RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 15.0260 0.406394
2 to 25 15.49 23.0069 0.850974
3 to 26 15.61 17.0544 0.549313
4 to 27 15.87 21.6369 0.800911
5 to 28 15.84 12.3293 0.220199
6 to 29 15.93 18.9039 0.665923
7 to 30 15.93 16.3522 0.500982
8 to 31 15.85 16.4488 0.507731
9 to 32 15.94 12.8291 0.252450
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.665310
Tough bday spacings test for dh-ranFile-2018-07-10_08:31: 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 42 50 93 105 93 51 23 16 10 8
(O-E)^2/E 0.0 0.8 7.4 0.2 0.5 2.8 0.0 1.5 0.1 1.7 3.8
Birthday Spacings: Sum(O-E)^2/E= 18.955, p= 0.959
RESULTS OF GCD FOR dh-ranFile-2018-07-10_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.796125
p-value, dist. of gcd's: 0.799373
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.624 0.591 0.279 0.394 0.587 0.479 0.901 0.182
Bits 8 to 15---> 0.495 0.833 0.207 0.180 0.753 0.222 0.906 0.192
Bits 16 to 23---> 0.462 0.363 0.442 0.882 0.125 0.258 0.742 0.546
Bits 24 to 31---> 0.699 0.640 0.551 0.869 0.465 0.297 0.108 0.832
KS test for the above 32 p values: 0.406
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_08:31,
p-values for 5 runs: 0.2015, 0.4807, 0.7843, 0.5440, 0.7004
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5213 5134.0 1.215 1.745
r= 30 23027 23103.0 0.250 1.995
r= 31 11538 11551.5 0.016 2.011
chi-square = 2.011 with df = 3; p-value = 0.430
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 242 211.4 4.424 4.424
r= 30 5142 5134.0 0.012 4.436
r= 31 23220 23103.0 0.592 5.028
r= 32 11396 11551.5 2.094 7.122
chi-square = 7.122 with df = 3; p-value = 0.932
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_08:31
b-rank test for bits 1 to 8, p=0.92610
b-rank test for bits 2 to 9, p=0.67087
b-rank test for bits 3 to 10, p=0.82469
b-rank test for bits 4 to 11, p=0.91872
b-rank test for bits 5 to 12, p=0.27434
b-rank test for bits 6 to 13, p=0.83579
b-rank test for bits 7 to 14, p=0.31589
b-rank test for bits 8 to 15, p=0.14062
b-rank test for bits 9 to 16, p=0.20303
b-rank test for bits 10 to 17, p=0.23254
b-rank test for bits 11 to 18, p=0.03053
b-rank test for bits 12 to 19, p=0.27404
b-rank test for bits 13 to 20, p=0.10669
b-rank test for bits 14 to 21, p=0.78341
b-rank test for bits 15 to 22, p=0.15902
b-rank test for bits 16 to 23, p=0.84583
b-rank test for bits 17 to 24, p=0.11197
b-rank test for bits 18 to 25, p=0.03465
b-rank test for bits 19 to 26, p=0.87897
b-rank test for bits 20 to 27, p=0.39394
b-rank test for bits 21 to 28, p=0.79866
b-rank test for bits 22 to 29, p=0.18805
b-rank test for bits 23 to 30, p=0.93642
b-rank test for bits 24 to 31, p=0.63215
b-rank test for bits 25 to 32, p=0.40742
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 = 0.423391
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_08:31
(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 142661 1.76 0.960476
2 142205 0.69 0.755160
3 141745 -0.38 0.350508
4 141978 0.16 0.563734
5 141845 -0.15 0.440263
6 141552 -0.83 0.201892
7 141718 -0.45 0.327426
8 142125 0.50 0.692835
9 141642 -0.62 0.266116
10 141996 0.20 0.580237
11 141563 -0.81 0.209205
12 142619 1.66 0.951352
13 141682 -0.53 0.297659
14 142128 0.51 0.695293
15 141940 0.07 0.528563
16 142751 1.97 0.975381
17 142429 1.21 0.887661
18 141212 -1.63 0.051627
19 141882 -0.06 0.474543
20 141383 -1.23 0.109397
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_08:31
Bits used No. missing words z-score p-value
23 to 32 141645 -0.9115 0.181021
22 to 31 142359 1.5506 0.939500
21 to 30 141285 -2.1529 0.015665
20 to 29 142002 0.3196 0.625346
19 to 28 141539 -1.2770 0.100801
18 to 27 141720 -0.6529 0.256923
17 to 26 142005 0.3299 0.629261
16 to 25 142005 0.3299 0.629261
15 to 24 141608 -1.0391 0.149386
14 to 23 141794 -0.3977 0.345430
13 to 22 142324 1.4299 0.923627
12 to 21 141712 -0.6804 0.248110
11 to 20 142322 1.4230 0.922632
10 to 19 141990 0.2782 0.609560
9 to 18 142109 0.6885 0.754436
8 to 17 141782 -0.4391 0.330306
7 to 16 142044 0.4644 0.678812
6 to 15 141755 -0.5322 0.297303
5 to 14 142000 0.3127 0.622729
4 to 13 141783 -0.4356 0.331556
3 to 12 141586 -1.1149 0.132440
2 to 11 141989 0.2747 0.608236
1 to 10 141449 -1.5873 0.056217
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_08:31
Bits used No. missing words z-score p-value
28 to 32 142098 0.6396 0.738770
27 to 31 142069 0.5413 0.705834
26 to 30 142054 0.4904 0.688077
25 to 29 141788 -0.4113 0.340431
24 to 28 142344 1.4735 0.929686
23 to 27 141887 -0.0757 0.469831
22 to 26 141397 -1.7367 0.041219
21 to 25 142038 0.4362 0.668643
20 to 24 141667 -0.8215 0.205693
19 to 23 142240 1.1209 0.868838
18 to 22 142259 1.1853 0.882055
17 to 21 141660 -0.8452 0.199003
16 to 20 142100 0.6463 0.740970
15 to 19 141893 -0.0554 0.477928
14 to 18 141879 -0.1028 0.459056
13 to 17 142085 0.5955 0.724243
12 to 16 142134 0.7616 0.776849
11 to 15 142003 0.3175 0.624578
10 to 14 141695 -0.7265 0.233753
9 to 13 141346 -1.9096 0.028093
8 to 12 141171 -2.5028 0.006161
7 to 11 141464 -1.5096 0.065574
6 to 10 141993 0.2836 0.611652
5 to 9 142334 1.4396 0.925004
4 to 8 141859 -0.1706 0.432265
3 to 7 141420 -1.6587 0.048584
2 to 6 141993 0.2836 0.611652
1 to 5 142097 0.6362 0.737667
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_08:31
Bits used No. missing words z-score p-value
31 to 32 141329 -1.7119 0.043459
30 to 31 142776 2.5565 0.994714
29 to 30 142240 0.9754 0.835326
28 to 29 142317 1.2026 0.885428
27 to 28 141991 0.2409 0.595189
26 to 27 142202 0.8633 0.806023
25 to 26 141748 -0.4759 0.317073
24 to 25 142786 2.5860 0.995146
23 to 24 141759 -0.4435 0.328720
22 to 23 141722 -0.5526 0.290270
21 to 22 142684 2.2852 0.988848
20 to 21 142055 0.4297 0.666295
19 to 20 141633 -0.8151 0.207498
18 to 19 142260 1.0344 0.849531
17 to 18 142575 1.9636 0.975213
16 to 17 141701 -0.6145 0.269428
15 to 16 141682 -0.6706 0.251241
14 to 15 142007 0.2881 0.613370
13 to 14 142631 2.1288 0.983365
12 to 13 142046 0.4032 0.656583
11 to 12 142024 0.3383 0.632416
10 to 11 141932 0.0669 0.526659
9 to 10 141797 -0.3314 0.370187
8 to 9 142549 1.8869 0.970415
7 to 8 141458 -1.3314 0.091536
6 to 7 142283 1.1023 0.864828
5 to 6 141569 -1.0039 0.157708
4 to 5 142204 0.8692 0.807640
3 to 4 141792 -0.3461 0.364632
2 to 3 141987 0.2291 0.590610
1 to 2 142276 1.0816 0.860290
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2607.24 1.517 0.935318
Test results for specific bytes for dh-ranFile-2018-07-10_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2448.89 -0.723 0.234883
2 to 9 2352.21 -2.090 0.018308
3 to 10 2430.91 -0.977 0.164265
4 to 11 2474.25 -0.364 0.357887
5 to 12 2431.94 -0.962 0.167905
6 to 13 2663.95 2.319 0.989791
7 to 14 2392.36 -1.522 0.063977
8 to 15 2450.19 -0.704 0.240564
9 to 16 2620.77 1.708 0.956179
10 to 17 2475.96 -0.340 0.366920
11 to 18 2593.57 1.323 0.907138
12 to 19 2578.37 1.108 0.866129
13 to 20 2505.90 0.084 0.533275
14 to 21 2559.53 0.842 0.800073
15 to 22 2433.71 -0.937 0.174272
16 to 23 2508.38 0.119 0.547179
17 to 24 2413.42 -1.224 0.110408
18 to 25 2549.54 0.701 0.758207
19 to 26 2469.63 -0.430 0.333775
20 to 27 2527.57 0.390 0.651683
21 to 28 2571.09 1.005 0.842635
22 to 29 2431.71 -0.966 0.167072
23 to 30 2450.17 -0.705 0.240484
24 to 31 2551.34 0.726 0.766103
25 to 32 2363.17 -1.935 0.026488
CDPARK for dh-ranFile-2018-07-10_08:31: 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
3481 -1.9178 0.027568
3546 1.0502 0.853193
3515 -0.3653 0.357445
3511 -0.5479 0.291865
3539 0.7306 0.767486
3542 0.8676 0.807188
3537 0.6393 0.738676
3516 -0.3196 0.374623
3506 -0.7763 0.218799
3504 -0.8676 0.192812
Square side=100, avg. no. parked=3519.70 sample std.=19.76
p-value of the KSTEST for those 10 p-values: 0.811431
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_08:31
0.9725,0.6427,0.3341,0.3423,0.1870,0.1273,0.8292,0.1826,0.6193,0.1924,
The KS test for those 10 p-values: 0.623552
The 3DSPHERES test for dh-ranFile-2018-07-10_08:31
sample no r^3 equiv. uni.
1 95.649 0.958758
2 51.082 0.817817
3 43.597 0.766186
4 46.002 0.784199
5 2.208 0.070965
6 15.071 0.394908
7 28.254 0.610071
8 2.076 0.066854
9 115.169 0.978484
10 18.139 0.453726
11 15.972 0.412802
12 30.156 0.634029
13 6.915 0.205870
14 9.903 0.281149
15 27.020 0.593708
16 23.178 0.538190
17 113.981 0.977615
18 64.802 0.884682
19 54.086 0.835172
20 35.699 0.695765
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.217554
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -2.0 1.3 0.2 0.5 0.0
-0.9 1.1 0.4 0.3 0.6 0.0
-0.1 -0.0 -0.8 1.7 0.3 -1.5
-0.5 0.3 1.0 0.2 0.2 -1.8
-1.3 -0.7 -0.0 -0.5 1.9 1.5
-0.3 0.6 0.3 -0.5 -1.6 1.0
0.7 0.5 -0.4 1.5 0.9 -1.0
0.8
Chi-square with 42 degrees of freedom:36.775570
z-score=-0.570032, p-value=0.300854
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_08:31
Test no p-value
1 0.348101
2 0.599354
3 0.020195
4 0.743220
5 0.270237
6 0.034111
7 0.458399
8 0.160840
9 0.639276
10 0.043506
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.076335
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_08:31:
(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 66689 0.01 66745 0.09
3 25000.00 25157 0.99 25003 0.00
4 6666.67 6499 4.22 6560 1.71
5 1388.89 1383 0.02 1411 0.35
6 238.10 225 0.72 240 0.02
7 34.72 41 1.14 38 0.31
8 4.96 5 0.00 2 1.77
p=0.68756 p=0.35613
Number of rngs required: 687275, p-value: 0.095
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_08:31
No. of wins: Observed Expected
98561 98585.9
z-score=-0.111, pvalue=0.45574
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66391 66666.7 1.140 1.140
2 37739 37654.3 0.190 1.330
3 27222 26954.7 2.650 3.980
4 19294 19313.5 0.020 4.000
5 13857 13851.4 0.002 4.002
6 10034 9943.5 0.823 4.825
7 6996 7145.0 3.108 7.933
8 5210 5139.1 0.979 8.912
9 3677 3699.9 0.141 9.054
10 2691 2666.3 0.229 9.282
11 1908 1923.3 0.122 9.405
12 1394 1388.7 0.020 9.425
13 981 1003.7 0.514 9.939
14 714 726.1 0.203 10.142
15 495 525.8 1.808 11.950
16 387 381.2 0.090 12.040
17 276 276.5 0.001 12.041
18 192 200.8 0.388 12.429
19 128 146.0 2.216 14.645
20 115 106.2 0.727 15.371
21 299 287.1 0.492 15.863
Chisq= 15.86 for 20 degrees of freedom, p= 0.27492
SUMMARY of craptest
p-value for no. of wins: 0.455736
p-value for throws/game: 0.274922
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_08:31
No. of wins: Observed Expected
98450 98585.9
z-score=-0.608, pvalue=0.27171
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66728 66666.7 0.056 0.056
2 37664 37654.3 0.002 0.059
3 26643 26954.7 3.605 3.664
4 19458 19313.5 1.082 4.746
5 13814 13851.4 0.101 4.847
6 9979 9943.5 0.126 4.973
7 7205 7145.0 0.503 5.477
8 5226 5139.1 1.470 6.947
9 3666 3699.9 0.310 7.257
10 2608 2666.3 1.275 8.532
11 2002 1923.3 3.218 11.750
12 1444 1388.7 2.199 13.949
13 947 1003.7 3.205 17.153
14 729 726.1 0.011 17.164
15 528 525.8 0.009 17.173
16 382 381.2 0.002 17.175
17 265 276.5 0.482 17.657
18 198 200.8 0.040 17.697
19 127 146.0 2.469 20.165
20 92 106.2 1.902 22.068
21 295 287.1 0.217 22.285
Chisq= 22.28 for 20 degrees of freedom, p= 0.67473
SUMMARY of craptest
p-value for no. of wins: 0.271714
p-value for throws/game: 0.674728
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0062,0.0157,0.0183,0.0202,0.0265,0.0276,0.0281,0.0305,0.0341,0.0347,
0.0412,0.0435,0.0435,0.0486,0.0516,0.0562,0.0640,0.0656,0.0669,0.0710,
0.0763,0.0915,0.0945,0.1008,0.1067,0.1085,0.1094,0.1104,0.1120,0.1249,
0.1273,0.1324,0.1406,0.1494,0.1577,0.1590,0.1608,0.1643,0.1671,0.1679,
0.1743,0.1799,0.1810,0.1818,0.1826,0.1870,0.1881,0.1924,0.1924,0.1928,
0.1990,0.2015,0.2019,0.2030,0.2057,0.2059,0.2071,0.2075,0.2092,0.2176,
0.2188,0.2202,0.2216,0.2325,0.2338,0.2349,0.2405,0.2406,0.2481,0.2512,
0.2525,0.2569,0.2577,0.2661,0.2694,0.2702,0.2717,0.2740,0.2743,0.2749,
0.2788,0.2811,0.2903,0.2919,0.2971,0.2973,0.2977,0.3009,0.3159,0.3171,
0.3274,0.3287,0.3303,0.3316,0.3338,0.3341,0.3404,0.3423,0.3454,0.3481,
0.3505,0.3561,0.3574,0.3579,0.3630,0.3646,0.3669,0.3702,0.3746,0.3939,
0.3945,0.3949,0.4062,0.4064,0.4074,0.4128,0.4234,0.4299,0.4323,0.4403,
0.4417,0.4537,0.4557,0.4584,0.4591,0.4616,0.4647,0.4698,0.4745,0.4779,
0.4788,0.4807,0.4948,0.5010,0.5077,0.5267,0.5286,0.5333,0.5382,0.5440,
0.5465,0.5472,0.5493,0.5510,0.5637,0.5802,0.5871,0.5906,0.5912,0.5937,
0.5952,0.5994,0.6082,0.6096,0.6101,0.6117,0.6117,0.6134,0.6193,0.6227,
0.6236,0.6244,0.6246,0.6253,0.6293,0.6293,0.6322,0.6324,0.6340,0.6393,
0.6399,0.6427,0.6517,0.6566,0.6653,0.6659,0.6663,0.6686,0.6709,0.6747,
0.6788,0.6876,0.6881,0.6928,0.6953,0.6958,0.6992,0.7004,0.7058,0.7242,
0.7377,0.7387,0.7388,0.7410,0.7418,0.7432,0.7529,0.7544,0.7552,0.7582,
0.7661,0.7662,0.7675,0.7768,0.7834,0.7842,0.7843,0.7961,0.7987,0.7994,
0.8001,0.8009,0.8060,0.8072,0.8076,0.8114,0.8178,0.8247,0.8292,0.8315,
0.8327,0.8352,0.8353,0.8358,0.8426,0.8458,0.8495,0.8510,0.8532,0.8603,
0.8648,0.8661,0.8688,0.8692,0.8790,0.8817,0.8821,0.8847,0.8854,0.8877,
0.9011,0.9056,0.9071,0.9187,0.9226,0.9236,0.9250,0.9261,0.9297,0.9319,
0.9353,0.9364,0.9395,0.9514,0.9562,0.9588,0.9592,0.9605,0.9704,0.9725,
0.9752,0.9754,0.9776,0.9785,0.9834,0.9888,0.9898,0.9947,0.9951,
Overall p-value after applying KStest on 269 p-values = 0.830251
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.