RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.67 25.6615 0.919147
2 to 25 15.88 25.7756 0.921352
3 to 26 15.90 14.4905 0.367868
4 to 27 15.77 15.2074 0.419452
5 to 28 15.72 13.2334 0.279575
6 to 29 15.98 20.8794 0.768270
7 to 30 15.86 15.0905 0.411040
8 to 31 15.51 19.7821 0.714474
9 to 32 16.00 22.3014 0.826596
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.278567
Tough bday spacings test for dh-ranFile-2018-06-16_16:31: 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 11 34 72 96 101 61 63 33 18 5 6
(O-E)^2/E 0.4 0.2 0.0 0.0 0.1 3.8 2.3 0.4 0.7 0.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 9.083, p= 0.476
RESULTS OF GCD FOR dh-ranFile-2018-06-16_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.727002
p-value, dist. of gcd's: 0.803293
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.845 0.558 0.485 0.366 0.645 0.308 0.174 0.650
Bits 8 to 15---> 0.351 0.659 0.372 0.526 0.827 0.805 0.589 0.852
Bits 16 to 23---> 0.769 0.442 0.406 0.014 0.059 0.415 0.886 0.757
Bits 24 to 31---> 0.148 0.331 0.227 0.871 0.951 0.029 0.103 0.954
KS test for the above 32 p values: 0.014
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_16:31,
p-values for 5 runs: 0.6597, 0.7335, 0.1861, 0.4877, 0.4401
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5164 5134.0 0.175 1.450
r= 30 22982 23103.0 0.634 2.084
r= 31 11659 11551.5 1.000 3.084
chi-square = 3.084 with df = 3; p-value = 0.621
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 196 211.4 1.124 1.124
r= 30 5176 5134.0 0.343 1.468
r= 31 23128 23103.0 0.027 1.495
r= 32 11500 11551.5 0.230 1.725
chi-square = 1.725 with df = 3; p-value = 0.369
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_16:31
b-rank test for bits 1 to 8, p=0.64119
b-rank test for bits 2 to 9, p=0.03621
b-rank test for bits 3 to 10, p=0.23559
b-rank test for bits 4 to 11, p=0.93817
b-rank test for bits 5 to 12, p=0.77288
b-rank test for bits 6 to 13, p=0.15370
b-rank test for bits 7 to 14, p=0.70475
b-rank test for bits 8 to 15, p=0.77759
b-rank test for bits 9 to 16, p=0.15785
b-rank test for bits 10 to 17, p=0.70746
b-rank test for bits 11 to 18, p=0.33953
b-rank test for bits 12 to 19, p=0.06513
b-rank test for bits 13 to 20, p=0.34853
b-rank test for bits 14 to 21, p=0.97292
b-rank test for bits 15 to 22, p=0.79214
b-rank test for bits 16 to 23, p=0.48008
b-rank test for bits 17 to 24, p=0.05051
b-rank test for bits 18 to 25, p=0.93376
b-rank test for bits 19 to 26, p=0.95133
b-rank test for bits 20 to 27, p=0.37020
b-rank test for bits 21 to 28, p=0.07625
b-rank test for bits 22 to 29, p=0.11892
b-rank test for bits 23 to 30, p=0.57689
b-rank test for bits 24 to 31, p=0.86880
b-rank test for bits 25 to 32, p=0.69161
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 = 0.651610
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_16:31
(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 141645 -0.62 0.268422
2 141751 -0.37 0.355717
3 141523 -0.90 0.183358
4 141517 -0.92 0.179661
5 142698 1.84 0.967313
6 142062 0.36 0.639344
7 141932 0.05 0.521121
8 141920 0.02 0.509945
9 143027 2.61 0.995491
10 141997 0.20 0.581150
11 142055 0.34 0.633204
12 141635 -0.64 0.260775
13 141711 -0.46 0.321543
14 142034 0.29 0.614583
15 142660 1.75 0.960276
16 142515 1.42 0.921483
17 142058 0.35 0.635840
18 141759 -0.35 0.362705
19 141585 -0.76 0.224291
20 141711 -0.46 0.321543
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_16:31
Bits used No. missing words z-score p-value
23 to 32 141712 -0.6804 0.248110
22 to 31 141791 -0.4080 0.341624
21 to 30 141418 -1.6942 0.045110
20 to 29 142103 0.6678 0.747878
19 to 28 142074 0.5678 0.714924
18 to 27 141708 -0.6942 0.243765
17 to 26 142095 0.6402 0.738992
16 to 25 141827 -0.2839 0.388245
15 to 24 141789 -0.4149 0.339096
14 to 23 141773 -0.4701 0.319141
13 to 22 142101 0.6609 0.745672
12 to 21 141404 -1.7425 0.040709
11 to 20 142454 1.8782 0.969821
10 to 19 142076 0.5747 0.717261
9 to 18 142248 1.1678 0.878562
8 to 17 142009 0.3437 0.634460
7 to 16 141990 0.2782 0.609560
6 to 15 141741 -0.5804 0.280806
5 to 14 141860 -0.1701 0.432464
4 to 13 141502 -1.4046 0.080072
3 to 12 141912 0.0092 0.503673
2 to 11 141866 -0.1494 0.440614
1 to 10 141870 -0.1356 0.446061
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_16:31
Bits used No. missing words z-score p-value
28 to 32 141882 -0.0926 0.463093
27 to 31 141909 -0.0011 0.499554
26 to 30 142179 0.9141 0.819677
25 to 29 141137 -2.6181 0.004421
24 to 28 141920 0.0362 0.514426
23 to 27 141868 -0.1401 0.444290
22 to 26 142025 0.3921 0.652509
21 to 25 142033 0.4192 0.662473
20 to 24 142119 0.7107 0.761379
19 to 23 142122 0.7209 0.764519
18 to 22 141747 -0.5503 0.291067
17 to 21 142089 0.6091 0.728755
16 to 20 141538 -1.2587 0.104061
15 to 19 141944 0.1175 0.546778
14 to 18 141554 -1.2045 0.114197
13 to 17 141559 -1.1876 0.117504
12 to 16 142190 0.9514 0.829305
11 to 15 142135 0.7650 0.777859
10 to 14 142046 0.4633 0.678421
9 to 13 141747 -0.5503 0.291067
8 to 12 141824 -0.2893 0.386193
7 to 11 142079 0.5752 0.717406
6 to 10 142181 0.9209 0.821453
5 to 9 142085 0.5955 0.724243
4 to 8 141731 -0.6045 0.272753
3 to 7 141720 -0.6418 0.260503
2 to 6 141742 -0.5672 0.285282
1 to 5 142060 0.5107 0.695236
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_16:31
Bits used No. missing words z-score p-value
31 to 32 142278 1.0875 0.861597
30 to 31 141982 0.2144 0.584869
29 to 30 141416 -1.4553 0.072800
28 to 29 142086 0.5212 0.698869
27 to 28 142338 1.2645 0.896977
26 to 27 142139 0.6775 0.750953
25 to 26 142335 1.2557 0.895381
24 to 25 141757 -0.4494 0.326589
23 to 24 141473 -1.2871 0.099028
22 to 23 141926 0.0492 0.519610
21 to 22 142558 1.9135 0.972157
20 to 21 141489 -1.2399 0.107504
19 to 20 141000 -2.6824 0.003655
18 to 19 141781 -0.3786 0.352509
17 to 18 142327 1.2321 0.891038
16 to 17 141777 -0.3904 0.348137
15 to 16 141194 -2.1101 0.017424
14 to 15 141344 -1.6676 0.047694
13 to 14 141892 -0.0511 0.479615
12 to 13 141686 -0.6588 0.255015
11 to 12 142131 0.6539 0.743410
10 to 11 141871 -0.1131 0.454988
9 to 10 142370 1.3589 0.912912
8 to 9 141365 -1.6057 0.054171
7 to 8 141811 -0.2901 0.385886
6 to 7 141548 -1.0659 0.143241
5 to 6 142095 0.5477 0.708051
4 to 5 142347 1.2911 0.901659
3 to 4 141705 -0.6027 0.273340
2 to 3 141290 -1.8269 0.033855
1 to 2 141622 -0.8476 0.198336
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2491.94 -0.114 0.454636
Test results for specific bytes for dh-ranFile-2018-06-16_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2487.98 -0.170 0.432512
2 to 9 2485.57 -0.204 0.419175
3 to 10 2538.17 0.540 0.705318
4 to 11 2469.15 -0.436 0.331295
5 to 12 2686.44 2.637 0.995814
6 to 13 2424.94 -1.061 0.144236
7 to 14 2512.68 0.179 0.571166
8 to 15 2536.13 0.511 0.695297
9 to 16 2525.38 0.359 0.640195
10 to 17 2490.70 -0.132 0.447670
11 to 18 2455.82 -0.625 0.266053
12 to 19 2503.43 0.049 0.519362
13 to 20 2499.95 -0.001 0.499707
14 to 21 2596.75 1.368 0.914384
15 to 22 2624.64 1.763 0.961024
16 to 23 2553.39 0.755 0.774899
17 to 24 2408.53 -1.294 0.097915
18 to 25 2517.55 0.248 0.598025
19 to 26 2427.75 -1.022 0.153429
20 to 27 2525.52 0.361 0.640927
21 to 28 2628.53 1.818 0.965447
22 to 29 2350.34 -2.117 0.017148
23 to 30 2560.59 0.857 0.804242
24 to 31 2562.92 0.890 0.813209
25 to 32 2623.18 1.742 0.959246
CDPARK for dh-ranFile-2018-06-16_16:31: 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
3533 0.4566 0.676028
3514 -0.4110 0.340551
3517 -0.2740 0.392053
3523 0.0000 0.500000
3534 0.5023 0.692266
3574 2.3288 0.990064
3542 0.8676 0.807188
3508 -0.6849 0.246694
3516 -0.3196 0.374623
3544 0.9589 0.831196
Square side=100, avg. no. parked=3530.50 sample std.=18.58
p-value of the KSTEST for those 10 p-values: 0.471316
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_16:31
0.9145,0.8661,0.6177,0.6378,0.7718,0.5101,0.4349,0.9251,0.8566,0.3399,
The KS test for those 10 p-values: 0.061213
The 3DSPHERES test for dh-ranFile-2018-06-16_16:31
sample no r^3 equiv. uni.
1 38.547 0.723324
2 75.348 0.918862
3 6.211 0.187005
4 90.703 0.951365
5 6.267 0.188521
6 55.562 0.843087
7 5.218 0.159645
8 32.117 0.657187
9 124.395 0.984180
10 24.236 0.554198
11 30.229 0.634918
12 88.657 0.947934
13 32.569 0.662313
14 14.996 0.393384
15 109.919 0.974369
16 0.113 0.003767
17 1.759 0.056938
18 74.449 0.916393
19 23.105 0.537062
20 49.539 0.808201
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.070193
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 0.6 0.5 -0.5 -0.2
-1.2 0.1 -0.1 0.2 0.4 0.3
-0.5 -1.0 -1.2 0.1 -1.3 1.1
1.2 0.2 1.7 0.3 -1.6 1.4
-0.9 -0.3 0.4 0.3 -0.0 -1.0
0.8 -0.2 1.6 -0.5 -0.8 -1.4
-0.5 0.2 -0.4 1.5 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:30.848872
z-score=-1.216688, p-value=0.101982
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_16:31
Test no p-value
1 0.016224
2 0.305130
3 0.113725
4 0.033768
5 0.008398
6 0.913317
7 0.218320
8 0.007064
9 0.072229
10 0.128814
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000035
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_16:31:
(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 66669 0.00 66719 0.04
3 25000.00 25125 0.62 24986 0.01
4 6666.67 6579 1.15 6661 0.00
5 1388.89 1366 0.38 1371 0.23
6 238.10 217 1.87 224 0.83
7 34.72 39 0.53 34 0.01
8 4.96 4 0.19 4 0.19
p=0.42213 p=0.02942
Number of rngs required: 688106, p-value: 0.366
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_16:31
No. of wins: Observed Expected
99454 98585.9
z-score= 3.883, pvalue=0.99995
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67158 66666.7 3.621 3.621
2 37484 37654.3 0.770 4.392
3 26992 26954.7 0.052 4.443
4 19207 19313.5 0.587 5.030
5 13705 13851.4 1.548 6.578
6 9877 9943.5 0.445 7.023
7 7082 7145.0 0.556 7.579
8 5123 5139.1 0.050 7.629
9 3748 3699.9 0.626 8.255
10 2735 2666.3 1.770 10.026
11 1957 1923.3 0.589 10.615
12 1342 1388.7 1.573 12.188
13 1004 1003.7 0.000 12.188
14 725 726.1 0.002 12.190
15 476 525.8 4.723 16.913
16 378 381.2 0.026 16.939
17 276 276.5 0.001 16.940
18 210 200.8 0.419 17.359
19 143 146.0 0.061 17.420
20 105 106.2 0.014 17.434
21 273 287.1 0.694 18.128
Chisq= 18.13 for 20 degrees of freedom, p= 0.42102
SUMMARY of craptest
p-value for no. of wins: 0.999948
p-value for throws/game: 0.421016
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_16:31
No. of wins: Observed Expected
98587 98585.9
z-score= 0.005, pvalue=0.50204
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66651 66666.7 0.004 0.004
2 37482 37654.3 0.789 0.792
3 26890 26954.7 0.155 0.948
4 19395 19313.5 0.344 1.292
5 13865 13851.4 0.013 1.305
6 10024 9943.5 0.651 1.956
7 7241 7145.0 1.289 3.245
8 5155 5139.1 0.049 3.295
9 3715 3699.9 0.062 3.357
10 2601 2666.3 1.599 4.956
11 1937 1923.3 0.097 5.053
12 1392 1388.7 0.008 5.061
13 973 1003.7 0.940 6.001
14 719 726.1 0.070 6.071
15 545 525.8 0.698 6.769
16 378 381.2 0.026 6.795
17 293 276.5 0.980 7.775
18 202 200.8 0.007 7.782
19 141 146.0 0.170 7.952
20 91 106.2 2.180 10.132
21 310 287.1 1.824 11.956
Chisq= 11.96 for 20 degrees of freedom, p= 0.08242
SUMMARY of craptest
p-value for no. of wins: 0.502037
p-value for throws/game: 0.082415
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0037,0.0038,0.0044,0.0071,0.0084,0.0137,0.0140,0.0162,0.0171,
0.0174,0.0288,0.0294,0.0338,0.0339,0.0362,0.0407,0.0451,0.0477,0.0505,
0.0542,0.0569,0.0587,0.0612,0.0651,0.0702,0.0722,0.0728,0.0763,0.0801,
0.0824,0.0979,0.0990,0.1020,0.1029,0.1041,0.1075,0.1137,0.1142,0.1175,
0.1189,0.1288,0.1432,0.1442,0.1483,0.1534,0.1537,0.1578,0.1596,0.1742,
0.1797,0.1834,0.1861,0.1870,0.1885,0.1983,0.2183,0.2243,0.2269,0.2356,
0.2438,0.2467,0.2481,0.2550,0.2605,0.2608,0.2661,0.2684,0.2728,0.2733,
0.2786,0.2796,0.2808,0.2853,0.2911,0.2911,0.3051,0.3080,0.3191,0.3215,
0.3215,0.3266,0.3307,0.3313,0.3391,0.3395,0.3399,0.3406,0.3416,0.3481,
0.3485,0.3507,0.3525,0.3557,0.3627,0.3662,0.3665,0.3679,0.3685,0.3702,
0.3717,0.3746,0.3859,0.3862,0.3882,0.3921,0.3934,0.4064,0.4110,0.4153,
0.4192,0.4195,0.4210,0.4221,0.4325,0.4325,0.4349,0.4401,0.4406,0.4419,
0.4443,0.4461,0.4477,0.4546,0.4550,0.4631,0.4713,0.4758,0.4796,0.4801,
0.4849,0.4877,0.4996,0.4997,0.5000,0.5020,0.5037,0.5099,0.5101,0.5144,
0.5194,0.5196,0.5211,0.5258,0.5371,0.5468,0.5542,0.5581,0.5712,0.5769,
0.5812,0.5849,0.5890,0.5980,0.6096,0.6146,0.6177,0.6212,0.6332,0.6345,
0.6349,0.6358,0.6378,0.6393,0.6402,0.6409,0.6412,0.6453,0.6498,0.6516,
0.6525,0.6572,0.6592,0.6597,0.6623,0.6625,0.6760,0.6784,0.6916,0.6923,
0.6952,0.6953,0.6989,0.7047,0.7053,0.7075,0.7081,0.7145,0.7149,0.7173,
0.7174,0.7233,0.7242,0.7270,0.7288,0.7335,0.7390,0.7434,0.7457,0.7479,
0.7510,0.7571,0.7614,0.7645,0.7683,0.7690,0.7718,0.7729,0.7749,0.7776,
0.7779,0.7921,0.8033,0.8042,0.8053,0.8072,0.8082,0.8132,0.8197,0.8215,
0.8266,0.8270,0.8293,0.8312,0.8431,0.8449,0.8518,0.8566,0.8616,0.8661,
0.8688,0.8705,0.8786,0.8856,0.8910,0.8954,0.8970,0.9017,0.9129,0.9133,
0.9144,0.9145,0.9164,0.9189,0.9191,0.9214,0.9215,0.9251,0.9338,0.9382,
0.9479,0.9511,0.9513,0.9514,0.9538,0.9592,0.9603,0.9610,0.9654,0.9673,
0.9698,0.9722,0.9729,0.9744,0.9842,0.9901,0.9955,0.9958,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.566148
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.