RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.89 7.0172 0.016674
2 to 25 16.01 17.2602 0.563126
3 to 26 15.98 10.2029 0.105113
4 to 27 15.85 15.3038 0.426389
5 to 28 15.74 24.7188 0.898816
6 to 29 15.82 5.7264 0.005156
7 to 30 15.80 21.8812 0.810667
8 to 31 15.99 14.1023 0.340155
9 to 32 15.58 12.5861 0.236574
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.183922
Tough bday spacings test for dh-ranFile-2018-07-03_01:31: 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 95 101 92 35 34 9 8 4
(O-E)^2/E 0.1 0.0 0.2 0.1 0.1 2.5 5.6 0.6 2.3 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 11.813, p= 0.702
RESULTS OF GCD FOR dh-ranFile-2018-07-03_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.780608
p-value, dist. of gcd's: 0.492308
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.748 0.120 0.460 0.419 0.870 0.155 0.168 0.235
Bits 8 to 15---> 0.691 0.047 0.409 0.041 0.423 0.581 0.250 0.321
Bits 16 to 23---> 0.328 0.696 0.602 0.758 0.779 0.251 0.479 0.667
Bits 24 to 31---> 0.408 0.062 0.527 0.492 0.758 0.329 0.704 0.342
KS test for the above 32 p values: 0.791
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_01:31,
p-values for 5 runs: 0.0001, 0.3094, 0.7672, 0.5372, 0.5238
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 230 211.4 1.633 1.633
r= 29 5157 5134.0 0.103 1.736
r= 30 23044 23103.0 0.151 1.887
r= 31 11569 11551.5 0.026 1.914
chi-square = 1.914 with df = 3; p-value = 0.409
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5226 5134.0 1.648 1.787
r= 31 22984 23103.0 0.613 2.401
r= 32 11584 11551.5 0.091 2.492
chi-square = 2.492 with df = 3; p-value = 0.523
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_01:31
b-rank test for bits 1 to 8, p=0.72514
b-rank test for bits 2 to 9, p=0.45861
b-rank test for bits 3 to 10, p=0.71396
b-rank test for bits 4 to 11, p=0.20347
b-rank test for bits 5 to 12, p=0.36815
b-rank test for bits 6 to 13, p=0.12368
b-rank test for bits 7 to 14, p=0.36715
b-rank test for bits 8 to 15, p=0.59741
b-rank test for bits 9 to 16, p=0.09389
b-rank test for bits 10 to 17, p=0.54496
b-rank test for bits 11 to 18, p=0.46328
b-rank test for bits 12 to 19, p=0.26350
b-rank test for bits 13 to 20, p=0.50309
b-rank test for bits 14 to 21, p=0.04544
b-rank test for bits 15 to 22, p=0.07255
b-rank test for bits 16 to 23, p=0.53484
b-rank test for bits 17 to 24, p=0.31687
b-rank test for bits 18 to 25, p=0.09300
b-rank test for bits 19 to 26, p=0.64956
b-rank test for bits 20 to 27, p=0.55554
b-rank test for bits 21 to 28, p=0.58187
b-rank test for bits 22 to 29, p=0.74393
b-rank test for bits 23 to 30, p=0.56850
b-rank test for bits 24 to 31, p=0.68443
b-rank test for bits 25 to 32, p=0.10795
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 = 0.102070
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_01:31
(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 141898 -0.03 0.489440
2 142532 1.45 0.927143
3 141696 -0.50 0.309089
4 141984 0.17 0.569249
5 142168 0.60 0.727201
6 142373 1.08 0.860672
7 141743 -0.39 0.348778
8 141333 -1.35 0.089060
9 141456 -1.06 0.144758
10 141863 -0.11 0.456900
11 142816 2.12 0.982929
12 142216 0.72 0.763164
13 141407 -1.17 0.120264
14 141365 -1.27 0.101722
15 141412 -1.16 0.122621
16 142190 0.66 0.744014
17 141914 0.01 0.504353
18 141891 -0.04 0.482920
19 142464 1.30 0.902505
20 141390 -1.21 0.112491
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_01:31
Bits used No. missing words z-score p-value
23 to 32 141768 -0.4873 0.313007
22 to 31 142615 2.4333 0.992520
21 to 30 141993 0.2885 0.613525
20 to 29 141928 0.0644 0.525666
19 to 28 142012 0.3540 0.638344
18 to 27 142025 0.3989 0.655003
17 to 26 141520 -1.3425 0.089714
16 to 25 141695 -0.7391 0.229933
15 to 24 142119 0.7230 0.765160
14 to 23 141652 -0.8873 0.187447
13 to 22 141745 -0.5667 0.285474
12 to 21 141887 -0.0770 0.469312
11 to 20 141619 -1.0011 0.158380
10 to 19 142259 1.2058 0.886045
9 to 18 141447 -1.5942 0.055441
8 to 17 142073 0.5644 0.713752
7 to 16 141694 -0.7425 0.228887
6 to 15 141980 0.2437 0.596264
5 to 14 142030 0.4161 0.661333
4 to 13 141535 -1.2908 0.098388
3 to 12 142181 0.9368 0.825568
2 to 11 141975 0.2264 0.589574
1 to 10 141921 0.0402 0.516050
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_01:31
Bits used No. missing words z-score p-value
28 to 32 141891 -0.0621 0.475227
27 to 31 141780 -0.4384 0.330546
26 to 30 141962 0.1785 0.570852
25 to 29 141611 -1.0113 0.155939
24 to 28 141737 -0.5842 0.279553
23 to 27 142571 2.2429 0.987550
22 to 26 141873 -0.1232 0.450993
21 to 25 142153 0.8260 0.795598
20 to 24 141401 -1.7232 0.042430
19 to 23 142421 1.7345 0.958583
18 to 22 141740 -0.5740 0.282984
17 to 21 141720 -0.6418 0.260503
16 to 20 141965 0.1887 0.574841
15 to 19 142065 0.5277 0.701145
14 to 18 142314 1.3718 0.914931
13 to 17 142038 0.4362 0.668643
12 to 16 142370 1.5616 0.940808
11 to 15 141964 0.1853 0.573512
10 to 14 142035 0.4260 0.664946
9 to 13 142057 0.5006 0.691665
8 to 12 141650 -0.8791 0.189678
7 to 11 141969 0.2023 0.580148
6 to 10 141873 -0.1232 0.450993
5 to 9 141957 0.1616 0.564187
4 to 8 141667 -0.8215 0.205693
3 to 7 142110 0.6802 0.751823
2 to 6 142177 0.9074 0.817891
1 to 5 141413 -1.6825 0.046238
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_01:31
Bits used No. missing words z-score p-value
31 to 32 142157 0.7306 0.767485
30 to 31 141522 -1.1426 0.126609
29 to 30 141903 -0.0187 0.492551
28 to 29 141886 -0.0688 0.472566
27 to 28 141948 0.1141 0.545409
26 to 27 141546 -1.0718 0.141912
25 to 26 141596 -0.9243 0.177671
24 to 25 142217 0.9076 0.817950
23 to 24 141587 -0.9508 0.170846
22 to 23 141972 0.1849 0.573333
21 to 22 142104 0.5742 0.717100
20 to 21 141647 -0.7738 0.219514
19 to 20 141844 -0.1927 0.423592
18 to 19 142183 0.8073 0.790249
17 to 18 141700 -0.6175 0.268455
16 to 17 142190 0.8279 0.796146
15 to 16 142055 0.4297 0.666295
14 to 15 141623 -0.8446 0.199158
13 to 14 142122 0.6273 0.734784
12 to 13 141958 0.1436 0.557080
11 to 12 142067 0.4651 0.679071
10 to 11 141380 -1.5614 0.059209
9 to 10 142259 1.0315 0.848841
8 to 9 141785 -0.3668 0.356901
7 to 8 141425 -1.4287 0.076545
6 to 7 141436 -1.3963 0.081319
5 to 6 142382 1.3943 0.918388
4 to 5 142303 1.1613 0.877234
3 to 4 141958 0.1436 0.557080
2 to 3 141244 -1.9626 0.024845
1 to 2 141564 -1.0187 0.154179
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2555.66 0.787 0.784397
Test results for specific bytes for dh-ranFile-2018-07-03_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2582.16 1.162 0.877352
2 to 9 2432.55 -0.954 0.170064
3 to 10 2525.24 0.357 0.639415
4 to 11 2444.11 -0.790 0.214635
5 to 12 2510.34 0.146 0.558114
6 to 13 2582.55 1.167 0.878493
7 to 14 2407.38 -1.310 0.095135
8 to 15 2588.00 1.244 0.893335
9 to 16 2553.33 0.754 0.774655
10 to 17 2537.98 0.537 0.704403
11 to 18 2521.10 0.298 0.617278
12 to 19 2607.23 1.516 0.935290
13 to 20 2520.35 0.288 0.613251
14 to 21 2440.51 -0.841 0.200088
15 to 22 2570.61 0.999 0.840984
16 to 23 2491.32 -0.123 0.451177
17 to 24 2359.47 -1.987 0.023442
18 to 25 2406.79 -1.318 0.093717
19 to 26 2599.74 1.410 0.920801
20 to 27 2383.75 -1.644 0.050090
21 to 28 2484.25 -0.223 0.411848
22 to 29 2382.98 -1.655 0.048973
23 to 30 2570.88 1.002 0.841925
24 to 31 2473.62 -0.373 0.354564
25 to 32 2649.42 2.113 0.982702
CDPARK for dh-ranFile-2018-07-03_01:31: 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
3519 -0.1826 0.427537
3510 -0.5936 0.276387
3493 -1.3699 0.085365
3499 -1.0959 0.136563
3524 0.0457 0.518210
3501 -1.0046 0.157553
3501 -1.0046 0.157553
3499 -1.0959 0.136563
3538 0.6849 0.753306
Square side=100, avg. no. parked=3512.30 sample std.=15.94
p-value of the KSTEST for those 10 p-values: 0.097765
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_01:31
0.0088,0.8228,0.7221,0.6783,0.9993,0.8265,0.5451,0.9257,0.5185,0.3560,
The KS test for those 10 p-values: 0.119477
The 3DSPHERES test for dh-ranFile-2018-07-03_01:31
sample no r^3 equiv. uni.
1 10.668 0.299251
2 22.907 0.533995
3 8.463 0.245790
4 4.492 0.139054
5 7.470 0.220427
6 65.447 0.887134
7 16.464 0.422357
8 26.509 0.586720
9 39.806 0.734691
10 50.733 0.815683
11 23.788 0.547490
12 13.482 0.361991
13 0.233 0.007744
14 10.414 0.293289
15 11.583 0.320304
16 25.825 0.577194
17 7.816 0.229367
18 16.155 0.416386
19 13.644 0.365426
20 2.276 0.073055
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.161160
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.1 -0.4 -0.7 -0.5 0.9
-0.1 -0.7 -0.6 -1.8 1.9 0.2
-1.4 0.0 -1.2 1.7 -1.1 -0.0
1.4 1.2 0.9 -0.7 -0.8 0.3
0.1 -0.1 -0.9 -0.5 1.4 -2.0
-0.6 -0.2 0.6 1.3 -1.5 0.1
-0.2 0.5 0.1 0.4 -0.6 -1.0
0.8
Chi-square with 42 degrees of freedom:40.641096
z-score=-0.148269, p-value=0.469359
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_01:31
Test no p-value
1 0.891307
2 0.277281
3 0.001699
4 0.704321
5 0.482007
6 0.078481
7 0.889815
8 0.561286
9 0.146865
10 0.534469
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.665374
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_01:31:
(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 66914 0.92 66793 0.24
3 25000.00 24825 1.23 25105 0.44
4 6666.67 6668 0.00 6455 6.72
5 1388.89 1342 1.58 1368 0.31
6 238.10 206 4.33 242 0.06
7 34.72 39 0.53 33 0.09
8 4.96 5 0.00 3 0.77
p=0.80140 p=0.80508
Number of rngs required: 688775, p-value: 0.666
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_01:31
No. of wins: Observed Expected
98337 98585.9
z-score=-1.113, pvalue=0.13285
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66897 66666.7 0.796 0.796
2 37390 37654.3 1.855 2.651
3 27179 26954.7 1.866 4.517
4 19219 19313.5 0.462 4.979
5 13970 13851.4 1.015 5.994
6 9975 9943.5 0.100 6.094
7 7189 7145.0 0.271 6.365
8 5049 5139.1 1.579 7.943
9 3563 3699.9 5.063 13.006
10 2615 2666.3 0.987 13.993
11 1965 1923.3 0.903 14.896
12 1359 1388.7 0.637 15.533
13 1022 1003.7 0.333 15.866
14 738 726.1 0.194 16.060
15 532 525.8 0.072 16.132
16 371 381.2 0.270 16.402
17 275 276.5 0.009 16.411
18 180 200.8 2.160 18.571
19 139 146.0 0.334 18.905
20 98 106.2 0.635 19.541
21 275 287.1 0.511 20.052
Chisq= 20.05 for 20 degrees of freedom, p= 0.54531
SUMMARY of craptest
p-value for no. of wins: 0.132845
p-value for throws/game: 0.545308
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_01:31
No. of wins: Observed Expected
98845 98585.9
z-score= 1.159, pvalue=0.87678
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66662 66666.7 0.000 0.000
2 37439 37654.3 1.231 1.232
3 27293 26954.7 4.245 5.477
4 19195 19313.5 0.727 6.203
5 13819 13851.4 0.076 6.279
6 9842 9943.5 1.037 7.316
7 7210 7145.0 0.591 7.907
8 5109 5139.1 0.176 8.083
9 3637 3699.9 1.068 9.151
10 2656 2666.3 0.040 9.191
11 1961 1923.3 0.738 9.929
12 1396 1388.7 0.038 9.967
13 1066 1003.7 3.865 13.832
14 734 726.1 0.085 13.917
15 528 525.8 0.009 13.926
16 426 381.2 5.277 19.203
17 282 276.5 0.108 19.311
18 213 200.8 0.737 20.048
19 143 146.0 0.061 20.109
20 114 106.2 0.571 20.680
21 275 287.1 0.511 21.191
Chisq= 21.19 for 20 degrees of freedom, p= 0.61403
SUMMARY of craptest
p-value for no. of wins: 0.876778
p-value for throws/game: 0.614035
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0017,0.0052,0.0077,0.0088,0.0167,0.0234,0.0248,0.0406,0.0424,
0.0454,0.0462,0.0472,0.0490,0.0501,0.0554,0.0592,0.0617,0.0726,0.0731,
0.0765,0.0785,0.0813,0.0854,0.0891,0.0897,0.0930,0.0937,0.0939,0.0951,
0.0978,0.0984,0.1017,0.1021,0.1051,0.1080,0.1125,0.1195,0.1202,0.1203,
0.1226,0.1237,0.1266,0.1328,0.1366,0.1366,0.1391,0.1419,0.1448,0.1469,
0.1542,0.1547,0.1559,0.1576,0.1576,0.1584,0.1612,0.1680,0.1701,0.1708,
0.1777,0.1839,0.1874,0.1897,0.1992,0.2001,0.2035,0.2057,0.2146,0.2195,
0.2204,0.2289,0.2294,0.2299,0.2348,0.2366,0.2458,0.2504,0.2511,0.2605,
0.2635,0.2685,0.2764,0.2773,0.2796,0.2830,0.2855,0.2933,0.2993,0.3091,
0.3094,0.3130,0.3169,0.3203,0.3207,0.3275,0.3286,0.3305,0.3402,0.3415,
0.3488,0.3546,0.3560,0.3569,0.3620,0.3654,0.3671,0.3681,0.4082,0.4088,
0.4094,0.4118,0.4164,0.4193,0.4224,0.4228,0.4236,0.4264,0.4275,0.4510,
0.4510,0.4512,0.4569,0.4586,0.4601,0.4633,0.4693,0.4694,0.4726,0.4752,
0.4786,0.4820,0.4829,0.4894,0.4917,0.4923,0.4926,0.5031,0.5044,0.5160,
0.5182,0.5185,0.5232,0.5238,0.5257,0.5267,0.5340,0.5345,0.5348,0.5372,
0.5450,0.5451,0.5453,0.5454,0.5475,0.5555,0.5571,0.5571,0.5581,0.5613,
0.5631,0.5642,0.5685,0.5692,0.5709,0.5733,0.5735,0.5748,0.5772,0.5801,
0.5809,0.5819,0.5867,0.5896,0.5963,0.5974,0.6017,0.6133,0.6135,0.6140,
0.6173,0.6383,0.6394,0.6496,0.6550,0.6613,0.6649,0.6654,0.6659,0.6663,
0.6666,0.6686,0.6783,0.6791,0.6844,0.6909,0.6917,0.6962,0.7011,0.7022,
0.7043,0.7043,0.7044,0.7138,0.7140,0.7171,0.7221,0.7251,0.7272,0.7347,
0.7348,0.7439,0.7440,0.7479,0.7518,0.7533,0.7578,0.7585,0.7632,0.7652,
0.7672,0.7675,0.7675,0.7747,0.7793,0.7806,0.7844,0.7902,0.7909,0.7956,
0.7961,0.8014,0.8051,0.8107,0.8157,0.8179,0.8180,0.8228,0.8256,0.8265,
0.8410,0.8419,0.8488,0.8607,0.8697,0.8768,0.8772,0.8774,0.8785,0.8860,
0.8871,0.8898,0.8913,0.8933,0.8988,0.9025,0.9149,0.9184,0.9208,0.9257,
0.9271,0.9353,0.9408,0.9586,0.9827,0.9829,0.9875,0.9925,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.068335
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.