RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.71 12.2517 0.215336
2 to 25 15.97 14.5828 0.374493
3 to 26 15.83 11.4407 0.167242
4 to 27 15.76 20.0660 0.729131
5 to 28 15.73 29.2681 0.967867
6 to 29 15.72 25.1372 0.908320
7 to 30 15.71 12.1968 0.211923
8 to 31 15.57 17.4128 0.573242
9 to 32 15.58 19.9568 0.723556
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.863373
Tough bday spacings test for dh-ranFile-2018-06-21_07:31: 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 9 39 83 90 97 72 54 27 15 9 5
(O-E)^2/E 0.0 0.2 1.3 0.6 0.0 0.5 0.1 0.3 0.0 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 3.945, p= 0.050
RESULTS OF GCD FOR dh-ranFile-2018-06-21_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.978525
p-value, dist. of gcd's: 0.763944
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.865 0.533 0.691 0.156 0.310 0.502 0.510 0.848
Bits 8 to 15---> 0.213 0.415 0.522 0.560 0.916 0.702 0.595 0.255
Bits 16 to 23---> 0.747 0.751 0.031 0.358 0.380 0.419 0.209 0.391
Bits 24 to 31---> 0.564 0.138 0.680 0.274 0.964 0.348 0.344 0.700
KS test for the above 32 p values: 0.504
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_07:31,
p-values for 5 runs: 0.6612, 0.6684, 0.7208, 0.2437, 0.5112
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 197 211.4 0.983 0.983
r= 29 5144 5134.0 0.019 1.003
r= 30 23031 23103.0 0.225 1.227
r= 31 11628 11551.5 0.506 1.734
chi-square = 1.734 with df = 3; p-value = 0.371
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 208 211.4 0.055 0.055
r= 30 5146 5134.0 0.028 0.083
r= 31 23035 23103.0 0.200 0.284
r= 32 11611 11551.5 0.306 0.590
chi-square = 0.590 with df = 3; p-value = 0.101
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_07:31
b-rank test for bits 1 to 8, p=0.84078
b-rank test for bits 2 to 9, p=0.66479
b-rank test for bits 3 to 10, p=0.66875
b-rank test for bits 4 to 11, p=0.10448
b-rank test for bits 5 to 12, p=0.38508
b-rank test for bits 6 to 13, p=0.75278
b-rank test for bits 7 to 14, p=0.05324
b-rank test for bits 8 to 15, p=0.21782
b-rank test for bits 9 to 16, p=0.94080
b-rank test for bits 10 to 17, p=0.60031
b-rank test for bits 11 to 18, p=0.44626
b-rank test for bits 12 to 19, p=0.21213
b-rank test for bits 13 to 20, p=0.49166
b-rank test for bits 14 to 21, p=0.09396
b-rank test for bits 15 to 22, p=0.67116
b-rank test for bits 16 to 23, p=0.83679
b-rank test for bits 17 to 24, p=0.26493
b-rank test for bits 18 to 25, p=0.61525
b-rank test for bits 19 to 26, p=0.35432
b-rank test for bits 20 to 27, p=0.78658
b-rank test for bits 21 to 28, p=0.76070
b-rank test for bits 22 to 29, p=0.46079
b-rank test for bits 23 to 30, p=0.35870
b-rank test for bits 24 to 31, p=0.93444
b-rank test for bits 25 to 32, p=0.55722
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 = 0.891585
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_07:31
(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 142433 1.22 0.889435
2 141224 -1.60 0.054662
3 142294 0.90 0.815610
4 141916 0.02 0.506217
5 142050 0.33 0.628797
6 141129 -1.82 0.034136
7 141774 -0.32 0.375929
8 141010 -2.10 0.017810
9 141191 -1.68 0.046640
10 141897 -0.03 0.488509
11 141334 -1.34 0.089437
12 142251 0.80 0.787650
13 141803 -0.25 0.401899
14 142345 1.02 0.845642
15 142029 0.28 0.610109
16 142137 0.53 0.702616
17 142185 0.64 0.740241
18 142021 0.26 0.602920
19 140805 -2.58 0.004937
20 142367 1.07 0.857538
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_07:31
Bits used No. missing words z-score p-value
23 to 32 141946 0.1264 0.550312
22 to 31 142023 0.3920 0.652458
21 to 30 142077 0.5782 0.718426
20 to 29 141729 -0.6218 0.267028
19 to 28 142025 0.3989 0.655003
18 to 27 142280 1.2782 0.899406
17 to 26 142547 2.1989 0.986056
16 to 25 141967 0.1989 0.578815
15 to 24 142460 1.8989 0.971209
14 to 23 141956 0.1609 0.563926
13 to 22 141604 -1.0529 0.146202
12 to 21 142577 2.3023 0.989341
11 to 20 142519 2.1023 0.982237
10 to 19 141655 -0.8770 0.190243
9 to 18 141955 0.1575 0.562568
8 to 17 141594 -1.0873 0.138442
7 to 16 142354 1.5333 0.937405
6 to 15 142134 0.7747 0.780749
5 to 14 142075 0.5713 0.716094
4 to 13 142010 0.3471 0.635756
3 to 12 142288 1.3058 0.904183
2 to 11 141944 0.1196 0.547581
1 to 10 141919 0.0333 0.513300
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_07:31
Bits used No. missing words z-score p-value
28 to 32 141848 -0.2079 0.417654
27 to 31 142151 0.8192 0.793670
26 to 30 141914 0.0158 0.506315
25 to 29 141766 -0.4859 0.313532
24 to 28 141878 -0.1062 0.457711
23 to 27 142103 0.6565 0.744252
22 to 26 141980 0.2396 0.594664
21 to 25 141884 -0.0859 0.465787
20 to 24 142076 0.5650 0.713957
19 to 23 142373 1.5718 0.941997
18 to 22 141785 -0.4215 0.336711
17 to 21 141405 -1.7096 0.043671
16 to 20 141491 -1.4181 0.078086
15 to 19 142020 0.3752 0.646227
14 to 18 141791 -0.4011 0.344166
13 to 17 141424 -1.6452 0.049966
12 to 16 141734 -0.5943 0.276143
11 to 15 142634 2.4565 0.992985
10 to 14 142395 1.6463 0.950153
9 to 13 142321 1.3955 0.918566
8 to 12 142314 1.3718 0.914931
7 to 11 142228 1.0802 0.859982
6 to 10 142521 2.0735 0.980935
5 to 9 141741 -0.5706 0.284132
4 to 8 142012 0.3480 0.636093
3 to 7 142382 1.6023 0.945452
2 to 6 141552 -1.2113 0.112893
1 to 5 141682 -0.7706 0.220469
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_07:31
Bits used No. missing words z-score p-value
31 to 32 142123 0.6303 0.735749
30 to 31 141977 0.1996 0.579110
29 to 30 142074 0.4858 0.686429
28 to 29 142405 1.4622 0.928150
27 to 28 141514 -1.1662 0.121774
26 to 27 141548 -1.0659 0.143241
25 to 26 141702 -0.6116 0.270404
24 to 25 141572 -0.9951 0.159850
23 to 24 141661 -0.7325 0.231921
22 to 23 142095 0.5477 0.708051
21 to 22 141733 -0.5201 0.301480
20 to 21 141626 -0.8358 0.201639
19 to 20 142384 1.4002 0.919274
18 to 19 141240 -1.9744 0.024167
17 to 18 142164 0.7512 0.773746
16 to 17 142251 1.0079 0.843243
15 to 16 141995 0.2527 0.599755
14 to 15 142390 1.4179 0.921891
13 to 14 142316 1.1996 0.884856
12 to 13 142182 0.8043 0.789399
11 to 12 142002 0.2734 0.607713
10 to 11 141876 -0.0983 0.460840
9 to 10 142232 0.9518 0.829408
8 to 9 141702 -0.6116 0.270404
7 to 8 141732 -0.5231 0.300453
6 to 7 142327 1.2321 0.891038
5 to 6 141871 -0.1131 0.454988
4 to 5 142584 1.9902 0.976714
3 to 4 142181 0.8014 0.788546
2 to 3 142411 1.4799 0.930544
1 to 2 142310 1.1819 0.881381
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2502.88 0.041 0.516244
Test results for specific bytes for dh-ranFile-2018-06-21_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2396.70 -1.461 0.072028
2 to 9 2408.69 -1.291 0.098285
3 to 10 2483.99 -0.226 0.410460
4 to 11 2460.91 -0.553 0.290188
5 to 12 2484.01 -0.226 0.410550
6 to 13 2386.98 -1.598 0.054985
7 to 14 2405.41 -1.338 0.090501
8 to 15 2512.23 0.173 0.568639
9 to 16 2590.00 1.273 0.898464
10 to 17 2421.19 -1.115 0.132522
11 to 18 2548.63 0.688 0.754169
12 to 19 2474.20 -0.365 0.357602
13 to 20 2407.68 -1.306 0.095838
14 to 21 2517.90 0.253 0.599936
15 to 22 2461.16 -0.549 0.291428
16 to 23 2529.45 0.416 0.661460
17 to 24 2471.12 -0.408 0.341457
18 to 25 2397.43 -1.451 0.073442
19 to 26 2548.45 0.685 0.753399
20 to 27 2616.32 1.645 0.950014
21 to 28 2459.74 -0.569 0.284532
22 to 29 2538.44 0.544 0.706652
23 to 30 2494.75 -0.074 0.470427
24 to 31 2494.42 -0.079 0.468546
25 to 32 2625.39 1.773 0.961911
CDPARK for dh-ranFile-2018-06-21_07:31: 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
3516 -0.3196 0.374623
3459 -2.9224 0.001737
3557 1.5525 0.939730
3529 0.2740 0.607947
3526 0.1370 0.554479
3504 -0.8676 0.192812
3520 -0.1370 0.445521
3527 0.1826 0.572463
3561 1.7352 0.958644
3524 0.0457 0.518210
Square side=100, avg. no. parked=3522.30 sample std.=26.78
p-value of the KSTEST for those 10 p-values: 0.577851
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_07:31
0.4720,0.2042,0.0986,0.5232,0.1399,0.0981,0.5413,0.3898,0.7280,0.6936,
The KS test for those 10 p-values: 0.312574
The 3DSPHERES test for dh-ranFile-2018-06-21_07:31
sample no r^3 equiv. uni.
1 14.694 0.387243
2 2.114 0.068033
3 25.512 0.572751
4 2.135 0.068709
5 25.798 0.576806
6 66.320 0.890374
7 26.055 0.580416
8 3.934 0.122894
9 21.055 0.504327
10 21.757 0.515793
11 89.180 0.948834
12 21.053 0.504298
13 67.842 0.895794
14 23.150 0.537755
15 71.333 0.907244
16 14.597 0.385262
17 52.784 0.827864
18 27.356 0.598225
19 6.181 0.186190
20 3.489 0.109796
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.760130
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 0.1 -0.3 -0.4 -1.2
2.1 1.1 -0.7 -1.0 -0.3 0.0
-1.1 0.4 2.8 -0.2 -1.3 0.4
0.1 1.1 -1.1 0.0 -0.5 0.2
-0.1 0.9 -1.5 -1.9 0.4 -0.2
0.6 0.1 -0.0 1.0 0.5 0.8
0.7 0.5 -1.2 0.4 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:36.120996
z-score=-0.641452, p-value=0.274124
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_07:31
Test no p-value
1 0.206994
2 0.022781
3 0.902036
4 0.464743
5 0.013015
6 0.982770
7 0.029117
8 0.000733
9 0.002138
10 0.406529
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000366
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_07:31:
(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 66611 0.05 66676 0.00
3 25000.00 24955 0.08 24938 0.15
4 6666.67 6738 0.76 6741 0.83
5 1388.89 1410 0.32 1366 0.38
6 238.10 245 0.20 244 0.15
7 34.72 36 0.05 27 1.72
8 4.96 4 0.19 7 0.84
p=0.05070 p=0.33186
Number of rngs required: 687904, p-value: 0.283
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_07:31
No. of wins: Observed Expected
98747 98585.9
z-score= 0.721, pvalue=0.76446
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66856 66666.7 0.538 0.538
2 37754 37654.3 0.264 0.802
3 27251 26954.7 3.256 4.058
4 19077 19313.5 2.895 6.953
5 13765 13851.4 0.539 7.492
6 9870 9943.5 0.544 8.036
7 6979 7145.0 3.858 11.894
8 5039 5139.1 1.949 13.843
9 3744 3699.9 0.526 14.369
10 2701 2666.3 0.452 14.821
11 1911 1923.3 0.079 14.900
12 1383 1388.7 0.024 14.924
13 1032 1003.7 0.797 15.721
14 724 726.1 0.006 15.727
15 523 525.8 0.015 15.742
16 397 381.2 0.659 16.401
17 270 276.5 0.155 16.556
18 175 200.8 3.322 19.878
19 154 146.0 0.440 20.318
20 104 106.2 0.046 20.364
21 291 287.1 0.053 20.417
Chisq= 20.42 for 20 degrees of freedom, p= 0.56787
SUMMARY of craptest
p-value for no. of wins: 0.764459
p-value for throws/game: 0.567871
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_07:31
No. of wins: Observed Expected
98753 98585.9
z-score= 0.748, pvalue=0.77264
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67127 66666.7 3.179 3.179
2 37472 37654.3 0.883 4.061
3 26806 26954.7 0.821 4.882
4 19193 19313.5 0.751 5.633
5 13762 13851.4 0.577 6.211
6 10073 9943.5 1.685 7.896
7 7135 7145.0 0.014 7.910
8 5029 5139.1 2.358 10.268
9 3722 3699.9 0.132 10.400
10 2746 2666.3 2.383 12.783
11 1910 1923.3 0.092 12.875
12 1352 1388.7 0.972 13.847
13 982 1003.7 0.470 14.317
14 672 726.1 4.037 18.354
15 569 525.8 3.543 21.897
16 426 381.2 5.277 27.174
17 273 276.5 0.045 27.219
18 219 200.8 1.644 28.863
19 134 146.0 0.984 29.847
20 109 106.2 0.073 29.920
21 289 287.1 0.012 29.933
Chisq= 29.93 for 20 degrees of freedom, p= 0.92905
SUMMARY of craptest
p-value for no. of wins: 0.772635
p-value for throws/game: 0.929048
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0007,0.0017,0.0021,0.0049,0.0130,0.0178,0.0228,0.0242,0.0291,
0.0306,0.0341,0.0437,0.0466,0.0500,0.0502,0.0507,0.0532,0.0547,0.0550,
0.0680,0.0687,0.0720,0.0734,0.0781,0.0894,0.0905,0.0940,0.0958,0.0981,
0.0983,0.0986,0.1013,0.1045,0.1098,0.1129,0.1218,0.1229,0.1325,0.1379,
0.1384,0.1399,0.1432,0.1462,0.1561,0.1599,0.1672,0.1862,0.1902,0.1928,
0.2016,0.2042,0.2070,0.2089,0.2119,0.2121,0.2126,0.2153,0.2178,0.2205,
0.2319,0.2437,0.2555,0.2649,0.2670,0.2704,0.2704,0.2741,0.2743,0.2761,
0.2825,0.2841,0.2845,0.2902,0.2914,0.3005,0.3015,0.3102,0.3126,0.3135,
0.3319,0.3367,0.3415,0.3436,0.3442,0.3475,0.3543,0.3576,0.3585,0.3587,
0.3705,0.3745,0.3746,0.3759,0.3798,0.3851,0.3853,0.3872,0.3898,0.3914,
0.4019,0.4065,0.4105,0.4105,0.4152,0.4177,0.4188,0.4455,0.4463,0.4550,
0.4577,0.4608,0.4608,0.4647,0.4658,0.4685,0.4704,0.4720,0.4885,0.4917,
0.5025,0.5037,0.5043,0.5043,0.5062,0.5063,0.5101,0.5112,0.5133,0.5158,
0.5162,0.5182,0.5215,0.5232,0.5333,0.5378,0.5413,0.5476,0.5503,0.5545,
0.5572,0.5600,0.5626,0.5637,0.5639,0.5679,0.5686,0.5725,0.5728,0.5732,
0.5768,0.5779,0.5788,0.5791,0.5804,0.5947,0.5949,0.5982,0.5998,0.5999,
0.6003,0.6029,0.6077,0.6079,0.6101,0.6153,0.6288,0.6358,0.6361,0.6462,
0.6525,0.6550,0.6612,0.6615,0.6648,0.6684,0.6687,0.6712,0.6796,0.6864,
0.6911,0.6936,0.7002,0.7023,0.7026,0.7067,0.7081,0.7140,0.7161,0.7184,
0.7208,0.7236,0.7280,0.7291,0.7357,0.7402,0.7443,0.7466,0.7509,0.7528,
0.7534,0.7542,0.7601,0.7607,0.7639,0.7645,0.7726,0.7737,0.7807,0.7866,
0.7877,0.7885,0.7894,0.7937,0.8156,0.8279,0.8294,0.8368,0.8408,0.8432,
0.8456,0.8482,0.8575,0.8600,0.8634,0.8648,0.8814,0.8849,0.8894,0.8904,
0.8910,0.8916,0.8958,0.8985,0.8994,0.9020,0.9042,0.9072,0.9083,0.9149,
0.9159,0.9186,0.9193,0.9219,0.9282,0.9290,0.9305,0.9344,0.9374,0.9397,
0.9408,0.9420,0.9455,0.9488,0.9500,0.9502,0.9586,0.9619,0.9640,0.9679,
0.9712,0.9767,0.9785,0.9809,0.9822,0.9828,0.9861,0.9893,0.9930,
Overall p-value after applying KStest on 269 p-values = 0.438836
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.