RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.82 23.0603 0.852702
2 to 25 16.17 8.3835 0.042355
3 to 26 15.88 11.8237 0.189308
4 to 27 15.66 17.5364 0.581361
5 to 28 15.65 12.2380 0.214484
6 to 29 15.98 11.7495 0.184935
7 to 30 15.88 9.7857 0.087645
8 to 31 15.91 27.2113 0.944959
9 to 32 16.00 18.9874 0.670744
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.460004
Tough bday spacings test for dh-ranFile-2018-07-06_14:31: 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 41 73 84 112 71 55 30 18 8 1
(O-E)^2/E 0.5 0.5 0.0 1.9 2.1 0.7 0.2 0.0 0.7 0.3 2.3
Birthday Spacings: Sum(O-E)^2/E= 9.116, p= 0.479
RESULTS OF GCD FOR dh-ranFile-2018-07-06_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.290542
p-value, dist. of gcd's: 0.095377
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.641 0.584 0.731 0.690 0.823 0.959 0.913 0.596
Bits 8 to 15---> 0.745 0.154 0.956 0.796 0.276 0.455 0.711 0.647
Bits 16 to 23---> 0.970 0.460 0.031 0.695 0.201 0.545 0.084 0.726
Bits 24 to 31---> 0.112 0.351 0.446 0.262 0.975 0.796 0.351 0.675
KS test for the above 32 p values: 0.770
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_14:31,
p-values for 5 runs: 0.2192, 0.9104, 0.8701, 0.8411, 0.9771
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 210 211.4 0.010 0.010
r= 29 5124 5134.0 0.020 0.029
r= 30 23072 23103.0 0.042 0.071
r= 31 11594 11551.5 0.156 0.227
chi-square = 0.227 with df = 3; p-value = 0.027
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 194 211.4 1.435 1.435
r= 30 5139 5134.0 0.005 1.440
r= 31 22892 23103.0 1.928 3.368
r= 32 11775 11551.5 4.323 7.691
chi-square = 7.691 with df = 3; p-value = 0.947
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_14:31
b-rank test for bits 1 to 8, p=0.87693
b-rank test for bits 2 to 9, p=0.98425
b-rank test for bits 3 to 10, p=0.21913
b-rank test for bits 4 to 11, p=0.07592
b-rank test for bits 5 to 12, p=0.53140
b-rank test for bits 6 to 13, p=0.12157
b-rank test for bits 7 to 14, p=0.04783
b-rank test for bits 8 to 15, p=0.67333
b-rank test for bits 9 to 16, p=0.88691
b-rank test for bits 10 to 17, p=0.22539
b-rank test for bits 11 to 18, p=0.55231
b-rank test for bits 12 to 19, p=0.01515
b-rank test for bits 13 to 20, p=0.00242
b-rank test for bits 14 to 21, p=0.37794
b-rank test for bits 15 to 22, p=0.37238
b-rank test for bits 16 to 23, p=0.31371
b-rank test for bits 17 to 24, p=0.62452
b-rank test for bits 18 to 25, p=0.57128
b-rank test for bits 19 to 26, p=0.65960
b-rank test for bits 20 to 27, p=0.99828
b-rank test for bits 21 to 28, p=0.28773
b-rank test for bits 22 to 29, p=0.64107
b-rank test for bits 23 to 30, p=0.05962
b-rank test for bits 24 to 31, p=0.55121
b-rank test for bits 25 to 32, p=0.35518
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 = 0.303282
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_14:31
(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 141527 -0.89 0.185850
2 140901 -2.36 0.009239
3 141469 -1.03 0.151785
4 141815 -0.22 0.412781
5 142240 0.77 0.780119
6 141565 -0.80 0.210551
7 141927 0.04 0.516466
8 141836 -0.17 0.431981
9 142474 1.32 0.906469
10 141768 -0.33 0.370621
11 142382 1.10 0.865284
12 140690 -2.85 0.002194
13 142620 1.66 0.951587
14 141286 -1.46 0.072644
15 142028 0.28 0.609212
16 142021 0.26 0.602920
17 141925 0.04 0.514603
18 142081 0.40 0.655826
19 142155 0.57 0.717015
20 141856 -0.12 0.450419
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_14:31
Bits used No. missing words z-score p-value
23 to 32 142021 0.3851 0.649907
22 to 31 141883 -0.0908 0.463829
21 to 30 141924 0.0506 0.520172
20 to 29 142072 0.5609 0.712578
19 to 28 141868 -0.1425 0.443336
18 to 27 141758 -0.5218 0.300895
17 to 26 142468 1.9264 0.972976
16 to 25 142169 0.8954 0.814717
15 to 24 141959 0.1713 0.567997
14 to 23 141918 0.0299 0.511925
13 to 22 142004 0.3264 0.627957
12 to 21 142372 1.5954 0.944690
11 to 20 141926 0.0575 0.522920
10 to 19 141810 -0.3425 0.365981
9 to 18 141888 -0.0736 0.470684
8 to 17 141701 -0.7184 0.236262
7 to 16 141893 -0.0563 0.477547
6 to 15 141912 0.0092 0.503673
5 to 14 142277 1.2678 0.897570
4 to 13 141947 0.1299 0.551676
3 to 12 142031 0.4196 0.662594
2 to 11 141659 -0.8632 0.194012
1 to 10 141624 -0.9839 0.162583
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_14:31
Bits used No. missing words z-score p-value
28 to 32 141737 -0.5842 0.279553
27 to 31 141717 -0.6520 0.257212
26 to 30 141569 -1.1537 0.124320
25 to 29 142269 1.2192 0.888620
24 to 28 142500 2.0023 0.977372
23 to 27 141648 -0.8859 0.187845
22 to 26 142236 1.1074 0.865930
21 to 25 142032 0.4158 0.661233
20 to 24 141884 -0.0859 0.465787
19 to 23 142127 0.7379 0.769702
18 to 22 141416 -1.6723 0.047232
17 to 21 142087 0.6023 0.726503
16 to 20 142769 2.9141 0.998217
15 to 19 141594 -1.0689 0.142554
14 to 18 142067 0.5345 0.703493
13 to 17 141677 -0.7876 0.215477
12 to 16 141868 -0.1401 0.444290
11 to 15 141794 -0.3909 0.347917
10 to 14 141805 -0.3537 0.361797
9 to 13 141472 -1.4825 0.069107
8 to 12 141913 0.0124 0.504963
7 to 11 142086 0.5989 0.725374
6 to 10 142406 1.6836 0.953873
5 to 9 142321 1.3955 0.918566
4 to 8 142052 0.4836 0.685675
3 to 7 141686 -0.7571 0.224510
2 to 6 142307 1.3480 0.911176
1 to 5 142140 0.7819 0.782873
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_14:31
Bits used No. missing words z-score p-value
31 to 32 142188 0.8220 0.794472
30 to 31 141265 -1.9007 0.028672
29 to 30 142140 0.6804 0.751888
28 to 29 141462 -1.3196 0.093491
27 to 28 142387 1.4091 0.920591
26 to 27 141905 -0.0128 0.494905
25 to 26 140768 -3.3668 0.000380
24 to 25 142195 0.8427 0.800298
23 to 24 142349 1.2970 0.902678
22 to 23 141352 -1.6440 0.050084
21 to 22 142015 0.3117 0.622370
20 to 21 142593 2.0167 0.978138
19 to 20 141323 -1.7296 0.041852
18 to 19 142238 0.9695 0.833859
17 to 18 141752 -0.4641 0.321288
16 to 17 141558 -1.0364 0.150014
15 to 16 142035 0.3707 0.644573
14 to 15 142297 1.1436 0.873599
13 to 14 141955 0.1347 0.553583
12 to 13 142037 0.3766 0.646767
11 to 12 141587 -0.9508 0.170846
10 to 11 141978 0.2026 0.580263
9 to 10 141975 0.1937 0.576801
8 to 9 142091 0.5359 0.703986
7 to 8 142138 0.6745 0.750017
6 to 7 141892 -0.0511 0.479615
5 to 6 141759 -0.4435 0.328720
4 to 5 142146 0.6981 0.757456
3 to 4 141963 0.1583 0.562897
2 to 3 141869 -0.1190 0.452651
1 to 2 141137 -2.2783 0.011356
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2586.99 1.230 0.890700
Test results for specific bytes for dh-ranFile-2018-07-06_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2429.22 -1.001 0.158435
2 to 9 2435.08 -0.918 0.179273
3 to 10 2378.45 -1.719 0.042807
4 to 11 2413.00 -1.230 0.109289
5 to 12 2464.88 -0.497 0.309694
6 to 13 2492.98 -0.099 0.460439
7 to 14 2576.22 1.078 0.859465
8 to 15 2518.14 0.257 0.601251
9 to 16 2469.10 -0.437 0.331035
10 to 17 2694.64 2.753 0.997044
11 to 18 2458.38 -0.589 0.278064
12 to 19 2660.56 2.271 0.988414
13 to 20 2530.47 0.431 0.666716
14 to 21 2580.27 1.135 0.871860
15 to 22 2513.36 0.189 0.574929
16 to 23 2557.51 0.813 0.791999
17 to 24 2490.51 -0.134 0.446604
18 to 25 2456.71 -0.612 0.270188
19 to 26 2591.55 1.295 0.902281
20 to 27 2547.38 0.670 0.748573
21 to 28 2509.12 0.129 0.551289
22 to 29 2481.12 -0.267 0.394734
23 to 30 2592.10 1.302 0.903625
24 to 31 2482.38 -0.249 0.401625
25 to 32 2480.55 -0.275 0.391612
CDPARK for dh-ranFile-2018-07-06_14:31: 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
3561 1.7352 0.958644
3512 -0.5023 0.307734
3502 -0.9589 0.168804
3534 0.5023 0.692266
3516 -0.3196 0.374623
3537 0.6393 0.738676
3523 0.0000 0.500000
3522 -0.0457 0.481790
3504 -0.8676 0.192812
3515 -0.3653 0.357445
Square side=100, avg. no. parked=3522.60 sample std.=16.72
p-value of the KSTEST for those 10 p-values: 0.786082
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_14:31
0.8416,0.2721,0.9046,0.4296,0.5730,0.2877,0.5207,0.2854,0.0278,0.4474,
The KS test for those 10 p-values: 0.769122
The 3DSPHERES test for dh-ranFile-2018-07-06_14:31
sample no r^3 equiv. uni.
1 1.820 0.058861
2 3.824 0.119687
3 40.737 0.742802
4 14.439 0.382015
5 7.230 0.214151
6 1.083 0.035448
7 8.924 0.257290
8 29.191 0.622063
9 41.080 0.745728
10 3.886 0.121491
11 34.682 0.685283
12 25.529 0.573000
13 56.715 0.849002
14 15.812 0.409660
15 34.395 0.682257
16 0.304 0.010090
17 1.541 0.050081
18 40.192 0.738084
19 38.316 0.721187
20 30.676 0.640320
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.217969
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 0.3 1.4 -0.5 1.4
-1.1 0.7 2.9 -0.8 -0.3 -0.6
0.9 0.4 1.2 0.1 -0.4 0.3
-0.2 -0.5 -0.3 -0.5 0.6 -0.6
-0.6 -1.9 -0.2 -0.4 1.5 -1.1
1.0 -0.7 -0.5 -0.8 0.5 -0.5
1.0 0.8 -1.6 0.4 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:35.388389
z-score=-0.721386, p-value=0.245308
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_14:31
Test no p-value
1 0.004584
2 0.268215
3 0.063300
4 0.904770
5 0.811085
6 0.277740
7 0.299493
8 0.233150
9 0.344742
10 0.507570
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.193982
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_14:31:
(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 66834 0.42 66753 0.11
3 25000.00 24825 1.23 24856 0.83
4 6666.67 6674 0.01 6684 0.05
5 1388.89 1378 0.09 1423 0.84
6 238.10 244 0.15 230 0.28
7 34.72 38 0.31 45 3.04
8 4.96 6 0.22 8 1.86
p=0.12190 p=0.67972
Number of rngs required: 688525, p-value: 0.556
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_14:31
No. of wins: Observed Expected
98272 98585.9
z-score=-1.404, pvalue=0.08020
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66869 66666.7 0.614 0.614
2 37788 37654.3 0.475 1.089
3 26684 26954.7 2.719 3.808
4 19314 19313.5 0.000 3.808
5 14031 13851.4 2.328 6.136
6 9807 9943.5 1.875 8.011
7 6983 7145.0 3.674 11.685
8 5130 5139.1 0.016 11.701
9 3745 3699.9 0.551 12.252
10 2722 2666.3 1.164 13.416
11 1894 1923.3 0.447 13.863
12 1309 1388.7 4.579 18.442
13 988 1003.7 0.246 18.688
14 731 726.1 0.033 18.720
15 537 525.8 0.237 18.957
16 389 381.2 0.162 19.119
17 270 276.5 0.155 19.273
18 225 200.8 2.909 22.182
19 173 146.0 4.999 27.182
20 124 106.2 2.978 30.160
21 287 287.1 0.000 30.160
Chisq= 30.16 for 20 degrees of freedom, p= 0.93269
SUMMARY of craptest
p-value for no. of wins: 0.080195
p-value for throws/game: 0.932693
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_14:31
No. of wins: Observed Expected
98545 98585.9
z-score=-0.183, pvalue=0.42750
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66592 66666.7 0.084 0.084
2 37674 37654.3 0.010 0.094
3 27050 26954.7 0.337 0.431
4 19134 19313.5 1.668 2.098
5 13854 13851.4 0.000 2.099
6 10004 9943.5 0.368 2.466
7 7178 7145.0 0.152 2.618
8 5232 5139.1 1.680 4.299
9 3739 3699.9 0.414 4.713
10 2619 2666.3 0.839 5.552
11 1938 1923.3 0.112 5.664
12 1400 1388.7 0.091 5.755
13 1023 1003.7 0.371 6.125
14 692 726.1 1.605 7.731
15 538 525.8 0.281 8.012
16 364 381.2 0.772 8.784
17 273 276.5 0.045 8.829
18 177 200.8 2.828 11.657
19 130 146.0 1.750 13.407
20 88 106.2 3.124 16.531
21 301 287.1 0.672 17.202
Chisq= 17.20 for 20 degrees of freedom, p= 0.36020
SUMMARY of craptest
p-value for no. of wins: 0.427500
p-value for throws/game: 0.360195
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0022,0.0024,0.0046,0.0092,0.0101,0.0114,0.0152,0.0269,0.0278,
0.0287,0.0307,0.0354,0.0419,0.0424,0.0428,0.0472,0.0478,0.0501,0.0501,
0.0589,0.0596,0.0633,0.0691,0.0726,0.0759,0.0802,0.0844,0.0876,0.0935,
0.0954,0.1093,0.1122,0.1197,0.1215,0.1216,0.1219,0.1243,0.1426,0.1500,
0.1518,0.1540,0.1584,0.1626,0.1688,0.1708,0.1793,0.1849,0.1858,0.1878,
0.1893,0.1928,0.1940,0.1940,0.2009,0.2106,0.2142,0.2145,0.2155,0.2180,
0.2191,0.2192,0.2245,0.2254,0.2332,0.2363,0.2453,0.2572,0.2573,0.2622,
0.2682,0.2702,0.2721,0.2756,0.2777,0.2781,0.2796,0.2854,0.2877,0.2877,
0.2905,0.2995,0.3009,0.3033,0.3077,0.3097,0.3137,0.3213,0.3287,0.3310,
0.3447,0.3479,0.3505,0.3515,0.3552,0.3574,0.3602,0.3618,0.3660,0.3706,
0.3724,0.3746,0.3779,0.3820,0.3916,0.3947,0.4016,0.4097,0.4128,0.4275,
0.4296,0.4320,0.4433,0.4443,0.4456,0.4466,0.4474,0.4504,0.4527,0.4545,
0.4600,0.4602,0.4604,0.4638,0.4658,0.4707,0.4775,0.4789,0.4796,0.4818,
0.4949,0.5000,0.5037,0.5050,0.5076,0.5119,0.5146,0.5165,0.5202,0.5207,
0.5229,0.5314,0.5451,0.5512,0.5513,0.5517,0.5523,0.5536,0.5558,0.5629,
0.5680,0.5713,0.5730,0.5730,0.5749,0.5768,0.5803,0.5814,0.5839,0.5961,
0.6013,0.6029,0.6092,0.6221,0.6224,0.6245,0.6280,0.6403,0.6411,0.6414,
0.6446,0.6468,0.6473,0.6499,0.6558,0.6596,0.6612,0.6626,0.6667,0.6707,
0.6733,0.6748,0.6797,0.6823,0.6853,0.6857,0.6903,0.6923,0.6952,0.7035,
0.7040,0.7107,0.7126,0.7170,0.7212,0.7254,0.7262,0.7265,0.7312,0.7381,
0.7387,0.7428,0.7452,0.7457,0.7486,0.7500,0.7519,0.7575,0.7691,0.7695,
0.7697,0.7801,0.7829,0.7861,0.7920,0.7945,0.7962,0.7964,0.8003,0.8111,
0.8147,0.8228,0.8339,0.8411,0.8416,0.8490,0.8527,0.8595,0.8653,0.8659,
0.8701,0.8719,0.8736,0.8769,0.8869,0.8886,0.8907,0.8976,0.9023,0.9027,
0.9036,0.9046,0.9048,0.9065,0.9104,0.9112,0.9135,0.9186,0.9206,0.9327,
0.9447,0.9450,0.9472,0.9516,0.9539,0.9564,0.9586,0.9593,0.9698,0.9730,
0.9747,0.9771,0.9774,0.9781,0.9843,0.9884,0.9970,0.9982,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.949393
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.