RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 22.6439 0.838795
2 to 25 15.72 16.8996 0.538814
3 to 26 15.79 21.2908 0.786448
4 to 27 15.86 14.4670 0.366190
5 to 28 15.55 15.4281 0.435321
6 to 29 15.69 12.6526 0.240886
7 to 30 16.37 16.5783 0.516728
8 to 31 15.53 23.6398 0.870444
9 to 32 15.54 29.1810 0.967107
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.371639
Tough bday spacings test for dh-ranFile-2018-07-09_14:31: 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 34 73 96 108 80 55 26 13 5 1
(O-E)^2/E 0.0 0.2 0.0 0.0 1.1 0.0 0.2 0.5 0.2 0.4 2.3
Birthday Spacings: Sum(O-E)^2/E= 4.940, p= 0.105
RESULTS OF GCD FOR dh-ranFile-2018-07-09_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.429005
p-value, dist. of gcd's: 0.602634
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.139 0.866 0.335 0.394 0.421 0.341 0.049 0.478
Bits 8 to 15---> 0.453 0.396 0.811 0.893 0.449 0.796 0.766 0.331
Bits 16 to 23---> 0.652 0.949 0.943 0.043 0.913 0.669 0.888 0.560
Bits 24 to 31---> 0.266 0.907 0.250 0.383 0.534 0.677 0.595 0.192
KS test for the above 32 p values: 0.415
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_14:31,
p-values for 5 runs: 0.9893, 0.3809, 0.9867, 0.8171, 0.0000
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5198 5134.0 0.798 0.853
r= 30 23030 23103.0 0.231 1.084
r= 31 11564 11551.5 0.013 1.097
chi-square = 1.097 with df = 3; p-value = 0.222
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 189 211.4 2.377 2.377
r= 30 5212 5134.0 1.185 3.562
r= 31 23177 23103.0 0.237 3.799
r= 32 11422 11551.5 1.452 5.251
chi-square = 5.251 with df = 3; p-value = 0.846
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_14:31
b-rank test for bits 1 to 8, p=0.43108
b-rank test for bits 2 to 9, p=0.94291
b-rank test for bits 3 to 10, p=0.90077
b-rank test for bits 4 to 11, p=0.60932
b-rank test for bits 5 to 12, p=0.71059
b-rank test for bits 6 to 13, p=0.24507
b-rank test for bits 7 to 14, p=0.56982
b-rank test for bits 8 to 15, p=0.18152
b-rank test for bits 9 to 16, p=0.02692
b-rank test for bits 10 to 17, p=0.09270
b-rank test for bits 11 to 18, p=0.72587
b-rank test for bits 12 to 19, p=0.55101
b-rank test for bits 13 to 20, p=0.18355
b-rank test for bits 14 to 21, p=0.29076
b-rank test for bits 15 to 22, p=0.76553
b-rank test for bits 16 to 23, p=0.95356
b-rank test for bits 17 to 24, p=0.37615
b-rank test for bits 18 to 25, p=0.31412
b-rank test for bits 19 to 26, p=0.04043
b-rank test for bits 20 to 27, p=0.32404
b-rank test for bits 21 to 28, p=0.37006
b-rank test for bits 22 to 29, p=0.95791
b-rank test for bits 23 to 30, p=0.79220
b-rank test for bits 24 to 31, p=0.31758
b-rank test for bits 25 to 32, p=0.18961
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 = 0.878236
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_14:31
(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 142328 0.98 0.836013
2 141961 0.12 0.548045
3 142291 0.89 0.813737
4 142015 0.25 0.597504
5 141551 -0.84 0.201235
6 141963 0.13 0.549895
7 141238 -1.57 0.058379
8 142092 0.43 0.665237
9 141461 -1.05 0.147435
10 142497 1.37 0.915133
11 141792 -0.27 0.391990
12 141392 -1.21 0.113386
13 142326 0.97 0.834855
14 142458 1.28 0.900068
15 142968 2.47 0.993311
16 142139 0.54 0.704232
17 141517 -0.92 0.179661
18 141738 -0.40 0.344466
19 141938 0.07 0.526704
20 142066 0.37 0.642837
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_14:31
Bits used No. missing words z-score p-value
23 to 32 142156 0.8506 0.802500
22 to 31 142387 1.6471 0.950235
21 to 30 142106 0.6782 0.751169
20 to 29 142191 0.9713 0.834295
19 to 28 142017 0.3713 0.644784
18 to 27 141309 -2.0701 0.019221
17 to 26 141785 -0.4287 0.334062
16 to 25 141745 -0.5667 0.285474
15 to 24 141740 -0.5839 0.279645
14 to 23 141943 0.1161 0.546215
13 to 22 142012 0.3540 0.638344
12 to 21 141616 -1.0115 0.155893
11 to 20 141751 -0.5460 0.292545
10 to 19 141668 -0.8322 0.202656
9 to 18 141987 0.2678 0.605584
8 to 17 142188 0.9609 0.831707
7 to 16 141444 -1.6046 0.054292
6 to 15 142517 2.0954 0.981933
5 to 14 142109 0.6885 0.754436
4 to 13 141449 -1.5873 0.056217
3 to 12 141760 -0.5149 0.303301
2 to 11 142033 0.4264 0.665109
1 to 10 141668 -0.8322 0.202656
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_14:31
Bits used No. missing words z-score p-value
28 to 32 142759 2.8802 0.998013
27 to 31 142010 0.3413 0.633544
26 to 30 141976 0.2260 0.589399
25 to 29 142039 0.4396 0.669872
24 to 28 141998 0.3006 0.618131
23 to 27 141847 -0.2113 0.416331
22 to 26 142216 1.0396 0.850728
21 to 25 141773 -0.4621 0.321992
20 to 24 141336 -1.9435 0.025978
19 to 23 141743 -0.5638 0.286435
18 to 22 141661 -0.8418 0.199951
17 to 21 142452 1.8396 0.967084
16 to 20 141735 -0.5909 0.277277
15 to 19 141428 -1.6316 0.051379
14 to 18 142083 0.5887 0.721973
13 to 17 141251 -2.2316 0.012820
12 to 16 142085 0.5955 0.724243
11 to 15 141855 -0.1842 0.426940
10 to 14 142251 1.1582 0.876610
9 to 13 142217 1.0429 0.851514
8 to 12 142122 0.7209 0.764519
7 to 11 142098 0.6396 0.738770
6 to 10 142009 0.3379 0.632267
5 to 9 141729 -0.6113 0.270504
4 to 8 141938 0.0972 0.538711
3 to 7 142082 0.5853 0.720834
2 to 6 141958 0.1650 0.565521
1 to 5 141962 0.1785 0.570852
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_14:31
Bits used No. missing words z-score p-value
31 to 32 141774 -0.3992 0.344872
30 to 31 141420 -1.4435 0.074447
29 to 30 141753 -0.4612 0.322345
28 to 29 142035 0.3707 0.644573
27 to 28 142177 0.7896 0.785116
26 to 27 141918 0.0256 0.510202
25 to 26 141295 -1.8122 0.034979
24 to 25 142050 0.4150 0.660913
23 to 24 142338 1.2645 0.896977
22 to 23 141652 -0.7591 0.223901
21 to 22 142267 1.0551 0.854304
20 to 21 142045 0.4002 0.655498
19 to 20 142500 1.7424 0.959280
18 to 19 141845 -0.1898 0.424747
17 to 18 142718 2.3855 0.991471
16 to 17 141819 -0.2665 0.394942
15 to 16 141658 -0.7414 0.229230
14 to 15 142284 1.1052 0.865468
13 to 14 141082 -2.4405 0.007333
12 to 13 142668 2.2380 0.987388
11 to 12 141849 -0.1780 0.429375
10 to 11 141611 -0.8800 0.189422
9 to 10 141858 -0.1514 0.439824
8 to 9 141366 -1.6027 0.054496
7 to 8 141765 -0.4258 0.335144
6 to 7 141819 -0.2665 0.394942
5 to 6 141570 -1.0010 0.158420
4 to 5 141735 -0.5142 0.303539
3 to 4 141607 -0.8918 0.186242
2 to 3 142591 2.0108 0.977828
1 to 2 142096 0.5506 0.709063
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2592.47 1.308 0.904512
Test results for specific bytes for dh-ranFile-2018-07-09_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2495.90 -0.058 0.476871
2 to 9 2492.63 -0.104 0.458499
3 to 10 2475.07 -0.353 0.362224
4 to 11 2546.48 0.657 0.744516
5 to 12 2519.03 0.269 0.606091
6 to 13 2530.35 0.429 0.666140
7 to 14 2564.35 0.910 0.818615
8 to 15 2604.04 1.471 0.929408
9 to 16 2633.95 1.894 0.970911
10 to 17 2473.89 -0.369 0.355951
11 to 18 2601.53 1.436 0.924486
12 to 19 2572.71 1.028 0.848100
13 to 20 2489.12 -0.154 0.438862
14 to 21 2636.73 1.934 0.973418
15 to 22 2571.27 1.008 0.843256
16 to 23 2512.21 0.173 0.568538
17 to 24 2578.98 1.117 0.867999
18 to 25 2608.86 1.540 0.938165
19 to 26 2562.39 0.882 0.811197
20 to 27 2500.50 0.007 0.502842
21 to 28 2520.79 0.294 0.615642
22 to 29 2527.28 0.386 0.650160
23 to 30 2574.88 1.059 0.855188
24 to 31 2594.60 1.338 0.909529
25 to 32 2621.04 1.712 0.956527
CDPARK for dh-ranFile-2018-07-09_14:31: 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
3523 0.0000 0.500000
3463 -2.7397 0.003075
3533 0.4566 0.676028
3500 -1.0502 0.146807
3537 0.6393 0.738676
3525 0.0913 0.536383
3480 -1.9635 0.024796
3479 -2.0091 0.022262
3524 0.0457 0.518210
3512 -0.5023 0.307734
Square side=100, avg. no. parked=3507.60 sample std.=24.42
p-value of the KSTEST for those 10 p-values: 0.052697
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_14:31
0.2523,0.4405,0.1513,0.1931,0.0947,0.8699,0.8656,0.2846,0.1886,0.4333,
The KS test for those 10 p-values: 0.198834
The 3DSPHERES test for dh-ranFile-2018-07-09_14:31
sample no r^3 equiv. uni.
1 26.920 0.592348
2 17.450 0.441031
3 18.147 0.453877
4 44.599 0.773866
5 13.593 0.364352
6 16.046 0.414250
7 27.952 0.606134
8 120.307 0.981871
9 32.543 0.662018
10 42.934 0.760959
11 2.808 0.089339
12 4.951 0.152146
13 26.314 0.584021
14 21.199 0.506698
15 17.857 0.448575
16 88.706 0.948018
17 33.001 0.667139
18 28.801 0.617125
19 18.980 0.468818
20 16.792 0.428644
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.221800
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 -0.6 1.2 1.4 0.1
-0.9 -0.3 2.0 -0.1 -0.5 2.2
-0.1 -0.2 1.8 -1.5 0.3 1.6
-2.0 0.4 -1.0 -0.9 -0.4 -0.1
-0.7 1.0 -2.0 1.0 1.2 -0.7
-0.2 1.0 0.3 -1.2 -0.1 0.6
-1.2 1.1 0.9 0.4 -1.3 0.0
0.8
Chi-square with 42 degrees of freedom:46.658437
z-score=0.508277, p-value=0.713211
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_14:31
Test no p-value
1 0.214621
2 0.519014
3 0.344222
4 0.422205
5 0.974390
6 0.222877
7 0.717770
8 0.889391
9 0.182025
10 0.036282
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.847254
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_14:31:
(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 66673 0.00 66398 1.08
3 25000.00 25045 0.08 25077 0.24
4 6666.67 6641 0.10 6759 1.28
5 1388.89 1358 0.69 1481 6.11
6 238.10 244 0.15 246 0.26
7 34.72 34 0.01 32 0.21
8 4.96 4 0.19 6 0.22
p=0.02384 p=0.84774
Number of rngs required: 689460, p-value: 0.890
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_14:31
No. of wins: Observed Expected
98567 98585.9
z-score=-0.084, pvalue=0.46639
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66453 66666.7 0.685 0.685
2 37756 37654.3 0.275 0.959
3 26894 26954.7 0.137 1.096
4 19411 19313.5 0.493 1.589
5 13961 13851.4 0.867 2.456
6 9869 9943.5 0.559 3.015
7 7141 7145.0 0.002 3.017
8 5140 5139.1 0.000 3.017
9 3666 3699.9 0.310 3.327
10 2648 2666.3 0.126 3.452
11 1890 1923.3 0.578 4.030
12 1438 1388.7 1.747 5.777
13 1028 1003.7 0.588 6.365
14 768 726.1 2.413 8.778
15 542 525.8 0.497 9.275
16 385 381.2 0.039 9.314
17 277 276.5 0.001 9.314
18 187 200.8 0.952 10.267
19 137 146.0 0.553 10.820
20 111 106.2 0.216 11.035
21 298 287.1 0.413 11.448
Chisq= 11.45 for 20 degrees of freedom, p= 0.06623
SUMMARY of craptest
p-value for no. of wins: 0.466390
p-value for throws/game: 0.066235
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_14:31
No. of wins: Observed Expected
98429 98585.9
z-score=-0.702, pvalue=0.24148
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66924 66666.7 0.993 0.993
2 37292 37654.3 3.486 4.480
3 26849 26954.7 0.415 4.894
4 19194 19313.5 0.739 5.633
5 13891 13851.4 0.113 5.746
6 10030 9943.5 0.752 6.498
7 7198 7145.0 0.393 6.891
8 5118 5139.1 0.086 6.977
9 3783 3699.9 1.868 8.845
10 2700 2666.3 0.426 9.271
11 1940 1923.3 0.144 9.416
12 1431 1388.7 1.286 10.702
13 995 1003.7 0.076 10.778
14 726 726.1 0.000 10.778
15 525 525.8 0.001 10.779
16 391 381.2 0.255 11.033
17 270 276.5 0.155 11.188
18 203 200.8 0.023 11.211
19 142 146.0 0.109 11.320
20 124 106.2 2.978 14.298
21 274 287.1 0.599 14.897
Chisq= 14.90 for 20 degrees of freedom, p= 0.21774
SUMMARY of craptest
p-value for no. of wins: 0.241476
p-value for throws/game: 0.217735
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0031,0.0073,0.0128,0.0192,0.0223,0.0238,0.0248,0.0260,0.0269,
0.0350,0.0363,0.0404,0.0426,0.0492,0.0514,0.0527,0.0543,0.0545,0.0562,
0.0584,0.0662,0.0744,0.0893,0.0927,0.0947,0.1048,0.1134,0.1390,0.1468,
0.1474,0.1513,0.1521,0.1559,0.1584,0.1797,0.1815,0.1820,0.1835,0.1862,
0.1886,0.1894,0.1896,0.1917,0.1931,0.1988,0.2000,0.2012,0.2027,0.2027,
0.2146,0.2177,0.2218,0.2223,0.2229,0.2239,0.2292,0.2409,0.2415,0.2451,
0.2498,0.2523,0.2665,0.2705,0.2773,0.2796,0.2846,0.2855,0.2864,0.2908,
0.2925,0.3033,0.3035,0.3077,0.3141,0.3176,0.3220,0.3223,0.3240,0.3307,
0.3341,0.3346,0.3351,0.3409,0.3442,0.3445,0.3449,0.3560,0.3622,0.3644,
0.3662,0.3701,0.3716,0.3762,0.3809,0.3831,0.3920,0.3940,0.3949,0.3949,
0.3959,0.4142,0.4154,0.4163,0.4206,0.4222,0.4247,0.4269,0.4286,0.4290,
0.4294,0.4311,0.4333,0.4353,0.4389,0.4398,0.4405,0.4410,0.4486,0.4490,
0.4532,0.4539,0.4585,0.4664,0.4688,0.4769,0.4782,0.5000,0.5028,0.5067,
0.5102,0.5167,0.5182,0.5190,0.5267,0.5341,0.5364,0.5387,0.5388,0.5462,
0.5480,0.5499,0.5510,0.5596,0.5655,0.5685,0.5698,0.5709,0.5840,0.5894,
0.5923,0.5950,0.5975,0.6026,0.6056,0.6061,0.6061,0.6093,0.6156,0.6171,
0.6181,0.6323,0.6335,0.6383,0.6428,0.6446,0.6448,0.6502,0.6524,0.6555,
0.6609,0.6620,0.6651,0.6652,0.6661,0.6671,0.6689,0.6699,0.6760,0.6765,
0.7042,0.7091,0.7106,0.7132,0.7178,0.7208,0.7220,0.7242,0.7259,0.7387,
0.7388,0.7445,0.7512,0.7544,0.7610,0.7645,0.7655,0.7659,0.7739,0.7851,
0.7864,0.7922,0.7955,0.8025,0.8109,0.8112,0.8137,0.8171,0.8186,0.8317,
0.8343,0.8349,0.8360,0.8388,0.8433,0.8457,0.8473,0.8477,0.8481,0.8507,
0.8515,0.8543,0.8552,0.8655,0.8656,0.8660,0.8680,0.8699,0.8704,0.8766,
0.8782,0.8875,0.8894,0.8905,0.8927,0.8970,0.9001,0.9008,0.9045,0.9070,
0.9095,0.9133,0.9151,0.9245,0.9294,0.9382,0.9429,0.9429,0.9480,0.9490,
0.9502,0.9536,0.9565,0.9579,0.9593,0.9671,0.9671,0.9709,0.9734,0.9744,
0.9778,0.9819,0.9819,0.9867,0.9874,0.9893,0.9915,0.9933,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.236189
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.