RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.83 26.7264 0.937795
2 to 25 15.56 21.3887 0.790615
3 to 26 15.88 20.0960 0.730654
4 to 27 15.78 16.3210 0.498795
5 to 28 15.43 25.2059 0.909804
6 to 29 15.28 31.9459 0.984717
7 to 30 15.55 16.7464 0.528328
8 to 31 15.59 32.8043 0.988067
9 to 32 15.99 18.2606 0.627417
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.003850
Tough bday spacings test for dh-ranFile-2018-07-04_09:31: 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 5 34 69 106 96 81 41 36 23 6 3
(O-E)^2/E 1.9 0.2 0.2 0.7 0.0 0.1 2.4 1.3 4.4 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 11.595, p= 0.687
RESULTS OF GCD FOR dh-ranFile-2018-07-04_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.141606
p-value, dist. of gcd's: 0.378823
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.189 0.241 0.037 0.559 0.198 0.347 0.343 0.847
Bits 8 to 15---> 0.584 0.652 0.281 0.928 0.105 0.461 0.942 0.029
Bits 16 to 23---> 0.138 0.742 0.217 0.035 0.774 0.985 0.598 0.535
Bits 24 to 31---> 0.447 0.465 0.362 0.109 0.309 0.842 0.342 0.321
KS test for the above 32 p values: 0.629
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_09:31,
p-values for 5 runs: 0.4157, 0.1309, 0.3714, 0.3893, 0.5954
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5084 5134.0 0.487 0.586
r= 30 23174 23103.0 0.218 0.804
r= 31 11526 11551.5 0.056 0.861
chi-square = 0.861 with df = 3; p-value = 0.165
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 168 211.4 8.917 8.917
r= 30 5230 5134.0 1.795 10.711
r= 31 23165 23103.0 0.166 10.877
r= 32 11437 11551.5 1.135 12.013
chi-square = 12.013 with df = 3; p-value = 0.993
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_09:31
b-rank test for bits 1 to 8, p=0.59080
b-rank test for bits 2 to 9, p=0.57220
b-rank test for bits 3 to 10, p=0.01904
b-rank test for bits 4 to 11, p=0.76129
b-rank test for bits 5 to 12, p=0.66544
b-rank test for bits 6 to 13, p=0.85556
b-rank test for bits 7 to 14, p=0.02627
b-rank test for bits 8 to 15, p=0.77184
b-rank test for bits 9 to 16, p=0.28234
b-rank test for bits 10 to 17, p=0.79081
b-rank test for bits 11 to 18, p=0.16493
b-rank test for bits 12 to 19, p=0.45261
b-rank test for bits 13 to 20, p=0.41922
b-rank test for bits 14 to 21, p=0.48351
b-rank test for bits 15 to 22, p=0.76437
b-rank test for bits 16 to 23, p=0.77668
b-rank test for bits 17 to 24, p=0.71584
b-rank test for bits 18 to 25, p=0.36902
b-rank test for bits 19 to 26, p=0.40063
b-rank test for bits 20 to 27, p=0.91758
b-rank test for bits 21 to 28, p=0.02553
b-rank test for bits 22 to 29, p=0.25822
b-rank test for bits 23 to 30, p=0.57597
b-rank test for bits 24 to 31, p=0.34487
b-rank test for bits 25 to 32, p=0.46505
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 = 0.611774
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_09:31
(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 142580 1.57 0.941441
2 142162 0.59 0.722522
3 142975 2.49 0.993611
4 141809 -0.23 0.407331
5 142323 0.97 0.833108
6 141952 0.10 0.539707
7 141435 -1.11 0.133877
8 142347 1.02 0.846750
9 142365 1.06 0.856483
10 142149 0.56 0.712252
11 141713 -0.46 0.323219
12 141848 -0.14 0.443029
13 142150 0.56 0.713049
14 142291 0.89 0.813737
15 141786 -0.29 0.386614
16 142363 1.06 0.855422
17 141903 -0.01 0.494100
18 142273 0.85 0.802253
19 141902 -0.02 0.493168
20 141733 -0.41 0.340175
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_09:31
Bits used No. missing words z-score p-value
23 to 32 141502 -1.4046 0.080072
22 to 31 141567 -1.1804 0.118911
21 to 30 141558 -1.2115 0.112855
20 to 29 142058 0.5127 0.695904
19 to 28 142158 0.8575 0.804411
18 to 27 141949 0.1368 0.554403
17 to 26 142317 1.4058 0.920102
16 to 25 141841 -0.2356 0.406864
15 to 24 141926 0.0575 0.522920
14 to 23 141701 -0.7184 0.236262
13 to 22 141734 -0.6046 0.272727
12 to 21 141881 -0.0977 0.461089
11 to 20 141792 -0.4046 0.342891
10 to 19 142585 2.3299 0.990094
9 to 18 141772 -0.4736 0.317910
8 to 17 142455 1.8816 0.970056
7 to 16 141767 -0.4908 0.311786
6 to 15 141853 -0.1942 0.422994
5 to 14 141977 0.2333 0.592253
4 to 13 141630 -0.9632 0.167722
3 to 12 141628 -0.9701 0.165998
2 to 11 142087 0.6127 0.729948
1 to 10 142058 0.5127 0.695904
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_09:31
Bits used No. missing words z-score p-value
28 to 32 141739 -0.5774 0.281838
27 to 31 142014 0.3548 0.638635
26 to 30 141506 -1.3672 0.085778
25 to 29 141764 -0.4926 0.311132
24 to 28 141991 0.2768 0.609051
23 to 27 141863 -0.1571 0.437602
22 to 26 141492 -1.4147 0.078581
21 to 25 141723 -0.6316 0.263815
20 to 24 142320 1.3921 0.918054
19 to 23 142153 0.8260 0.795598
18 to 22 141989 0.2701 0.606446
17 to 21 142290 1.2904 0.901545
16 to 20 141637 -0.9232 0.177964
15 to 19 141410 -1.6926 0.045262
14 to 18 141728 -0.6147 0.269384
13 to 17 141519 -1.3232 0.092892
12 to 16 141984 0.2531 0.599912
11 to 15 141925 0.0531 0.521181
10 to 14 141745 -0.5571 0.288746
9 to 13 142201 0.9887 0.838598
8 to 12 141739 -0.5774 0.281838
7 to 11 141429 -1.6282 0.051737
6 to 10 141673 -0.8011 0.211532
5 to 9 141953 0.1480 0.558842
4 to 8 142238 1.1141 0.867390
3 to 7 141945 0.1209 0.548121
2 to 6 142085 0.5955 0.724243
1 to 5 142335 1.4429 0.925483
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_09:31
Bits used No. missing words z-score p-value
31 to 32 142528 1.8250 0.965998
30 to 31 141579 -0.9744 0.164923
29 to 30 141693 -0.6381 0.261691
28 to 29 142522 1.8073 0.964641
27 to 28 142034 0.3678 0.643473
26 to 27 141982 0.2144 0.584869
25 to 26 142287 1.1141 0.867376
24 to 25 141770 -0.4110 0.340535
23 to 24 141623 -0.8446 0.199158
22 to 23 141777 -0.3904 0.348137
21 to 22 141531 -1.1160 0.132207
20 to 21 141775 -0.3963 0.345959
19 to 20 141901 -0.0246 0.490198
18 to 19 142377 1.3796 0.916139
17 to 18 142036 0.3737 0.645671
16 to 17 141884 -0.0747 0.470219
15 to 16 141520 -1.1485 0.125388
14 to 15 141533 -1.1101 0.133474
13 to 14 142319 1.2085 0.886566
12 to 13 142389 1.4150 0.921459
11 to 12 141548 -1.0659 0.143241
10 to 11 142289 1.1200 0.868637
9 to 10 141490 -1.2370 0.108051
8 to 9 141926 0.0492 0.519610
7 to 8 141773 -0.4022 0.343786
6 to 7 142089 0.5300 0.701944
5 to 6 142503 1.7512 0.960048
4 to 5 142169 0.7660 0.778158
3 to 4 141941 0.0934 0.537216
2 to 3 142024 0.3383 0.632416
1 to 2 142356 1.3176 0.906183
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2503.43 0.049 0.519350
Test results for specific bytes for dh-ranFile-2018-07-04_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2554.52 0.771 0.779642
2 to 9 2516.37 0.231 0.591531
3 to 10 2576.83 1.087 0.861385
4 to 11 2379.55 -1.703 0.044246
5 to 12 2482.37 -0.249 0.401572
6 to 13 2569.26 0.979 0.836319
7 to 14 2454.80 -0.639 0.261354
8 to 15 2470.83 -0.413 0.339964
9 to 16 2572.21 1.021 0.846411
10 to 17 2547.48 0.671 0.749039
11 to 18 2581.46 1.152 0.875356
12 to 19 2536.92 0.522 0.699228
13 to 20 2481.18 -0.266 0.395071
14 to 21 2554.59 0.772 0.779939
15 to 22 2432.07 -0.961 0.168364
16 to 23 2555.28 0.782 0.782828
17 to 24 2596.29 1.362 0.913364
18 to 25 2544.75 0.633 0.736594
19 to 26 2573.06 1.033 0.849251
20 to 27 2575.42 1.067 0.856934
21 to 28 2415.60 -1.194 0.116323
22 to 29 2575.96 1.074 0.858626
23 to 30 2483.16 -0.238 0.405899
24 to 31 2608.90 1.540 0.938223
25 to 32 2361.23 -1.963 0.024851
CDPARK for dh-ranFile-2018-07-04_09:31: 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
3494 -1.3242 0.092718
3499 -1.0959 0.136563
3498 -1.1416 0.126820
3539 0.7306 0.767486
3547 1.0959 0.863437
3521 -0.0913 0.463617
3517 -0.2740 0.392053
3540 0.7763 0.781201
3492 -1.4155 0.078457
3507 -0.7306 0.232514
Square side=100, avg. no. parked=3515.40 sample std.=19.60
p-value of the KSTEST for those 10 p-values: 0.305852
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_09:31
0.4992,0.0180,0.6015,0.3321,0.2388,0.6282,0.8745,0.8814,0.5385,0.4358,
The KS test for those 10 p-values: 0.872794
The 3DSPHERES test for dh-ranFile-2018-07-04_09:31
sample no r^3 equiv. uni.
1 6.915 0.205864
2 35.399 0.692712
3 30.264 0.635343
4 45.155 0.778023
5 10.557 0.296638
6 46.107 0.784953
7 34.877 0.687318
8 12.875 0.348941
9 10.429 0.293639
10 3.913 0.122283
11 83.601 0.938375
12 5.808 0.176015
13 9.999 0.283456
14 21.196 0.506655
15 14.608 0.385483
16 7.257 0.214875
17 8.588 0.248939
18 20.198 0.489957
19 44.326 0.771799
20 38.658 0.724341
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.556916
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 1.8 0.1 0.8 0.5 -0.6
-2.0 -0.1 -1.0 -1.0 -0.3 -2.1
0.1 1.2 1.8 -1.2 1.9 0.2
-1.2 0.4 0.7 -0.9 -0.6 0.4
-0.5 1.3 -0.9 -0.0 1.0 -2.1
1.5 1.2 0.8 -0.4 1.3 1.0
0.0 -0.4 -0.4 0.4 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:44.598644
z-score=0.283535, p-value=0.636960
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_09:31
Test no p-value
1 0.313168
2 0.000090
3 0.426837
4 0.342476
5 0.161794
6 0.450943
7 0.060410
8 0.467830
9 0.059376
10 0.168234
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004524
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_09:31:
(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 66432 0.83 66577 0.12
3 25000.00 25161 1.04 25001 0.00
4 6666.67 6720 0.43 6773 1.70
5 1388.89 1417 0.57 1343 1.52
6 238.10 236 0.02 254 1.06
7 34.72 28 1.30 46 3.66
8 4.96 5 0.00 5 0.00
p=0.34738 p=0.76628
Number of rngs required: 688751, p-value: 0.656
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_09:31
No. of wins: Observed Expected
98596 98585.9
z-score= 0.045, pvalue=0.51809
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66795 66666.7 0.247 0.247
2 37246 37654.3 4.428 4.675
3 27131 26954.7 1.153 5.828
4 19336 19313.5 0.026 5.854
5 13684 13851.4 2.024 7.877
6 10129 9943.5 3.459 11.336
7 7096 7145.0 0.336 11.673
8 5254 5139.1 2.570 14.243
9 3672 3699.9 0.210 14.453
10 2641 2666.3 0.240 14.693
11 1869 1923.3 1.535 16.227
12 1394 1388.7 0.020 16.247
13 963 1003.7 1.652 17.899
14 751 726.1 0.851 18.750
15 530 525.8 0.033 18.783
16 426 381.2 5.277 24.060
17 286 276.5 0.324 24.384
18 230 200.8 4.237 28.621
19 147 146.0 0.007 28.628
20 131 106.2 5.783 34.411
21 289 287.1 0.012 34.424
Chisq= 34.42 for 20 degrees of freedom, p= 0.97660
SUMMARY of craptest
p-value for no. of wins: 0.518089
p-value for throws/game: 0.976603
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_09:31
No. of wins: Observed Expected
98377 98585.9
z-score=-0.934, pvalue=0.17512
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66473 66666.7 0.563 0.563
2 37690 37654.3 0.034 0.596
3 27108 26954.7 0.871 1.468
4 19255 19313.5 0.177 1.645
5 13723 13851.4 1.191 2.835
6 9962 9943.5 0.034 2.870
7 7194 7145.0 0.336 3.205
8 5198 5139.1 0.676 3.881
9 3734 3699.9 0.315 4.196
10 2664 2666.3 0.002 4.198
11 1977 1923.3 1.498 5.696
12 1353 1388.7 0.920 6.616
13 1006 1003.7 0.005 6.621
14 722 726.1 0.024 6.644
15 506 525.8 0.748 7.393
16 417 381.2 3.372 10.764
17 279 276.5 0.022 10.786
18 190 200.8 0.584 11.370
19 154 146.0 0.440 11.810
20 106 106.2 0.000 11.811
21 289 287.1 0.012 11.823
Chisq= 11.82 for 20 degrees of freedom, p= 0.07798
SUMMARY of craptest
p-value for no. of wins: 0.175117
p-value for throws/game: 0.077977
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0038,0.0045,0.0180,0.0190,0.0249,0.0255,0.0263,0.0291,0.0346,
0.0370,0.0442,0.0453,0.0517,0.0594,0.0604,0.0780,0.0785,0.0786,0.0801,
0.0858,0.0927,0.0929,0.1047,0.1081,0.1090,0.1129,0.1163,0.1189,0.1223,
0.1254,0.1268,0.1309,0.1322,0.1335,0.1339,0.1366,0.1379,0.1416,0.1432,
0.1618,0.1649,0.1649,0.1651,0.1660,0.1677,0.1682,0.1684,0.1751,0.1760,
0.1780,0.1895,0.1981,0.1992,0.2059,0.2115,0.2149,0.2172,0.2325,0.2363,
0.2388,0.2411,0.2489,0.2582,0.2614,0.2617,0.2638,0.2694,0.2727,0.2809,
0.2818,0.2818,0.2823,0.2835,0.2887,0.2936,0.2966,0.3059,0.3093,0.3111,
0.3118,0.3132,0.3179,0.3206,0.3232,0.3321,0.3400,0.3402,0.3405,0.3422,
0.3425,0.3429,0.3429,0.3438,0.3449,0.3460,0.3468,0.3474,0.3481,0.3489,
0.3619,0.3690,0.3714,0.3788,0.3855,0.3866,0.3893,0.3921,0.3951,0.4006,
0.4016,0.4059,0.4069,0.4073,0.4157,0.4192,0.4230,0.4268,0.4358,0.4376,
0.4430,0.4466,0.4509,0.4526,0.4611,0.4614,0.4636,0.4648,0.4651,0.4678,
0.4702,0.4835,0.4900,0.4902,0.4932,0.4941,0.4988,0.4992,0.5067,0.5181,
0.5193,0.5196,0.5212,0.5229,0.5283,0.5351,0.5372,0.5385,0.5397,0.5481,
0.5544,0.5569,0.5587,0.5588,0.5722,0.5760,0.5839,0.5849,0.5908,0.5915,
0.5923,0.5954,0.5979,0.5999,0.6015,0.6064,0.6091,0.6118,0.6274,0.6282,
0.6292,0.6324,0.6353,0.6370,0.6386,0.6435,0.6457,0.6521,0.6557,0.6654,
0.6869,0.6873,0.6927,0.6959,0.6959,0.6992,0.7019,0.7123,0.7130,0.7158,
0.7225,0.7242,0.7243,0.7299,0.7307,0.7366,0.7421,0.7490,0.7613,0.7644,
0.7663,0.7675,0.7718,0.7718,0.7738,0.7767,0.7780,0.7782,0.7796,0.7799,
0.7812,0.7828,0.7850,0.7906,0.7908,0.7956,0.8023,0.8044,0.8137,0.8331,
0.8363,0.8386,0.8421,0.8464,0.8467,0.8468,0.8493,0.8554,0.8556,0.8565,
0.8569,0.8586,0.8614,0.8634,0.8674,0.8674,0.8686,0.8728,0.8745,0.8754,
0.8814,0.8866,0.9015,0.9062,0.9098,0.9134,0.9161,0.9176,0.9181,0.9201,
0.9215,0.9255,0.9277,0.9378,0.9382,0.9384,0.9414,0.9421,0.9600,0.9646,
0.9660,0.9701,0.9766,0.9847,0.9850,0.9881,0.9901,0.9927,0.9936,
Overall p-value after applying KStest on 269 p-values = 0.990404
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.