RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.69 22.3131 0.827024
2 to 25 15.60 18.9622 0.669292
3 to 26 15.57 26.4869 0.933965
4 to 27 15.77 19.0599 0.674895
5 to 28 15.93 22.9872 0.850331
6 to 29 15.66 16.0606 0.480460
7 to 30 15.82 18.0012 0.611236
8 to 31 15.86 26.2796 0.930485
9 to 32 15.65 10.8871 0.137630
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.093753
Tough bday spacings test for dh-ranFile-2018-06-29_06:31: 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 7 40 72 102 99 78 52 24 16 5 5
(O-E)^2/E 0.5 0.3 0.0 0.2 0.0 0.0 0.0 1.1 0.1 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 2.860, p= 0.015
RESULTS OF GCD FOR dh-ranFile-2018-06-29_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.740644
p-value, dist. of gcd's: 0.505206
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.639 0.307 0.837 0.143 0.785 0.701 0.729 0.244
Bits 8 to 15---> 0.978 0.096 0.553 0.780 0.853 0.344 0.135 0.950
Bits 16 to 23---> 0.171 0.313 0.336 0.857 0.189 0.841 0.253 0.734
Bits 24 to 31---> 0.773 0.894 0.436 0.179 0.776 0.034 0.062 0.150
KS test for the above 32 p values: 0.396
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_06:31,
p-values for 5 runs: 0.4421, 0.8540, 0.3974, 0.5165, 0.6545
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5097 5134.0 0.267 0.539
r= 30 23032 23103.0 0.218 0.757
r= 31 11652 11551.5 0.874 1.631
chi-square = 1.631 with df = 3; p-value = 0.348
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 229 211.4 1.462 1.462
r= 30 4838 5134.0 17.067 18.529
r= 31 23315 23103.0 1.944 20.474
r= 32 11618 11551.5 0.383 20.856
chi-square = 20.856 with df = 3; p-value = 1.000
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_06:31
b-rank test for bits 1 to 8, p=0.20149
b-rank test for bits 2 to 9, p=0.43365
b-rank test for bits 3 to 10, p=0.55827
b-rank test for bits 4 to 11, p=0.47255
b-rank test for bits 5 to 12, p=0.53746
b-rank test for bits 6 to 13, p=0.71958
b-rank test for bits 7 to 14, p=0.86238
b-rank test for bits 8 to 15, p=0.78840
b-rank test for bits 9 to 16, p=0.82630
b-rank test for bits 10 to 17, p=0.99535
b-rank test for bits 11 to 18, p=0.84188
b-rank test for bits 12 to 19, p=0.18166
b-rank test for bits 13 to 20, p=0.35518
b-rank test for bits 14 to 21, p=0.23766
b-rank test for bits 15 to 22, p=0.73884
b-rank test for bits 16 to 23, p=0.66735
b-rank test for bits 17 to 24, p=0.03516
b-rank test for bits 18 to 25, p=0.35356
b-rank test for bits 19 to 26, p=0.23656
b-rank test for bits 20 to 27, p=0.63631
b-rank test for bits 21 to 28, p=0.95536
b-rank test for bits 22 to 29, p=0.80393
b-rank test for bits 23 to 30, p=0.34203
b-rank test for bits 24 to 31, p=0.00520
b-rank test for bits 25 to 32, p=0.44151
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 = 0.892450
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_06:31
(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 141788 -0.28 0.388404
2 142271 0.85 0.800951
3 141826 -0.19 0.422815
4 141953 0.10 0.540635
5 142387 1.12 0.867800
6 142027 0.27 0.608315
7 141945 0.08 0.533210
8 141475 -1.01 0.155103
9 141585 -0.76 0.224291
10 141352 -1.30 0.096429
11 142470 1.31 0.904898
12 141545 -0.85 0.197319
13 142489 1.35 0.912191
14 141534 -0.88 0.190260
15 142052 0.33 0.630562
16 142278 0.86 0.805485
17 141740 -0.40 0.346189
18 142231 0.75 0.773844
19 141926 0.04 0.515534
20 143111 2.81 0.997505
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_06:31
Bits used No. missing words z-score p-value
23 to 32 141980 0.2437 0.596264
22 to 31 141952 0.1471 0.558488
21 to 30 141747 -0.5598 0.287822
20 to 29 141418 -1.6942 0.045110
19 to 28 141458 -1.5563 0.059817
18 to 27 141748 -0.5563 0.288999
17 to 26 141953 0.1506 0.559849
16 to 25 142212 1.0437 0.851686
15 to 24 141738 -0.5908 0.277330
14 to 23 141743 -0.5736 0.283136
13 to 22 142058 0.5127 0.695904
12 to 21 141923 0.0471 0.518798
11 to 20 141184 -2.5011 0.006190
10 to 19 142033 0.4264 0.665109
9 to 18 142279 1.2747 0.898797
8 to 17 142506 2.0575 0.980180
7 to 16 142174 0.9127 0.819288
6 to 15 141831 -0.2701 0.393540
5 to 14 142015 0.3644 0.642213
4 to 13 141506 -1.3908 0.082144
3 to 12 141867 -0.1460 0.441974
2 to 11 142066 0.5402 0.705485
1 to 10 142428 1.7885 0.963154
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_06:31
Bits used No. missing words z-score p-value
28 to 32 141986 0.2599 0.602529
27 to 31 142076 0.5650 0.713957
26 to 30 142179 0.9141 0.819677
25 to 29 141797 -0.3808 0.351683
24 to 28 141723 -0.6316 0.263815
23 to 27 142124 0.7277 0.766600
22 to 26 141865 -0.1503 0.440275
21 to 25 141743 -0.5638 0.286435
20 to 24 141732 -0.6011 0.273881
19 to 23 142201 0.9887 0.838598
18 to 22 142189 0.9480 0.828444
17 to 21 142634 2.4565 0.992985
16 to 20 141848 -0.2079 0.417654
15 to 19 142100 0.6463 0.740970
14 to 18 141788 -0.4113 0.340431
13 to 17 142442 1.8057 0.964514
12 to 16 142010 0.3413 0.633544
11 to 15 142280 1.2565 0.895534
10 to 14 142258 1.1819 0.881384
9 to 13 142167 0.8735 0.808793
8 to 12 142141 0.7853 0.783868
7 to 11 141985 0.2565 0.601221
6 to 10 141784 -0.4248 0.335474
5 to 9 141146 -2.5876 0.004833
4 to 8 142009 0.3379 0.632267
3 to 7 141781 -0.4350 0.331775
2 to 6 141560 -1.1842 0.118173
1 to 5 141461 -1.5198 0.064285
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_06:31
Bits used No. missing words z-score p-value
31 to 32 142286 1.1111 0.866742
30 to 31 142011 0.2999 0.617878
29 to 30 141893 -0.0482 0.480790
28 to 29 141840 -0.2045 0.418976
27 to 28 142259 1.0315 0.848841
26 to 27 142042 0.3914 0.652233
25 to 26 141581 -0.9685 0.166391
24 to 25 141784 -0.3697 0.355801
23 to 24 141715 -0.5732 0.283240
22 to 23 142130 0.6509 0.742459
21 to 22 141913 0.0108 0.504319
20 to 21 141992 0.2439 0.596332
19 to 20 141803 -0.3137 0.376891
18 to 19 141733 -0.5201 0.301480
17 to 18 141898 -0.0334 0.486669
16 to 17 142196 0.8456 0.801122
15 to 16 142017 0.3176 0.624610
14 to 15 142074 0.4858 0.686429
13 to 14 141294 -1.8151 0.034752
12 to 13 141439 -1.3874 0.082659
11 to 12 141650 -0.7650 0.222140
10 to 11 141630 -0.8240 0.204975
9 to 10 141915 0.0167 0.506672
8 to 9 142684 2.2852 0.988848
7 to 8 141723 -0.5496 0.291281
6 to 7 141800 -0.3225 0.373534
5 to 6 141848 -0.1809 0.428217
4 to 5 142198 0.8515 0.802764
3 to 4 141303 -1.7886 0.036841
2 to 3 141822 -0.2576 0.398354
1 to 2 142057 0.4356 0.668438
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2536.26 0.513 0.695948
Test results for specific bytes for dh-ranFile-2018-06-29_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2524.06 0.340 0.633179
2 to 9 2396.34 -1.466 0.071318
3 to 10 2316.28 -2.598 0.004686
4 to 11 2538.12 0.539 0.705082
5 to 12 2656.41 2.212 0.986514
6 to 13 2521.38 0.302 0.618798
7 to 14 2592.27 1.305 0.904028
8 to 15 2443.04 -0.806 0.210237
9 to 16 2497.32 -0.038 0.484886
10 to 17 2503.70 0.052 0.520857
11 to 18 2458.61 -0.585 0.279146
12 to 19 2556.58 0.800 0.788191
13 to 20 2640.99 1.994 0.976919
14 to 21 2561.22 0.866 0.806679
15 to 22 2525.07 0.354 0.638515
16 to 23 2479.02 -0.297 0.383363
17 to 24 2390.31 -1.551 0.060419
18 to 25 2449.53 -0.714 0.237691
19 to 26 2462.48 -0.531 0.297855
20 to 27 2491.60 -0.119 0.452746
21 to 28 2476.01 -0.339 0.367180
22 to 29 2507.80 0.110 0.543942
23 to 30 2634.65 1.904 0.971556
24 to 31 2550.24 0.711 0.761325
25 to 32 2608.62 1.536 0.937753
CDPARK for dh-ranFile-2018-06-29_06:31: 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
3499 -1.0959 0.136563
3514 -0.4110 0.340551
3531 0.3653 0.642555
3528 0.2283 0.590298
3507 -0.7306 0.232514
3584 2.7854 0.997327
3539 0.7306 0.767486
3551 1.2785 0.899470
3516 -0.3196 0.374623
3523 0.0000 0.500000
Square side=100, avg. no. parked=3529.20 sample std.=23.30
p-value of the KSTEST for those 10 p-values: 0.763366
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_06:31
0.2171,0.7411,0.3033,0.0465,0.5148,0.6966,0.0513,0.2117,0.5555,0.6848,
The KS test for those 10 p-values: 0.411320
The 3DSPHERES test for dh-ranFile-2018-06-29_06:31
sample no r^3 equiv. uni.
1 10.583 0.297259
2 17.296 0.438163
3 21.677 0.514500
4 18.715 0.464111
5 28.664 0.615366
6 38.493 0.722825
7 36.104 0.699850
8 66.309 0.890334
9 16.012 0.413582
10 5.279 0.161367
11 66.772 0.892010
12 4.733 0.145937
13 8.475 0.246106
14 46.284 0.786215
15 40.076 0.737073
16 139.917 0.990570
17 32.752 0.664362
18 0.843 0.027693
19 0.047 0.001556
20 35.096 0.689587
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.843289
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 2.6 0.6 -0.4 -1.2 0.3
1.5 -0.0 -1.3 1.1 0.3 1.3
0.3 -0.1 -0.4 0.5 -0.6 -0.8
-0.2 -0.3 0.3 -3.1 0.8 2.3
-0.9 0.0 0.9 -0.8 0.8 0.0
0.3 1.1 2.7 0.4 -1.0 -1.2
0.5 0.8 -0.4 0.4 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:48.447643
z-score=0.703496, p-value=0.771062
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_06:31
Test no p-value
1 0.571318
2 0.048049
3 0.166474
4 0.147375
5 0.529615
6 0.194192
7 0.248072
8 0.052853
9 0.997440
10 0.181723
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.028606
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_06:31:
(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 66646 0.01 66837 0.44
3 25000.00 24970 0.04 24813 1.40
4 6666.67 6739 0.78 6680 0.03
5 1388.89 1378 0.09 1380 0.06
6 238.10 228 0.43 235 0.04
7 34.72 32 0.21 45 3.04
8 4.96 6 0.22 9 3.29
p=0.06055 p=0.78253
Number of rngs required: 687985, p-value: 0.315
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_06:31
No. of wins: Observed Expected
98866 98585.9
z-score= 1.253, pvalue=0.89489
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66435 66666.7 0.805 0.805
2 37973 37654.3 2.697 3.502
3 27038 26954.7 0.257 3.759
4 19349 19313.5 0.065 3.825
5 13765 13851.4 0.539 4.364
6 9830 9943.5 1.297 5.660
7 7067 7145.0 0.852 6.512
8 5114 5139.1 0.122 6.635
9 3707 3699.9 0.014 6.649
10 2676 2666.3 0.035 6.684
11 1951 1923.3 0.398 7.082
12 1411 1388.7 0.357 7.439
13 1005 1003.7 0.002 7.440
14 734 726.1 0.085 7.525
15 551 525.8 1.204 8.730
16 371 381.2 0.270 9.000
17 280 276.5 0.043 9.043
18 197 200.8 0.073 9.116
19 146 146.0 0.000 9.116
20 114 106.2 0.571 9.687
21 286 287.1 0.004 9.691
Chisq= 9.69 for 20 degrees of freedom, p= 0.02657
SUMMARY of craptest
p-value for no. of wins: 0.894889
p-value for throws/game: 0.026569
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_06:31
No. of wins: Observed Expected
98633 98585.9
z-score= 0.211, pvalue=0.58350
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66853 66666.7 0.521 0.521
2 37415 37654.3 1.521 2.042
3 27106 26954.7 0.849 2.891
4 19367 19313.5 0.148 3.039
5 13803 13851.4 0.169 3.208
6 9982 9943.5 0.149 3.357
7 7034 7145.0 1.725 5.082
8 5213 5139.1 1.063 6.146
9 3646 3699.9 0.784 6.930
10 2684 2666.3 0.118 7.048
11 1921 1923.3 0.003 7.050
12 1373 1388.7 0.178 7.229
13 993 1003.7 0.114 7.343
14 733 726.1 0.065 7.408
15 479 525.8 4.172 11.580
16 395 381.2 0.503 12.083
17 282 276.5 0.108 12.191
18 192 200.8 0.388 12.579
19 152 146.0 0.248 12.827
20 104 106.2 0.046 12.873
21 273 287.1 0.694 13.567
Chisq= 13.57 for 20 degrees of freedom, p= 0.14824
SUMMARY of craptest
p-value for no. of wins: 0.583495
p-value for throws/game: 0.148238
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0047,0.0048,0.0052,0.0062,0.0155,0.0266,0.0277,0.0286,0.0340,
0.0348,0.0352,0.0368,0.0451,0.0465,0.0480,0.0513,0.0529,0.0598,0.0604,
0.0605,0.0619,0.0643,0.0713,0.0821,0.0827,0.0938,0.0964,0.0964,0.1182,
0.1351,0.1366,0.1376,0.1431,0.1459,0.1474,0.1482,0.1499,0.1551,0.1614,
0.1664,0.1665,0.1714,0.1792,0.1817,0.1817,0.1886,0.1903,0.1942,0.1973,
0.2015,0.2050,0.2102,0.2117,0.2171,0.2221,0.2243,0.2325,0.2366,0.2377,
0.2377,0.2438,0.2461,0.2481,0.2525,0.2638,0.2739,0.2773,0.2791,0.2831,
0.2832,0.2864,0.2878,0.2890,0.2913,0.2973,0.2979,0.3015,0.3033,0.3068,
0.3131,0.3150,0.3318,0.3355,0.3359,0.3404,0.3406,0.3420,0.3439,0.3462,
0.3477,0.3517,0.3536,0.3552,0.3558,0.3672,0.3735,0.3746,0.3769,0.3834,
0.3884,0.3935,0.3955,0.3974,0.3984,0.4113,0.4136,0.4177,0.4190,0.4228,
0.4282,0.4337,0.4359,0.4382,0.4403,0.4415,0.4420,0.4421,0.4527,0.4641,
0.4725,0.4805,0.4808,0.4849,0.4867,0.5000,0.5043,0.5052,0.5067,0.5145,
0.5148,0.5155,0.5165,0.5188,0.5209,0.5296,0.5332,0.5375,0.5406,0.5439,
0.5529,0.5555,0.5583,0.5585,0.5598,0.5713,0.5835,0.5903,0.5963,0.5963,
0.6012,0.6025,0.6083,0.6112,0.6154,0.6179,0.6188,0.6246,0.6306,0.6323,
0.6332,0.6335,0.6363,0.6385,0.6391,0.6422,0.6426,0.6522,0.6545,0.6644,
0.6651,0.6674,0.6684,0.6693,0.6749,0.6848,0.6864,0.6896,0.6959,0.6959,
0.6966,0.6999,0.7013,0.7051,0.7055,0.7140,0.7196,0.7228,0.7292,0.7337,
0.7371,0.7388,0.7406,0.7410,0.7411,0.7425,0.7613,0.7634,0.7666,0.7675,
0.7711,0.7730,0.7738,0.7765,0.7804,0.7825,0.7839,0.7854,0.7862,0.7882,
0.7884,0.8010,0.8011,0.8028,0.8039,0.8055,0.8067,0.8088,0.8193,0.8197,
0.8263,0.8270,0.8284,0.8366,0.8386,0.8415,0.8419,0.8433,0.8488,0.8503,
0.8517,0.8527,0.8540,0.8566,0.8624,0.8667,0.8678,0.8814,0.8903,0.8920,
0.8925,0.8941,0.8949,0.8955,0.8988,0.8995,0.9040,0.9049,0.9122,0.9305,
0.9340,0.9378,0.9495,0.9554,0.9632,0.9645,0.9716,0.9769,0.9782,0.9802,
0.9865,0.9888,0.9906,0.9930,0.9954,0.9973,0.9974,0.9975,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.519242
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.