RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_22:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.49 20.5121 0.751123
2 to 25 15.76 15.4560 0.437329
3 to 26 15.63 20.7300 0.761401
4 to 27 15.67 16.7734 0.530186
5 to 28 15.79 23.9203 0.878384
6 to 29 15.64 20.2483 0.738274
7 to 30 16.01 16.9028 0.539032
8 to 31 15.67 22.4831 0.833152
9 to 32 15.70 16.1032 0.483471
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.087583
Tough bday spacings test for dh-ranFile-2018-07-08_22:31: 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 10 32 66 108 100 74 50 28 18 9 5
(O-E)^2/E 0.1 0.6 0.7 1.1 0.1 0.2 0.1 0.1 0.7 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 4.663, p= 0.087
RESULTS OF GCD FOR dh-ranFile-2018-07-08_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.741146
p-value, dist. of gcd's: 0.163056
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.342 0.089 0.996 0.439 0.985 0.181 0.313 0.325
Bits 8 to 15---> 0.054 0.143 0.201 0.010 0.197 0.578 0.117 0.197
Bits 16 to 23---> 0.595 0.138 0.088 0.318 0.083 0.442 0.392 0.231
Bits 24 to 31---> 0.697 0.157 0.166 0.619 0.543 0.464 0.865 0.767
KS test for the above 32 p values: 0.990
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_22:31,
p-values for 5 runs: 0.0527, 0.9468, 0.3648, 0.2535, 0.1571
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5167 5134.0 0.212 0.472
r= 30 23061 23103.0 0.077 0.549
r= 31 11568 11551.5 0.024 0.572
chi-square = 0.572 with df = 3; p-value = 0.097
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5152 5134.0 0.063 0.411
r= 31 23134 23103.0 0.041 0.453
r= 32 11494 11551.5 0.286 0.739
chi-square = 0.739 with df = 3; p-value = 0.136
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_22:31
b-rank test for bits 1 to 8, p=0.40742
b-rank test for bits 2 to 9, p=0.50539
b-rank test for bits 3 to 10, p=0.59515
b-rank test for bits 4 to 11, p=0.69477
b-rank test for bits 5 to 12, p=0.70175
b-rank test for bits 6 to 13, p=0.91895
b-rank test for bits 7 to 14, p=0.87701
b-rank test for bits 8 to 15, p=0.65759
b-rank test for bits 9 to 16, p=0.76710
b-rank test for bits 10 to 17, p=0.08261
b-rank test for bits 11 to 18, p=0.59204
b-rank test for bits 12 to 19, p=0.18360
b-rank test for bits 13 to 20, p=0.18062
b-rank test for bits 14 to 21, p=0.76522
b-rank test for bits 15 to 22, p=0.04580
b-rank test for bits 16 to 23, p=0.42014
b-rank test for bits 17 to 24, p=0.57327
b-rank test for bits 18 to 25, p=0.74065
b-rank test for bits 19 to 26, p=0.23331
b-rank test for bits 20 to 27, p=0.36610
b-rank test for bits 21 to 28, p=0.79294
b-rank test for bits 22 to 29, p=0.95926
b-rank test for bits 23 to 30, p=0.71810
b-rank test for bits 24 to 31, p=0.05200
b-rank test for bits 25 to 32, p=0.14797
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 = 0.867360
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_22:31
(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 141825 -0.20 0.421901
2 141882 -0.06 0.474543
3 141505 -0.94 0.172407
4 141775 -0.31 0.376816
5 142885 2.28 0.988684
6 142002 0.22 0.585708
7 141262 -1.51 0.065209
8 141877 -0.08 0.469894
9 141387 -1.22 0.111157
10 141110 -1.87 0.030909
11 141968 0.14 0.554516
12 142266 0.83 0.797674
13 141312 -1.40 0.081413
14 141091 -1.91 0.027939
15 141584 -0.76 0.223592
16 141391 -1.21 0.112938
17 142177 0.63 0.734145
18 142210 0.70 0.758816
19 140910 -2.33 0.009775
20 141739 -0.40 0.345327
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_22:31
Bits used No. missing words z-score p-value
23 to 32 141527 -1.3184 0.093688
22 to 31 142080 0.5885 0.721907
21 to 30 142039 0.4471 0.672612
20 to 29 142122 0.7333 0.768326
19 to 28 142571 2.2816 0.988744
18 to 27 141911 0.0058 0.502297
17 to 26 141956 0.1609 0.563926
16 to 25 141955 0.1575 0.562568
15 to 24 141971 0.2127 0.584202
14 to 23 142115 0.7092 0.760902
13 to 22 142142 0.8023 0.788813
12 to 21 142193 0.9782 0.836006
11 to 20 141718 -0.6598 0.254704
10 to 19 141712 -0.6804 0.248110
9 to 18 141672 -0.8184 0.206570
8 to 17 141511 -1.3736 0.084790
7 to 16 142244 1.1540 0.875757
6 to 15 141901 -0.0287 0.488542
5 to 14 141721 -0.6494 0.258036
4 to 13 142000 0.3127 0.622729
3 to 12 141923 0.0471 0.518798
2 to 11 142293 1.3230 0.907082
1 to 10 142385 1.6402 0.949523
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_22:31
Bits used No. missing words z-score p-value
28 to 32 141764 -0.4926 0.311132
27 to 31 141814 -0.3232 0.373290
26 to 30 141802 -0.3638 0.357992
25 to 29 142100 0.6463 0.740970
24 to 28 142550 2.1718 0.985063
23 to 27 142021 0.3785 0.647486
22 to 26 142319 1.3887 0.917540
21 to 25 142091 0.6158 0.730997
20 to 24 142118 0.7074 0.760327
19 to 23 142260 1.1887 0.882723
18 to 22 141647 -0.8893 0.186933
17 to 21 142227 1.0768 0.859226
16 to 20 141742 -0.5672 0.285282
15 to 19 142046 0.4633 0.678421
14 to 18 141949 0.1345 0.553486
13 to 17 141260 -2.2011 0.013864
12 to 16 142599 2.3379 0.990303
11 to 15 142061 0.5141 0.696421
10 to 14 141670 -0.8113 0.208600
9 to 13 141591 -1.0791 0.140275
8 to 12 141723 -0.6316 0.263815
7 to 11 141719 -0.6452 0.259403
6 to 10 141599 -1.0520 0.146408
5 to 9 142125 0.7311 0.767636
4 to 8 141774 -0.4587 0.323208
3 to 7 141643 -0.9028 0.183312
2 to 6 142576 2.2599 0.988086
1 to 5 141895 -0.0486 0.480629
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_22:31
Bits used No. missing words z-score p-value
31 to 32 141981 0.2114 0.583719
30 to 31 141661 -0.7325 0.231921
29 to 30 142556 1.9076 0.971777
28 to 29 141735 -0.5142 0.303539
27 to 28 142013 0.3058 0.620126
26 to 27 142426 1.5241 0.936258
25 to 26 141782 -0.3756 0.353605
24 to 25 142097 0.5536 0.710073
23 to 24 141811 -0.2901 0.385886
22 to 23 142864 2.8161 0.997570
21 to 22 141449 -1.3579 0.087247
20 to 21 141799 -0.3255 0.372418
19 to 20 141810 -0.2930 0.384758
18 to 19 141817 -0.2724 0.392673
17 to 18 141636 -0.8063 0.210040
16 to 17 141734 -0.5172 0.302509
15 to 16 141317 -1.7473 0.040294
14 to 15 142002 0.2734 0.607713
13 to 14 141883 -0.0777 0.469045
12 to 13 141570 -1.0010 0.158420
11 to 12 142071 0.4769 0.683284
10 to 11 141266 -1.8977 0.028866
9 to 10 141884 -0.0747 0.470219
8 to 9 142080 0.5035 0.692677
7 to 8 142101 0.5654 0.714099
6 to 7 142174 0.7807 0.782522
5 to 6 142172 0.7748 0.780782
4 to 5 141751 -0.4671 0.320232
3 to 4 141704 -0.6057 0.272359
2 to 3 141951 0.1229 0.548915
1 to 2 141844 -0.1927 0.423592
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2580.27 1.135 0.871859
Test results for specific bytes for dh-ranFile-2018-07-08_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2587.48 1.237 0.891977
2 to 9 2453.55 -0.657 0.255608
3 to 10 2536.05 0.510 0.694910
4 to 11 2525.61 0.362 0.641398
5 to 12 2546.21 0.654 0.743286
6 to 13 2505.29 0.075 0.529795
7 to 14 2269.40 -3.261 0.000555
8 to 15 2569.37 0.981 0.836697
9 to 16 2486.64 -0.189 0.425089
10 to 17 2461.29 -0.548 0.292015
11 to 18 2616.93 1.654 0.950893
12 to 19 2421.14 -1.115 0.132384
13 to 20 2463.70 -0.513 0.303841
14 to 21 2454.81 -0.639 0.261394
15 to 22 2426.70 -1.037 0.149948
16 to 23 2350.36 -2.116 0.017160
17 to 24 2532.45 0.459 0.676855
18 to 25 2491.65 -0.118 0.452997
19 to 26 2461.12 -0.550 0.291209
20 to 27 2381.14 -1.681 0.046383
21 to 28 2516.48 0.233 0.592160
22 to 29 2521.29 0.301 0.618342
23 to 30 2661.33 2.282 0.988743
24 to 31 2583.81 1.185 0.882028
25 to 32 2465.54 -0.487 0.313007
CDPARK for dh-ranFile-2018-07-08_22:31: 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
3498 -1.1416 0.126820
3535 0.5479 0.708135
3517 -0.2740 0.392053
3551 1.2785 0.899470
3536 0.5936 0.723613
3504 -0.8676 0.192812
3569 2.1005 0.982156
3534 0.5023 0.692266
3514 -0.4110 0.340551
3515 -0.3653 0.357445
Square side=100, avg. no. parked=3527.30 sample std.=20.78
p-value of the KSTEST for those 10 p-values: 0.867543
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_22:31
0.8204,0.4832,0.6527,0.7703,0.1448,0.3473,0.4336,0.7064,0.2314,0.3293,
The KS test for those 10 p-values: 0.788007
The 3DSPHERES test for dh-ranFile-2018-07-08_22:31
sample no r^3 equiv. uni.
1 20.535 0.495656
2 126.178 0.985093
3 20.140 0.488970
4 108.515 0.973141
5 96.099 0.959373
6 52.936 0.828734
7 20.123 0.488677
8 15.868 0.410759
9 46.483 0.787628
10 0.178 0.005915
11 29.458 0.625411
12 5.145 0.157595
13 4.448 0.137808
14 52.345 0.825324
15 35.864 0.697435
16 3.197 0.101087
17 6.346 0.190668
18 1.537 0.049932
19 15.618 0.405828
20 39.943 0.735901
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.736249
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 -2.3 1.8 0.0 -0.7
-1.4 0.1 -0.1 -0.1 1.6 0.1
0.1 0.6 0.7 -0.8 -0.1 -2.1
0.4 -0.7 -0.2 1.5 -0.6 1.1
0.3 -0.1 1.6 -0.2 0.9 -1.3
-1.1 -2.4 1.5 -1.4 -0.5 1.5
-0.2 -2.0 0.5 -0.7 0.9 0.0
0.8
Chi-square with 42 degrees of freedom:50.245984
z-score=0.899711, p-value=0.820815
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_22:31
Test no p-value
1 0.419814
2 0.144250
3 0.414396
4 0.732318
5 0.334991
6 0.016124
7 0.226223
8 0.199465
9 0.036862
10 0.166701
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.017013
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_22:31:
(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 66544 0.23 66557 0.18
3 25000.00 25190 1.44 25146 0.85
4 6666.67 6666 0.00 6645 0.07
5 1388.89 1343 1.52 1380 0.06
6 238.10 216 2.05 228 0.43
7 34.72 37 0.15 36 0.05
8 4.96 3 0.77 7 0.84
p=0.59457 p=0.12871
Number of rngs required: 688706, p-value: 0.636
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_22:31
No. of wins: Observed Expected
98324 98585.9
z-score=-1.171, pvalue=0.12076
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66327 66666.7 1.731 1.731
2 37623 37654.3 0.026 1.757
3 27035 26954.7 0.239 1.996
4 19420 19313.5 0.588 2.583
5 13805 13851.4 0.156 2.739
6 9968 9943.5 0.060 2.799
7 7078 7145.0 0.629 3.428
8 5379 5139.1 11.202 14.629
9 3743 3699.9 0.503 15.132
10 2694 2666.3 0.288 15.420
11 1844 1923.3 3.272 18.692
12 1413 1388.7 0.424 19.116
13 1027 1003.7 0.540 19.656
14 755 726.1 1.147 20.803
15 498 525.8 1.474 22.277
16 367 381.2 0.525 22.802
17 269 276.5 0.206 23.007
18 214 200.8 0.864 23.871
19 165 146.0 2.477 26.348
20 94 106.2 1.405 27.753
21 282 287.1 0.091 27.844
Chisq= 27.84 for 20 degrees of freedom, p= 0.88685
SUMMARY of craptest
p-value for no. of wins: 0.120762
p-value for throws/game: 0.886855
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_22:31
No. of wins: Observed Expected
98672 98585.9
z-score= 0.385, pvalue=0.64998
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66685 66666.7 0.005 0.005
2 37162 37654.3 6.437 6.442
3 27082 26954.7 0.601 7.043
4 19523 19313.5 2.273 9.316
5 14135 13851.4 5.806 15.122
6 9809 9943.5 1.820 16.942
7 7131 7145.0 0.028 16.970
8 5199 5139.1 0.699 17.669
9 3732 3699.9 0.279 17.948
10 2617 2666.3 0.911 18.859
11 1853 1923.3 2.572 21.431
12 1376 1388.7 0.117 21.548
13 970 1003.7 1.132 22.680
14 757 726.1 1.311 23.992
15 549 525.8 1.020 25.012
16 411 381.2 2.338 27.350
17 248 276.5 2.945 30.295
18 207 200.8 0.190 30.485
19 153 146.0 0.337 30.822
20 115 106.2 0.727 31.549
21 286 287.1 0.004 31.553
Chisq= 31.55 for 20 degrees of freedom, p= 0.95170
SUMMARY of craptest
p-value for no. of wins: 0.649983
p-value for throws/game: 0.951698
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0059,0.0098,0.0104,0.0139,0.0161,0.0170,0.0172,0.0279,0.0289,
0.0309,0.0369,0.0403,0.0458,0.0464,0.0499,0.0520,0.0527,0.0544,0.0652,
0.0814,0.0826,0.0831,0.0848,0.0872,0.0875,0.0876,0.0881,0.0887,0.0937,
0.0973,0.1011,0.1112,0.1129,0.1166,0.1208,0.1268,0.1287,0.1324,0.1361,
0.1378,0.1384,0.1403,0.1433,0.1443,0.1448,0.1464,0.1480,0.1499,0.1567,
0.1571,0.1576,0.1584,0.1631,0.1659,0.1667,0.1724,0.1806,0.1807,0.1833,
0.1836,0.1869,0.1907,0.1928,0.1972,0.1974,0.1995,0.2006,0.2066,0.2086,
0.2100,0.2236,0.2262,0.2306,0.2314,0.2319,0.2333,0.2481,0.2535,0.2547,
0.2556,0.2580,0.2594,0.2614,0.2638,0.2724,0.2853,0.2912,0.2920,0.3025,
0.3035,0.3038,0.3111,0.3128,0.3130,0.3185,0.3202,0.3232,0.3255,0.3293,
0.3350,0.3406,0.3424,0.3453,0.3473,0.3536,0.3574,0.3580,0.3648,0.3661,
0.3724,0.3733,0.3768,0.3848,0.3859,0.3915,0.3921,0.3927,0.4058,0.4074,
0.4108,0.4144,0.4198,0.4201,0.4219,0.4236,0.4251,0.4336,0.4373,0.4392,
0.4418,0.4530,0.4641,0.4690,0.4699,0.4702,0.4745,0.4806,0.4832,0.4835,
0.4885,0.4887,0.4890,0.4957,0.5023,0.5054,0.5188,0.5298,0.5302,0.5390,
0.5425,0.5489,0.5535,0.5545,0.5626,0.5639,0.5733,0.5779,0.5837,0.5842,
0.5857,0.5920,0.5922,0.5946,0.5952,0.5954,0.6077,0.6183,0.6190,0.6201,
0.6227,0.6254,0.6364,0.6414,0.6475,0.6500,0.6527,0.6576,0.6726,0.6769,
0.6784,0.6833,0.6923,0.6927,0.6948,0.6949,0.6964,0.6974,0.6974,0.7017,
0.7064,0.7081,0.7101,0.7141,0.7181,0.7219,0.7236,0.7310,0.7323,0.7341,
0.7359,0.7362,0.7383,0.7407,0.7410,0.7411,0.7433,0.7511,0.7588,0.7603,
0.7609,0.7614,0.7652,0.7671,0.7672,0.7676,0.7683,0.7703,0.7808,0.7825,
0.7876,0.7880,0.7888,0.7929,0.7977,0.8204,0.8208,0.8253,0.8287,0.8332,
0.8360,0.8367,0.8592,0.8653,0.8674,0.8675,0.8719,0.8758,0.8770,0.8784,
0.8820,0.8827,0.8869,0.8920,0.8995,0.9071,0.9175,0.9189,0.9363,0.9468,
0.9495,0.9509,0.9517,0.9593,0.9594,0.9718,0.9731,0.9822,0.9850,0.9851,
0.9851,0.9881,0.9887,0.9887,0.9887,0.9901,0.9903,0.9956,0.9976,
Overall p-value after applying KStest on 269 p-values = 0.265946
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.