RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 21.8132 0.807991
2 to 25 15.64 16.5828 0.517042
3 to 26 15.96 20.8088 0.765042
4 to 27 15.91 13.2878 0.283281
5 to 28 15.90 20.0514 0.728392
6 to 29 15.71 20.9148 0.769874
7 to 30 15.76 23.7901 0.874748
8 to 31 15.88 21.1581 0.780703
9 to 32 15.73 18.8506 0.662825
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.043481
Tough bday spacings test for dh-ranFile-2018-07-11_15:31: 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 37 77 82 115 78 52 29 16 4 2
(O-E)^2/E 0.1 0.0 0.2 2.5 3.1 0.0 0.0 0.0 0.1 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.116, p= 0.383
RESULTS OF GCD FOR dh-ranFile-2018-07-11_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.438076
p-value, dist. of gcd's: 0.140957
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.460 0.654 0.897 0.489 0.554 0.396 0.107 0.365
Bits 8 to 15---> 0.290 0.810 0.766 0.195 0.456 0.923 0.644 0.904
Bits 16 to 23---> 0.919 0.860 0.651 0.648 0.135 0.097 0.409 0.565
Bits 24 to 31---> 0.889 0.077 0.966 0.184 0.662 0.592 0.382 0.819
KS test for the above 32 p values: 0.547
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_15:31,
p-values for 5 runs: 0.8712, 0.9499, 0.7232, 0.6725, 0.6481
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 217 211.4 0.147 0.147
r= 29 5123 5134.0 0.024 0.171
r= 30 22910 23103.0 1.613 1.784
r= 31 11750 11551.5 3.410 5.194
chi-square = 5.194 with df = 3; p-value = 0.842
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 239 211.4 3.598 3.598
r= 30 5127 5134.0 0.010 3.608
r= 31 22946 23103.0 1.068 4.676
r= 32 11688 11551.5 1.612 6.288
chi-square = 6.288 with df = 3; p-value = 0.902
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_15:31
b-rank test for bits 1 to 8, p=0.96785
b-rank test for bits 2 to 9, p=0.92201
b-rank test for bits 3 to 10, p=0.12376
b-rank test for bits 4 to 11, p=0.46142
b-rank test for bits 5 to 12, p=0.67767
b-rank test for bits 6 to 13, p=0.80191
b-rank test for bits 7 to 14, p=0.75155
b-rank test for bits 8 to 15, p=0.07784
b-rank test for bits 9 to 16, p=0.20952
b-rank test for bits 10 to 17, p=0.78781
b-rank test for bits 11 to 18, p=0.82834
b-rank test for bits 12 to 19, p=0.13328
b-rank test for bits 13 to 20, p=0.64714
b-rank test for bits 14 to 21, p=0.67602
b-rank test for bits 15 to 22, p=0.05643
b-rank test for bits 16 to 23, p=0.21548
b-rank test for bits 17 to 24, p=0.81498
b-rank test for bits 18 to 25, p=0.14948
b-rank test for bits 19 to 26, p=0.20106
b-rank test for bits 20 to 27, p=0.48002
b-rank test for bits 21 to 28, p=0.32518
b-rank test for bits 22 to 29, p=0.68472
b-rank test for bits 23 to 30, p=0.08183
b-rank test for bits 24 to 31, p=0.15788
b-rank test for bits 25 to 32, p=0.69655
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 = 0.556163
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_15:31
(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 141440 -1.10 0.136416
2 142345 1.02 0.845642
3 141809 -0.23 0.407331
4 141663 -0.58 0.282464
5 141853 -0.13 0.447646
6 141813 -0.23 0.410962
7 141253 -1.53 0.062579
8 142270 0.84 0.800298
9 142043 0.31 0.622599
10 142395 1.13 0.871759
11 142259 0.82 0.793032
12 142142 0.54 0.706649
13 141363 -1.28 0.100894
14 142224 0.74 0.768894
15 141547 -0.85 0.198619
16 142290 0.89 0.813110
17 141897 -0.03 0.488509
18 141825 -0.20 0.421901
19 141548 -0.84 0.199271
20 141932 0.05 0.521121
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_15:31
Bits used No. missing words z-score p-value
23 to 32 141567 -1.1804 0.118911
22 to 31 142124 0.7402 0.770423
21 to 30 142291 1.3161 0.905930
20 to 29 142147 0.8196 0.793764
19 to 28 142145 0.8127 0.791792
18 to 27 141830 -0.2736 0.392215
17 to 26 142173 0.9092 0.818380
16 to 25 141976 0.2299 0.590914
15 to 24 142215 1.0540 0.854066
14 to 23 142076 0.5747 0.717261
13 to 22 141698 -0.7287 0.233085
12 to 21 141682 -0.7839 0.216550
11 to 20 141931 0.0747 0.529783
10 to 19 141968 0.2023 0.580163
9 to 18 141775 -0.4632 0.321608
8 to 17 141587 -1.1115 0.133180
7 to 16 141966 0.1954 0.577466
6 to 15 141862 -0.1632 0.435178
5 to 14 142006 0.3333 0.630563
4 to 13 142136 0.7816 0.782781
3 to 12 141933 0.0816 0.532526
2 to 11 141968 0.2023 0.580163
1 to 10 141791 -0.4080 0.341624
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_15:31
Bits used No. missing words z-score p-value
28 to 32 141406 -1.7062 0.043985
27 to 31 141547 -1.2282 0.109679
26 to 30 142092 0.6192 0.732114
25 to 29 141857 -0.1774 0.429601
24 to 28 142274 1.2362 0.891802
23 to 27 142163 0.8599 0.805077
22 to 26 142292 1.2972 0.902717
21 to 25 141750 -0.5401 0.294564
20 to 24 141620 -0.9808 0.163351
19 to 23 142328 1.4192 0.922083
18 to 22 142182 0.9243 0.822336
17 to 21 142097 0.6362 0.737667
16 to 20 142093 0.6226 0.733230
15 to 19 142444 1.8124 0.965041
14 to 18 142186 0.9379 0.825843
13 to 17 141689 -0.7469 0.227568
12 to 16 141947 0.1277 0.550805
11 to 15 142116 0.7006 0.758216
10 to 14 142501 2.0057 0.977554
9 to 13 141719 -0.6452 0.259403
8 to 12 142600 2.3413 0.990390
7 to 11 141830 -0.2689 0.393998
6 to 10 141574 -1.1367 0.127829
5 to 9 142081 0.5819 0.719694
4 to 8 142033 0.4192 0.662473
3 to 7 141895 -0.0486 0.480629
2 to 6 142116 0.7006 0.758216
1 to 5 142124 0.7277 0.766600
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_15:31
Bits used No. missing words z-score p-value
31 to 32 141899 -0.0305 0.487845
30 to 31 142137 0.6716 0.749079
29 to 30 142069 0.4710 0.681181
28 to 29 141810 -0.2930 0.384758
27 to 28 141900 -0.0275 0.489022
26 to 27 142258 1.0285 0.848149
25 to 26 141953 0.1288 0.551250
24 to 25 141241 -1.9715 0.024335
23 to 24 142364 1.3412 0.910074
22 to 23 142035 0.3707 0.644573
21 to 22 141992 0.2439 0.596332
20 to 21 141978 0.2026 0.580263
19 to 20 142304 1.1642 0.877832
18 to 19 141845 -0.1898 0.424747
17 to 18 141474 -1.2842 0.099543
16 to 17 142656 2.2026 0.986187
15 to 16 141460 -1.3255 0.092510
14 to 15 142063 0.4533 0.674835
13 to 14 141887 -0.0659 0.473741
12 to 13 142407 1.4681 0.928955
11 to 12 141453 -1.3461 0.089134
10 to 11 142249 1.0020 0.841823
9 to 10 142065 0.4592 0.676956
8 to 9 142060 0.4445 0.671643
7 to 8 142107 0.5831 0.720086
6 to 7 141695 -0.6322 0.263614
5 to 6 142157 0.7306 0.767485
4 to 5 142047 0.4061 0.657668
3 to 4 142462 1.6303 0.948480
2 to 3 142767 2.5300 0.994297
1 to 2 141928 0.0551 0.521960
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2601.03 1.429 0.923459
Test results for specific bytes for dh-ranFile-2018-07-11_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2553.29 0.754 0.774466
2 to 9 2585.96 1.216 0.887937
3 to 10 2457.06 -0.607 0.271826
4 to 11 2468.81 -0.441 0.329562
5 to 12 2495.83 -0.059 0.476491
6 to 13 2564.75 0.916 0.820101
7 to 14 2486.00 -0.198 0.421502
8 to 15 2482.79 -0.243 0.403826
9 to 16 2556.99 0.806 0.789863
10 to 17 2480.35 -0.278 0.390525
11 to 18 2363.77 -1.927 0.027016
12 to 19 2514.37 0.203 0.580529
13 to 20 2485.61 -0.204 0.419366
14 to 21 2471.14 -0.408 0.341591
15 to 22 2576.67 1.084 0.860884
16 to 23 2519.47 0.275 0.608467
17 to 24 2656.22 2.209 0.986424
18 to 25 2458.85 -0.582 0.280279
19 to 26 2417.16 -1.172 0.120679
20 to 27 2433.42 -0.942 0.173206
21 to 28 2562.37 0.882 0.811106
22 to 29 2654.52 2.185 0.985562
23 to 30 2559.15 0.836 0.798547
24 to 31 2522.12 0.313 0.622815
25 to 32 2562.40 0.882 0.811227
CDPARK for dh-ranFile-2018-07-11_15:31: 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
3512 -0.5023 0.307734
3513 -0.4566 0.323972
3535 0.5479 0.708135
3538 0.6849 0.753306
3500 -1.0502 0.146807
3539 0.7306 0.767486
3579 2.5571 0.994722
3555 1.4612 0.928018
3535 0.5479 0.708135
3534 0.5023 0.692266
Square side=100, avg. no. parked=3534.00 sample std.=21.42
p-value of the KSTEST for those 10 p-values: 0.178509
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_15:31
0.7522,0.2422,0.3985,0.8959,0.2626,0.4675,0.8638,0.0763,0.3034,0.9129,
The KS test for those 10 p-values: 0.875739
The 3DSPHERES test for dh-ranFile-2018-07-11_15:31
sample no r^3 equiv. uni.
1 0.311 0.010298
2 37.343 0.711993
3 11.841 0.326116
4 0.494 0.016341
5 10.607 0.297822
6 4.206 0.130814
7 4.351 0.135012
8 15.841 0.410245
9 25.423 0.571481
10 10.201 0.288260
11 11.317 0.314241
12 0.014 0.000451
13 8.394 0.244066
14 60.155 0.865364
15 23.852 0.548454
16 4.177 0.129963
17 19.550 0.478824
18 29.393 0.624607
19 6.359 0.191015
20 126.992 0.985492
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.034913
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -0.8 0.2 -0.5 1.1
1.7 1.1 0.1 -0.5 1.2 0.7
-0.5 -1.8 -0.9 -0.8 0.6 -1.0
-0.5 1.1 2.2 0.1 0.3 0.3
-0.3 0.5 -0.6 1.1 -0.7 -1.8
-1.0 -0.1 -0.6 -0.1 -1.0 1.1
-0.2 -0.4 0.5 -0.7 0.1 2.0
-0.1
Chi-square with 42 degrees of freedom:36.213306
z-score=-0.631380, p-value=0.277841
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_15:31
Test no p-value
1 0.563402
2 0.162026
3 0.025301
4 0.119640
5 0.270066
6 0.099641
7 0.398012
8 0.454819
9 0.333147
10 0.772521
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.087114
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_15:31:
(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 66399 1.07 66840 0.45
3 25000.00 25195 1.52 24943 0.13
4 6666.67 6737 0.74 6538 2.48
5 1388.89 1383 0.02 1395 0.03
6 238.10 237 0.01 235 0.04
7 34.72 38 0.31 47 4.34
8 4.96 10 5.12 1 3.16
p=0.81479 p=0.89970
Number of rngs required: 688144, p-value: 0.383
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_15:31
No. of wins: Observed Expected
98267 98585.9
z-score=-1.426, pvalue=0.07692
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66196 66666.7 3.323 3.323
2 37780 37654.3 0.419 3.742
3 26872 26954.7 0.254 3.996
4 19477 19313.5 1.385 5.381
5 13906 13851.4 0.215 5.596
6 10039 9943.5 0.916 6.513
7 7062 7145.0 0.965 7.477
8 5196 5139.1 0.631 8.108
9 3730 3699.9 0.245 8.353
10 2649 2666.3 0.112 8.466
11 1933 1923.3 0.049 8.514
12 1447 1388.7 2.444 10.958
13 1053 1003.7 2.420 13.378
14 757 726.1 1.311 14.690
15 476 525.8 4.723 19.413
16 335 381.2 5.588 25.001
17 293 276.5 0.980 25.981
18 232 200.8 4.838 30.819
19 154 146.0 0.440 31.259
20 114 106.2 0.571 31.829
21 299 287.1 0.492 32.321
Chisq= 32.32 for 20 degrees of freedom, p= 0.96001
SUMMARY of craptest
p-value for no. of wins: 0.076917
p-value for throws/game: 0.960007
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_15:31
No. of wins: Observed Expected
99196 98585.9
z-score= 2.729, pvalue=0.99682
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66739 66666.7 0.078 0.078
2 37550 37654.3 0.289 0.368
3 27147 26954.7 1.371 1.739
4 19377 19313.5 0.209 1.948
5 13813 13851.4 0.107 2.055
6 9911 9943.5 0.107 2.161
7 7138 7145.0 0.007 2.168
8 5091 5139.1 0.450 2.618
9 3742 3699.9 0.480 3.097
10 2637 2666.3 0.322 3.419
11 1980 1923.3 1.670 5.089
12 1344 1388.7 1.441 6.531
13 976 1003.7 0.765 7.296
14 689 726.1 1.900 9.196
15 504 525.8 0.907 10.102
16 389 381.2 0.162 10.264
17 277 276.5 0.001 10.265
18 190 200.8 0.584 10.849
19 133 146.0 1.155 12.004
20 103 106.2 0.097 12.101
21 270 287.1 1.020 13.121
Chisq= 13.12 for 20 degrees of freedom, p= 0.12787
SUMMARY of craptest
p-value for no. of wins: 0.996823
p-value for throws/game: 0.127869
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0103,0.0163,0.0243,0.0253,0.0270,0.0349,0.0435,0.0440,0.0564,
0.0626,0.0763,0.0769,0.0769,0.0778,0.0818,0.0871,0.0891,0.0925,0.0973,
0.0995,0.0996,0.1009,0.1073,0.1097,0.1189,0.1196,0.1207,0.1238,0.1278,
0.1279,0.1300,0.1308,0.1332,0.1333,0.1350,0.1353,0.1364,0.1410,0.1468,
0.1495,0.1579,0.1620,0.1634,0.1732,0.1785,0.1838,0.1910,0.1945,0.1986,
0.1993,0.2011,0.2095,0.2155,0.2166,0.2276,0.2331,0.2422,0.2441,0.2594,
0.2626,0.2636,0.2701,0.2718,0.2778,0.2803,0.2825,0.2833,0.2883,0.2901,
0.2946,0.2978,0.3034,0.3077,0.3142,0.3216,0.3240,0.3252,0.3261,0.3296,
0.3331,0.3416,0.3416,0.3652,0.3816,0.3825,0.3828,0.3848,0.3905,0.3922,
0.3940,0.3964,0.3980,0.3985,0.4038,0.4073,0.4091,0.4102,0.4110,0.4194,
0.4215,0.4219,0.4247,0.4296,0.4352,0.4381,0.4476,0.4548,0.4563,0.4602,
0.4614,0.4675,0.4737,0.4765,0.4788,0.4800,0.4806,0.4878,0.4885,0.4890,
0.4893,0.5170,0.5211,0.5220,0.5298,0.5325,0.5470,0.5485,0.5508,0.5513,
0.5542,0.5562,0.5634,0.5648,0.5715,0.5775,0.5802,0.5802,0.5803,0.5805,
0.5909,0.5920,0.5963,0.6085,0.6226,0.6228,0.6246,0.6306,0.6440,0.6446,
0.6471,0.6481,0.6482,0.6511,0.6538,0.6577,0.6623,0.6625,0.6628,0.6716,
0.6725,0.6748,0.6760,0.6770,0.6777,0.6812,0.6847,0.6923,0.6966,0.7066,
0.7081,0.7081,0.7120,0.7173,0.7197,0.7201,0.7232,0.7284,0.7321,0.7332,
0.7377,0.7491,0.7515,0.7522,0.7533,0.7582,0.7582,0.7650,0.7660,0.7666,
0.7675,0.7675,0.7689,0.7699,0.7704,0.7725,0.7745,0.7807,0.7828,0.7878,
0.7899,0.7918,0.7930,0.7938,0.7985,0.8003,0.8019,0.8051,0.8080,0.8101,
0.8111,0.8112,0.8131,0.8148,0.8150,0.8184,0.8187,0.8201,0.8223,0.8258,
0.8283,0.8418,0.8419,0.8456,0.8481,0.8541,0.8603,0.8609,0.8638,0.8654,
0.8712,0.8718,0.8747,0.8757,0.8778,0.8879,0.8885,0.8918,0.8959,0.8971,
0.8997,0.9016,0.9027,0.9037,0.9059,0.9101,0.9129,0.9191,0.9220,0.9221,
0.9234,0.9235,0.9280,0.9290,0.9485,0.9499,0.9600,0.9650,0.9661,0.9679,
0.9776,0.9855,0.9856,0.9862,0.9864,0.9904,0.9943,0.9947,0.9968,
Overall p-value after applying KStest on 269 p-values = 0.038230
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.