RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.63 15.5453 0.443734
2 to 25 15.62 18.0952 0.617142
3 to 26 15.88 14.3088 0.354868
4 to 27 15.81 24.2905 0.888245
5 to 28 16.08 9.3343 0.070812
6 to 29 16.02 12.4105 0.225333
7 to 30 15.89 13.3833 0.289829
8 to 31 15.88 8.5361 0.046299
9 to 32 16.21 19.9413 0.722757
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.643798
Tough bday spacings test for dh-ranFile-2018-06-23_21:31: 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 32 73 96 98 87 55 27 13 6 2
(O-E)^2/E 0.4 0.6 0.0 0.0 0.0 1.0 0.2 0.3 0.2 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 3.755, p= 0.042
RESULTS OF GCD FOR dh-ranFile-2018-06-23_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.564482
p-value, dist. of gcd's: 0.138749
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.249 0.312 0.610 0.154 0.516 0.693 0.470 0.552
Bits 8 to 15---> 0.023 0.962 0.601 0.282 0.560 0.949 0.875 0.445
Bits 16 to 23---> 0.121 0.211 0.427 0.756 0.554 0.798 0.737 0.230
Bits 24 to 31---> 0.344 0.629 0.497 0.105 0.537 0.857 0.874 0.963
KS test for the above 32 p values: 0.172
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_21:31,
p-values for 5 runs: 0.7176, 0.4950, 0.1067, 0.3867, 0.4568
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5075 5134.0 0.678 0.950
r= 30 23196 23103.0 0.374 1.324
r= 31 11510 11551.5 0.149 1.473
chi-square = 1.473 with df = 3; p-value = 0.312
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5137 5134.0 0.002 0.149
r= 31 23121 23103.0 0.014 0.163
r= 32 11525 11551.5 0.061 0.224
chi-square = 0.224 with df = 3; p-value = 0.026
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_21:31
b-rank test for bits 1 to 8, p=0.95375
b-rank test for bits 2 to 9, p=0.64429
b-rank test for bits 3 to 10, p=0.10119
b-rank test for bits 4 to 11, p=0.39179
b-rank test for bits 5 to 12, p=0.33764
b-rank test for bits 6 to 13, p=0.10388
b-rank test for bits 7 to 14, p=0.63116
b-rank test for bits 8 to 15, p=0.79795
b-rank test for bits 9 to 16, p=0.26827
b-rank test for bits 10 to 17, p=0.20049
b-rank test for bits 11 to 18, p=0.15727
b-rank test for bits 12 to 19, p=0.13670
b-rank test for bits 13 to 20, p=0.09516
b-rank test for bits 14 to 21, p=0.03293
b-rank test for bits 15 to 22, p=0.71036
b-rank test for bits 16 to 23, p=0.43486
b-rank test for bits 17 to 24, p=0.11555
b-rank test for bits 18 to 25, p=0.25343
b-rank test for bits 19 to 26, p=0.13529
b-rank test for bits 20 to 27, p=0.30033
b-rank test for bits 21 to 28, p=0.88578
b-rank test for bits 22 to 29, p=0.39299
b-rank test for bits 23 to 30, p=0.86126
b-rank test for bits 24 to 31, p=0.49644
b-rank test for bits 25 to 32, p=0.61436
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 = 0.131839
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_21:31
(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 142096 0.44 0.668634
2 142003 0.22 0.586619
3 141563 -0.81 0.209205
4 141982 0.17 0.567412
5 141712 -0.46 0.322381
6 142152 0.57 0.714638
7 141673 -0.55 0.290415
8 142010 0.24 0.592977
9 141861 -0.11 0.455047
10 141316 -1.39 0.082830
11 141964 0.13 0.550820
12 141838 -0.17 0.433819
13 141852 -0.13 0.446722
14 141123 -1.84 0.033089
15 141603 -0.72 0.237081
16 142191 0.66 0.744765
17 142348 1.02 0.847302
18 141230 -1.59 0.056231
19 142029 0.28 0.610109
20 141490 -0.98 0.163607
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_21:31
Bits used No. missing words z-score p-value
23 to 32 142348 1.5127 0.934816
22 to 31 141263 -2.2287 0.012916
21 to 30 142062 0.5264 0.700712
20 to 29 142419 1.7575 0.960582
19 to 28 141535 -1.2908 0.098388
18 to 27 141892 -0.0598 0.476174
17 to 26 141438 -1.6253 0.052052
16 to 25 142369 1.5851 0.943525
15 to 24 142232 1.1127 0.867072
14 to 23 141949 0.1368 0.554403
13 to 22 141510 -1.3770 0.084256
12 to 21 142051 0.4885 0.687408
11 to 20 141765 -0.4977 0.309351
10 to 19 141913 0.0127 0.505049
9 to 18 141960 0.1747 0.569352
8 to 17 142089 0.6196 0.732224
7 to 16 142199 0.9989 0.841069
6 to 15 142107 0.6816 0.752261
5 to 14 141628 -0.9701 0.165998
4 to 13 142012 0.3540 0.638344
3 to 12 142263 1.2196 0.888683
2 to 11 141379 -1.8287 0.033720
1 to 10 142201 1.0058 0.842734
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_21:31
Bits used No. missing words z-score p-value
28 to 32 142078 0.5718 0.716259
27 to 31 141787 -0.4147 0.339189
26 to 30 141900 -0.0316 0.487385
25 to 29 142161 0.8531 0.803203
24 to 28 141862 -0.1604 0.436267
23 to 27 142052 0.4836 0.685675
22 to 26 141751 -0.5367 0.295733
21 to 25 141829 -0.2723 0.392694
20 to 24 141789 -0.4079 0.341674
19 to 23 141786 -0.4181 0.337949
18 to 22 141994 0.2870 0.612950
17 to 21 141596 -1.0621 0.144087
16 to 20 141740 -0.5740 0.282984
15 to 19 142161 0.8531 0.803203
14 to 18 141784 -0.4248 0.335474
13 to 17 141907 -0.0079 0.496849
12 to 16 141918 0.0294 0.511723
11 to 15 141773 -0.4621 0.321992
10 to 14 141695 -0.7265 0.233753
9 to 13 141948 0.1311 0.552146
8 to 12 141586 -1.0960 0.136532
7 to 11 142115 0.6972 0.757157
6 to 10 141799 -0.3740 0.354202
5 to 9 141702 -0.7028 0.241086
4 to 8 141702 -0.7028 0.241086
3 to 7 142681 2.6158 0.995549
2 to 6 141759 -0.5096 0.305168
1 to 5 142168 0.8768 0.809715
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_21:31
Bits used No. missing words z-score p-value
31 to 32 141914 0.0138 0.505496
30 to 31 141928 0.0551 0.521960
29 to 30 141761 -0.4376 0.330856
28 to 29 141881 -0.0836 0.466699
27 to 28 141870 -0.1160 0.453819
26 to 27 142137 0.6716 0.749079
25 to 26 142198 0.8515 0.802764
24 to 25 141368 -1.5968 0.055150
23 to 24 141389 -1.5349 0.062405
22 to 23 142685 2.2881 0.988935
21 to 22 141659 -0.7384 0.230125
20 to 21 141594 -0.9302 0.176140
19 to 20 141704 -0.6057 0.272359
18 to 19 142284 1.1052 0.865468
17 to 18 142296 1.1406 0.872986
16 to 17 141865 -0.1308 0.447980
15 to 16 141511 -1.1750 0.119994
14 to 15 141623 -0.8446 0.199158
13 to 14 141879 -0.0895 0.464355
12 to 13 142377 1.3796 0.916139
11 to 12 141376 -1.5732 0.057831
10 to 11 142222 0.9223 0.821822
9 to 10 142039 0.3825 0.648958
8 to 9 142316 1.1996 0.884856
7 to 8 142606 2.0551 0.980064
6 to 7 141498 -1.2134 0.112496
5 to 6 141446 -1.3668 0.085851
4 to 5 142375 1.3737 0.915226
3 to 4 141717 -0.5673 0.285240
2 to 3 141629 -0.8269 0.204138
1 to 2 141824 -0.2517 0.400632
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2413.64 -1.221 0.110991
Test results for specific bytes for dh-ranFile-2018-06-23_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2572.36 1.023 0.846928
2 to 9 2612.58 1.592 0.944316
3 to 10 2391.75 -1.531 0.062894
4 to 11 2432.73 -0.951 0.170724
5 to 12 2491.44 -0.121 0.451813
6 to 13 2440.77 -0.838 0.201133
7 to 14 2500.39 0.006 0.502221
8 to 15 2533.07 0.468 0.680019
9 to 16 2480.28 -0.279 0.390164
10 to 17 2513.87 0.196 0.577752
11 to 18 2471.25 -0.407 0.342138
12 to 19 2444.02 -0.792 0.214274
13 to 20 2554.48 0.770 0.779494
14 to 21 2525.93 0.367 0.643084
15 to 22 2568.74 0.972 0.834517
16 to 23 2496.18 -0.054 0.478434
17 to 24 2526.26 0.371 0.644808
18 to 25 2545.70 0.646 0.740976
19 to 26 2409.13 -1.285 0.099378
20 to 27 2617.82 1.666 0.952167
21 to 28 2548.59 0.687 0.754001
22 to 29 2527.60 0.390 0.651840
23 to 30 2640.40 1.986 0.976462
24 to 31 2487.38 -0.179 0.429150
25 to 32 2492.06 -0.112 0.455297
CDPARK for dh-ranFile-2018-06-23_21:31: 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
3493 -1.3699 0.085365
3528 0.2283 0.590298
3519 -0.1826 0.427537
3516 -0.3196 0.374623
3518 -0.2283 0.409702
3569 2.1005 0.982156
3549 1.1872 0.882429
3574 2.3288 0.990064
3535 0.5479 0.708135
3537 0.6393 0.738676
Square side=100, avg. no. parked=3533.80 sample std.=23.63
p-value of the KSTEST for those 10 p-values: 0.226312
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_21:31
0.8578,0.4186,0.7559,0.8418,0.1865,0.6191,0.5421,0.1894,0.8612,0.3623,
The KS test for those 10 p-values: 0.668775
The 3DSPHERES test for dh-ranFile-2018-06-23_21:31
sample no r^3 equiv. uni.
1 63.811 0.880808
2 7.720 0.226877
3 2.004 0.064627
4 47.726 0.796253
5 3.849 0.120397
6 15.905 0.411496
7 17.221 0.436747
8 3.021 0.095799
9 1.445 0.047011
10 15.902 0.411439
11 82.486 0.936042
12 26.224 0.582771
13 77.635 0.924818
14 36.129 0.700095
15 35.263 0.691311
16 8.101 0.236650
17 30.268 0.635387
18 67.011 0.892867
19 63.076 0.877853
20 27.659 0.602259
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.827361
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 0.1 0.2 0.1 -0.1
0.2 -0.8 0.7 -0.8 -0.6 -0.7
0.7 -0.0 1.8 -0.2 1.3 -0.5
-1.0 -0.4 -0.5 1.2 -1.3 0.8
-0.5 -1.4 0.5 0.1 0.8 0.5
-0.1 -0.1 0.0 -0.4 -0.4 -0.1
-0.7 0.5 0.9 0.4 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:20.889188
z-score=-2.303378, p-value=0.002626
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_21:31
Test no p-value
1 0.071904
2 0.237779
3 0.531240
4 0.000102
5 0.045959
6 0.571487
7 0.168191
8 0.428735
9 0.064327
10 0.030085
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000718
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_21:31:
(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 66695 0.01
3 25000.00 25113 0.51 24949 0.10
4 6666.67 6586 0.98 6692 0.10
5 1388.89 1368 0.31 1387 0.00
6 238.10 230 0.28 236 0.02
7 34.72 30 0.64 35 0.00
8 4.96 8 1.86 5 0.00
p=0.40149 p=0.00025
Number of rngs required: 687945, p-value: 0.299
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_21:31
No. of wins: Observed Expected
98568 98585.9
z-score=-0.080, pvalue=0.46817
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66957 66666.7 1.264 1.264
2 37374 37654.3 2.087 3.351
3 26792 26954.7 0.982 4.334
4 19444 19313.5 0.882 5.216
5 13940 13851.4 0.566 5.782
6 9883 9943.5 0.369 6.151
7 7066 7145.0 0.874 7.025
8 5182 5139.1 0.359 7.384
9 3695 3699.9 0.006 7.390
10 2654 2666.3 0.057 7.447
11 1854 1923.3 2.499 9.946
12 1462 1388.7 3.865 13.811
13 996 1003.7 0.059 13.870
14 773 726.1 3.024 16.894
15 522 525.8 0.028 16.922
16 407 381.2 1.753 18.675
17 298 276.5 1.665 20.340
18 182 200.8 1.765 22.106
19 127 146.0 2.469 24.575
20 117 106.2 1.095 25.670
21 275 287.1 0.511 26.181
Chisq= 26.18 for 20 degrees of freedom, p= 0.84008
SUMMARY of craptest
p-value for no. of wins: 0.468169
p-value for throws/game: 0.840076
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_21:31
No. of wins: Observed Expected
98297 98585.9
z-score=-1.292, pvalue=0.09819
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66247 66666.7 2.642 2.642
2 37697 37654.3 0.048 2.690
3 27056 26954.7 0.380 3.071
4 19596 19313.5 4.133 7.204
5 13805 13851.4 0.156 7.359
6 9876 9943.5 0.459 7.818
7 7185 7145.0 0.224 8.042
8 5258 5139.1 2.752 10.794
9 3727 3699.9 0.199 10.993
10 2637 2666.3 0.322 11.315
11 1843 1923.3 3.355 14.670
12 1417 1388.7 0.575 15.245
13 1012 1003.7 0.068 15.313
14 698 726.1 1.091 16.404
15 499 525.8 1.370 17.774
16 390 381.2 0.205 17.979
17 270 276.5 0.155 18.134
18 246 200.8 10.160 28.293
19 144 146.0 0.027 28.320
20 106 106.2 0.000 28.321
21 291 287.1 0.053 28.373
Chisq= 28.37 for 20 degrees of freedom, p= 0.89915
SUMMARY of craptest
p-value for no. of wins: 0.098188
p-value for throws/game: 0.899146
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0003,0.0007,0.0026,0.0129,0.0227,0.0264,0.0301,0.0329,0.0331,
0.0337,0.0423,0.0460,0.0463,0.0470,0.0521,0.0552,0.0562,0.0578,0.0624,
0.0629,0.0643,0.0646,0.0708,0.0719,0.0828,0.0843,0.0854,0.0859,0.0952,
0.0958,0.0982,0.0984,0.0994,0.1012,0.1039,0.1054,0.1067,0.1110,0.1125,
0.1156,0.1200,0.1204,0.1211,0.1318,0.1353,0.1365,0.1367,0.1387,0.1441,
0.1544,0.1573,0.1636,0.1660,0.1682,0.1707,0.1722,0.1761,0.1865,0.1894,
0.1992,0.2005,0.2011,0.2041,0.2092,0.2106,0.2143,0.2253,0.2263,0.2269,
0.2296,0.2301,0.2338,0.2366,0.2371,0.2378,0.2411,0.2411,0.2485,0.2534,
0.2683,0.2724,0.2824,0.2830,0.2852,0.2898,0.2904,0.2957,0.2988,0.3003,
0.3052,0.3094,0.3116,0.3124,0.3220,0.3224,0.3309,0.3355,0.3376,0.3379,
0.3392,0.3417,0.3421,0.3435,0.3542,0.3549,0.3623,0.3746,0.3867,0.3902,
0.3918,0.3927,0.3930,0.4006,0.4015,0.4097,0.4114,0.4115,0.4186,0.4271,
0.4275,0.4287,0.4291,0.4338,0.4349,0.4363,0.4367,0.4437,0.4453,0.4467,
0.4480,0.4518,0.4538,0.4550,0.4553,0.4568,0.4644,0.4667,0.4682,0.4696,
0.4762,0.4784,0.4874,0.4950,0.4964,0.4967,0.4968,0.5022,0.5050,0.5055,
0.5117,0.5163,0.5220,0.5312,0.5368,0.5421,0.5508,0.5521,0.5522,0.5544,
0.5545,0.5596,0.5645,0.5674,0.5694,0.5715,0.5778,0.5828,0.5866,0.5903,
0.5930,0.6010,0.6023,0.6097,0.6101,0.6130,0.6144,0.6171,0.6191,0.6294,
0.6312,0.6354,0.6383,0.6431,0.6438,0.6443,0.6448,0.6490,0.6518,0.6686,
0.6688,0.6800,0.6857,0.6874,0.6913,0.6928,0.7001,0.7007,0.7081,0.7104,
0.7146,0.7163,0.7176,0.7228,0.7322,0.7371,0.7387,0.7410,0.7448,0.7491,
0.7523,0.7540,0.7559,0.7562,0.7572,0.7795,0.7963,0.7980,0.7985,0.8028,
0.8032,0.8032,0.8097,0.8218,0.8274,0.8345,0.8401,0.8411,0.8418,0.8427,
0.8469,0.8473,0.8575,0.8578,0.8612,0.8613,0.8655,0.8671,0.8730,0.8744,
0.8748,0.8779,0.8808,0.8824,0.8849,0.8858,0.8882,0.8887,0.8929,0.8991,
0.9152,0.9161,0.9248,0.9348,0.9360,0.9435,0.9443,0.9490,0.9522,0.9537,
0.9606,0.9619,0.9626,0.9765,0.9801,0.9822,0.9889,0.9901,0.9955,
Overall p-value after applying KStest on 269 p-values = 0.192356
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.