RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_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 15.76 14.8723 0.395318
2 to 25 15.92 15.9468 0.472391
3 to 26 16.28 13.1632 0.274804
4 to 27 15.77 15.3034 0.426362
5 to 28 15.56 30.4127 0.976482
6 to 29 15.99 14.6822 0.381637
7 to 30 15.70 15.0228 0.406163
8 to 31 15.66 20.7127 0.760595
9 to 32 15.90 23.5641 0.868228
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.455039
Tough bday spacings test for dh-ranFile-2018-07-10_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 12 39 77 96 95 82 36 35 17 7 4
(O-E)^2/E 0.9 0.2 0.2 0.0 0.1 0.2 5.0 0.9 0.3 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.735, p= 0.345
RESULTS OF GCD FOR dh-ranFile-2018-07-10_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.552854
p-value, dist. of gcd's: 0.391117
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.550 0.391 0.178 0.641 0.431 0.411 0.363 0.228
Bits 8 to 15---> 0.254 0.556 0.956 0.380 0.317 0.295 0.847 0.302
Bits 16 to 23---> 0.379 0.531 0.004 0.946 0.889 0.647 0.402 0.235
Bits 24 to 31---> 0.404 0.911 0.456 0.484 0.019 0.501 0.631 0.070
KS test for the above 32 p values: 0.765
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_20:31,
p-values for 5 runs: 0.3186, 0.6389, 0.2253, 0.9137, 0.5488
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 194 211.4 1.435 1.435
r= 29 5044 5134.0 1.578 3.013
r= 30 23247 23103.0 0.897 3.910
r= 31 11515 11551.5 0.115 4.026
chi-square = 4.026 with df = 3; p-value = 0.741
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5155 5134.0 0.086 0.225
r= 31 23062 23103.0 0.073 0.298
r= 32 11577 11551.5 0.056 0.354
chi-square = 0.354 with df = 3; p-value = 0.050
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_20:31
b-rank test for bits 1 to 8, p=0.17541
b-rank test for bits 2 to 9, p=0.62612
b-rank test for bits 3 to 10, p=0.92138
b-rank test for bits 4 to 11, p=0.17823
b-rank test for bits 5 to 12, p=0.02124
b-rank test for bits 6 to 13, p=0.67750
b-rank test for bits 7 to 14, p=0.26092
b-rank test for bits 8 to 15, p=0.76819
b-rank test for bits 9 to 16, p=0.68866
b-rank test for bits 10 to 17, p=0.47479
b-rank test for bits 11 to 18, p=0.69738
b-rank test for bits 12 to 19, p=0.70807
b-rank test for bits 13 to 20, p=0.94897
b-rank test for bits 14 to 21, p=0.08260
b-rank test for bits 15 to 22, p=0.00677
b-rank test for bits 16 to 23, p=0.75103
b-rank test for bits 17 to 24, p=0.27707
b-rank test for bits 18 to 25, p=0.65760
b-rank test for bits 19 to 26, p=0.62778
b-rank test for bits 20 to 27, p=0.93899
b-rank test for bits 21 to 28, p=0.72357
b-rank test for bits 22 to 29, p=0.60721
b-rank test for bits 23 to 30, p=0.73205
b-rank test for bits 24 to 31, p=0.33050
b-rank test for bits 25 to 32, p=0.57212
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 = 0.395613
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_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 142484 1.34 0.910313
2 141181 -1.70 0.044405
3 142346 1.02 0.846197
4 141924 0.03 0.513671
5 141925 0.04 0.514603
6 140770 -2.66 0.003884
7 141352 -1.30 0.096429
8 140792 -2.61 0.004519
9 141700 -0.49 0.312389
10 142155 0.57 0.717015
11 142741 1.94 0.974001
12 141706 -0.48 0.317369
13 142200 0.68 0.751474
14 141783 -0.30 0.383935
15 140719 -2.78 0.002708
16 141683 -0.53 0.298469
17 142207 0.70 0.756626
18 141495 -0.97 0.166507
19 143064 2.70 0.996510
20 142807 2.10 0.982019
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_20:31
Bits used No. missing words z-score p-value
23 to 32 141626 -0.9770 0.164285
22 to 31 141566 -1.1839 0.118227
21 to 30 141261 -2.2356 0.012688
20 to 29 141707 -0.6977 0.242686
19 to 28 141975 0.2264 0.589574
18 to 27 142500 2.0368 0.979165
17 to 26 141852 -0.1977 0.421644
16 to 25 142327 1.4402 0.925100
15 to 24 141831 -0.2701 0.393540
14 to 23 142197 0.9920 0.839393
13 to 22 142020 0.3816 0.648629
12 to 21 142128 0.7540 0.774586
11 to 20 141682 -0.7839 0.216550
10 to 19 141681 -0.7873 0.215540
9 to 18 141638 -0.9356 0.174734
8 to 17 141930 0.0713 0.528411
7 to 16 141569 -1.1736 0.120287
6 to 15 142092 0.6299 0.735619
5 to 14 141838 -0.2460 0.402855
4 to 13 141498 -1.4184 0.078040
3 to 12 141787 -0.4218 0.336575
2 to 11 141822 -0.3011 0.381655
1 to 10 141912 0.0092 0.503673
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_20:31
Bits used No. missing words z-score p-value
28 to 32 141679 -0.7808 0.217466
27 to 31 142041 0.4463 0.672324
26 to 30 141573 -1.1401 0.127122
25 to 29 141797 -0.3808 0.351683
24 to 28 141475 -1.4723 0.070469
23 to 27 141719 -0.6452 0.259403
22 to 26 142064 0.5243 0.699967
21 to 25 141453 -1.5469 0.060946
20 to 24 142208 1.0124 0.844336
19 to 23 142188 0.9446 0.827580
18 to 22 141634 -0.9333 0.175327
17 to 21 141944 0.1175 0.546778
16 to 20 141519 -1.3232 0.092892
15 to 19 142102 0.6531 0.743160
14 to 18 141995 0.2904 0.614248
13 to 17 142474 1.9141 0.972199
12 to 16 141937 0.0938 0.537365
11 to 15 142133 0.7582 0.775835
10 to 14 142241 1.1243 0.869558
9 to 13 141811 -0.3333 0.369446
8 to 12 141961 0.1752 0.569520
7 to 11 142055 0.4938 0.689275
6 to 10 142200 0.9853 0.837767
5 to 9 141326 -1.9774 0.023999
4 to 8 141464 -1.5096 0.065574
3 to 7 141946 0.1243 0.549463
2 to 6 142003 0.3175 0.624578
1 to 5 142078 0.5718 0.716259
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_20:31
Bits used No. missing words z-score p-value
31 to 32 141569 -1.0039 0.157708
30 to 31 141454 -1.3432 0.089611
29 to 30 141892 -0.0511 0.479615
28 to 29 141579 -0.9744 0.164923
27 to 28 142094 0.5447 0.707037
26 to 27 142058 0.4386 0.669508
25 to 26 141612 -0.8771 0.190222
24 to 25 142479 1.6804 0.953564
23 to 24 141736 -0.5113 0.304571
22 to 23 141795 -0.3373 0.367962
21 to 22 141756 -0.4523 0.325526
20 to 21 141967 0.1701 0.567541
19 to 20 142222 0.9223 0.821822
18 to 19 141827 -0.2429 0.404056
17 to 18 141857 -0.1544 0.438661
16 to 17 141626 -0.8358 0.201639
15 to 16 142315 1.1967 0.884282
14 to 15 141737 -0.5083 0.305605
13 to 14 142077 0.4946 0.689559
12 to 13 142349 1.2970 0.902678
11 to 12 141811 -0.2901 0.385886
10 to 11 142364 1.3412 0.910074
9 to 10 141482 -1.2606 0.103734
8 to 9 141695 -0.6322 0.263614
7 to 8 142117 0.6126 0.729928
6 to 7 142109 0.5890 0.722068
5 to 6 142142 0.6863 0.753751
4 to 5 141989 0.2350 0.592901
3 to 4 141419 -1.4464 0.074032
2 to 3 141563 -1.0216 0.153480
1 to 2 141834 -0.2222 0.412074
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2461.49 -0.545 0.293021
Test results for specific bytes for dh-ranFile-2018-07-10_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2623.41 1.745 0.959537
2 to 9 2580.40 1.137 0.872249
3 to 10 2534.67 0.490 0.688029
4 to 11 2504.04 0.057 0.522773
5 to 12 2415.49 -1.195 0.116003
6 to 13 2555.09 0.779 0.782046
7 to 14 2573.73 1.043 0.851469
8 to 15 2423.77 -1.078 0.140502
9 to 16 2480.87 -0.270 0.393391
10 to 17 2521.87 0.309 0.621425
11 to 18 2400.59 -1.406 0.079881
12 to 19 2543.58 0.616 0.731174
13 to 20 2485.00 -0.212 0.415999
14 to 21 2489.00 -0.156 0.438204
15 to 22 2423.99 -1.075 0.141187
16 to 23 2501.74 0.025 0.509811
17 to 24 2533.32 0.471 0.681247
18 to 25 2438.87 -0.865 0.193646
19 to 26 2495.76 -0.060 0.476100
20 to 27 2399.12 -1.427 0.076844
21 to 28 2493.05 -0.098 0.460832
22 to 29 2469.33 -0.434 0.332223
23 to 30 2597.92 1.385 0.916942
24 to 31 2550.78 0.718 0.763653
25 to 32 2592.43 1.307 0.904414
CDPARK for dh-ranFile-2018-07-10_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
3552 1.3242 0.907282
3545 1.0046 0.842447
3508 -0.6849 0.246694
3498 -1.1416 0.126820
3531 0.3653 0.642555
3484 -1.7808 0.037471
3512 -0.5023 0.307734
3541 0.8219 0.794438
3521 -0.0913 0.463617
3528 0.2283 0.590298
Square side=100, avg. no. parked=3522.00 sample std.=20.55
p-value of the KSTEST for those 10 p-values: 0.999253
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_20:31
0.5125,0.1968,0.6221,0.3860,0.5023,0.0608,0.7031,0.7138,0.4726,0.1105,
The KS test for those 10 p-values: 0.507528
The 3DSPHERES test for dh-ranFile-2018-07-10_20:31
sample no r^3 equiv. uni.
1 0.879 0.028860
2 24.619 0.559842
3 12.002 0.329733
4 88.663 0.947944
5 10.397 0.292888
6 9.970 0.282741
7 54.526 0.837572
8 18.330 0.457196
9 6.085 0.183573
10 17.455 0.441133
11 13.233 0.356662
12 2.833 0.090113
13 14.332 0.379812
14 6.434 0.193034
15 10.207 0.288408
16 7.388 0.218285
17 39.753 0.734222
18 0.045 0.001505
19 26.553 0.587332
20 101.785 0.966387
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.206161
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.3 2.0 -0.3 0.6 -0.6
0.5 -0.8 -0.9 0.0 0.5 -0.2
0.7 0.1 -1.1 1.0 -0.5 -0.7
-0.9 0.8 0.7 -1.8 0.4 1.1
1.2 0.2 -0.6 0.6 -0.9 0.5
0.6 1.8 -0.5 -0.9 -0.2 0.2
0.7 3.0 1.3 -1.3 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:41.885587
z-score=-0.012484, p-value=0.524059
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_20:31
Test no p-value
1 0.116068
2 0.648276
3 0.099956
4 0.243605
5 0.780248
6 0.447220
7 0.004024
8 0.212816
9 0.229393
10 0.070877
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.022359
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_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 66689 0.01 66921 0.97
3 25000.00 24961 0.06 24770 2.12
4 6666.67 6680 0.03 6681 0.03
5 1388.89 1373 0.18 1342 1.58
6 238.10 249 0.50 247 0.33
7 34.72 41 1.14 32 0.21
8 4.96 6 0.22 6 0.22
p=0.09265 p=0.51422
Number of rngs required: 687262, p-value: 0.092
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_20:31
No. of wins: Observed Expected
98446 98585.9
z-score=-0.626, pvalue=0.26581
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66638 66666.7 0.012 0.012
2 37855 37654.3 1.070 1.082
3 26704 26954.7 2.332 3.414
4 19215 19313.5 0.502 3.916
5 13763 13851.4 0.564 4.481
6 10044 9943.5 1.015 5.495
7 7097 7145.0 0.323 5.818
8 5155 5139.1 0.049 5.868
9 3854 3699.9 6.421 12.289
10 2641 2666.3 0.240 12.529
11 1939 1923.3 0.128 12.657
12 1388 1388.7 0.000 12.657
13 993 1003.7 0.114 12.771
14 741 726.1 0.304 13.075
15 555 525.8 1.618 14.693
16 380 381.2 0.003 14.696
17 287 276.5 0.396 15.092
18 197 200.8 0.073 15.165
19 166 146.0 2.744 17.909
20 108 106.2 0.030 17.939
21 280 287.1 0.176 18.116
Chisq= 18.12 for 20 degrees of freedom, p= 0.42021
SUMMARY of craptest
p-value for no. of wins: 0.265812
p-value for throws/game: 0.420210
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_20:31
No. of wins: Observed Expected
98805 98585.9
z-score= 0.980, pvalue=0.83649
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66489 66666.7 0.473 0.473
2 37590 37654.3 0.110 0.583
3 26988 26954.7 0.041 0.624
4 19227 19313.5 0.387 1.011
5 13888 13851.4 0.097 1.108
6 9939 9943.5 0.002 1.110
7 7218 7145.0 0.745 1.855
8 5206 5139.1 0.872 2.727
9 3798 3699.9 2.603 5.330
10 2708 2666.3 0.652 5.982
11 1937 1923.3 0.097 6.079
12 1395 1388.7 0.028 6.108
13 954 1003.7 2.462 8.570
14 762 726.1 1.771 10.341
15 496 525.8 1.693 12.034
16 410 381.2 2.184 14.217
17 260 276.5 0.989 15.207
18 183 200.8 1.583 16.790
19 150 146.0 0.110 16.900
20 119 106.2 1.539 18.439
21 283 287.1 0.059 18.498
Chisq= 18.50 for 20 degrees of freedom, p= 0.44536
SUMMARY of craptest
p-value for no. of wins: 0.836489
p-value for throws/game: 0.445356
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0015,0.0027,0.0036,0.0039,0.0040,0.0045,0.0068,0.0127,0.0191,0.0212,
0.0224,0.0240,0.0289,0.0375,0.0444,0.0504,0.0608,0.0609,0.0656,0.0702,
0.0705,0.0709,0.0740,0.0768,0.0780,0.0799,0.0826,0.0896,0.0901,0.0920,
0.0927,0.0929,0.0964,0.1000,0.1037,0.1105,0.1160,0.1161,0.1182,0.1203,
0.1268,0.1271,0.1405,0.1412,0.1535,0.1577,0.1643,0.1649,0.1665,0.1747,
0.1753,0.1754,0.1782,0.1784,0.1836,0.1902,0.1930,0.1936,0.1968,0.2016,
0.2062,0.2128,0.2155,0.2166,0.2175,0.2183,0.2253,0.2281,0.2294,0.2354,
0.2427,0.2436,0.2467,0.2545,0.2594,0.2609,0.2636,0.2658,0.2748,0.2771,
0.2827,0.2884,0.2929,0.2930,0.2946,0.2985,0.3016,0.3046,0.3056,0.3077,
0.3124,0.3174,0.3174,0.3186,0.3255,0.3297,0.3305,0.3322,0.3366,0.3453,
0.3517,0.3567,0.3628,0.3680,0.3694,0.3794,0.3798,0.3798,0.3816,0.3817,
0.3839,0.3859,0.3860,0.3907,0.3911,0.3934,0.3935,0.3953,0.3956,0.4021,
0.4029,0.4041,0.4043,0.4062,0.4113,0.4121,0.4160,0.4202,0.4216,0.4264,
0.4309,0.4382,0.4387,0.4411,0.4454,0.4472,0.4550,0.4562,0.4572,0.4608,
0.4636,0.4724,0.4726,0.4748,0.4761,0.4796,0.4836,0.5011,0.5023,0.5037,
0.5075,0.5098,0.5125,0.5137,0.5142,0.5146,0.5228,0.5241,0.5284,0.5312,
0.5374,0.5468,0.5488,0.5495,0.5497,0.5529,0.5560,0.5598,0.5675,0.5695,
0.5721,0.5873,0.5896,0.5903,0.5929,0.6072,0.6142,0.6214,0.6221,0.6246,
0.6261,0.6278,0.6309,0.6389,0.6411,0.6426,0.6473,0.6483,0.6486,0.6576,
0.6695,0.6723,0.6775,0.6812,0.6880,0.6887,0.6893,0.6896,0.6974,0.7000,
0.7031,0.7070,0.7081,0.7138,0.7163,0.7170,0.7221,0.7236,0.7299,0.7312,
0.7320,0.7342,0.7356,0.7413,0.7432,0.7510,0.7515,0.7538,0.7566,0.7606,
0.7637,0.7649,0.7682,0.7746,0.7758,0.7802,0.7820,0.7944,0.8218,0.8276,
0.8365,0.8376,0.8378,0.8394,0.8424,0.8443,0.8462,0.8475,0.8515,0.8682,
0.8696,0.8722,0.8843,0.8888,0.9027,0.9044,0.9073,0.9101,0.9103,0.9106,
0.9137,0.9169,0.9214,0.9251,0.9390,0.9464,0.9479,0.9490,0.9536,0.9556,
0.9595,0.9664,0.9722,0.9740,0.9765,0.9792,0.9820,0.9965,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.097806
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.