RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.44 21.1411 0.779958
2 to 25 15.77 16.3513 0.500919
3 to 26 15.56 15.1503 0.415344
4 to 27 15.68 33.0714 0.988961
5 to 28 15.80 18.2779 0.628483
6 to 29 15.67 11.2717 0.157901
7 to 30 15.72 19.2740 0.686969
8 to 31 15.85 14.3822 0.360114
9 to 32 16.18 23.4098 0.863623
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.548942
Tough bday spacings test for dh-ranFile-2018-06-27_04:31: 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 17 35 62 107 95 84 49 28 18 3 2
(O-E)^2/E 6.7 0.1 1.7 0.9 0.1 0.4 0.2 0.1 0.7 2.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 13.887, p= 0.822
RESULTS OF GCD FOR dh-ranFile-2018-06-27_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.354227
p-value, dist. of gcd's: 0.104837
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.614 0.959 0.032 0.175 0.712 0.939 0.595 0.709
Bits 8 to 15---> 0.613 0.029 0.935 0.296 0.377 0.742 0.869 0.080
Bits 16 to 23---> 0.054 0.360 0.718 0.741 0.476 0.553 0.748 0.507
Bits 24 to 31---> 0.715 0.557 0.149 0.095 0.694 0.945 0.858 0.167
KS test for the above 32 p values: 0.442
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_04:31,
p-values for 5 runs: 0.6031, 0.9766, 0.8904, 0.7089, 0.8501
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 217 211.4 0.147 0.147
r= 29 5055 5134.0 1.216 1.363
r= 30 23277 23103.0 1.310 2.673
r= 31 11451 11551.5 0.875 3.548
chi-square = 3.548 with df = 3; p-value = 0.685
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5182 5134.0 0.449 0.596
r= 31 22862 23103.0 2.515 3.111
r= 32 11739 11551.5 3.043 6.154
chi-square = 6.154 with df = 3; p-value = 0.896
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_04:31
b-rank test for bits 1 to 8, p=0.52823
b-rank test for bits 2 to 9, p=0.10386
b-rank test for bits 3 to 10, p=0.09416
b-rank test for bits 4 to 11, p=0.35817
b-rank test for bits 5 to 12, p=0.21663
b-rank test for bits 6 to 13, p=0.07328
b-rank test for bits 7 to 14, p=0.75701
b-rank test for bits 8 to 15, p=0.75769
b-rank test for bits 9 to 16, p=0.85758
b-rank test for bits 10 to 17, p=0.84469
b-rank test for bits 11 to 18, p=0.23881
b-rank test for bits 12 to 19, p=0.06209
b-rank test for bits 13 to 20, p=0.84236
b-rank test for bits 14 to 21, p=0.90000
b-rank test for bits 15 to 22, p=0.25505
b-rank test for bits 16 to 23, p=0.57169
b-rank test for bits 17 to 24, p=0.34032
b-rank test for bits 18 to 25, p=0.09143
b-rank test for bits 19 to 26, p=0.39749
b-rank test for bits 20 to 27, p=0.10420
b-rank test for bits 21 to 28, p=0.37117
b-rank test for bits 22 to 29, p=0.53741
b-rank test for bits 23 to 30, p=0.25364
b-rank test for bits 24 to 31, p=0.47828
b-rank test for bits 25 to 32, p=0.38888
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 = 0.205326
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_04:31
(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 141259 -1.52 0.064323
2 141899 -0.02 0.490372
3 140881 -2.40 0.008139
4 141153 -1.77 0.038604
5 142293 0.90 0.814987
6 141866 -0.10 0.459681
7 141920 0.02 0.509945
8 142684 1.81 0.964850
9 142352 1.03 0.849496
10 142703 1.85 0.968157
11 141619 -0.68 0.248778
12 141781 -0.30 0.382151
13 142029 0.28 0.610109
14 142079 0.40 0.654104
15 141477 -1.01 0.156220
16 141490 -0.98 0.163607
17 142260 0.82 0.793699
18 142384 1.11 0.866294
19 142038 0.30 0.618152
20 141168 -1.73 0.041630
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_04:31
Bits used No. missing words z-score p-value
23 to 32 141661 -0.8563 0.195913
22 to 31 141712 -0.6804 0.248110
21 to 30 142237 1.1299 0.870740
20 to 29 141605 -1.0494 0.146994
19 to 28 141540 -1.2736 0.101411
18 to 27 142449 1.8609 0.968623
17 to 26 141749 -0.5529 0.290179
16 to 25 141775 -0.4632 0.321608
15 to 24 142201 1.0058 0.842734
14 to 23 142002 0.3196 0.625346
13 to 22 142488 1.9954 0.977001
12 to 21 141836 -0.2529 0.400187
11 to 20 141426 -1.6667 0.047792
10 to 19 141721 -0.6494 0.258036
9 to 18 141955 0.1575 0.562568
8 to 17 141902 -0.0253 0.489918
7 to 16 142161 0.8678 0.807256
6 to 15 142308 1.3747 0.915392
5 to 14 142400 1.6920 0.954674
4 to 13 142258 1.2023 0.885378
3 to 12 141603 -1.0563 0.145413
2 to 11 141721 -0.6494 0.258036
1 to 10 141626 -0.9770 0.164285
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_04:31
Bits used No. missing words z-score p-value
28 to 32 142240 1.1209 0.868838
27 to 31 142302 1.3311 0.908419
26 to 30 141717 -0.6520 0.257212
25 to 29 141878 -0.1062 0.457711
24 to 28 141804 -0.3571 0.360527
23 to 27 141548 -1.2248 0.110316
22 to 26 142591 2.3107 0.989577
21 to 25 142041 0.4463 0.672324
20 to 24 141686 -0.7571 0.224510
19 to 23 141739 -0.5774 0.281838
18 to 22 141841 -0.2316 0.408414
17 to 21 142076 0.5650 0.713957
16 to 20 142331 1.4294 0.923554
15 to 19 142192 0.9582 0.831020
14 to 18 142040 0.4429 0.671099
13 to 17 141005 -3.0655 0.001086
12 to 16 141704 -0.6960 0.243204
11 to 15 142112 0.6870 0.753964
10 to 14 141995 0.2904 0.614248
9 to 13 142489 1.9650 0.975292
8 to 12 141615 -0.9977 0.159205
7 to 11 142315 1.3752 0.915458
6 to 10 142152 0.8226 0.794635
5 to 9 141930 0.0701 0.527930
4 to 8 141228 -2.3096 0.010455
3 to 7 142133 0.7582 0.775835
2 to 6 142324 1.4057 0.920088
1 to 5 141862 -0.1604 0.436267
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_04:31
Bits used No. missing words z-score p-value
31 to 32 141520 -1.1485 0.125388
30 to 31 142066 0.4622 0.678014
29 to 30 142108 0.5860 0.721078
28 to 29 141603 -0.9036 0.183096
27 to 28 141898 -0.0334 0.486669
26 to 27 141507 -1.1868 0.117650
25 to 26 142229 0.9430 0.827154
24 to 25 141648 -0.7709 0.220388
23 to 24 141392 -1.5260 0.063499
22 to 23 142560 1.9194 0.972532
21 to 22 142004 0.2793 0.609978
20 to 21 142116 0.6096 0.728952
19 to 20 142365 1.3442 0.910552
18 to 19 142142 0.6863 0.753751
17 to 18 142271 1.0669 0.856985
16 to 17 141786 -0.3638 0.358002
15 to 16 141997 0.2586 0.602033
14 to 15 142775 2.5536 0.994669
13 to 14 141964 0.1613 0.564059
12 to 13 141491 -1.2340 0.108599
11 to 12 141444 -1.3727 0.084930
10 to 11 141998 0.2616 0.603171
9 to 10 142158 0.7335 0.768385
8 to 9 141299 -1.8004 0.035900
7 to 8 141759 -0.4435 0.328720
6 to 7 142184 0.8102 0.791098
5 to 6 141856 -0.1573 0.437498
4 to 5 141943 0.0993 0.539559
3 to 4 141605 -0.8977 0.184665
2 to 3 141341 -1.6765 0.046821
1 to 2 141541 -1.0865 0.138625
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2565.70 0.929 0.823604
Test results for specific bytes for dh-ranFile-2018-06-27_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2593.76 1.326 0.907576
2 to 9 2542.03 0.594 0.723868
3 to 10 2615.61 1.635 0.948968
4 to 11 2387.27 -1.594 0.055435
5 to 12 2528.56 0.404 0.656847
6 to 13 2519.90 0.281 0.610785
7 to 14 2541.49 0.587 0.721317
8 to 15 2440.04 -0.848 0.198212
9 to 16 2512.30 0.174 0.569021
10 to 17 2444.36 -0.787 0.215694
11 to 18 2487.09 -0.183 0.427553
12 to 19 2579.24 1.121 0.868769
13 to 20 2504.15 0.059 0.523380
14 to 21 2453.94 -0.651 0.257405
15 to 22 2363.75 -1.927 0.026999
16 to 23 2608.23 1.531 0.937069
17 to 24 2430.42 -0.984 0.162550
18 to 25 2507.14 0.101 0.540215
19 to 26 2588.43 1.251 0.894450
20 to 27 2442.48 -0.814 0.207964
21 to 28 2527.04 0.382 0.648902
22 to 29 2423.40 -1.083 0.139331
23 to 30 2492.37 -0.108 0.457018
24 to 31 2496.05 -0.056 0.477698
25 to 32 2495.24 -0.067 0.473161
CDPARK for dh-ranFile-2018-06-27_04:31: 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
3528 0.2283 0.590298
3519 -0.1826 0.427537
3532 0.4110 0.659449
3522 -0.0457 0.481790
3519 -0.1826 0.427537
3521 -0.0913 0.463617
3491 -1.4612 0.071982
3541 0.8219 0.794438
3519 -0.1826 0.427537
3491 -1.4612 0.071982
Square side=100, avg. no. parked=3518.30 sample std.=15.20
p-value of the KSTEST for those 10 p-values: 0.378757
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_04:31
0.3858,0.2165,0.1484,0.6501,0.0294,0.3288,0.6806,0.7280,0.1245,0.4524,
The KS test for those 10 p-values: 0.298577
The 3DSPHERES test for dh-ranFile-2018-06-27_04:31
sample no r^3 equiv. uni.
1 5.388 0.164399
2 2.931 0.093090
3 36.794 0.706673
4 10.686 0.299656
5 17.924 0.449797
6 5.831 0.176653
7 152.472 0.993795
8 6.177 0.186083
9 49.730 0.809416
10 8.577 0.248654
11 14.012 0.373161
12 27.539 0.600668
13 62.645 0.876086
14 21.594 0.513157
15 35.926 0.698061
16 13.659 0.365743
17 26.307 0.583928
18 27.974 0.606424
19 2.093 0.067391
20 4.118 0.128259
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.662228
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 -0.4 -0.5 -1.0 0.1
0.9 -0.1 -0.9 -0.8 -1.8 -0.3
1.9 0.6 -0.3 0.8 -0.2 -0.5
0.3 -0.0 -0.5 0.2 -1.4 -0.1
1.5 0.8 1.1 0.1 0.2 -2.1
0.9 -0.3 0.8 -1.3 0.3 1.3
0.0 -0.1 -0.4 -0.7 1.6 -1.0
0.8
Chi-square with 42 degrees of freedom:35.070033
z-score=-0.756121, p-value=0.233195
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_04:31
Test no p-value
1 0.010050
2 0.181969
3 0.640968
4 0.362403
5 0.319772
6 0.293531
7 0.549648
8 0.160814
9 0.861542
10 0.093232
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.164900
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_04:31:
(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 66598 0.07 67029 1.97
3 25000.00 25153 0.94 24857 0.82
4 6666.67 6584 1.03 6539 2.44
5 1388.89 1378 0.09 1319 3.52
6 238.10 242 0.06 204 4.88
7 34.72 37 0.15 44 2.48
8 4.96 7 0.84 7 0.84
p=0.21283 p=0.99053
Number of rngs required: 688820, p-value: 0.685
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_04:31
No. of wins: Observed Expected
98533 98585.9
z-score=-0.236, pvalue=0.40656
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66867 66666.7 0.602 0.602
2 37669 37654.3 0.006 0.608
3 26799 26954.7 0.900 1.507
4 19163 19313.5 1.172 2.680
5 14019 13851.4 2.027 4.707
6 9911 9943.5 0.107 4.814
7 7211 7145.0 0.609 5.423
8 5147 5139.1 0.012 5.435
9 3700 3699.9 0.000 5.435
10 2629 2666.3 0.522 5.957
11 1867 1923.3 1.650 7.606
12 1345 1388.7 1.378 8.984
13 1009 1003.7 0.028 9.012
14 739 726.1 0.228 9.240
15 532 525.8 0.072 9.312
16 363 381.2 0.864 10.176
17 289 276.5 0.561 10.738
18 199 200.8 0.017 10.754
19 159 146.0 1.160 11.915
20 113 106.2 0.433 12.348
21 270 287.1 1.020 13.368
Chisq= 13.37 for 20 degrees of freedom, p= 0.13898
SUMMARY of craptest
p-value for no. of wins: 0.406556
p-value for throws/game: 0.138975
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_04:31
No. of wins: Observed Expected
98328 98585.9
z-score=-1.153, pvalue=0.12439
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66606 66666.7 0.055 0.055
2 37939 37654.3 2.152 2.207
3 26845 26954.7 0.447 2.654
4 19393 19313.5 0.328 2.982
5 13636 13851.4 3.350 6.332
6 9951 9943.5 0.006 6.338
7 7150 7145.0 0.003 6.341
8 5068 5139.1 0.983 7.324
9 3755 3699.9 0.822 8.146
10 2743 2666.3 2.207 10.352
11 1903 1923.3 0.215 10.567
12 1384 1388.7 0.016 10.583
13 961 1003.7 1.818 12.401
14 731 726.1 0.033 12.434
15 551 525.8 1.204 13.638
16 371 381.2 0.270 13.908
17 298 276.5 1.665 15.574
18 179 200.8 2.373 17.946
19 137 146.0 0.553 18.499
20 115 106.2 0.727 19.226
21 284 287.1 0.034 19.260
Chisq= 19.26 for 20 degrees of freedom, p= 0.49499
SUMMARY of craptest
p-value for no. of wins: 0.124395
p-value for throws/game: 0.494990
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0081,0.0101,0.0105,0.0270,0.0290,0.0294,0.0320,0.0359,0.0386,
0.0416,0.0468,0.0478,0.0543,0.0554,0.0621,0.0635,0.0643,0.0674,0.0720,
0.0720,0.0733,0.0805,0.0849,0.0914,0.0931,0.0932,0.0942,0.0947,0.1014,
0.1039,0.1042,0.1048,0.1086,0.1103,0.1177,0.1244,0.1245,0.1254,0.1283,
0.1386,0.1390,0.1393,0.1454,0.1470,0.1484,0.1493,0.1562,0.1579,0.1592,
0.1608,0.1626,0.1636,0.1643,0.1644,0.1649,0.1670,0.1754,0.1767,0.1820,
0.1831,0.1847,0.1861,0.1959,0.1982,0.2053,0.2080,0.2128,0.2157,0.2165,
0.2166,0.2204,0.2245,0.2332,0.2388,0.2432,0.2481,0.2487,0.2488,0.2536,
0.2550,0.2572,0.2574,0.2580,0.2580,0.2818,0.2902,0.2935,0.2962,0.2986,
0.2997,0.3198,0.3216,0.3287,0.3288,0.3403,0.3542,0.3580,0.3582,0.3601,
0.3603,0.3605,0.3624,0.3657,0.3712,0.3732,0.3772,0.3788,0.3822,0.3858,
0.3889,0.3975,0.4002,0.4066,0.4084,0.4153,0.4275,0.4275,0.4275,0.4276,
0.4363,0.4375,0.4423,0.4498,0.4524,0.4570,0.4577,0.4597,0.4636,0.4732,
0.4765,0.4777,0.4783,0.4818,0.4867,0.4899,0.4904,0.4950,0.5009,0.5066,
0.5099,0.5132,0.5234,0.5279,0.5282,0.5374,0.5396,0.5402,0.5489,0.5496,
0.5526,0.5569,0.5626,0.5641,0.5690,0.5717,0.5839,0.5903,0.5949,0.6007,
0.6020,0.6031,0.6032,0.6064,0.6100,0.6101,0.6108,0.6126,0.6136,0.6142,
0.6182,0.6253,0.6285,0.6410,0.6489,0.6501,0.6541,0.6568,0.6594,0.6622,
0.6711,0.6723,0.6780,0.6806,0.6846,0.6854,0.6870,0.6936,0.6981,0.7067,
0.7089,0.7093,0.7116,0.7140,0.7150,0.7184,0.7211,0.7213,0.7239,0.7280,
0.7290,0.7406,0.7423,0.7485,0.7538,0.7540,0.7570,0.7577,0.7684,0.7758,
0.7800,0.7911,0.7937,0.7944,0.7946,0.8073,0.8094,0.8150,0.8218,0.8236,
0.8272,0.8310,0.8424,0.8427,0.8447,0.8495,0.8501,0.8570,0.8576,0.8580,
0.8615,0.8636,0.8663,0.8688,0.8688,0.8688,0.8707,0.8761,0.8854,0.8904,
0.8944,0.8956,0.9000,0.9076,0.9084,0.9106,0.9154,0.9155,0.9201,0.9236,
0.9354,0.9371,0.9389,0.9447,0.9490,0.9547,0.9591,0.9649,0.9682,0.9686,
0.9725,0.9753,0.9766,0.9770,0.9890,0.9896,0.9905,0.9938,0.9947,
Overall p-value after applying KStest on 269 p-values = 0.702257
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.