RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_22:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.98 17.6361 0.587863
2 to 25 15.60 20.8305 0.766034
3 to 26 15.93 14.4793 0.367067
4 to 27 15.83 16.3758 0.502629
5 to 28 15.90 10.0542 0.098676
6 to 29 15.65 20.8636 0.767550
7 to 30 15.72 14.5077 0.369104
8 to 31 16.06 14.5815 0.374403
9 to 32 16.00 14.0698 0.337845
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.523494
Tough bday spacings test for dh-ranFile-2018-06-17_22:31: 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 36 82 99 99 70 56 32 11 5 2
(O-E)^2/E 0.1 0.0 1.0 0.0 0.0 0.8 0.3 0.2 1.0 0.4 1.0
Birthday Spacings: Sum(O-E)^2/E= 5.002, p= 0.109
RESULTS OF GCD FOR dh-ranFile-2018-06-17_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.098638
p-value, dist. of gcd's: 0.521790
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.005 0.815 0.550 0.420 0.178 0.602 0.277 0.163
Bits 8 to 15---> 0.500 0.913 0.362 0.616 0.340 0.585 0.317 0.860
Bits 16 to 23---> 0.682 0.349 0.937 0.541 0.457 0.152 0.260 0.643
Bits 24 to 31---> 0.621 0.087 0.360 0.813 0.629 0.189 0.468 0.612
KS test for the above 32 p values: 0.527
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_22:31,
p-values for 5 runs: 0.0564, 0.2983, 0.3230, 0.2310, 0.9116
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 210 211.4 0.010 0.010
r= 29 5073 5134.0 0.725 0.735
r= 30 23123 23103.0 0.017 0.752
r= 31 11594 11551.5 0.156 0.908
chi-square = 0.908 with df = 3; p-value = 0.176
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5208 5134.0 1.066 1.401
r= 31 22957 23103.0 0.923 2.325
r= 32 11632 11551.5 0.561 2.885
chi-square = 2.885 with df = 3; p-value = 0.590
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_22:31
b-rank test for bits 1 to 8, p=0.56064
b-rank test for bits 2 to 9, p=0.08638
b-rank test for bits 3 to 10, p=0.53740
b-rank test for bits 4 to 11, p=0.19512
b-rank test for bits 5 to 12, p=0.42396
b-rank test for bits 6 to 13, p=0.18327
b-rank test for bits 7 to 14, p=0.72943
b-rank test for bits 8 to 15, p=0.97093
b-rank test for bits 9 to 16, p=0.65231
b-rank test for bits 10 to 17, p=0.54579
b-rank test for bits 11 to 18, p=0.94522
b-rank test for bits 12 to 19, p=0.90890
b-rank test for bits 13 to 20, p=0.68366
b-rank test for bits 14 to 21, p=0.60567
b-rank test for bits 15 to 22, p=0.27089
b-rank test for bits 16 to 23, p=0.50247
b-rank test for bits 17 to 24, p=0.47648
b-rank test for bits 18 to 25, p=0.61656
b-rank test for bits 19 to 26, p=0.32910
b-rank test for bits 20 to 27, p=0.34521
b-rank test for bits 21 to 28, p=0.30418
b-rank test for bits 22 to 29, p=0.62195
b-rank test for bits 23 to 30, p=0.80664
b-rank test for bits 24 to 31, p=0.90475
b-rank test for bits 25 to 32, p=0.88789
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 = 0.367074
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_22:31
(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 142019 0.26 0.601117
2 142211 0.70 0.759544
3 142191 0.66 0.744765
4 141925 0.04 0.514603
5 142061 0.35 0.638469
6 141395 -1.20 0.114739
7 141975 0.15 0.560972
8 142056 0.34 0.634083
9 142262 0.82 0.795029
10 141544 -0.85 0.196670
11 142611 1.64 0.949437
12 141482 -1.00 0.159034
13 141499 -0.96 0.168851
14 141998 0.21 0.582063
15 142303 0.92 0.821159
16 142015 0.25 0.597504
17 141774 -0.32 0.375929
18 141906 -0.01 0.496896
19 141477 -1.01 0.156220
20 141954 0.10 0.541562
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_22:31
Bits used No. missing words z-score p-value
23 to 32 141537 -1.2839 0.099589
22 to 31 142184 0.9471 0.828216
21 to 30 141695 -0.7391 0.229933
20 to 29 142071 0.5575 0.711401
19 to 28 141561 -1.2011 0.114849
18 to 27 141821 -0.3046 0.380341
17 to 26 141252 -2.2667 0.011706
16 to 25 141832 -0.2667 0.394867
15 to 24 141696 -0.7356 0.230981
14 to 23 141708 -0.6942 0.243765
13 to 22 142325 1.4333 0.924120
12 to 21 142103 0.6678 0.747878
11 to 20 141911 0.0058 0.502297
10 to 19 141767 -0.4908 0.311786
9 to 18 141747 -0.5598 0.287822
8 to 17 141556 -1.2184 0.111540
7 to 16 141693 -0.7460 0.227844
6 to 15 142223 1.0816 0.860289
5 to 14 142197 0.9920 0.839393
4 to 13 142019 0.3782 0.647349
3 to 12 142380 1.6230 0.947705
2 to 11 141715 -0.6701 0.251396
1 to 10 141378 -1.8322 0.033463
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_22:31
Bits used No. missing words z-score p-value
28 to 32 141932 0.0768 0.530628
27 to 31 142203 0.9955 0.840251
26 to 30 141887 -0.0757 0.469831
25 to 29 141864 -0.1537 0.438939
24 to 28 141455 -1.5401 0.061768
23 to 27 141585 -1.0994 0.135792
22 to 26 142296 1.3107 0.905028
21 to 25 142133 0.7582 0.775835
20 to 24 142108 0.6735 0.749672
19 to 23 142377 1.5853 0.943553
18 to 22 142092 0.6192 0.732114
17 to 21 142501 2.0057 0.977554
16 to 20 142244 1.1345 0.871702
15 to 19 141859 -0.1706 0.432265
14 to 18 141768 -0.4791 0.315939
13 to 17 142050 0.4768 0.683265
12 to 16 141895 -0.0486 0.480629
11 to 15 141837 -0.2452 0.403156
10 to 14 142258 1.1819 0.881384
9 to 13 142383 1.6057 0.945826
8 to 12 141738 -0.5808 0.280695
7 to 11 142059 0.5074 0.694048
6 to 10 142179 0.9141 0.819677
5 to 9 141644 -0.8994 0.184214
4 to 8 141646 -0.8926 0.186024
3 to 7 142010 0.3413 0.633544
2 to 6 142377 1.5853 0.943553
1 to 5 141078 -2.8181 0.002416
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_22:31
Bits used No. missing words z-score p-value
31 to 32 142057 0.4356 0.668438
30 to 31 142273 1.0728 0.858314
29 to 30 142472 1.6598 0.951522
28 to 29 142116 0.6096 0.728952
27 to 28 141871 -0.1131 0.454988
26 to 27 141798 -0.3284 0.371302
25 to 26 141875 -0.1013 0.459669
24 to 25 142232 0.9518 0.829408
23 to 24 141908 -0.0039 0.498435
22 to 23 141604 -0.9007 0.183880
21 to 22 142433 1.5447 0.938797
20 to 21 141824 -0.2517 0.400632
19 to 20 141427 -1.4228 0.077397
18 to 19 142454 1.6067 0.945939
17 to 18 141722 -0.5526 0.290270
16 to 17 142140 0.6804 0.751888
15 to 16 142243 0.9843 0.837510
14 to 15 142655 2.1996 0.986083
13 to 14 141881 -0.0836 0.466699
12 to 13 142309 1.1790 0.880794
11 to 12 141681 -0.6735 0.250302
10 to 11 141481 -1.2635 0.103203
9 to 10 141408 -1.4788 0.069590
8 to 9 141885 -0.0718 0.471393
7 to 8 141901 -0.0246 0.490198
6 to 7 141528 -1.1249 0.130323
5 to 6 141974 0.1908 0.575646
4 to 5 141817 -0.2724 0.392673
3 to 4 142325 1.2262 0.889932
2 to 3 142240 0.9754 0.835326
1 to 2 142020 0.3265 0.627962
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2479.71 -0.287 0.387052
Test results for specific bytes for dh-ranFile-2018-06-17_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2497.76 -0.032 0.487354
2 to 9 2455.27 -0.633 0.263485
3 to 10 2497.69 -0.033 0.486990
4 to 11 2394.03 -1.499 0.066983
5 to 12 2385.33 -1.622 0.052438
6 to 13 2476.26 -0.336 0.368528
7 to 14 2327.43 -2.441 0.007332
8 to 15 2594.23 1.333 0.908666
9 to 16 2389.50 -1.563 0.059058
10 to 17 2466.29 -0.477 0.316774
11 to 18 2554.35 0.769 0.778936
12 to 19 2339.25 -2.273 0.011501
13 to 20 2603.05 1.457 0.927499
14 to 21 2454.81 -0.639 0.261372
15 to 22 2460.19 -0.563 0.286703
16 to 23 2585.77 1.213 0.887416
17 to 24 2488.23 -0.166 0.433895
18 to 25 2527.14 0.384 0.649436
19 to 26 2465.30 -0.491 0.311790
20 to 27 2504.00 0.057 0.522540
21 to 28 2485.60 -0.204 0.419300
22 to 29 2544.80 0.634 0.736806
23 to 30 2532.89 0.465 0.679077
24 to 31 2442.59 -0.812 0.208413
25 to 32 2485.18 -0.210 0.416983
CDPARK for dh-ranFile-2018-06-17_22:31: 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
3485 -1.7352 0.041356
3511 -0.5479 0.291865
3557 1.5525 0.939730
3533 0.4566 0.676028
3559 1.6438 0.949895
3503 -0.9132 0.180558
3534 0.5023 0.692266
3503 -0.9132 0.180558
3513 -0.4566 0.323972
3507 -0.7306 0.232514
Square side=100, avg. no. parked=3520.50 sample std.=23.14
p-value of the KSTEST for those 10 p-values: 0.615499
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_22:31
0.1630,0.1378,0.3914,0.3580,0.6622,0.8454,0.1693,0.3968,0.5860,0.9058,
The KS test for those 10 p-values: 0.855593
The 3DSPHERES test for dh-ranFile-2018-06-17_22:31
sample no r^3 equiv. uni.
1 18.989 0.468985
2 44.796 0.775347
3 13.746 0.367587
4 33.235 0.669722
5 3.891 0.121646
6 32.520 0.661761
7 20.454 0.494293
8 8.647 0.250414
9 240.430 0.999669
10 19.101 0.470957
11 59.047 0.860298
12 2.165 0.069632
13 3.860 0.120721
14 14.132 0.375669
15 59.172 0.860876
16 22.763 0.531751
17 9.762 0.277754
18 16.790 0.428594
19 29.085 0.620732
20 0.193 0.006403
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.752646
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 0.3 0.6 -0.7 -0.2
-0.8 0.9 -2.4 2.6 0.3 1.6
-0.7 -2.4 0.7 -0.1 -1.3 1.3
-1.5 0.9 1.0 0.1 -0.8 1.3
1.5 -1.6 1.5 -1.1 -0.1 -1.4
-0.2 1.8 -0.9 -1.8 -1.0 -0.3
-0.2 -0.4 -0.8 1.0 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:56.628197
z-score=1.596067, p-value=0.934746
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_22:31
Test no p-value
1 0.113500
2 0.137837
3 0.238256
4 0.164092
5 0.605880
6 0.024845
7 0.481036
8 0.007062
9 0.364662
10 0.396362
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.009640
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_22:31:
(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 66825 0.38 66877 0.66
3 25000.00 24840 1.02 24855 0.84
4 6666.67 6664 0.00 6597 0.73
5 1388.89 1404 0.16 1413 0.42
6 238.10 234 0.07 225 0.72
7 34.72 31 0.40 29 0.94
8 4.96 1 3.16 3 0.77
p=0.48108 p=0.46746
Number of rngs required: 689846, p-value: 0.955
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_22:31
No. of wins: Observed Expected
98190 98585.9
z-score=-1.771, pvalue=0.03832
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66485 66666.7 0.495 0.495
2 37648 37654.3 0.001 0.496
3 26926 26954.7 0.031 0.527
4 19630 19313.5 5.188 5.715
5 14203 13851.4 8.924 14.639
6 9827 9943.5 1.366 16.004
7 7117 7145.0 0.110 16.114
8 5055 5139.1 1.375 17.490
9 3603 3699.9 2.536 20.026
10 2680 2666.3 0.070 20.096
11 1909 1923.3 0.107 20.203
12 1387 1388.7 0.002 20.205
13 986 1003.7 0.313 20.518
14 702 726.1 0.803 21.320
15 524 525.8 0.006 21.327
16 349 381.2 2.712 24.039
17 267 276.5 0.329 24.368
18 186 200.8 1.095 25.463
19 135 146.0 0.827 26.289
20 103 106.2 0.097 26.387
21 278 287.1 0.289 26.676
Chisq= 26.68 for 20 degrees of freedom, p= 0.85537
SUMMARY of craptest
p-value for no. of wins: 0.038321
p-value for throws/game: 0.855371
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_22:31
No. of wins: Observed Expected
98819 98585.9
z-score= 1.043, pvalue=0.85147
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66883 66666.7 0.702 0.702
2 37499 37654.3 0.641 1.343
3 26883 26954.7 0.191 1.534
4 19213 19313.5 0.523 2.056
5 13791 13851.4 0.264 2.320
6 10101 9943.5 2.493 4.813
7 7152 7145.0 0.007 4.820
8 5136 5139.1 0.002 4.822
9 3743 3699.9 0.503 5.325
10 2617 2666.3 0.911 6.236
11 1935 1923.3 0.071 6.307
12 1296 1388.7 6.193 12.500
13 1076 1003.7 5.206 17.706
14 740 726.1 0.265 17.970
15 526 525.8 0.000 17.970
16 403 381.2 1.253 19.223
17 245 276.5 3.597 22.820
18 192 200.8 0.388 23.208
19 155 146.0 0.557 23.765
20 115 106.2 0.727 24.492
21 299 287.1 0.492 24.984
Chisq= 24.98 for 20 degrees of freedom, p= 0.79794
SUMMARY of craptest
p-value for no. of wins: 0.851467
p-value for throws/game: 0.797943
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0024,0.0051,0.0064,0.0071,0.0073,0.0096,0.0115,0.0117,0.0248,0.0335,
0.0383,0.0414,0.0524,0.0564,0.0591,0.0618,0.0670,0.0696,0.0696,0.0774,
0.0864,0.0868,0.0986,0.0987,0.0996,0.1032,0.1089,0.1115,0.1135,0.1147,
0.1148,0.1207,0.1216,0.1303,0.1358,0.1378,0.1378,0.1523,0.1562,0.1590,
0.1630,0.1632,0.1641,0.1689,0.1693,0.1765,0.1776,0.1806,0.1806,0.1833,
0.1839,0.1842,0.1860,0.1893,0.1951,0.1967,0.2084,0.2278,0.2299,0.2310,
0.2310,0.2325,0.2383,0.2438,0.2503,0.2504,0.2514,0.2601,0.2614,0.2635,
0.2709,0.2767,0.2778,0.2807,0.2867,0.2878,0.2903,0.2919,0.2983,0.3042,
0.3118,0.3118,0.3159,0.3168,0.3170,0.3230,0.3240,0.3291,0.3378,0.3400,
0.3452,0.3495,0.3580,0.3603,0.3622,0.3647,0.3671,0.3671,0.3676,0.3685,
0.3691,0.3713,0.3744,0.3757,0.3759,0.3803,0.3871,0.3914,0.3927,0.3949,
0.3964,0.3968,0.4006,0.4032,0.4170,0.4193,0.4198,0.4240,0.4286,0.4323,
0.4339,0.4389,0.4550,0.4575,0.4597,0.4667,0.4675,0.4680,0.4690,0.4698,
0.4710,0.4714,0.4765,0.4806,0.4810,0.4811,0.4870,0.4874,0.4902,0.4943,
0.4969,0.4984,0.4996,0.5023,0.5025,0.5026,0.5146,0.5218,0.5225,0.5235,
0.5268,0.5306,0.5318,0.5374,0.5411,0.5416,0.5458,0.5501,0.5606,0.5610,
0.5756,0.5821,0.5852,0.5860,0.5879,0.5904,0.5975,0.6011,0.6015,0.6057,
0.6059,0.6118,0.6155,0.6163,0.6166,0.6206,0.6207,0.6220,0.6280,0.6292,
0.6335,0.6341,0.6385,0.6431,0.6473,0.6494,0.6523,0.6618,0.6622,0.6684,
0.6697,0.6760,0.6791,0.6818,0.6833,0.6837,0.6923,0.6940,0.7114,0.7290,
0.7294,0.7321,0.7368,0.7448,0.7479,0.7497,0.7519,0.7526,0.7595,0.7660,
0.7676,0.7753,0.7758,0.7789,0.7950,0.7979,0.8066,0.8131,0.8154,0.8197,
0.8212,0.8282,0.8294,0.8353,0.8375,0.8394,0.8403,0.8454,0.8515,0.8554,
0.8556,0.8583,0.8596,0.8603,0.8603,0.8609,0.8717,0.8808,0.8814,0.8874,
0.8879,0.8899,0.9048,0.9050,0.9058,0.9087,0.9089,0.9116,0.9126,0.9241,
0.9275,0.9347,0.9373,0.9388,0.9397,0.9436,0.9436,0.9452,0.9458,0.9459,
0.9477,0.9494,0.9499,0.9515,0.9547,0.9709,0.9776,0.9861,0.9997,
Overall p-value after applying KStest on 269 p-values = 0.677673
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.