RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.04 9.6940 0.084049
2 to 25 16.18 17.0852 0.551389
3 to 26 15.88 16.8755 0.537171
4 to 27 15.88 24.4208 0.891555
5 to 28 15.60 21.2128 0.783083
6 to 29 15.55 20.6686 0.758532
7 to 30 15.96 11.7316 0.183889
8 to 31 15.98 9.8779 0.091349
9 to 32 16.12 20.8341 0.766199
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.777353
Tough bday spacings test for dh-ranFile-2018-06-20_00:31: 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 13 43 67 105 90 71 62 22 17 7 3
(O-E)^2/E 1.6 1.1 0.5 0.5 0.6 0.7 1.9 2.0 0.3 0.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 9.573, p= 0.521
RESULTS OF GCD FOR dh-ranFile-2018-06-20_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.960179
p-value, dist. of gcd's: 0.926364
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.756 0.707 0.714 0.976 0.595 0.237 0.742 0.431
Bits 8 to 15---> 0.873 0.229 0.006 0.688 0.103 0.937 0.172 0.486
Bits 16 to 23---> 0.726 0.654 0.281 0.966 0.610 0.663 0.977 0.722
Bits 24 to 31---> 0.963 0.032 0.109 0.523 0.046 0.577 0.511 0.141
KS test for the above 32 p values: 0.563
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_00:31,
p-values for 5 runs: 0.2845, 0.2402, 0.6318, 0.7318, 0.8380
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5155 5134.0 0.086 0.434
r= 30 22993 23103.0 0.524 0.958
r= 31 11632 11551.5 0.561 1.519
chi-square = 1.519 with df = 3; p-value = 0.322
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 228 211.4 1.301 1.301
r= 30 5128 5134.0 0.007 1.308
r= 31 23074 23103.0 0.037 1.344
r= 32 11570 11551.5 0.030 1.374
chi-square = 1.374 with df = 3; p-value = 0.288
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_00:31
b-rank test for bits 1 to 8, p=0.68117
b-rank test for bits 2 to 9, p=0.29898
b-rank test for bits 3 to 10, p=0.93004
b-rank test for bits 4 to 11, p=0.86081
b-rank test for bits 5 to 12, p=0.80523
b-rank test for bits 6 to 13, p=0.40600
b-rank test for bits 7 to 14, p=0.61678
b-rank test for bits 8 to 15, p=0.27034
b-rank test for bits 9 to 16, p=0.04517
b-rank test for bits 10 to 17, p=0.92565
b-rank test for bits 11 to 18, p=0.78697
b-rank test for bits 12 to 19, p=0.96227
b-rank test for bits 13 to 20, p=0.07694
b-rank test for bits 14 to 21, p=0.82243
b-rank test for bits 15 to 22, p=0.42642
b-rank test for bits 16 to 23, p=0.44909
b-rank test for bits 17 to 24, p=0.97930
b-rank test for bits 18 to 25, p=0.65859
b-rank test for bits 19 to 26, p=0.85431
b-rank test for bits 20 to 27, p=0.90734
b-rank test for bits 21 to 28, p=0.92323
b-rank test for bits 22 to 29, p=0.83683
b-rank test for bits 23 to 30, p=0.61627
b-rank test for bits 24 to 31, p=0.40166
b-rank test for bits 25 to 32, p=0.66615
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 = 0.013139
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_00:31
(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 141785 -0.29 0.385720
2 140895 -2.37 0.008896
3 142633 1.69 0.954564
4 141870 -0.09 0.463392
5 141886 -0.05 0.478265
6 141752 -0.37 0.356588
7 141793 -0.27 0.392888
8 141282 -1.47 0.071362
9 142018 0.25 0.600214
10 141952 0.10 0.539707
11 142091 0.42 0.664386
12 141745 -0.38 0.350508
13 141687 -0.52 0.301719
14 142212 0.71 0.760271
15 142244 0.78 0.782875
16 140906 -2.34 0.009533
17 142107 0.46 0.677904
18 141554 -0.83 0.203210
19 141840 -0.16 0.435658
20 141953 0.10 0.540635
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_00:31
Bits used No. missing words z-score p-value
23 to 32 142089 0.6196 0.732224
22 to 31 141687 -0.7667 0.221643
21 to 30 141732 -0.6115 0.270440
20 to 29 141789 -0.4149 0.339096
19 to 28 142789 3.0333 0.998791
18 to 27 142089 0.6196 0.732224
17 to 26 141591 -1.0977 0.136170
16 to 25 141872 -0.1287 0.448788
15 to 24 142171 0.9023 0.816554
14 to 23 142224 1.0851 0.861054
13 to 22 141742 -0.5770 0.281970
12 to 21 141952 0.1471 0.558488
11 to 20 141666 -0.8391 0.200715
10 to 19 142157 0.8540 0.803457
9 to 18 142032 0.4230 0.663852
8 to 17 141852 -0.1977 0.421644
7 to 16 141496 -1.4253 0.077039
6 to 15 142250 1.1747 0.879947
5 to 14 142117 0.7161 0.763036
4 to 13 141683 -0.7804 0.217564
3 to 12 141624 -0.9839 0.162583
2 to 11 142190 0.9678 0.833435
1 to 10 142118 0.7196 0.764100
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_00:31
Bits used No. missing words z-score p-value
28 to 32 142503 2.0124 0.977913
27 to 31 141820 -0.3028 0.381016
26 to 30 142114 0.6938 0.756095
25 to 29 141937 0.0938 0.537365
24 to 28 141990 0.2735 0.607749
23 to 27 142104 0.6599 0.745341
22 to 26 142222 1.0599 0.855405
21 to 25 142113 0.6904 0.755031
20 to 24 142114 0.6938 0.756095
19 to 23 141744 -0.5604 0.287589
18 to 22 142149 0.8124 0.791731
17 to 21 141875 -0.1164 0.453679
16 to 20 142057 0.5006 0.691665
15 to 19 142109 0.6768 0.750749
14 to 18 142706 2.7006 0.996539
13 to 17 142414 1.7107 0.956436
12 to 16 141975 0.2226 0.588081
11 to 15 141587 -1.0926 0.137275
10 to 14 142102 0.6531 0.743160
9 to 13 141818 -0.3096 0.378435
8 to 12 142334 1.4396 0.925004
7 to 11 141970 0.2057 0.581472
6 to 10 141953 0.1480 0.558842
5 to 9 141817 -0.3130 0.377147
4 to 8 142056 0.4972 0.690471
3 to 7 141850 -0.2011 0.420303
2 to 6 141660 -0.8452 0.199003
1 to 5 142496 1.9887 0.976634
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_00:31
Bits used No. missing words z-score p-value
31 to 32 141913 0.0108 0.504319
30 to 31 142310 1.1819 0.881381
29 to 30 141872 -0.1101 0.456158
28 to 29 141371 -1.5880 0.056144
27 to 28 141961 0.1524 0.560572
26 to 27 141574 -0.9892 0.161289
25 to 26 142230 0.9459 0.827908
24 to 25 141932 0.0669 0.526659
23 to 24 142045 0.4002 0.655498
22 to 23 141961 0.1524 0.560572
21 to 22 142014 0.3088 0.621248
20 to 21 141763 -0.4317 0.332997
19 to 20 142351 1.3029 0.903689
18 to 19 142430 1.5359 0.937719
17 to 18 141525 -1.1337 0.128457
16 to 17 140858 -3.1013 0.000963
15 to 16 141776 -0.3933 0.347048
14 to 15 142739 2.4474 0.992806
13 to 14 141497 -1.2163 0.111933
12 to 13 141520 -1.1485 0.125388
11 to 12 142444 1.5772 0.942625
10 to 11 142049 0.4120 0.659832
9 to 10 141876 -0.0983 0.460840
8 to 9 142620 2.0964 0.981975
7 to 8 142402 1.4533 0.926930
6 to 7 141646 -0.7768 0.218643
5 to 6 141644 -0.7827 0.216906
4 to 5 141228 -2.0098 0.022225
3 to 4 141966 0.1672 0.566381
2 to 3 141737 -0.5083 0.305605
1 to 2 142503 1.7512 0.960048
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2541.26 0.584 0.720229
Test results for specific bytes for dh-ranFile-2018-06-20_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2507.95 0.112 0.544748
2 to 9 2483.78 -0.229 0.409263
3 to 10 2553.73 0.760 0.776344
4 to 11 2578.14 1.105 0.865449
5 to 12 2524.53 0.347 0.635661
6 to 13 2443.10 -0.805 0.210485
7 to 14 2542.41 0.600 0.725662
8 to 15 2493.48 -0.092 0.463259
9 to 16 2463.14 -0.521 0.301095
10 to 17 2660.76 2.273 0.988501
11 to 18 2511.26 0.159 0.563263
12 to 19 2605.45 1.491 0.932066
13 to 20 2571.09 1.005 0.842628
14 to 21 2333.38 -2.356 0.009228
15 to 22 2601.26 1.432 0.923943
16 to 23 2601.76 1.439 0.924943
17 to 24 2500.78 0.011 0.504398
18 to 25 2501.88 0.027 0.510592
19 to 26 2488.19 -0.167 0.433696
20 to 27 2413.96 -1.217 0.111840
21 to 28 2519.18 0.271 0.606874
22 to 29 2474.79 -0.357 0.360732
23 to 30 2574.77 1.057 0.854846
24 to 31 2524.22 0.343 0.634016
25 to 32 2489.45 -0.149 0.440712
CDPARK for dh-ranFile-2018-06-20_00:31: 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
3498 -1.1416 0.126820
3516 -0.3196 0.374623
3553 1.3699 0.914635
3511 -0.5479 0.291865
3543 0.9132 0.819442
3516 -0.3196 0.374623
3501 -1.0046 0.157553
3541 0.8219 0.794438
3524 0.0457 0.518210
3545 1.0046 0.842447
Square side=100, avg. no. parked=3524.80 sample std.=18.51
p-value of the KSTEST for those 10 p-values: 0.901952
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_00:31
0.4774,0.3064,0.2689,0.9744,0.7438,0.7006,0.3733,0.4794,0.7507,0.5582,
The KS test for those 10 p-values: 0.506330
The 3DSPHERES test for dh-ranFile-2018-06-20_00:31
sample no r^3 equiv. uni.
1 55.927 0.844988
2 9.836 0.279541
3 36.672 0.705474
4 32.914 0.666174
5 10.653 0.298892
6 79.584 0.929546
7 61.829 0.872670
8 11.893 0.327290
9 31.532 0.650433
10 9.083 0.261220
11 16.850 0.429737
12 40.794 0.743285
13 8.815 0.254591
14 8.206 0.239303
15 32.895 0.665962
16 52.025 0.823450
17 28.669 0.615431
18 24.615 0.559784
19 32.147 0.657527
20 4.956 0.152282
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.395587
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 -1.3 -1.3 -1.0 -0.4
1.0 -0.2 0.0 -0.8 -0.7 -1.9
-0.1 0.1 0.0 0.7 0.9 -1.1
0.2 0.9 0.4 0.4 0.2 -0.3
-0.1 -0.3 -0.6 1.4 1.5 -2.0
-0.1 -1.3 1.2 1.1 1.2 0.6
0.7 0.8 0.1 -0.7 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:31.947974
z-score=-1.096766, p-value=0.130382
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_00:31
Test no p-value
1 0.350242
2 0.290634
3 0.079152
4 0.114079
5 0.034234
6 0.085321
7 0.507404
8 0.026044
9 0.015066
10 0.777772
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001414
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_00:31:
(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 66393 1.12 66591 0.09
3 25000.00 25235 2.21 25086 0.30
4 6666.67 6675 0.01 6629 0.21
5 1388.89 1403 0.14 1418 0.61
6 238.10 250 0.60 239 0.00
7 34.72 37 0.15 32 0.21
8 4.96 6 0.22 4 0.19
p=0.38388 p=0.04793
Number of rngs required: 687873, p-value: 0.270
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_00:31
No. of wins: Observed Expected
98837 98585.9
z-score= 1.123, pvalue=0.86933
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66939 66666.7 1.112 1.112
2 37601 37654.3 0.076 1.188
3 27195 26954.7 2.142 3.330
4 19391 19313.5 0.311 3.641
5 13650 13851.4 2.929 6.570
6 9932 9943.5 0.013 6.583
7 7116 7145.0 0.118 6.701
8 4991 5139.1 4.266 10.968
9 3701 3699.9 0.000 10.968
10 2651 2666.3 0.088 11.056
11 1906 1923.3 0.156 11.212
12 1388 1388.7 0.000 11.212
13 978 1003.7 0.659 11.871
14 667 726.1 4.817 16.688
15 563 525.8 2.627 19.314
16 364 381.2 0.772 20.086
17 278 276.5 0.008 20.094
18 155 200.8 10.459 30.552
19 129 146.0 1.976 32.528
20 105 106.2 0.014 32.542
21 300 287.1 0.578 33.121
Chisq= 33.12 for 20 degrees of freedom, p= 0.96727
SUMMARY of craptest
p-value for no. of wins: 0.869335
p-value for throws/game: 0.967274
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_00:31
No. of wins: Observed Expected
98164 98585.9
z-score=-1.887, pvalue=0.02959
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66371 66666.7 1.311 1.311
2 37856 37654.3 1.080 2.391
3 26836 26954.7 0.523 2.914
4 19741 19313.5 9.464 12.379
5 13935 13851.4 0.504 12.883
6 9794 9943.5 2.249 15.132
7 7097 7145.0 0.323 15.455
8 5090 5139.1 0.469 15.924
9 3656 3699.9 0.520 16.444
10 2682 2666.3 0.092 16.536
11 1939 1923.3 0.128 16.664
12 1404 1388.7 0.168 16.831
13 1020 1003.7 0.264 17.096
14 661 726.1 5.844 22.939
15 526 525.8 0.000 22.939
16 399 381.2 0.836 23.775
17 265 276.5 0.482 24.257
18 216 200.8 1.146 25.403
19 140 146.0 0.245 25.648
20 108 106.2 0.030 25.678
21 264 287.1 1.861 27.539
Chisq= 27.54 for 20 degrees of freedom, p= 0.87922
SUMMARY of craptest
p-value for no. of wins: 0.029594
p-value for throws/game: 0.879224
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0014,0.0057,0.0089,0.0092,0.0095,0.0131,0.0151,0.0222,0.0260,
0.0296,0.0317,0.0342,0.0452,0.0459,0.0479,0.0561,0.0714,0.0769,0.0770,
0.0792,0.0840,0.0853,0.0913,0.1026,0.1087,0.1118,0.1119,0.1141,0.1254,
0.1268,0.1285,0.1304,0.1362,0.1373,0.1411,0.1523,0.1576,0.1613,0.1626,
0.1720,0.1839,0.1990,0.2007,0.2032,0.2105,0.2169,0.2176,0.2186,0.2216,
0.2286,0.2367,0.2393,0.2402,0.2546,0.2612,0.2689,0.2703,0.2704,0.2705,
0.2795,0.2813,0.2820,0.2845,0.2876,0.2883,0.2906,0.2919,0.2989,0.2990,
0.3011,0.3017,0.3056,0.3064,0.3221,0.3273,0.3330,0.3391,0.3470,0.3502,
0.3505,0.3566,0.3607,0.3733,0.3746,0.3746,0.3771,0.3784,0.3810,0.3839,
0.3857,0.3929,0.3956,0.4017,0.4060,0.4093,0.4203,0.4216,0.4264,0.4297,
0.4314,0.4337,0.4357,0.4407,0.4488,0.4491,0.4537,0.4562,0.4608,0.4633,
0.4634,0.4774,0.4783,0.4794,0.4862,0.5043,0.5044,0.5063,0.5074,0.5106,
0.5111,0.5182,0.5213,0.5234,0.5267,0.5372,0.5374,0.5397,0.5406,0.5447,
0.5514,0.5582,0.5585,0.5588,0.5598,0.5606,0.5606,0.5633,0.5635,0.5664,
0.5768,0.5815,0.5881,0.5954,0.6002,0.6069,0.6077,0.6101,0.6154,0.6163,
0.6168,0.6212,0.6318,0.6340,0.6357,0.6504,0.6544,0.6555,0.6575,0.6586,
0.6598,0.6628,0.6639,0.6644,0.6660,0.6661,0.6662,0.6779,0.6812,0.6882,
0.6905,0.6917,0.7006,0.7055,0.7072,0.7137,0.7202,0.7219,0.7257,0.7257,
0.7318,0.7322,0.7322,0.7423,0.7432,0.7433,0.7438,0.7453,0.7507,0.7507,
0.7550,0.7561,0.7561,0.7562,0.7585,0.7603,0.7630,0.7641,0.7662,0.7763,
0.7774,0.7778,0.7829,0.7831,0.7870,0.7917,0.7944,0.8035,0.8052,0.8166,
0.8194,0.8224,0.8234,0.8279,0.8334,0.8368,0.8380,0.8424,0.8426,0.8450,
0.8543,0.8548,0.8554,0.8608,0.8611,0.8654,0.8693,0.8727,0.8732,0.8792,
0.8799,0.8814,0.8916,0.9020,0.9037,0.9073,0.9146,0.9232,0.9239,0.9249,
0.9250,0.9256,0.9264,0.9269,0.9295,0.9300,0.9321,0.9368,0.9377,0.9426,
0.9546,0.9564,0.9600,0.9602,0.9623,0.9631,0.9658,0.9673,0.9744,0.9762,
0.9766,0.9772,0.9779,0.9793,0.9820,0.9885,0.9928,0.9965,0.9988,
Overall p-value after applying KStest on 269 p-values = 0.038164
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.