RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.58 19.9752 0.724499
2 to 25 15.96 18.0181 0.612300
3 to 26 15.78 24.4049 0.891157
4 to 27 15.78 21.3605 0.789420
5 to 28 15.52 20.7515 0.762397
6 to 29 15.76 21.3995 0.791072
7 to 30 15.63 24.7838 0.900345
8 to 31 15.96 12.7513 0.247330
9 to 32 15.87 30.0818 0.974239
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.014675
Tough bday spacings test for dh-ranFile-2018-06-28_03:31: 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 5 29 69 109 98 94 53 28 11 2 2
(O-E)^2/E 1.9 1.6 0.2 1.3 0.0 3.2 0.0 0.1 1.0 3.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 13.659, p= 0.811
RESULTS OF GCD FOR dh-ranFile-2018-06-28_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.977218
p-value, dist. of gcd's: 0.672089
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.906 0.682 0.612 0.060 0.970 0.380 0.271 0.986
Bits 8 to 15---> 0.469 0.591 0.284 0.476 0.725 0.303 0.637 0.951
Bits 16 to 23---> 0.253 0.318 0.700 0.948 0.019 0.415 0.349 0.204
Bits 24 to 31---> 0.682 0.860 0.915 0.743 0.783 0.073 0.721 0.303
KS test for the above 32 p values: 0.468
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_03:31,
p-values for 5 runs: 0.2007, 0.6352, 0.6227, 0.0153, 0.6861
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5072 5134.0 0.749 1.097
r= 30 23080 23103.0 0.023 1.120
r= 31 11628 11551.5 0.506 1.627
chi-square = 1.627 with df = 3; p-value = 0.347
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 196 211.4 1.124 1.124
r= 30 5116 5134.0 0.063 1.188
r= 31 23128 23103.0 0.027 1.215
r= 32 11560 11551.5 0.006 1.221
chi-square = 1.221 with df = 3; p-value = 0.252
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_03:31
b-rank test for bits 1 to 8, p=0.04123
b-rank test for bits 2 to 9, p=0.07532
b-rank test for bits 3 to 10, p=0.01814
b-rank test for bits 4 to 11, p=0.36911
b-rank test for bits 5 to 12, p=0.92333
b-rank test for bits 6 to 13, p=0.04995
b-rank test for bits 7 to 14, p=0.65470
b-rank test for bits 8 to 15, p=0.34755
b-rank test for bits 9 to 16, p=0.50485
b-rank test for bits 10 to 17, p=0.85705
b-rank test for bits 11 to 18, p=0.91237
b-rank test for bits 12 to 19, p=0.00389
b-rank test for bits 13 to 20, p=0.67295
b-rank test for bits 14 to 21, p=0.38585
b-rank test for bits 15 to 22, p=0.77288
b-rank test for bits 16 to 23, p=0.50012
b-rank test for bits 17 to 24, p=0.17377
b-rank test for bits 18 to 25, p=0.40771
b-rank test for bits 19 to 26, p=0.79353
b-rank test for bits 20 to 27, p=0.97424
b-rank test for bits 21 to 28, p=0.92947
b-rank test for bits 22 to 29, p=0.56404
b-rank test for bits 23 to 30, p=0.92157
b-rank test for bits 24 to 31, p=0.63025
b-rank test for bits 25 to 32, p=0.76681
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 = 0.404208
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_03:31
(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 142032 0.29 0.612795
2 141005 -2.11 0.017304
3 142204 0.69 0.754425
4 142010 0.24 0.592977
5 141835 -0.17 0.431063
6 141871 -0.09 0.464320
7 142029 0.28 0.610109
8 142385 1.11 0.866797
9 141694 -0.50 0.307444
10 141505 -0.94 0.172407
11 142035 0.29 0.615476
12 141539 -0.87 0.193449
13 142288 0.88 0.811852
14 141300 -1.42 0.077271
15 142410 1.17 0.878957
16 141547 -0.85 0.198619
17 141921 0.03 0.510876
18 142249 0.79 0.786292
19 142473 1.32 0.906078
20 141459 -1.05 0.146360
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_03:31
Bits used No. missing words z-score p-value
23 to 32 141972 0.2161 0.585547
22 to 31 142162 0.8713 0.808198
21 to 30 142559 2.2402 0.987462
20 to 29 142550 2.2092 0.986420
19 to 28 141708 -0.6942 0.243765
18 to 27 141670 -0.8253 0.204608
17 to 26 141631 -0.9598 0.168588
16 to 25 141975 0.2264 0.589574
15 to 24 141482 -1.4736 0.070301
14 to 23 142252 1.1816 0.881322
13 to 22 141871 -0.1322 0.447424
12 to 21 142444 1.8437 0.967386
11 to 20 141816 -0.3218 0.373792
10 to 19 141984 0.2575 0.601597
9 to 18 141804 -0.3632 0.358225
8 to 17 141565 -1.1873 0.117546
7 to 16 141692 -0.7494 0.226804
6 to 15 141758 -0.5218 0.300895
5 to 14 142532 2.1471 0.984109
4 to 13 141809 -0.3460 0.364684
3 to 12 141799 -0.3804 0.351806
2 to 11 142226 1.0920 0.862576
1 to 10 141985 0.2609 0.602927
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_03:31
Bits used No. missing words z-score p-value
28 to 32 142312 1.3650 0.913871
27 to 31 141823 -0.2926 0.384897
26 to 30 141779 -0.4418 0.329318
25 to 29 141608 -1.0215 0.153519
24 to 28 141481 -1.4520 0.073256
23 to 27 142044 0.4565 0.675988
22 to 26 142023 0.3853 0.650001
21 to 25 141652 -0.8723 0.191521
20 to 24 141832 -0.2621 0.396609
19 to 23 142349 1.4904 0.931941
18 to 22 142159 0.8463 0.801318
17 to 21 142134 0.7616 0.776849
16 to 20 141743 -0.5638 0.286435
15 to 19 141617 -0.9909 0.160855
14 to 18 141948 0.1311 0.552146
13 to 17 142055 0.4938 0.689275
12 to 16 141939 0.1006 0.540057
11 to 15 141823 -0.2926 0.384897
10 to 14 141556 -1.1977 0.115511
9 to 13 141828 -0.2757 0.391391
8 to 12 141842 -0.2282 0.409731
7 to 11 142261 1.1921 0.883389
6 to 10 142722 2.7548 0.997064
5 to 9 141740 -0.5740 0.282984
4 to 8 142273 1.2328 0.891171
3 to 7 142013 0.3514 0.637365
2 to 6 142093 0.6226 0.733230
1 to 5 141656 -0.8587 0.195240
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_03:31
Bits used No. missing words z-score p-value
31 to 32 142106 0.5801 0.719092
30 to 31 141782 -0.3756 0.353605
29 to 30 141941 0.0934 0.537216
28 to 29 141792 -0.3461 0.364632
27 to 28 142112 0.5978 0.725029
26 to 27 142784 2.5801 0.995062
25 to 26 141923 0.0403 0.516083
24 to 25 141766 -0.4228 0.336220
23 to 24 141762 -0.4346 0.331926
22 to 23 142364 1.3412 0.910074
21 to 22 141960 0.1495 0.559408
20 to 21 141867 -0.1249 0.450314
19 to 20 141995 0.2527 0.599755
18 to 19 142112 0.5978 0.725029
17 to 18 141239 -1.9774 0.024000
16 to 17 142062 0.4504 0.673772
15 to 16 142434 1.5477 0.939153
14 to 15 141929 0.0580 0.523135
13 to 14 142065 0.4592 0.676956
12 to 13 142047 0.4061 0.657668
11 to 12 142077 0.4946 0.689559
10 to 11 142092 0.5388 0.705005
9 to 10 141599 -0.9154 0.179984
8 to 9 142398 1.4415 0.925279
7 to 8 142400 1.4474 0.926108
6 to 7 141950 0.1200 0.547747
5 to 6 141604 -0.9007 0.183880
4 to 5 141647 -0.7738 0.219514
3 to 4 141827 -0.2429 0.404056
2 to 3 142327 1.2321 0.891038
1 to 2 141362 -1.6145 0.053205
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2540.70 0.576 0.717555
Test results for specific bytes for dh-ranFile-2018-06-28_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2334.25 -2.344 0.009538
2 to 9 2584.17 1.190 0.883044
3 to 10 2420.98 -1.118 0.131875
4 to 11 2436.12 -0.903 0.183165
5 to 12 2526.73 0.378 0.647287
6 to 13 2518.02 0.255 0.600582
7 to 14 2557.79 0.817 0.793116
8 to 15 2557.19 0.809 0.790689
9 to 16 2428.49 -1.011 0.155927
10 to 17 2474.81 -0.356 0.360853
11 to 18 2476.53 -0.332 0.370000
12 to 19 2550.19 0.710 0.761067
13 to 20 2423.87 -1.077 0.140825
14 to 21 2435.48 -0.912 0.180774
15 to 22 2563.53 0.898 0.815533
16 to 23 2523.23 0.329 0.628767
17 to 24 2534.96 0.494 0.689476
18 to 25 2482.18 -0.252 0.400503
19 to 26 2609.56 1.549 0.939362
20 to 27 2455.23 -0.633 0.263338
21 to 28 2552.73 0.746 0.772086
22 to 29 2469.46 -0.432 0.332913
23 to 30 2521.00 0.297 0.616767
24 to 31 2540.71 0.576 0.717590
25 to 32 2489.86 -0.143 0.442989
CDPARK for dh-ranFile-2018-06-28_03:31: 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
3511 -0.5479 0.291865
3539 0.7306 0.767486
3530 0.3196 0.625377
3523 0.0000 0.500000
3570 2.1461 0.984068
3535 0.5479 0.708135
3564 1.8721 0.969407
3525 0.0913 0.536383
3511 -0.5479 0.291865
3530 0.3196 0.625377
Square side=100, avg. no. parked=3533.80 sample std.=18.74
p-value of the KSTEST for those 10 p-values: 0.191492
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_03:31
0.7864,0.3801,0.5562,0.1733,0.4287,0.3837,0.3975,0.6329,0.1005,0.3699,
The KS test for those 10 p-values: 0.307487
The 3DSPHERES test for dh-ranFile-2018-06-28_03:31
sample no r^3 equiv. uni.
1 51.898 0.822701
2 0.083 0.002777
3 22.456 0.526947
4 12.899 0.349470
5 198.971 0.998683
6 74.325 0.916048
7 7.951 0.232807
8 11.724 0.323487
9 13.434 0.360960
10 118.761 0.980912
11 37.054 0.709205
12 39.417 0.731230
13 33.238 0.669755
14 110.566 0.974917
15 103.900 0.968674
16 9.123 0.262203
17 62.254 0.874460
18 9.511 0.271688
19 24.720 0.561329
20 3.624 0.113778
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.120989
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 0.6 0.3 0.6 -0.2
1.8 0.8 -1.0 -0.7 1.0 -0.4
-0.8 -0.7 -0.4 1.1 -1.5 0.7
-0.9 -0.3 -0.1 0.9 0.1 1.4
1.0 -0.1 -0.0 -1.1 0.7 -0.8
1.6 -0.4 0.8 1.1 -1.7 0.8
-0.5 0.2 -0.4 -0.7 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:32.400902
z-score=-1.047347, p-value=0.143321
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_03:31
Test no p-value
1 0.120545
2 0.301217
3 0.151219
4 0.679013
5 0.151926
6 0.075170
7 0.748310
8 0.140647
9 0.255932
10 0.029086
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.009903
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_03:31:
(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 66694 0.01 66627 0.02
3 25000.00 25059 0.14 25163 1.06
4 6666.67 6554 1.90 6607 0.53
5 1388.89 1422 0.79 1336 2.01
6 238.10 240 0.02 229 0.35
7 34.72 24 3.31 34 0.01
8 4.96 6 0.22 3 0.77
p=0.61875 p=0.42655
Number of rngs required: 687815, p-value: 0.249
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_03:31
No. of wins: Observed Expected
98611 98585.9
z-score= 0.112, pvalue=0.54477
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66585 66666.7 0.100 0.100
2 37460 37654.3 1.003 1.103
3 26974 26954.7 0.014 1.117
4 19702 19313.5 7.816 8.933
5 13769 13851.4 0.490 9.423
6 9865 9943.5 0.620 10.044
7 7092 7145.0 0.394 10.437
8 5071 5139.1 0.902 11.339
9 3731 3699.9 0.262 11.601
10 2718 2666.3 1.003 12.604
11 1947 1923.3 0.291 12.895
12 1368 1388.7 0.310 13.205
13 1004 1003.7 0.000 13.205
14 748 726.1 0.658 13.863
15 535 525.8 0.160 14.023
16 388 381.2 0.123 14.146
17 308 276.5 3.579 17.725
18 208 200.8 0.256 17.981
19 137 146.0 0.553 18.534
20 88 106.2 3.124 21.657
21 302 287.1 0.772 22.429
Chisq= 22.43 for 20 degrees of freedom, p= 0.68232
SUMMARY of craptest
p-value for no. of wins: 0.544766
p-value for throws/game: 0.682321
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_03:31
No. of wins: Observed Expected
98773 98585.9
z-score= 0.837, pvalue=0.79871
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66742 66666.7 0.085 0.085
2 37649 37654.3 0.001 0.086
3 26774 26954.7 1.212 1.298
4 19419 19313.5 0.577 1.874
5 13935 13851.4 0.504 2.379
6 9785 9943.5 2.528 4.907
7 7348 7145.0 5.766 10.673
8 5128 5139.1 0.024 10.696
9 3611 3699.9 2.134 12.831
10 2644 2666.3 0.186 13.017
11 1871 1923.3 1.424 14.441
12 1400 1388.7 0.091 14.532
13 1038 1003.7 1.171 15.704
14 763 726.1 1.871 17.575
15 542 525.8 0.497 18.071
16 352 381.2 2.229 20.301
17 280 276.5 0.043 20.344
18 192 200.8 0.388 20.732
19 136 146.0 0.683 21.415
20 116 106.2 0.901 22.317
21 275 287.1 0.511 22.828
Chisq= 22.83 for 20 degrees of freedom, p= 0.70267
SUMMARY of craptest
p-value for no. of wins: 0.798705
p-value for throws/game: 0.702669
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0028,0.0039,0.0095,0.0099,0.0147,0.0153,0.0173,0.0181,0.0187,0.0240,
0.0291,0.0412,0.0499,0.0532,0.0599,0.0703,0.0727,0.0733,0.0752,0.0753,
0.0773,0.1005,0.1138,0.1155,0.1175,0.1205,0.1210,0.1319,0.1406,0.1408,
0.1433,0.1464,0.1512,0.1519,0.1535,0.1559,0.1609,0.1686,0.1724,0.1733,
0.1738,0.1800,0.1808,0.1832,0.1839,0.1915,0.1915,0.1934,0.1952,0.1986,
0.2007,0.2044,0.2046,0.2195,0.2268,0.2328,0.2438,0.2473,0.2487,0.2520,
0.2530,0.2559,0.2622,0.2633,0.2708,0.2717,0.2830,0.2844,0.2864,0.2919,
0.2919,0.3009,0.3012,0.3027,0.3033,0.3074,0.3075,0.3178,0.3235,0.3293,
0.3319,0.3329,0.3362,0.3466,0.3475,0.3493,0.3495,0.3518,0.3536,0.3582,
0.3609,0.3610,0.3646,0.3647,0.3691,0.3699,0.3700,0.3738,0.3801,0.3803,
0.3837,0.3849,0.3849,0.3858,0.3914,0.3966,0.3975,0.4005,0.4041,0.4042,
0.4077,0.4097,0.4155,0.4266,0.4287,0.4311,0.4430,0.4474,0.4503,0.4643,
0.4684,0.4691,0.4764,0.5000,0.5001,0.5048,0.5109,0.5161,0.5231,0.5269,
0.5364,0.5372,0.5401,0.5448,0.5477,0.5521,0.5562,0.5594,0.5613,0.5640,
0.5855,0.5896,0.5910,0.5930,0.5998,0.6006,0.6016,0.6029,0.6101,0.6122,
0.6123,0.6128,0.6155,0.6168,0.6187,0.6227,0.6254,0.6254,0.6288,0.6303,
0.6329,0.6352,0.6373,0.6374,0.6473,0.6500,0.6547,0.6577,0.6698,0.6721,
0.6730,0.6738,0.6760,0.6770,0.6790,0.6815,0.6815,0.6823,0.6861,0.6893,
0.6895,0.6896,0.6999,0.7027,0.7050,0.7081,0.7092,0.7176,0.7176,0.7191,
0.7205,0.7245,0.7250,0.7250,0.7253,0.7312,0.7332,0.7433,0.7483,0.7544,
0.7611,0.7624,0.7668,0.7675,0.7721,0.7729,0.7768,0.7826,0.7863,0.7864,
0.7894,0.7907,0.7911,0.7931,0.7935,0.7987,0.8013,0.8082,0.8109,0.8119,
0.8155,0.8227,0.8571,0.8603,0.8626,0.8668,0.8745,0.8790,0.8813,0.8830,
0.8834,0.8910,0.8912,0.8912,0.9003,0.9061,0.9062,0.9101,0.9124,0.9139,
0.9148,0.9160,0.9216,0.9233,0.9253,0.9261,0.9295,0.9319,0.9392,0.9394,
0.9482,0.9506,0.9674,0.9687,0.9694,0.9697,0.9742,0.9742,0.9749,0.9772,
0.9809,0.9841,0.9841,0.9863,0.9864,0.9875,0.9951,0.9971,0.9987,
Overall p-value after applying KStest on 269 p-values = 0.268124
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.