RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.01 12.8417 0.253286
2 to 25 15.90 18.1072 0.617891
3 to 26 15.99 18.6322 0.649951
4 to 27 15.95 16.9702 0.543610
5 to 28 15.97 22.1935 0.822609
6 to 29 16.04 11.1264 0.150083
7 to 30 15.62 26.8017 0.938960
8 to 31 15.77 17.6559 0.589145
9 to 32 15.93 14.3268 0.356154
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.851550
Tough bday spacings test for dh-ranFile-2018-07-07_20:31: 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 6 35 69 100 102 75 55 24 18 11 5
(O-E)^2/E 1.1 0.1 0.2 0.1 0.2 0.1 0.2 1.1 0.7 2.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 6.834, p= 0.259
RESULTS OF GCD FOR dh-ranFile-2018-07-07_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.437652
p-value, dist. of gcd's: 0.015881
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.503 0.660 0.938 0.937 0.174 0.403 0.815 0.478
Bits 8 to 15---> 0.386 0.077 0.192 0.349 0.722 0.090 0.490 0.414
Bits 16 to 23---> 0.911 0.024 0.348 0.770 0.627 0.111 0.806 0.994
Bits 24 to 31---> 0.257 0.247 0.315 0.808 0.533 0.395 0.095 0.574
KS test for the above 32 p values: 0.026
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_20:31,
p-values for 5 runs: 0.0724, 0.0920, 0.5035, 0.1994, 0.6852
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 231 211.4 1.814 1.814
r= 29 5004 5134.0 3.292 5.106
r= 30 23101 23103.0 0.000 5.106
r= 31 11664 11551.5 1.095 6.201
chi-square = 6.201 with df = 3; p-value = 0.898
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 192 211.4 1.783 1.783
r= 30 5142 5134.0 0.012 1.796
r= 31 22923 23103.0 1.403 3.199
r= 32 11743 11551.5 3.174 6.373
chi-square = 6.373 with df = 3; p-value = 0.905
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_20:31
b-rank test for bits 1 to 8, p=0.35537
b-rank test for bits 2 to 9, p=0.64587
b-rank test for bits 3 to 10, p=0.80715
b-rank test for bits 4 to 11, p=0.86482
b-rank test for bits 5 to 12, p=0.65010
b-rank test for bits 6 to 13, p=0.56215
b-rank test for bits 7 to 14, p=0.80570
b-rank test for bits 8 to 15, p=0.76230
b-rank test for bits 9 to 16, p=0.47462
b-rank test for bits 10 to 17, p=0.24239
b-rank test for bits 11 to 18, p=0.76505
b-rank test for bits 12 to 19, p=0.62155
b-rank test for bits 13 to 20, p=0.94372
b-rank test for bits 14 to 21, p=0.99887
b-rank test for bits 15 to 22, p=0.95195
b-rank test for bits 16 to 23, p=0.96533
b-rank test for bits 17 to 24, p=0.24519
b-rank test for bits 18 to 25, p=0.23576
b-rank test for bits 19 to 26, p=0.28019
b-rank test for bits 20 to 27, p=0.58201
b-rank test for bits 21 to 28, p=0.32095
b-rank test for bits 22 to 29, p=0.62448
b-rank test for bits 23 to 30, p=0.28739
b-rank test for bits 24 to 31, p=0.37086
b-rank test for bits 25 to 32, p=0.61451
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 = 0.095311
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_20:31
(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 141863 -0.11 0.456900
2 142678 1.80 0.963749
3 142252 0.80 0.788327
4 141648 -0.61 0.270738
5 142270 0.84 0.800298
6 142153 0.57 0.715431
7 142300 0.91 0.819321
8 142183 0.64 0.738724
9 141715 -0.45 0.324899
10 141669 -0.56 0.287222
11 142166 0.60 0.725646
12 141866 -0.10 0.459681
13 141477 -1.01 0.156220
14 141450 -1.07 0.141591
15 141997 0.20 0.581150
16 142296 0.90 0.816852
17 141557 -0.82 0.205197
18 141807 -0.24 0.405518
19 141810 -0.23 0.408238
20 141971 0.14 0.557285
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_20:31
Bits used No. missing words z-score p-value
23 to 32 142173 0.9092 0.818380
22 to 31 142265 1.2264 0.889985
21 to 30 141814 -0.3287 0.371182
20 to 29 142166 0.8851 0.811940
19 to 28 141787 -0.4218 0.336575
18 to 27 141711 -0.6839 0.247020
17 to 26 141901 -0.0287 0.488542
16 to 25 142021 0.3851 0.649907
15 to 24 142096 0.6437 0.740112
14 to 23 141754 -0.5356 0.296110
13 to 22 141959 0.1713 0.567997
12 to 21 141667 -0.8356 0.201684
11 to 20 142120 0.7264 0.766218
10 to 19 141726 -0.6322 0.263637
9 to 18 142186 0.9540 0.829967
8 to 17 142065 0.5368 0.704295
7 to 16 141728 -0.6253 0.265895
6 to 15 141639 -0.9322 0.175624
5 to 14 141544 -1.2598 0.103878
4 to 13 141760 -0.5149 0.303301
3 to 12 141733 -0.6080 0.271582
2 to 11 141926 0.0575 0.522920
1 to 10 141716 -0.6667 0.252496
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_20:31
Bits used No. missing words z-score p-value
28 to 32 141891 -0.0621 0.475227
27 to 31 142579 2.2701 0.988398
26 to 30 142322 1.3989 0.919076
25 to 29 141850 -0.2011 0.420303
24 to 28 142334 1.4396 0.925004
23 to 27 141923 0.0463 0.518480
22 to 26 141473 -1.4791 0.069559
21 to 25 142280 1.2565 0.895534
20 to 24 141785 -0.4215 0.336711
19 to 23 141880 -0.0994 0.460401
18 to 22 141952 0.1446 0.557504
17 to 21 141974 0.2192 0.586761
16 to 20 141926 0.0565 0.522532
15 to 19 142347 1.4836 0.931046
14 to 18 141981 0.2429 0.595978
13 to 17 142144 0.7955 0.786836
12 to 16 141959 0.1684 0.566855
11 to 15 141906 -0.0113 0.495497
10 to 14 142821 3.0904 0.999001
9 to 13 141753 -0.5299 0.298080
8 to 12 141808 -0.3435 0.365614
7 to 11 142042 0.4497 0.673547
6 to 10 141790 -0.4045 0.342919
5 to 9 141980 0.2396 0.594664
4 to 8 142173 0.8938 0.814285
3 to 7 141884 -0.0859 0.465787
2 to 6 141704 -0.6960 0.243204
1 to 5 141818 -0.3096 0.378435
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_20:31
Bits used No. missing words z-score p-value
31 to 32 141680 -0.6765 0.249365
30 to 31 142230 0.9459 0.827908
29 to 30 142156 0.7276 0.766583
28 to 29 141304 -1.7856 0.037079
27 to 28 141770 -0.4110 0.340535
26 to 27 141080 -2.4464 0.007215
25 to 26 142074 0.4858 0.686429
24 to 25 141938 0.0846 0.533699
23 to 24 142123 0.6303 0.735749
22 to 23 141726 -0.5408 0.294324
21 to 22 142325 1.2262 0.889932
20 to 21 142109 0.5890 0.722068
19 to 20 142217 0.9076 0.817950
18 to 19 141967 0.1701 0.567541
17 to 18 141921 0.0344 0.513731
16 to 17 142311 1.1849 0.881965
15 to 16 142063 0.4533 0.674835
14 to 15 142031 0.3589 0.640168
13 to 14 142129 0.6480 0.741506
12 to 13 141672 -0.7001 0.241936
11 to 12 142006 0.2852 0.612240
10 to 11 142594 2.0197 0.978291
9 to 10 141780 -0.3815 0.351415
8 to 9 141423 -1.4346 0.075700
7 to 8 142141 0.6834 0.752821
6 to 7 142305 1.1672 0.878429
5 to 6 142289 1.1200 0.868637
4 to 5 141538 -1.0954 0.136678
3 to 4 142298 1.1465 0.874210
2 to 3 141460 -1.3255 0.092510
1 to 2 141676 -0.6883 0.245635
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2495.92 -0.058 0.476970
Test results for specific bytes for dh-ranFile-2018-07-07_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2551.67 0.731 0.767540
2 to 9 2442.56 -0.812 0.208291
3 to 10 2509.24 0.131 0.551991
4 to 11 2433.34 -0.943 0.172923
5 to 12 2494.21 -0.082 0.467380
6 to 13 2412.91 -1.232 0.109054
7 to 14 2420.68 -1.122 0.130993
8 to 15 2467.91 -0.454 0.324995
9 to 16 2477.09 -0.324 0.372948
10 to 17 2602.49 1.449 0.926401
11 to 18 2597.66 1.381 0.916370
12 to 19 2563.93 0.904 0.817047
13 to 20 2535.60 0.504 0.692703
14 to 21 2601.22 1.431 0.923842
15 to 22 2505.74 0.081 0.532355
16 to 23 2491.87 -0.115 0.454238
17 to 24 2565.18 0.922 0.821677
18 to 25 2442.77 -0.809 0.209174
19 to 26 2516.89 0.239 0.594409
20 to 27 2469.54 -0.431 0.333307
21 to 28 2434.98 -0.920 0.178905
22 to 29 2506.22 0.088 0.535068
23 to 30 2443.71 -0.796 0.213000
24 to 31 2493.02 -0.099 0.460658
25 to 32 2409.30 -1.283 0.099804
CDPARK for dh-ranFile-2018-07-07_20:31: 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
3548 1.1416 0.873180
3583 2.7397 0.996925
3556 1.5068 0.934075
3512 -0.5023 0.307734
3553 1.3699 0.914635
3519 -0.1826 0.427537
3535 0.5479 0.708135
3538 0.6849 0.753306
3542 0.8676 0.807188
3511 -0.5479 0.291865
Square side=100, avg. no. parked=3539.70 sample std.=21.06
p-value of the KSTEST for those 10 p-values: 0.031672
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_20:31
0.4499,0.1745,0.4191,0.7652,0.5522,0.1254,0.8663,0.0066,0.9575,0.7703,
The KS test for those 10 p-values: 0.915103
The 3DSPHERES test for dh-ranFile-2018-07-07_20:31
sample no r^3 equiv. uni.
1 43.140 0.762599
2 58.511 0.857778
3 18.509 0.460426
4 7.521 0.221750
5 64.012 0.881606
6 30.391 0.636884
7 74.271 0.915895
8 2.352 0.075414
9 33.993 0.677971
10 7.478 0.220621
11 11.747 0.324007
12 12.874 0.348927
13 38.793 0.725584
14 3.202 0.101238
15 12.231 0.334825
16 2.644 0.084370
17 0.529 0.017463
18 6.294 0.189252
19 10.770 0.301635
20 31.582 0.651018
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.588510
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.9 -0.4 -0.1 1.4 -0.6
0.1 -0.6 -0.9 1.0 1.0 0.2
0.3 -0.9 0.3 -0.5 0.9 -1.3
-0.5 -0.4 2.1 -1.9 0.1 0.9
-0.9 1.3 -0.3 0.6 0.0 -0.1
-0.4 -0.1 0.6 -0.3 1.2 -0.8
-1.6 -0.4 0.9 0.4 -0.6 1.0
0.8
Chi-square with 42 degrees of freedom:35.066227
z-score=-0.756537, p-value=0.233052
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_20:31
Test no p-value
1 0.000052
2 0.012167
3 0.127537
4 0.149078
5 0.050334
6 0.626015
7 0.419631
8 0.456920
9 0.374454
10 0.001522
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000254
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_20:31:
(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 66664 0.00 66756 0.12
3 25000.00 25099 0.39 24874 0.64
4 6666.67 6585 1.00 6779 1.89
5 1388.89 1403 0.14 1329 2.58
6 238.10 214 2.44 229 0.35
7 34.72 31 0.40 27 1.72
8 4.96 3 0.77 5 0.00
p=0.47496 p=0.70551
Number of rngs required: 687509, p-value: 0.150
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_20:31
No. of wins: Observed Expected
98549 98585.9
z-score=-0.165, pvalue=0.43453
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66833 66666.7 0.415 0.415
2 37687 37654.3 0.028 0.443
3 26846 26954.7 0.439 0.882
4 19182 19313.5 0.895 1.777
5 13921 13851.4 0.350 2.126
6 9926 9943.5 0.031 2.157
7 7258 7145.0 1.786 3.944
8 5005 5139.1 3.498 7.441
9 3761 3699.9 1.010 8.452
10 2651 2666.3 0.088 8.539
11 1880 1923.3 0.976 9.515
12 1381 1388.7 0.043 9.559
13 997 1003.7 0.045 9.603
14 723 726.1 0.014 9.617
15 515 525.8 0.223 9.840
16 413 381.2 2.661 12.502
17 277 276.5 0.001 12.503
18 207 200.8 0.190 12.692
19 150 146.0 0.110 12.803
20 94 106.2 1.405 14.207
21 293 287.1 0.121 14.328
Chisq= 14.33 for 20 degrees of freedom, p= 0.18652
SUMMARY of craptest
p-value for no. of wins: 0.434530
p-value for throws/game: 0.186517
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_20:31
No. of wins: Observed Expected
98538 98585.9
z-score=-0.214, pvalue=0.41525
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66702 66666.7 0.019 0.019
2 37392 37654.3 1.827 1.846
3 27137 26954.7 1.232 3.079
4 19315 19313.5 0.000 3.079
5 13842 13851.4 0.006 3.085
6 9828 9943.5 1.343 4.428
7 7162 7145.0 0.040 4.468
8 5131 5139.1 0.013 4.481
9 3662 3699.9 0.388 4.868
10 2781 2666.3 4.934 9.803
11 1905 1923.3 0.175 9.977
12 1387 1388.7 0.002 9.980
13 973 1003.7 0.940 10.920
14 767 726.1 2.299 13.219
15 546 525.8 0.773 13.992
16 417 381.2 3.372 17.364
17 319 276.5 6.519 23.883
18 178 200.8 2.595 26.478
19 164 146.0 2.223 28.702
20 98 106.2 0.635 29.337
21 294 287.1 0.165 29.502
Chisq= 29.50 for 20 degrees of freedom, p= 0.92167
SUMMARY of craptest
p-value for no. of wins: 0.415253
p-value for throws/game: 0.921671
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0003,0.0015,0.0066,0.0072,0.0122,0.0159,0.0175,0.0239,0.0255,
0.0317,0.0371,0.0503,0.0696,0.0724,0.0754,0.0757,0.0773,0.0844,0.0902,
0.0920,0.0925,0.0949,0.0953,0.0998,0.1012,0.1039,0.1091,0.1105,0.1254,
0.1275,0.1310,0.1367,0.1416,0.1491,0.1500,0.1501,0.1562,0.1729,0.1743,
0.1745,0.1756,0.1789,0.1865,0.1893,0.1924,0.1994,0.2017,0.2052,0.2083,
0.2092,0.2130,0.2206,0.2217,0.2331,0.2358,0.2419,0.2424,0.2432,0.2452,
0.2456,0.2470,0.2475,0.2494,0.2525,0.2533,0.2571,0.2590,0.2636,0.2659,
0.2707,0.2716,0.2802,0.2872,0.2874,0.2919,0.2943,0.2961,0.2981,0.3016,
0.3033,0.3077,0.3147,0.3209,0.3240,0.3249,0.3250,0.3333,0.3348,0.3366,
0.3367,0.3405,0.3429,0.3482,0.3489,0.3490,0.3514,0.3554,0.3562,0.3656,
0.3709,0.3712,0.3729,0.3745,0.3784,0.3858,0.3946,0.4032,0.4055,0.4082,
0.4137,0.4153,0.4191,0.4196,0.4203,0.4275,0.4345,0.4377,0.4499,0.4542,
0.4569,0.4569,0.4597,0.4604,0.4604,0.4607,0.4658,0.4674,0.4746,0.4750,
0.4752,0.4770,0.4777,0.4885,0.4900,0.4955,0.5029,0.5035,0.5137,0.5185,
0.5225,0.5229,0.5324,0.5335,0.5337,0.5351,0.5436,0.5520,0.5522,0.5573,
0.5575,0.5622,0.5669,0.5675,0.5680,0.5743,0.5812,0.5820,0.5868,0.5885,
0.5891,0.5944,0.5947,0.5960,0.6122,0.6145,0.6179,0.6216,0.6245,0.6260,
0.6266,0.6369,0.6402,0.6459,0.6499,0.6500,0.6501,0.6510,0.6601,0.6735,
0.6748,0.6780,0.6852,0.6864,0.6927,0.7043,0.7055,0.7081,0.7154,0.7221,
0.7221,0.7256,0.7256,0.7357,0.7387,0.7401,0.7415,0.7528,0.7533,0.7623,
0.7626,0.7650,0.7652,0.7662,0.7666,0.7675,0.7698,0.7703,0.7868,0.7883,
0.8003,0.8057,0.8060,0.8071,0.8072,0.8080,0.8119,0.8143,0.8152,0.8169,
0.8170,0.8180,0.8184,0.8193,0.8217,0.8226,0.8279,0.8300,0.8516,0.8578,
0.8648,0.8663,0.8686,0.8732,0.8742,0.8784,0.8816,0.8820,0.8899,0.8900,
0.8955,0.8978,0.9052,0.9111,0.9146,0.9151,0.9159,0.9164,0.9191,0.9217,
0.9238,0.9250,0.9264,0.9310,0.9341,0.9369,0.9383,0.9390,0.9437,0.9520,
0.9575,0.9637,0.9653,0.9783,0.9884,0.9938,0.9969,0.9989,0.9990,
Overall p-value after applying KStest on 269 p-values = 0.865906
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.