RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.76 19.8403 0.717523
2 to 25 15.91 14.1323 0.342281
3 to 26 15.54 20.3933 0.745390
4 to 27 15.71 17.8678 0.602771
5 to 28 15.93 11.1263 0.150074
6 to 29 15.89 22.2717 0.825507
7 to 30 15.81 19.1145 0.678000
8 to 31 15.89 18.6332 0.650014
9 to 32 15.98 15.9813 0.474841
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.378624
Tough bday spacings test for dh-ranFile-2018-06-23_06:31: 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 3 48 70 92 98 78 61 26 14 7 3
(O-E)^2/E 4.1 3.5 0.1 0.3 0.0 0.0 1.5 0.5 0.1 0.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.499, p= 0.602
RESULTS OF GCD FOR dh-ranFile-2018-06-23_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.536468
p-value, dist. of gcd's: 0.805315
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.686 0.902 0.511 0.604 0.220 0.435 0.064 0.453
Bits 8 to 15---> 0.897 0.599 0.610 0.717 0.488 0.663 0.160 0.791
Bits 16 to 23---> 0.673 0.166 0.511 0.411 0.078 0.390 0.776 0.930
Bits 24 to 31---> 0.000 0.110 0.172 0.834 0.451 0.479 0.131 0.089
KS test for the above 32 p values: 0.439
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_06:31,
p-values for 5 runs: 0.2962, 0.1020, 0.7744, 0.0854, 0.0486
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5063 5134.0 0.982 1.187
r= 30 23234 23103.0 0.742 1.929
r= 31 11485 11551.5 0.383 2.312
chi-square = 2.312 with df = 3; p-value = 0.490
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 222 211.4 0.530 0.530
r= 30 5060 5134.0 1.067 1.597
r= 31 23134 23103.0 0.041 1.638
r= 32 11584 11551.5 0.091 1.729
chi-square = 1.729 with df = 3; p-value = 0.370
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_06:31
b-rank test for bits 1 to 8, p=0.42845
b-rank test for bits 2 to 9, p=0.07787
b-rank test for bits 3 to 10, p=0.23734
b-rank test for bits 4 to 11, p=0.53710
b-rank test for bits 5 to 12, p=0.57380
b-rank test for bits 6 to 13, p=0.34842
b-rank test for bits 7 to 14, p=0.98773
b-rank test for bits 8 to 15, p=0.34872
b-rank test for bits 9 to 16, p=0.31386
b-rank test for bits 10 to 17, p=0.20390
b-rank test for bits 11 to 18, p=0.52066
b-rank test for bits 12 to 19, p=0.49416
b-rank test for bits 13 to 20, p=0.70377
b-rank test for bits 14 to 21, p=0.08521
b-rank test for bits 15 to 22, p=0.94520
b-rank test for bits 16 to 23, p=0.26347
b-rank test for bits 17 to 24, p=0.26485
b-rank test for bits 18 to 25, p=0.69339
b-rank test for bits 19 to 26, p=0.98702
b-rank test for bits 20 to 27, p=0.36331
b-rank test for bits 21 to 28, p=0.76340
b-rank test for bits 22 to 29, p=0.20276
b-rank test for bits 23 to 30, p=0.97572
b-rank test for bits 24 to 31, p=0.96933
b-rank test for bits 25 to 32, p=0.02656
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 = 0.407115
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_06:31
(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 141427 -1.13 0.129884
2 141738 -0.40 0.344466
3 141364 -1.27 0.101308
4 142535 1.46 0.928108
5 141859 -0.12 0.453195
6 141935 0.06 0.523913
7 141591 -0.74 0.228510
8 142562 1.52 0.936362
9 142010 0.24 0.592977
10 141852 -0.13 0.446722
11 141691 -0.51 0.304985
12 141883 -0.06 0.475473
13 142130 0.52 0.696928
14 142229 0.75 0.772436
15 141499 -0.96 0.168851
16 142735 1.93 0.973143
17 142331 0.99 0.837740
18 141514 -0.92 0.177830
19 142238 0.77 0.778733
20 141795 -0.27 0.394686
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_06:31
Bits used No. missing words z-score p-value
23 to 32 141526 -1.3218 0.093113
22 to 31 141580 -1.1356 0.128058
21 to 30 142012 0.3540 0.638344
20 to 29 142167 0.8885 0.812869
19 to 28 142101 0.6609 0.745672
18 to 27 141802 -0.3701 0.355653
17 to 26 142274 1.2575 0.895711
16 to 25 142268 1.2368 0.891918
15 to 24 141973 0.2196 0.586890
14 to 23 141733 -0.6080 0.271582
13 to 22 141655 -0.8770 0.190243
12 to 21 141679 -0.7942 0.213528
11 to 20 142062 0.5264 0.700712
10 to 19 142198 0.9954 0.840233
9 to 18 141590 -1.1011 0.135418
8 to 17 141391 -1.7873 0.036941
7 to 16 141832 -0.2667 0.394867
6 to 15 142183 0.9437 0.827336
5 to 14 142166 0.8851 0.811940
4 to 13 142227 1.0954 0.863332
3 to 12 142592 2.3540 0.990715
2 to 11 142136 0.7816 0.782781
1 to 10 141726 -0.6322 0.263637
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_06:31
Bits used No. missing words z-score p-value
28 to 32 141555 -1.2011 0.114853
27 to 31 141421 -1.6554 0.048926
26 to 30 141596 -1.0621 0.144087
25 to 29 142213 1.0294 0.848352
24 to 28 141508 -1.3604 0.086845
23 to 27 141695 -0.7265 0.233753
22 to 26 141799 -0.3740 0.354202
21 to 25 141907 -0.0079 0.496849
20 to 24 142092 0.6192 0.732114
19 to 23 141966 0.1921 0.576169
18 to 22 141950 0.1379 0.554826
17 to 21 141968 0.1989 0.578822
16 to 20 141823 -0.2926 0.384897
15 to 19 142122 0.7209 0.764519
14 to 18 141466 -1.5028 0.066444
13 to 17 141919 0.0328 0.513075
12 to 16 141793 -0.3943 0.346665
11 to 15 141795 -0.3876 0.349171
10 to 14 142211 1.0226 0.846754
9 to 13 142287 1.2802 0.899769
8 to 12 142085 0.5955 0.724243
7 to 11 142313 1.3684 0.914402
6 to 10 142442 1.8057 0.964514
5 to 9 141653 -0.8689 0.192447
4 to 8 141948 0.1311 0.552146
3 to 7 141808 -0.3435 0.365614
2 to 6 141760 -0.5062 0.306357
1 to 5 142349 1.4904 0.931941
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_06:31
Bits used No. missing words z-score p-value
31 to 32 141830 -0.2340 0.407488
30 to 31 142099 0.5595 0.712089
29 to 30 142120 0.6214 0.732847
28 to 29 141611 -0.8800 0.189422
27 to 28 142005 0.2822 0.611110
26 to 27 141736 -0.5113 0.304571
25 to 26 142210 0.8869 0.812442
24 to 25 142059 0.4415 0.670576
23 to 24 141910 0.0020 0.500789
22 to 23 141665 -0.7207 0.235536
21 to 22 141845 -0.1898 0.424747
20 to 21 141536 -1.1013 0.135390
19 to 20 141659 -0.7384 0.230125
18 to 19 141717 -0.5673 0.285240
17 to 18 141963 0.1583 0.562897
16 to 17 141461 -1.3225 0.093000
15 to 16 142234 0.9577 0.830900
14 to 15 142216 0.9046 0.817170
13 to 14 142248 0.9990 0.841109
12 to 13 142035 0.3707 0.644573
11 to 12 142450 1.5949 0.944632
10 to 11 141897 -0.0364 0.485493
9 to 10 141518 -1.1544 0.124175
8 to 9 141534 -1.1072 0.134111
7 to 8 142060 0.4445 0.671643
6 to 7 142330 1.2409 0.892681
5 to 6 142011 0.2999 0.617878
4 to 5 141811 -0.2901 0.385886
3 to 4 141568 -1.0069 0.156998
2 to 3 141965 0.1642 0.565220
1 to 2 141973 0.1878 0.574490
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2560.84 0.860 0.805225
Test results for specific bytes for dh-ranFile-2018-06-23_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2428.46 -1.012 0.155831
2 to 9 2499.08 -0.013 0.494787
3 to 10 2431.23 -0.973 0.165375
4 to 11 2527.77 0.393 0.652729
5 to 12 2445.33 -0.773 0.219723
6 to 13 2577.59 1.097 0.863730
7 to 14 2523.63 0.334 0.630877
8 to 15 2546.16 0.653 0.743055
9 to 16 2452.41 -0.673 0.250478
10 to 17 2430.70 -0.980 0.163530
11 to 18 2558.84 0.832 0.797312
12 to 19 2637.89 1.950 0.974413
13 to 20 2564.69 0.915 0.819854
14 to 21 2485.51 -0.205 0.418810
15 to 22 2378.62 -1.717 0.043031
16 to 23 2571.52 1.011 0.844106
17 to 24 2444.81 -0.781 0.217537
18 to 25 2577.67 1.098 0.863993
19 to 26 2680.29 2.550 0.994610
20 to 27 2498.39 -0.023 0.490937
21 to 28 2523.85 0.337 0.632048
22 to 29 2541.40 0.586 0.720899
23 to 30 2469.47 -0.432 0.332979
24 to 31 2456.47 -0.616 0.269094
25 to 32 2564.65 0.914 0.819716
CDPARK for dh-ranFile-2018-06-23_06:31: 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
3539 0.7306 0.767486
3456 -3.0594 0.001109
3515 -0.3653 0.357445
3512 -0.5023 0.307734
3511 -0.5479 0.291865
3535 0.5479 0.708135
3501 -1.0046 0.157553
3544 0.9589 0.831196
3535 0.5479 0.708135
3484 -1.7808 0.037471
Square side=100, avg. no. parked=3513.20 sample std.=26.17
p-value of the KSTEST for those 10 p-values: 0.317649
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_06:31
0.7843,0.6194,0.2036,0.1208,0.2399,0.2975,0.5150,0.7804,0.7302,0.0155,
The KS test for those 10 p-values: 0.676759
The 3DSPHERES test for dh-ranFile-2018-06-23_06:31
sample no r^3 equiv. uni.
1 6.026 0.181965
2 4.117 0.128226
3 59.547 0.862608
4 13.577 0.364012
5 9.205 0.264227
6 2.176 0.069957
7 0.346 0.011472
8 28.661 0.615330
9 17.913 0.449596
10 35.727 0.696056
11 15.117 0.395828
12 10.144 0.286900
13 17.199 0.436332
14 12.929 0.350119
15 0.645 0.021279
16 2.095 0.067465
17 12.136 0.332716
18 37.739 0.715768
19 8.641 0.250264
20 89.061 0.948631
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.075096
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.7 -1.2 1.1 0.5 -0.9 0.7
-1.0 1.8 -0.6 -2.2 0.3 0.7
0.1 0.1 0.3 0.8 -0.9 -0.3
-0.4 -0.7 0.4 0.7 0.1 1.4
-0.5 -0.8 -0.1 -2.6 0.1 1.0
1.9 1.1 -0.0 -0.5 0.3 0.6
-0.5 0.2 -1.2 1.0 2.4 -1.0
1.8
Chi-square with 42 degrees of freedom:53.416756
z-score=1.245670, p-value=0.888615
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_06:31
Test no p-value
1 0.690516
2 0.081836
3 0.166165
4 0.615137
5 0.312558
6 0.204025
7 0.236970
8 0.821455
9 0.280068
10 0.115655
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.145229
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_06:31:
(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 66818 0.34 66595 0.08
3 25000.00 24943 0.13 24891 0.48
4 6666.67 6561 1.67 6869 6.14
5 1388.89 1392 0.01 1406 0.21
6 238.10 238 0.00 209 3.56
7 34.72 40 0.80 24 3.31
8 4.96 7 0.84 5 0.00
p=0.29593 p=0.96768
Number of rngs required: 688101, p-value: 0.364
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_06:31
No. of wins: Observed Expected
98608 98585.9
z-score= 0.099, pvalue=0.53944
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66844 66666.7 0.472 0.472
2 37476 37654.3 0.844 1.316
3 26825 26954.7 0.624 1.941
4 19559 19313.5 3.122 5.062
5 13776 13851.4 0.411 5.473
6 10114 9943.5 2.922 8.395
7 7296 7145.0 3.190 11.585
8 4951 5139.1 6.883 18.468
9 3594 3699.9 3.029 21.497
10 2583 2666.3 2.602 24.099
11 1941 1923.3 0.162 24.262
12 1378 1388.7 0.083 24.345
13 988 1003.7 0.246 24.591
14 710 726.1 0.359 24.949
15 538 525.8 0.281 25.231
16 392 381.2 0.309 25.540
17 298 276.5 1.665 27.205
18 207 200.8 0.190 27.395
19 124 146.0 3.311 30.705
20 109 106.2 0.073 30.778
21 297 287.1 0.340 31.119
Chisq= 31.12 for 20 degrees of freedom, p= 0.94636
SUMMARY of craptest
p-value for no. of wins: 0.539443
p-value for throws/game: 0.946358
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_06:31
No. of wins: Observed Expected
98981 98585.9
z-score= 1.767, pvalue=0.96141
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66506 66666.7 0.387 0.387
2 37804 37654.3 0.595 0.982
3 27043 26954.7 0.289 1.271
4 19338 19313.5 0.031 1.302
5 13987 13851.4 1.327 2.629
6 9888 9943.5 0.310 2.940
7 7119 7145.0 0.095 3.035
8 5094 5139.1 0.395 3.430
9 3621 3699.9 1.681 5.111
10 2610 2666.3 1.189 6.300
11 1930 1923.3 0.023 6.323
12 1344 1388.7 1.441 7.764
13 1033 1003.7 0.854 8.619
14 787 726.1 5.101 13.719
15 537 525.8 0.237 13.956
16 357 381.2 1.530 15.487
17 313 276.5 4.807 20.294
18 186 200.8 1.095 21.389
19 125 146.0 3.016 24.405
20 91 106.2 2.180 26.585
21 287 287.1 0.000 26.585
Chisq= 26.58 for 20 degrees of freedom, p= 0.85265
SUMMARY of craptest
p-value for no. of wins: 0.961411
p-value for throws/game: 0.852645
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0011,0.0115,0.0155,0.0213,0.0266,0.0369,0.0375,0.0430,0.0486,
0.0489,0.0636,0.0664,0.0675,0.0700,0.0751,0.0779,0.0781,0.0818,0.0852,
0.0854,0.0868,0.0887,0.0930,0.0931,0.1013,0.1020,0.1097,0.1149,0.1157,
0.1208,0.1242,0.1281,0.1282,0.1299,0.1308,0.1341,0.1354,0.1354,0.1441,
0.1452,0.1501,0.1558,0.1570,0.1576,0.1596,0.1635,0.1654,0.1655,0.1662,
0.1689,0.1723,0.1778,0.1820,0.1894,0.1902,0.1924,0.2028,0.2036,0.2039,
0.2040,0.2135,0.2175,0.2197,0.2202,0.2285,0.2301,0.2338,0.2355,0.2370,
0.2373,0.2399,0.2503,0.2505,0.2635,0.2636,0.2642,0.2648,0.2691,0.2716,
0.2801,0.2852,0.2869,0.2919,0.2959,0.2962,0.2975,0.3046,0.3050,0.3064,
0.3077,0.3126,0.3139,0.3176,0.3327,0.3330,0.3423,0.3445,0.3467,0.3484,
0.3487,0.3492,0.3501,0.3542,0.3557,0.3574,0.3633,0.3640,0.3640,0.3656,
0.3696,0.3786,0.3849,0.3859,0.3903,0.3947,0.3949,0.3958,0.4071,0.4075,
0.4112,0.4188,0.4247,0.4285,0.4349,0.4363,0.4392,0.4467,0.4496,0.4506,
0.4527,0.4532,0.4748,0.4755,0.4787,0.4855,0.4881,0.4899,0.4909,0.4942,
0.4948,0.4968,0.5008,0.5106,0.5114,0.5131,0.5150,0.5207,0.5239,0.5365,
0.5371,0.5394,0.5521,0.5548,0.5629,0.5652,0.5738,0.5745,0.5762,0.5788,
0.5869,0.5930,0.5990,0.6022,0.6028,0.6040,0.6097,0.6111,0.6151,0.6153,
0.6179,0.6194,0.6309,0.6320,0.6383,0.6446,0.6500,0.6527,0.6625,0.6706,
0.6716,0.6730,0.6768,0.6780,0.6857,0.6905,0.6934,0.6961,0.6969,0.7007,
0.7038,0.7081,0.7081,0.7121,0.7158,0.7171,0.7175,0.7209,0.7242,0.7302,
0.7321,0.7328,0.7431,0.7454,0.7457,0.7634,0.7645,0.7675,0.7724,0.7744,
0.7756,0.7787,0.7804,0.7828,0.7843,0.7909,0.7973,0.8052,0.8053,0.8119,
0.8124,0.8129,0.8172,0.8197,0.8199,0.8215,0.8255,0.8273,0.8309,0.8312,
0.8340,0.8377,0.8402,0.8411,0.8441,0.8468,0.8484,0.8526,0.8626,0.8633,
0.8637,0.8640,0.8886,0.8919,0.8927,0.8957,0.8966,0.8998,0.9016,0.9144,
0.9281,0.9303,0.9319,0.9364,0.9446,0.9452,0.9464,0.9486,0.9614,0.9645,
0.9677,0.9693,0.9731,0.9744,0.9757,0.9870,0.9877,0.9907,0.9946,
Overall p-value after applying KStest on 269 p-values = 0.677587
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.