RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-14_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.34 36.9052 0.996534
2 to 25 15.55 13.7743 0.316994
3 to 26 15.41 20.9718 0.772447
4 to 27 15.76 15.7962 0.461673
5 to 28 15.73 22.4542 0.832122
6 to 29 15.86 17.3358 0.568152
7 to 30 15.52 25.3420 0.912688
8 to 31 15.78 13.1396 0.273209
9 to 32 15.49 21.6615 0.801911
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.138488
Tough bday spacings test for dh-ranFile-2018-06-14_23:31: 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 45 73 91 109 74 50 28 12 8 3
(O-E)^2/E 0.5 1.9 0.0 0.5 1.3 0.2 0.1 0.1 0.6 0.3 0.3
Birthday Spacings: Sum(O-E)^2/E= 5.728, p= 0.162
RESULTS OF GCD FOR dh-ranFile-2018-06-14_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.239690
p-value, dist. of gcd's: 0.343140
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-14_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.316 0.416 0.172 0.486 0.504 0.736 0.935 0.153
Bits 8 to 15---> 0.438 0.448 0.318 0.042 0.195 0.929 0.250 0.683
Bits 16 to 23---> 0.675 0.937 0.824 0.617 0.763 0.746 0.274 0.275
Bits 24 to 31---> 0.958 0.239 0.077 0.155 0.943 0.502 0.025 0.349
KS test for the above 32 p values: 0.122
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-14_23:31,
p-values for 5 runs: 0.9859, 0.6968, 0.3696, 0.3869, 0.9431
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-14_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 221 211.4 0.434 0.434
r= 29 5031 5134.0 2.067 2.501
r= 30 23104 23103.0 0.000 2.501
r= 31 11644 11551.5 0.740 3.241
chi-square = 3.241 with df = 3; p-value = 0.644
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-14_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 244 211.4 5.021 5.021
r= 30 5016 5134.0 2.713 7.734
r= 31 23257 23103.0 1.026 8.760
r= 32 11483 11551.5 0.406 9.166
chi-square = 9.166 with df = 3; p-value = 0.973
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-14_23:31
b-rank test for bits 1 to 8, p=0.48998
b-rank test for bits 2 to 9, p=0.35748
b-rank test for bits 3 to 10, p=0.48724
b-rank test for bits 4 to 11, p=0.32474
b-rank test for bits 5 to 12, p=0.47372
b-rank test for bits 6 to 13, p=0.89139
b-rank test for bits 7 to 14, p=0.30302
b-rank test for bits 8 to 15, p=0.82771
b-rank test for bits 9 to 16, p=0.74125
b-rank test for bits 10 to 17, p=0.86309
b-rank test for bits 11 to 18, p=0.19565
b-rank test for bits 12 to 19, p=0.88302
b-rank test for bits 13 to 20, p=0.93579
b-rank test for bits 14 to 21, p=0.66369
b-rank test for bits 15 to 22, p=0.22404
b-rank test for bits 16 to 23, p=0.04562
b-rank test for bits 17 to 24, p=0.01403
b-rank test for bits 18 to 25, p=0.27056
b-rank test for bits 19 to 26, p=0.78433
b-rank test for bits 20 to 27, p=0.95979
b-rank test for bits 21 to 28, p=0.61931
b-rank test for bits 22 to 29, p=0.62025
b-rank test for bits 23 to 30, p=0.39739
b-rank test for bits 24 to 31, p=0.10732
b-rank test for bits 25 to 32, p=0.32289
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 = 0.992126
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-14_23:31
(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 142231 0.75 0.773844
2 142512 1.41 0.920450
3 141609 -0.70 0.241431
4 142070 0.38 0.646317
5 140987 -2.15 0.015582
6 142240 0.77 0.780119
7 142050 0.33 0.628797
8 141873 -0.08 0.466177
9 141662 -0.58 0.281675
10 141795 -0.27 0.394686
11 141604 -0.71 0.237803
12 141761 -0.35 0.364459
13 142091 0.42 0.664386
14 141525 -0.90 0.184602
15 141698 -0.49 0.310737
16 141516 -0.92 0.179049
17 141470 -1.03 0.152335
18 141741 -0.39 0.347051
19 141974 0.15 0.560051
20 142288 0.88 0.811852
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-14_23:31
Bits used No. missing words z-score p-value
23 to 32 142118 0.7196 0.764100
22 to 31 141866 -0.1494 0.440614
21 to 30 141408 -1.7287 0.041929
20 to 29 142144 0.8092 0.790802
19 to 28 141397 -1.7667 0.038643
18 to 27 142017 0.3713 0.644784
17 to 26 142216 1.0575 0.854854
16 to 25 141905 -0.0149 0.494044
15 to 24 141887 -0.0770 0.469312
14 to 23 141911 0.0058 0.502297
13 to 22 142014 0.3609 0.640925
12 to 21 142029 0.4127 0.660070
11 to 20 141948 0.1333 0.553040
10 to 19 142343 1.4954 0.932597
9 to 18 142217 1.0609 0.855639
8 to 17 141949 0.1368 0.554403
7 to 16 142269 1.2402 0.892557
6 to 15 141940 0.1058 0.542113
5 to 14 141873 -0.1253 0.450153
4 to 13 142024 0.3954 0.653731
3 to 12 141696 -0.7356 0.230981
2 to 11 141191 -2.4770 0.006625
1 to 10 141898 -0.0391 0.484418
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-14_23:31
Bits used No. missing words z-score p-value
28 to 32 141993 0.2836 0.611652
27 to 31 141595 -1.0655 0.143319
26 to 30 142363 1.5379 0.937959
25 to 29 141974 0.2192 0.586761
24 to 28 142107 0.6701 0.748593
23 to 27 142034 0.4226 0.663710
22 to 26 142097 0.6362 0.737667
21 to 25 141600 -1.0486 0.147187
20 to 24 141366 -1.8418 0.032752
19 to 23 141736 -0.5876 0.278414
18 to 22 141774 -0.4587 0.323208
17 to 21 142125 0.7311 0.767636
16 to 20 141556 -1.1977 0.115511
15 to 19 141636 -0.9265 0.177082
14 to 18 141825 -0.2859 0.387491
13 to 17 142096 0.6328 0.736561
12 to 16 141882 -0.0926 0.463093
11 to 15 141890 -0.0655 0.473878
10 to 14 141316 -2.0113 0.022148
9 to 13 141588 -1.0893 0.138021
8 to 12 142185 0.9345 0.824970
7 to 11 141598 -1.0554 0.145631
6 to 10 142007 0.3311 0.629710
5 to 9 141416 -1.6723 0.047232
4 to 8 142166 0.8701 0.807868
3 to 7 142241 1.1243 0.869558
2 to 6 141602 -1.0418 0.148753
1 to 5 142027 0.3989 0.655010
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-14_23:31
Bits used No. missing words z-score p-value
31 to 32 141444 -1.3727 0.084930
30 to 31 142382 1.3943 0.918388
29 to 30 141908 -0.0039 0.498435
28 to 29 142186 0.8161 0.792789
27 to 28 141851 -0.1721 0.431693
26 to 27 142268 1.0580 0.854978
25 to 26 142011 0.2999 0.617878
24 to 25 141618 -0.8594 0.195065
23 to 24 141987 0.2291 0.590610
22 to 23 142307 1.1731 0.879616
21 to 22 142314 1.1937 0.883706
20 to 21 141677 -0.6853 0.246565
19 to 20 141684 -0.6647 0.253124
18 to 19 141029 -2.5968 0.004704
17 to 18 141831 -0.2311 0.408633
16 to 17 141913 0.0108 0.504319
15 to 16 142283 1.1023 0.864828
14 to 15 141548 -1.0659 0.143241
13 to 14 142421 1.5094 0.934395
12 to 13 141120 -2.3284 0.009945
11 to 12 141944 0.1023 0.540729
10 to 11 142175 0.7837 0.783388
9 to 10 141653 -0.7561 0.224784
8 to 9 141476 -1.2783 0.100579
7 to 8 142353 1.3088 0.904692
6 to 7 142070 0.4740 0.682233
5 to 6 142033 0.3648 0.642373
4 to 5 142480 1.6834 0.953850
3 to 4 142797 2.6185 0.995584
2 to 3 141663 -0.7266 0.233724
1 to 2 141990 0.2380 0.594046
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-14_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2408.53 -1.294 0.097896
Test results for specific bytes for dh-ranFile-2018-06-14_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2493.60 -0.091 0.463927
2 to 9 2546.22 0.654 0.743319
3 to 10 2546.53 0.658 0.744728
4 to 11 2583.32 1.178 0.880675
5 to 12 2482.52 -0.247 0.402358
6 to 13 2474.25 -0.364 0.357846
7 to 14 2416.96 -1.174 0.120115
8 to 15 2468.00 -0.453 0.325413
9 to 16 2453.54 -0.657 0.255557
10 to 17 2582.07 1.161 0.877097
11 to 18 2502.32 0.033 0.513068
12 to 19 2477.58 -0.317 0.375594
13 to 20 2562.38 0.882 0.811164
14 to 21 2614.76 1.623 0.947703
15 to 22 2424.90 -1.062 0.144116
16 to 23 2504.47 0.063 0.525178
17 to 24 2575.60 1.069 0.857489
18 to 25 2537.38 0.529 0.701451
19 to 26 2494.09 -0.084 0.466716
20 to 27 2682.39 2.579 0.995051
21 to 28 2496.37 -0.051 0.479507
22 to 29 2393.45 -1.507 0.065917
23 to 30 2317.92 -2.575 0.005011
24 to 31 2487.60 -0.175 0.430392
25 to 32 2591.39 1.292 0.901891
CDPARK for dh-ranFile-2018-06-14_23:31: 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
3535 0.5479 0.708135
3530 0.3196 0.625377
3551 1.2785 0.899470
3498 -1.1416 0.126820
3565 1.9178 0.972432
3531 0.3653 0.642555
3542 0.8676 0.807188
3508 -0.6849 0.246694
3527 0.1826 0.572463
3544 0.9589 0.831196
Square side=100, avg. no. parked=3533.10 sample std.=18.58
p-value of the KSTEST for those 10 p-values: 0.196469
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-14_23:31
0.1856,0.4855,0.0081,0.6874,0.1850,0.1056,0.3019,0.0622,0.5118,0.7027,
The KS test for those 10 p-values: 0.080417
The 3DSPHERES test for dh-ranFile-2018-06-14_23:31
sample no r^3 equiv. uni.
1 46.033 0.784426
2 2.040 0.065742
3 6.350 0.190777
4 89.805 0.949889
5 11.878 0.326938
6 37.399 0.712529
7 32.945 0.666520
8 32.662 0.663355
9 35.517 0.693914
10 27.372 0.598446
11 49.971 0.810940
12 35.887 0.697670
13 9.366 0.268161
14 0.581 0.019190
15 58.813 0.859205
16 3.533 0.111086
17 29.148 0.621525
18 19.384 0.475937
19 59.392 0.861894
20 13.953 0.371927
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.710422
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-14_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 0.6 1.2 -1.6 -1.2
-0.6 -1.9 -0.2 1.6 0.4 -0.5
-0.4 -0.6 0.8 -0.7 -0.0 0.1
0.2 -0.7 1.2 0.9 2.0 -2.1
0.7 0.6 -0.5 -2.0 0.5 0.5
0.5 -0.7 -0.9 -0.1 -1.6 0.2
-0.2 -0.1 -0.4 -0.7 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:36.212538
z-score=-0.631464, p-value=0.277810
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-14_23:31
Test no p-value
1 0.078856
2 0.326600
3 0.541052
4 0.358033
5 0.570029
6 0.879345
7 0.748018
8 0.036883
9 0.450494
10 0.363777
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.700286
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-14_23:31:
(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 66759 0.13 66886 0.72
3 25000.00 24735 2.81 25010 0.00
4 6666.67 6793 2.39 6504 3.97
5 1388.89 1417 0.57 1321 3.32
6 238.10 250 0.60 241 0.04
7 34.72 39 0.53 33 0.09
8 4.96 6 0.22 4 0.19
p=0.70083 p=0.78440
Number of rngs required: 687738, p-value: 0.221
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-14_23:31
No. of wins: Observed Expected
98368 98585.9
z-score=-0.974, pvalue=0.16493
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66472 66666.7 0.568 0.568
2 37854 37654.3 1.059 1.627
3 26679 26954.7 2.821 4.448
4 19361 19313.5 0.117 4.565
5 13983 13851.4 1.250 5.815
6 10091 9943.5 2.187 8.002
7 7173 7145.0 0.110 8.111
8 5057 5139.1 1.311 9.422
9 3658 3699.9 0.474 9.896
10 2732 2666.3 1.619 11.515
11 1907 1923.3 0.139 11.653
12 1360 1388.7 0.595 12.248
13 1067 1003.7 3.990 16.238
14 738 726.1 0.194 16.432
15 518 525.8 0.117 16.549
16 368 381.2 0.454 17.002
17 249 276.5 2.743 19.745
18 205 200.8 0.087 19.831
19 138 146.0 0.437 20.268
20 112 106.2 0.315 20.583
21 278 287.1 0.289 20.872
Chisq= 20.87 for 20 degrees of freedom, p= 0.59533
SUMMARY of craptest
p-value for no. of wins: 0.164931
p-value for throws/game: 0.595329
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-14_23:31
No. of wins: Observed Expected
98496 98585.9
z-score=-0.402, pvalue=0.34388
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66839 66666.7 0.445 0.445
2 37739 37654.3 0.190 0.636
3 26711 26954.7 2.204 2.840
4 19343 19313.5 0.045 2.885
5 13978 13851.4 1.157 4.042
6 9891 9943.5 0.278 4.319
7 7103 7145.0 0.247 4.567
8 5165 5139.1 0.131 4.697
9 3656 3699.9 0.520 5.217
10 2624 2666.3 0.671 5.888
11 1965 1923.3 0.903 6.791
12 1341 1388.7 1.641 8.432
13 1014 1003.7 0.105 8.538
14 738 726.1 0.194 8.731
15 521 525.8 0.044 8.776
16 365 381.2 0.684 9.460
17 270 276.5 0.155 9.615
18 208 200.8 0.256 9.871
19 144 146.0 0.027 9.898
20 99 106.2 0.490 10.388
21 286 287.1 0.004 10.392
Chisq= 10.39 for 20 degrees of freedom, p= 0.03951
SUMMARY of craptest
p-value for no. of wins: 0.343879
p-value for throws/game: 0.039514
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0047,0.0050,0.0066,0.0081,0.0099,0.0140,0.0156,0.0192,0.0221,0.0247,
0.0328,0.0369,0.0386,0.0395,0.0416,0.0419,0.0456,0.0472,0.0622,0.0657,
0.0659,0.0766,0.0789,0.0804,0.0849,0.0979,0.1006,0.1056,0.1073,0.1111,
0.1155,0.1201,0.1217,0.1268,0.1380,0.1385,0.1432,0.1433,0.1441,0.1456,
0.1472,0.1488,0.1523,0.1531,0.1554,0.1624,0.1649,0.1724,0.1771,0.1790,
0.1846,0.1850,0.1856,0.1908,0.1949,0.1951,0.1957,0.1965,0.2212,0.2240,
0.2248,0.2310,0.2337,0.2378,0.2386,0.2397,0.2414,0.2466,0.2467,0.2499,
0.2531,0.2556,0.2682,0.2706,0.2732,0.2737,0.2755,0.2778,0.2784,0.2817,
0.3019,0.3030,0.3107,0.3161,0.3170,0.3182,0.3229,0.3232,0.3247,0.3254,
0.3266,0.3269,0.3431,0.3439,0.3471,0.3487,0.3575,0.3578,0.3580,0.3638,
0.3645,0.3696,0.3719,0.3756,0.3869,0.3875,0.3947,0.3974,0.4024,0.4086,
0.4158,0.4304,0.4317,0.4381,0.4406,0.4475,0.4502,0.4505,0.4617,0.4631,
0.4639,0.4662,0.4667,0.4693,0.4737,0.4739,0.4759,0.4795,0.4844,0.4855,
0.4856,0.4872,0.4900,0.4940,0.4984,0.5023,0.5025,0.5040,0.5043,0.5118,
0.5131,0.5252,0.5407,0.5411,0.5421,0.5530,0.5544,0.5601,0.5682,0.5700,
0.5725,0.5868,0.5906,0.5940,0.5953,0.5984,0.6117,0.6169,0.6179,0.6193,
0.6202,0.6215,0.6254,0.6288,0.6297,0.6409,0.6424,0.6426,0.6441,0.6448,
0.6463,0.6537,0.6550,0.6601,0.6634,0.6637,0.6637,0.6644,0.6665,0.6745,
0.6822,0.6834,0.6874,0.6939,0.6968,0.6977,0.7003,0.7008,0.7015,0.7027,
0.7081,0.7104,0.7125,0.7360,0.7366,0.7377,0.7413,0.7433,0.7447,0.7459,
0.7480,0.7486,0.7633,0.7641,0.7676,0.7724,0.7738,0.7801,0.7834,0.7843,
0.7844,0.7844,0.7908,0.7928,0.8019,0.8072,0.8079,0.8109,0.8112,0.8119,
0.8242,0.8250,0.8277,0.8312,0.8321,0.8549,0.8550,0.8556,0.8575,0.8592,
0.8619,0.8631,0.8648,0.8696,0.8771,0.8793,0.8796,0.8807,0.8830,0.8837,
0.8914,0.8926,0.8995,0.9019,0.9047,0.9127,0.9184,0.9205,0.9292,0.9326,
0.9344,0.9350,0.9358,0.9372,0.9380,0.9429,0.9431,0.9477,0.9499,0.9539,
0.9576,0.9598,0.9724,0.9728,0.9859,0.9921,0.9951,0.9956,0.9965,
Overall p-value after applying KStest on 269 p-values = 0.989360
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.