/game: 0.285302
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0025,0.0074,0.0079,0.0108,0.0159,0.0180,0.0216,0.0225,0.0282,
0.0345,0.0373,0.0404,0.0412,0.0418,0.0423,0.0523,0.0562,0.0657,0.0680,
0.0680,0.0718,0.0836,0.0868,0.0962,0.0997,0.1012,0.1067,0.1076,0.1112,
0.1165,0.1182,0.1274,0.1297,0.1375,0.1380,0.1490,0.1501,0.1567,0.1568,
0.1618,0.1632,0.1655,0.1751,0.1763,0.1902,0.1908,0.1928,0.1937,0.1971,
0.1996,0.2021,0.2056,0.2242,0.2244,0.2284,0.2310,0.2342,0.2345,0.2394,
0.2441,0.2499,0.2536,0.2569,0.2600,0.2753,0.2754,0.2754,0.2839,0.2853,
0.2893,0.2903,0.2937,0.2969,0.3067,0.3092,0.3165,0.3191,0.3214,0.3226,
0.3260,0.3309,0.3352,0.3378,0.3421,0.3444,0.3484,0.3622,0.3627,0.3680,
0.3699,0.3723,0.3746,0.3746,0.3767,0.3769,0.3907,0.3966,0.4045,0.4060,
0.4097,0.4125,0.4206,0.4239,0.4261,0.4275,0.4298,0.4305,0.4351,0.4375,
0.4564,0.4599,0.4623,0.4734,0.4806,0.4858,0.4876,0.4881,0.4902,0.4904,
0.4957,0.5041,0.5050,0.5092,0.5110,0.5130,0.5144,0.5176,0.5322,0.5336,
0.5342,0.5477,0.5489,0.5713,0.5734,0.5740,0.5762,0.5781,0.5947,0.5958,
0.5980,0.5986,0.6006,0.6028,0.6032,0.6079,0.6081,0.6111,0.6115,0.6134,
0.6138,0.6176,0.6188,0.6207,0.6254,0.6256,0.6259,0.6310,0.6344,0.6346,
0.6348,0.6397,0.6406,0.6426,0.6563,0.6601,0.6609,0.6613,0.6642,0.6703,
0.6718,0.6723,0.6810,0.6825,0.6833,0.6879,0.6914,0.6923,0.6974,0.6988,
0.7004,0.7023,0.7023,0.7075,0.7110,0.7138,0.7138,0.7141,0.7230,0.7258,
0.7328,0.7343,0.7355,0.7400,0.7413,0.7538,0.7572,0.7608,0.7626,0.7663,
0.7694,0.7738,0.7780,0.7799,0.7817,0.7877,0.7894,0.7932,0.8076,0.8155,
0.8199,0.8206,0.8207,0.8209,0.8211,0.8240,0.8271,0.8296,0.8297,0.8339,
0.8352,0.8358,0.8369,0.8382,0.8402,0.8461,0.8477,0.8491,0.8493,0.8507,
0.8530,0.8538,0.8541,0.8584,0.8604,0.8638,0.8676,0.8747,0.8778,0.8821,
0.8908,0.8979,0.9010,0.9045,0.9123,0.9149,0.9273,0.9303,0.9354,0.9375,
0.9381,0.9384,0.9438,0.9495,0.9515,0.9567,0.9650,0.9655,0.9694,0.9715,
0.9782,0.9788,0.9790,0.9822,0.9859,0.9901,0.9932,0.9972,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.243303
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.