RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 23.9846 0.880145
2 to 25 15.86 18.0780 0.616061
3 to 26 15.80 15.3373 0.428801
4 to 27 16.03 15.2540 0.422809
5 to 28 15.65 18.2465 0.626546
6 to 29 15.85 22.6599 0.839347
7 to 30 15.99 11.8286 0.189599
8 to 31 15.74 22.4587 0.832284
9 to 32 15.58 15.1186 0.413064
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.485057
Tough bday spacings test for dh-ranFile-2018-07-06_09:31: 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 8 27 83 106 78 81 45 37 17 12 6
(O-E)^2/E 0.1 2.5 1.3 0.7 4.0 0.1 1.0 1.8 0.3 4.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 17.077, p= 0.927
RESULTS OF GCD FOR dh-ranFile-2018-07-06_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.706295
p-value, dist. of gcd's: 0.842107
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.416 0.707 0.956 0.820 0.809 0.385 0.669 0.155
Bits 8 to 15---> 0.665 0.744 0.230 0.051 0.055 0.194 0.817 0.336
Bits 16 to 23---> 0.599 0.113 0.308 0.528 0.700 0.160 0.432 0.936
Bits 24 to 31---> 0.452 0.536 0.669 0.491 0.283 0.622 0.331 0.250
KS test for the above 32 p values: 0.187
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_09:31,
p-values for 5 runs: 0.3231, 0.8952, 0.9400, 0.8235, 0.1941
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 217 211.4 0.147 0.147
r= 29 5107 5134.0 0.142 0.289
r= 30 22999 23103.0 0.469 0.758
r= 31 11677 11551.5 1.363 2.121
chi-square = 2.121 with df = 3; p-value = 0.452
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 235 211.4 2.630 2.630
r= 30 5009 5134.0 3.044 5.674
r= 31 23257 23103.0 1.026 6.700
r= 32 11499 11551.5 0.239 6.939
chi-square = 6.939 with df = 3; p-value = 0.926
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_09:31
b-rank test for bits 1 to 8, p=0.12533
b-rank test for bits 2 to 9, p=0.73237
b-rank test for bits 3 to 10, p=0.28403
b-rank test for bits 4 to 11, p=0.68041
b-rank test for bits 5 to 12, p=0.90685
b-rank test for bits 6 to 13, p=0.33778
b-rank test for bits 7 to 14, p=0.40072
b-rank test for bits 8 to 15, p=0.88507
b-rank test for bits 9 to 16, p=0.59182
b-rank test for bits 10 to 17, p=0.64164
b-rank test for bits 11 to 18, p=0.82096
b-rank test for bits 12 to 19, p=0.87846
b-rank test for bits 13 to 20, p=0.83854
b-rank test for bits 14 to 21, p=0.11025
b-rank test for bits 15 to 22, p=0.41774
b-rank test for bits 16 to 23, p=0.75403
b-rank test for bits 17 to 24, p=0.87486
b-rank test for bits 18 to 25, p=0.15710
b-rank test for bits 19 to 26, p=0.68508
b-rank test for bits 20 to 27, p=0.95905
b-rank test for bits 21 to 28, p=0.89416
b-rank test for bits 22 to 29, p=0.62095
b-rank test for bits 23 to 30, p=0.62830
b-rank test for bits 24 to 31, p=0.95405
b-rank test for bits 25 to 32, p=0.02685
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 = 0.078439
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_09:31
(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 141689 -0.51 0.303350
2 141781 -0.30 0.382151
3 142507 1.40 0.918707
4 142755 1.98 0.975915
5 141658 -0.59 0.278528
6 141748 -0.38 0.353109
7 141749 -0.37 0.353978
8 141983 0.17 0.568331
9 141562 -0.81 0.208534
10 141568 -0.80 0.212580
11 141181 -1.70 0.044405
12 142275 0.85 0.803550
13 142009 0.23 0.592070
14 142372 1.08 0.860153
15 141773 -0.32 0.375042
16 142419 1.19 0.883137
17 142082 0.40 0.656686
18 142122 0.50 0.690368
19 141822 -0.20 0.419160
20 141401 -1.19 0.117478
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_09:31
Bits used No. missing words z-score p-value
23 to 32 141930 0.0713 0.528411
22 to 31 141779 -0.4494 0.326567
21 to 30 142568 2.2713 0.988435
20 to 29 142561 2.2471 0.987684
19 to 28 141997 0.3023 0.618792
18 to 27 141709 -0.6908 0.244848
17 to 26 142105 0.6747 0.750075
16 to 25 141954 0.1540 0.561209
15 to 24 142284 1.2920 0.901815
14 to 23 141948 0.1333 0.553040
13 to 22 141827 -0.2839 0.388245
12 to 21 142175 0.9161 0.820194
11 to 20 141975 0.2264 0.589574
10 to 19 141980 0.2437 0.596264
9 to 18 141559 -1.2080 0.113517
8 to 17 142183 0.9437 0.827336
7 to 16 141655 -0.8770 0.190243
6 to 15 141997 0.3023 0.618792
5 to 14 141957 0.1644 0.565284
4 to 13 142231 1.1092 0.866330
3 to 12 142062 0.5264 0.700712
2 to 11 142129 0.7575 0.775620
1 to 10 142283 1.2885 0.901217
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_09:31
Bits used No. missing words z-score p-value
28 to 32 142155 0.8328 0.797516
27 to 31 141851 -0.1977 0.421629
26 to 30 142171 0.8870 0.812465
25 to 29 142457 1.8565 0.968309
24 to 28 141795 -0.3876 0.349171
23 to 27 141721 -0.6384 0.261605
22 to 26 141840 -0.2350 0.407098
21 to 25 141402 -1.7198 0.042738
20 to 24 142062 0.5175 0.697605
19 to 23 142208 1.0124 0.844336
18 to 22 141514 -1.3401 0.090106
17 to 21 141986 0.2599 0.602529
16 to 20 141675 -0.7943 0.213499
15 to 19 141632 -0.9401 0.173583
14 to 18 141958 0.1650 0.565521
13 to 17 141712 -0.6689 0.251775
12 to 16 141158 -2.5469 0.005435
11 to 15 141701 -0.7062 0.240031
10 to 14 141688 -0.7503 0.226546
9 to 13 141354 -1.8825 0.029886
8 to 12 141422 -1.6520 0.049271
7 to 11 142268 1.2158 0.887975
6 to 10 141993 0.2836 0.611652
5 to 9 142468 1.8938 0.970874
4 to 8 142098 0.6396 0.738770
3 to 7 141681 -0.7740 0.219465
2 to 6 142102 0.6531 0.743160
1 to 5 141722 -0.6350 0.262709
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_09:31
Bits used No. missing words z-score p-value
31 to 32 142026 0.3442 0.634637
30 to 31 142265 1.0492 0.852951
29 to 30 141834 -0.2222 0.412074
28 to 29 141919 0.0285 0.511378
27 to 28 142023 0.3353 0.631304
26 to 27 142068 0.4681 0.680127
25 to 26 141647 -0.7738 0.219514
24 to 25 141593 -0.9331 0.175377
23 to 24 142806 2.6450 0.995916
22 to 23 141806 -0.3048 0.380256
21 to 22 141981 0.2114 0.583719
20 to 21 142425 1.5212 0.935889
19 to 20 142237 0.9666 0.833123
18 to 19 142023 0.3353 0.631304
17 to 18 142317 1.2026 0.885428
16 to 17 141638 -0.8004 0.211744
15 to 16 141839 -0.2075 0.417824
14 to 15 141771 -0.4081 0.341617
13 to 14 142451 1.5978 0.944961
12 to 13 141911 0.0049 0.501965
11 to 12 141545 -1.0747 0.141250
10 to 11 141862 -0.1396 0.444482
9 to 10 142055 0.4297 0.666295
8 to 9 141566 -1.0128 0.155584
7 to 8 142039 0.3825 0.648958
6 to 7 141961 0.1524 0.560572
5 to 6 141608 -0.8889 0.187034
4 to 5 141451 -1.3520 0.088187
3 to 4 141859 -0.1485 0.440988
2 to 3 142238 0.9695 0.833859
1 to 2 141780 -0.3815 0.351415
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2616.02 1.641 0.949581
Test results for specific bytes for dh-ranFile-2018-07-06_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2377.61 -1.731 0.041732
2 to 9 2347.34 -2.159 0.015429
3 to 10 2512.65 0.179 0.570978
4 to 11 2523.05 0.326 0.627778
5 to 12 2569.72 0.986 0.837927
6 to 13 2507.36 0.104 0.541466
7 to 14 2483.12 -0.239 0.405666
8 to 15 2446.36 -0.759 0.224039
9 to 16 2622.70 1.735 0.958651
10 to 17 2539.46 0.558 0.711574
11 to 18 2361.87 -1.954 0.025380
12 to 19 2497.40 -0.037 0.485355
13 to 20 2538.87 0.550 0.708748
14 to 21 2564.46 0.912 0.819024
15 to 22 2521.05 0.298 0.617027
16 to 23 2541.07 0.581 0.719305
17 to 24 2569.88 0.988 0.838493
18 to 25 2389.80 -1.558 0.059561
19 to 26 2528.36 0.401 0.655804
20 to 27 2497.23 -0.039 0.484365
21 to 28 2460.66 -0.556 0.289008
22 to 29 2408.61 -1.293 0.098089
23 to 30 2444.32 -0.787 0.215506
24 to 31 2488.70 -0.160 0.436536
25 to 32 2468.88 -0.440 0.329924
CDPARK for dh-ranFile-2018-07-06_09:31: 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
3524 0.0457 0.518210
3564 1.8721 0.969407
3491 -1.4612 0.071982
3515 -0.3653 0.357445
3504 -0.8676 0.192812
3528 0.2283 0.590298
3545 1.0046 0.842447
3526 0.1370 0.554479
3507 -0.7306 0.232514
3541 0.8219 0.794438
Square side=100, avg. no. parked=3524.50 sample std.=20.51
p-value of the KSTEST for those 10 p-values: 0.998153
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_09:31
0.0143,0.4009,0.4824,0.5680,0.5317,0.6088,0.7608,0.9869,0.9423,0.8582,
The KS test for those 10 p-values: 0.275476
The 3DSPHERES test for dh-ranFile-2018-07-06_09:31
sample no r^3 equiv. uni.
1 31.549 0.650638
2 3.384 0.106676
3 3.171 0.100304
4 20.826 0.500533
5 1.248 0.040757
6 7.348 0.217243
7 12.117 0.332288
8 17.866 0.448725
9 9.301 0.266574
10 188.604 0.998139
11 18.347 0.457492
12 12.012 0.329956
13 18.984 0.468890
14 0.480 0.015861
15 9.741 0.277246
16 18.742 0.464599
17 19.310 0.474642
18 9.021 0.259697
19 53.121 0.829784
20 74.916 0.917686
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.178063
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.6 -2.0 -0.1 0.8 0.5
0.5 -0.8 0.3 1.6 0.5 -0.1
0.4 -0.6 -0.8 0.3 0.4 -1.1
0.0 0.5 2.1 -1.6 0.4 -1.1
-0.0 -0.2 0.0 0.6 0.4 -0.8
-0.4 -0.3 -1.0 -0.6 0.5 1.7
-0.9 -1.0 0.9 1.0 1.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:37.217584
z-score=-0.521804, p-value=0.319354
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_09:31
Test no p-value
1 0.015005
2 0.054056
3 0.056991
4 0.649834
5 0.105469
6 0.010551
7 0.035712
8 0.632016
9 0.530087
10 0.415709
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001392
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_09:31:
(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 66580 0.11 66527 0.29
3 25000.00 24951 0.10 25174 1.21
4 6666.67 6762 1.36 6676 0.01
5 1388.89 1411 0.35 1347 1.26
6 238.10 263 2.61 242 0.06
7 34.72 30 0.64 30 0.64
8 4.96 2 1.77 3 0.77
p=0.67329 p=0.35851
Number of rngs required: 688063, p-value: 0.348
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_09:31
No. of wins: Observed Expected
98526 98585.9
z-score=-0.268, pvalue=0.39446
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66550 66666.7 0.204 0.204
2 37625 37654.3 0.023 0.227
3 27047 26954.7 0.316 0.543
4 19240 19313.5 0.279 0.822
5 13948 13851.4 0.673 1.496
6 9984 9943.5 0.165 1.660
7 6999 7145.0 2.984 4.645
8 5187 5139.1 0.447 5.092
9 3691 3699.9 0.021 5.113
10 2737 2666.3 1.875 6.988
11 1941 1923.3 0.162 7.150
12 1356 1388.7 0.772 7.922
13 1043 1003.7 1.538 9.460
14 773 726.1 3.024 12.483
15 543 525.8 0.560 13.044
16 383 381.2 0.009 13.053
17 253 276.5 2.004 15.056
18 184 200.8 1.410 16.467
19 126 146.0 2.736 19.203
20 112 106.2 0.315 19.518
21 278 287.1 0.289 19.807
Chisq= 19.81 for 20 degrees of freedom, p= 0.52993
SUMMARY of craptest
p-value for no. of wins: 0.394456
p-value for throws/game: 0.529935
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_09:31
No. of wins: Observed Expected
98168 98585.9
z-score=-1.869, pvalue=0.03082
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66586 66666.7 0.098 0.098
2 37599 37654.3 0.081 0.179
3 26847 26954.7 0.431 0.609
4 19340 19313.5 0.036 0.646
5 13906 13851.4 0.215 0.861
6 10166 9943.5 4.977 5.838
7 7172 7145.0 0.102 5.940
8 5074 5139.1 0.824 6.764
9 3812 3699.9 3.399 10.162
10 2621 2666.3 0.770 10.932
11 1976 1923.3 1.442 12.374
12 1353 1388.7 0.920 13.294
13 990 1003.7 0.187 13.481
14 702 726.1 0.803 14.284
15 508 525.8 0.605 14.889
16 363 381.2 0.864 15.753
17 263 276.5 0.663 16.416
18 184 200.8 1.410 17.826
19 148 146.0 0.028 17.854
20 111 106.2 0.216 18.070
21 279 287.1 0.229 18.299
Chisq= 18.30 for 20 degrees of freedom, p= 0.43229
SUMMARY of craptest
p-value for no. of wins: 0.030818
p-value for throws/game: 0.432293
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0054,0.0106,0.0143,0.0150,0.0154,0.0159,0.0254,0.0268,0.0299,
0.0308,0.0357,0.0408,0.0417,0.0427,0.0444,0.0493,0.0511,0.0541,0.0547,
0.0570,0.0596,0.0720,0.0784,0.0882,0.0901,0.0981,0.1003,0.1055,0.1067,
0.1103,0.1131,0.1135,0.1175,0.1253,0.1413,0.1547,0.1556,0.1571,0.1597,
0.1736,0.1754,0.1781,0.1870,0.1871,0.1896,0.1902,0.1928,0.1940,0.1941,
0.2085,0.2117,0.2126,0.2135,0.2155,0.2172,0.2195,0.2195,0.2240,0.2265,
0.2303,0.2325,0.2400,0.2448,0.2496,0.2518,0.2597,0.2616,0.2627,0.2666,
0.2755,0.2772,0.2785,0.2831,0.2840,0.2890,0.3034,0.3080,0.3194,0.3231,
0.3266,0.3299,0.3300,0.3314,0.3323,0.3359,0.3378,0.3416,0.3477,0.3492,
0.3514,0.3531,0.3540,0.3574,0.3585,0.3750,0.3803,0.3822,0.3849,0.3882,
0.3945,0.4007,0.4009,0.4057,0.4071,0.4121,0.4131,0.4156,0.4157,0.4177,
0.4178,0.4192,0.4216,0.4228,0.4288,0.4323,0.4324,0.4365,0.4410,0.4445,
0.4487,0.4521,0.4523,0.4575,0.4646,0.4689,0.4746,0.4824,0.4844,0.4851,
0.4854,0.4910,0.5005,0.5020,0.5114,0.5182,0.5284,0.5284,0.5299,0.5301,
0.5317,0.5364,0.5415,0.5530,0.5545,0.5606,0.5612,0.5653,0.5655,0.5680,
0.5683,0.5710,0.5837,0.5896,0.5903,0.5918,0.5921,0.5963,0.5988,0.6025,
0.6088,0.6117,0.6161,0.6170,0.6188,0.6188,0.6209,0.6217,0.6265,0.6278,
0.6283,0.6313,0.6313,0.6320,0.6346,0.6416,0.6490,0.6498,0.6506,0.6558,
0.6567,0.6646,0.6663,0.6690,0.6693,0.6733,0.6801,0.6804,0.6851,0.6904,
0.6976,0.7004,0.7007,0.7063,0.7071,0.7087,0.7116,0.7193,0.7324,0.7388,
0.7432,0.7442,0.7501,0.7540,0.7608,0.7756,0.7944,0.7975,0.8035,0.8090,
0.8125,0.8174,0.8190,0.8202,0.8203,0.8210,0.8235,0.8273,0.8298,0.8323,
0.8331,0.8339,0.8379,0.8385,0.8385,0.8393,0.8421,0.8424,0.8443,0.8530,
0.8582,0.8602,0.8663,0.8749,0.8785,0.8801,0.8831,0.8851,0.8854,0.8880,
0.8942,0.8952,0.9012,0.9018,0.9068,0.9177,0.9187,0.9261,0.9273,0.9359,
0.9364,0.9400,0.9423,0.9450,0.9496,0.9541,0.9564,0.9587,0.9591,0.9683,
0.9694,0.9709,0.9759,0.9869,0.9877,0.9884,0.9959,0.9981,0.9982,
Overall p-value after applying KStest on 269 p-values = 0.939692
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.