RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-14_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.40 22.0921 0.818796
2 to 25 15.58 14.3823 0.360117
3 to 26 15.77 8.2781 0.039768
4 to 27 15.80 27.6072 0.950258
5 to 28 16.00 12.7001 0.243983
6 to 29 15.69 11.2471 0.156568
7 to 30 15.48 27.2955 0.946127
8 to 31 15.96 16.9105 0.539555
9 to 32 15.64 27.6028 0.950202
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.333069
Tough bday spacings test for dh-ranFile-2018-06-14_12:31: 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 44 82 103 89 77 42 24 17 12 3
(O-E)^2/E 0.5 1.5 1.0 0.3 0.8 0.0 2.0 1.1 0.3 4.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 12.149, p= 0.725
RESULTS OF GCD FOR dh-ranFile-2018-06-14_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.053886
p-value, dist. of gcd's: 0.592072
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-14_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.300 0.058 0.203 0.222 0.760 0.827 0.743 0.417
Bits 8 to 15---> 0.611 0.105 0.086 0.780 0.635 0.802 0.752 0.775
Bits 16 to 23---> 0.145 0.661 0.332 0.261 0.304 0.871 0.963 0.258
Bits 24 to 31---> 0.018 0.669 0.814 0.253 0.334 0.709 0.321 0.016
KS test for the above 32 p values: 0.469
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-14_12:31,
p-values for 5 runs: 0.9020, 0.1588, 0.5693, 0.5427, 0.2485
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-14_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5184 5134.0 0.487 0.514
r= 30 23113 23103.0 0.004 0.519
r= 31 11494 11551.5 0.286 0.805
chi-square = 0.805 with df = 3; p-value = 0.152
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-14_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 242 211.4 4.424 4.424
r= 30 5118 5134.0 0.050 4.474
r= 31 23057 23103.0 0.092 4.565
r= 32 11583 11551.5 0.086 4.651
chi-square = 4.651 with df = 3; p-value = 0.801
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-14_12:31
b-rank test for bits 1 to 8, p=0.96785
b-rank test for bits 2 to 9, p=0.82382
b-rank test for bits 3 to 10, p=0.43685
b-rank test for bits 4 to 11, p=0.01266
b-rank test for bits 5 to 12, p=0.70807
b-rank test for bits 6 to 13, p=0.31649
b-rank test for bits 7 to 14, p=0.97732
b-rank test for bits 8 to 15, p=0.26925
b-rank test for bits 9 to 16, p=0.48825
b-rank test for bits 10 to 17, p=0.26835
b-rank test for bits 11 to 18, p=0.26092
b-rank test for bits 12 to 19, p=0.30080
b-rank test for bits 13 to 20, p=0.26631
b-rank test for bits 14 to 21, p=0.36749
b-rank test for bits 15 to 22, p=0.03297
b-rank test for bits 16 to 23, p=0.95360
b-rank test for bits 17 to 24, p=0.74902
b-rank test for bits 18 to 25, p=0.61816
b-rank test for bits 19 to 26, p=0.03507
b-rank test for bits 20 to 27, p=0.31139
b-rank test for bits 21 to 28, p=0.13576
b-rank test for bits 22 to 29, p=0.63422
b-rank test for bits 23 to 30, p=0.86270
b-rank test for bits 24 to 31, p=0.87582
b-rank test for bits 25 to 32, p=0.62797
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 = 0.804922
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-14_12:31
(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 141285 -1.46 0.072322
2 141964 0.13 0.550820
3 142159 0.58 0.720168
4 141450 -1.07 0.141591
5 141321 -1.37 0.084627
6 141949 0.09 0.536924
7 142615 1.65 0.950402
8 141968 0.14 0.554516
9 141614 -0.69 0.245090
10 142329 0.98 0.836590
11 141953 0.10 0.540635
12 142121 0.49 0.689543
13 141378 -1.24 0.107224
14 141617 -0.68 0.247299
15 142039 0.30 0.619043
16 142033 0.29 0.613690
17 142280 0.87 0.806769
18 141563 -0.81 0.209205
19 141967 0.13 0.553593
20 141961 0.12 0.548045
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-14_12:31
Bits used No. missing words z-score p-value
23 to 32 141865 -0.1529 0.439254
22 to 31 142144 0.8092 0.790802
21 to 30 141831 -0.2701 0.393540
20 to 29 142303 1.3575 0.912686
19 to 28 141900 -0.0322 0.487167
18 to 27 141564 -1.1908 0.116867
17 to 26 141955 0.1575 0.562568
16 to 25 142300 1.3471 0.911032
15 to 24 141885 -0.0839 0.466569
14 to 23 141750 -0.5494 0.291361
13 to 22 142326 1.4368 0.924612
12 to 21 141714 -0.6736 0.250298
11 to 20 142006 0.3333 0.630563
10 to 19 141963 0.1851 0.573413
9 to 18 141687 -0.7667 0.221643
8 to 17 142069 0.5506 0.709041
7 to 16 142014 0.3609 0.640925
6 to 15 142037 0.4402 0.670119
5 to 14 142485 1.9851 0.976432
4 to 13 141277 -2.1804 0.014612
3 to 12 141490 -1.4460 0.074093
2 to 11 142167 0.8885 0.812869
1 to 10 141816 -0.3218 0.373792
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-14_12:31
Bits used No. missing words z-score p-value
28 to 32 142233 1.0972 0.863720
27 to 31 141698 -0.7164 0.236881
26 to 30 141945 0.1209 0.548121
25 to 29 141777 -0.4486 0.326869
24 to 28 142028 0.4023 0.656258
23 to 27 142120 0.7141 0.762428
22 to 26 142087 0.6023 0.726503
21 to 25 141425 -1.6418 0.050316
20 to 24 142031 0.4124 0.659992
19 to 23 142344 1.4735 0.929686
18 to 22 141742 -0.5672 0.285282
17 to 21 142181 0.9209 0.821453
16 to 20 141767 -0.4825 0.314734
15 to 19 141907 -0.0079 0.496849
14 to 18 141808 -0.3435 0.365614
13 to 17 142121 0.7175 0.763475
12 to 16 142001 0.3107 0.622003
11 to 15 142087 0.6023 0.726503
10 to 14 141655 -0.8621 0.194306
9 to 13 141696 -0.7232 0.234793
8 to 12 142198 0.9785 0.836097
7 to 11 142131 0.7514 0.773801
6 to 10 142078 0.5718 0.716259
5 to 9 141482 -1.4486 0.073728
4 to 8 142163 0.8599 0.805077
3 to 7 141251 -2.2316 0.012820
2 to 6 141513 -1.3435 0.089556
1 to 5 142452 1.8396 0.967084
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-14_12:31
Bits used No. missing words z-score p-value
31 to 32 142026 0.3442 0.634637
30 to 31 142168 0.7630 0.777280
29 to 30 141865 -0.1308 0.447980
28 to 29 142672 2.2498 0.987768
27 to 28 141368 -1.5968 0.055150
26 to 27 142951 3.0728 0.998940
25 to 26 141752 -0.4641 0.321288
24 to 25 142502 1.7483 0.959793
23 to 24 141689 -0.6499 0.257865
22 to 23 141443 -1.3756 0.084472
21 to 22 142301 1.1554 0.876030
20 to 21 141141 -2.2665 0.011712
19 to 20 141586 -0.9538 0.170099
18 to 19 141761 -0.4376 0.330856
17 to 18 142126 0.6391 0.738636
16 to 17 142317 1.2026 0.885428
15 to 16 142102 0.5683 0.715101
14 to 15 141805 -0.3078 0.379133
13 to 14 141932 0.0669 0.526659
12 to 13 141758 -0.4464 0.327654
11 to 12 141745 -0.4847 0.313927
10 to 11 141530 -1.1190 0.131577
9 to 10 141919 0.0285 0.511378
8 to 9 142298 1.1465 0.874210
7 to 8 141925 0.0462 0.518434
6 to 7 142213 0.8958 0.814815
5 to 6 141699 -0.6204 0.267483
4 to 5 141658 -0.7414 0.229230
3 to 4 141371 -1.5880 0.056144
2 to 3 142014 0.3088 0.621248
1 to 2 141688 -0.6529 0.256913
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-14_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2597.89 1.384 0.916883
Test results for specific bytes for dh-ranFile-2018-06-14_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2552.85 0.747 0.772591
2 to 9 2440.45 -0.842 0.199853
3 to 10 2680.09 2.547 0.994565
4 to 11 2590.10 1.274 0.898706
5 to 12 2477.51 -0.318 0.375203
6 to 13 2491.38 -0.122 0.451514
7 to 14 2564.26 0.909 0.818273
8 to 15 2418.17 -1.157 0.123595
9 to 16 2438.96 -0.863 0.194003
10 to 17 2430.73 -0.980 0.163621
11 to 18 2463.06 -0.522 0.300681
12 to 19 2507.13 0.101 0.540180
13 to 20 2581.69 1.155 0.876009
14 to 21 2567.29 0.952 0.829373
15 to 22 2452.75 -0.668 0.251997
16 to 23 2566.60 0.942 0.826857
17 to 24 2496.83 -0.045 0.482131
18 to 25 2372.99 -1.796 0.036231
19 to 26 2502.44 0.035 0.513774
20 to 27 2394.29 -1.495 0.067470
21 to 28 2426.33 -1.042 0.148744
22 to 29 2437.04 -0.890 0.186639
23 to 30 2511.31 0.160 0.563549
24 to 31 2478.12 -0.309 0.378472
25 to 32 2504.74 0.067 0.526721
CDPARK for dh-ranFile-2018-06-14_12:31: 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
3542 0.8676 0.807188
3525 0.0913 0.536383
3478 -2.0548 0.019949
3522 -0.0457 0.481790
3575 2.3744 0.991212
3506 -0.7763 0.218799
3565 1.9178 0.972432
3536 0.5936 0.723613
3523 0.0000 0.500000
3532 0.4110 0.659449
Square side=100, avg. no. parked=3530.40 sample std.=26.17
p-value of the KSTEST for those 10 p-values: 0.380787
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-14_12:31
0.8736,0.1689,0.2226,0.0205,0.1772,0.3019,0.0309,0.6946,0.0959,0.7121,
The KS test for those 10 p-values: 0.059655
The 3DSPHERES test for dh-ranFile-2018-06-14_12:31
sample no r^3 equiv. uni.
1 171.292 0.996686
2 40.641 0.741979
3 26.830 0.591119
4 7.283 0.215536
5 56.738 0.849122
6 31.139 0.645822
7 5.431 0.165586
8 2.792 0.088882
9 47.784 0.796644
10 7.985 0.233695
11 1.311 0.042770
12 38.970 0.727199
13 6.887 0.205120
14 118.080 0.980474
15 14.456 0.382380
16 2.297 0.073711
17 72.078 0.909518
18 44.349 0.771973
19 35.068 0.689299
20 0.967 0.031716
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.463272
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-14_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.5 -0.6 0.3 0.0 -0.3
0.9 0.8 0.6 -0.3 0.1 2.6
-0.4 -0.1 -0.6 0.2 -1.8 -1.1
0.8 0.4 0.4 0.3 -1.5 1.0
-0.5 0.9 -0.3 0.1 0.3 -0.6
-0.6 -1.1 0.7 -0.6 1.5 0.2
-0.5 -1.0 0.9 2.1 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:34.216902
z-score=-0.849206, p-value=0.202091
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-14_12:31
Test no p-value
1 0.446949
2 0.999796
3 0.589997
4 0.031283
5 0.012083
6 0.036827
7 0.230032
8 0.964541
9 0.174430
10 0.604031
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.070765
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-14_12:31:
(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 66627 0.02 66693 0.01
3 25000.00 24989 0.00 24873 0.65
4 6666.67 6749 1.02 6740 0.81
5 1388.89 1361 0.56 1419 0.65
6 238.10 237 0.01 226 0.61
7 34.72 31 0.40 46 3.66
8 4.96 5 0.00 2 1.77
p=0.08115 p=0.77342
Number of rngs required: 687469, p-value: 0.139
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-14_12:31
No. of wins: Observed Expected
98657 98585.9
z-score= 0.318, pvalue=0.62483
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66550 66666.7 0.204 0.204
2 37512 37654.3 0.538 0.742
3 27127 26954.7 1.101 1.843
4 19336 19313.5 0.026 1.869
5 13838 13851.4 0.013 1.882
6 10099 9943.5 2.430 4.313
7 7218 7145.0 0.745 5.058
8 5136 5139.1 0.002 5.060
9 3702 3699.9 0.001 5.061
10 2666 2666.3 0.000 5.061
11 1870 1923.3 1.479 6.540
12 1337 1388.7 1.928 8.468
13 995 1003.7 0.076 8.543
14 709 726.1 0.405 8.948
15 535 525.8 0.160 9.108
16 374 381.2 0.134 9.242
17 277 276.5 0.001 9.242
18 210 200.8 0.419 9.661
19 135 146.0 0.827 10.488
20 103 106.2 0.097 10.585
21 271 287.1 0.904 11.489
Chisq= 11.49 for 20 degrees of freedom, p= 0.06747
SUMMARY of craptest
p-value for no. of wins: 0.624828
p-value for throws/game: 0.067469
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-14_12:31
No. of wins: Observed Expected
98539 98585.9
z-score=-0.210, pvalue=0.41700
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66614 66666.7 0.042 0.042
2 37739 37654.3 0.190 0.232
3 26992 26954.7 0.052 0.284
4 19050 19313.5 3.594 3.878
5 13635 13851.4 3.381 7.259
6 10006 9943.5 0.392 7.651
7 7095 7145.0 0.350 8.002
8 5250 5139.1 2.394 10.396
9 3855 3699.9 6.505 16.901
10 2726 2666.3 1.337 18.238
11 1918 1923.3 0.015 18.252
12 1404 1388.7 0.168 18.420
13 1025 1003.7 0.451 18.871
14 756 726.1 1.228 20.099
15 542 525.8 0.497 20.596
16 363 381.2 0.864 21.460
17 265 276.5 0.482 21.942
18 198 200.8 0.040 21.982
19 172 146.0 4.636 26.618
20 111 106.2 0.216 26.834
21 284 287.1 0.034 26.867
Chisq= 26.87 for 20 degrees of freedom, p= 0.86096
SUMMARY of craptest
p-value for no. of wins: 0.416998
p-value for throws/game: 0.860963
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0117,0.0121,0.0127,0.0128,0.0146,0.0162,0.0179,0.0199,0.0205,0.0309,
0.0313,0.0317,0.0330,0.0351,0.0362,0.0368,0.0398,0.0428,0.0503,0.0539,
0.0552,0.0561,0.0581,0.0597,0.0675,0.0675,0.0708,0.0723,0.0737,0.0737,
0.0741,0.0811,0.0845,0.0846,0.0863,0.0889,0.0896,0.0959,0.1051,0.1072,
0.1169,0.1236,0.1316,0.1358,0.1393,0.1416,0.1454,0.1487,0.1518,0.1566,
0.1588,0.1636,0.1656,0.1689,0.1701,0.1744,0.1772,0.1866,0.1940,0.1943,
0.1999,0.2021,0.2026,0.2051,0.2092,0.2155,0.2188,0.2216,0.2219,0.2226,
0.2292,0.2300,0.2337,0.2348,0.2369,0.2440,0.2451,0.2473,0.2485,0.2503,
0.2520,0.2532,0.2569,0.2576,0.2579,0.2609,0.2610,0.2663,0.2675,0.2684,
0.2692,0.2853,0.2914,0.2997,0.3007,0.3008,0.3019,0.3036,0.3114,0.3139,
0.3147,0.3165,0.3213,0.3213,0.3269,0.3277,0.3309,0.3320,0.3331,0.3341,
0.3601,0.3656,0.3675,0.3738,0.3752,0.3785,0.3791,0.3808,0.3824,0.3935,
0.4170,0.4173,0.4369,0.4393,0.4469,0.4480,0.4515,0.4633,0.4666,0.4693,
0.4818,0.4821,0.4872,0.4883,0.4968,0.5000,0.5114,0.5138,0.5184,0.5267,
0.5267,0.5364,0.5369,0.5396,0.5402,0.5406,0.5427,0.5480,0.5481,0.5508,
0.5536,0.5545,0.5626,0.5635,0.5693,0.5734,0.5900,0.5911,0.5921,0.6040,
0.6108,0.6137,0.6182,0.6190,0.6212,0.6220,0.6248,0.6280,0.6306,0.6342,
0.6346,0.6349,0.6409,0.6458,0.6563,0.6594,0.6600,0.6613,0.6686,0.6701,
0.6893,0.6895,0.6946,0.7081,0.7088,0.7090,0.7121,0.7151,0.7163,0.7202,
0.7236,0.7248,0.7265,0.7265,0.7272,0.7386,0.7420,0.7428,0.7490,0.7525,
0.7597,0.7624,0.7635,0.7720,0.7726,0.7734,0.7738,0.7750,0.7773,0.7805,
0.7908,0.7966,0.8008,0.8018,0.8049,0.8051,0.8068,0.8072,0.8129,0.8141,
0.8148,0.8183,0.8188,0.8215,0.8238,0.8269,0.8271,0.8294,0.8361,0.8366,
0.8491,0.8610,0.8627,0.8637,0.8715,0.8736,0.8742,0.8758,0.8760,0.8760,
0.8854,0.8987,0.9020,0.9095,0.9110,0.9127,0.9169,0.9246,0.9297,0.9461,
0.9502,0.9503,0.9504,0.9536,0.9598,0.9630,0.9645,0.9671,0.9678,0.9724,
0.9764,0.9773,0.9805,0.9878,0.9912,0.9946,0.9967,0.9989,0.9998,
Overall p-value after applying KStest on 269 p-values = 0.201031
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.