RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.78 20.2554 0.738625
2 to 25 15.80 8.3594 0.041754
3 to 26 15.77 18.7924 0.659424
4 to 27 15.75 24.1397 0.884311
5 to 28 15.81 16.2842 0.496217
6 to 29 15.88 19.3694 0.692256
7 to 30 15.74 23.7031 0.872272
8 to 31 15.84 14.6207 0.377215
9 to 32 15.54 23.2242 0.857906
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.260389
Tough bday spacings test for dh-ranFile-2018-07-10_12:31: 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 7 30 79 98 98 90 50 30 10 5 3
(O-E)^2/E 0.5 1.2 0.4 0.0 0.0 1.8 0.1 0.0 1.6 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.322, p= 0.212
RESULTS OF GCD FOR dh-ranFile-2018-07-10_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.768810
p-value, dist. of gcd's: 0.992805
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.077 0.464 0.083 0.970 0.897 0.836 0.822 0.311
Bits 8 to 15---> 0.738 0.203 0.071 0.949 0.384 0.374 0.202 0.056
Bits 16 to 23---> 0.566 0.162 0.304 0.123 0.603 0.462 0.516 0.567
Bits 24 to 31---> 0.845 0.636 0.382 0.672 0.100 0.435 0.573 0.110
KS test for the above 32 p values: 0.411
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_12:31,
p-values for 5 runs: 0.3707, 0.1209, 0.7289, 0.3857, 0.5387
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5109 5134.0 0.122 0.470
r= 30 22967 23103.0 0.801 1.271
r= 31 11704 11551.5 2.013 3.284
chi-square = 3.284 with df = 3; p-value = 0.650
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 202 211.4 0.420 0.420
r= 30 5087 5134.0 0.430 0.850
r= 31 23094 23103.0 0.004 0.854
r= 32 11617 11551.5 0.371 1.225
chi-square = 1.225 with df = 3; p-value = 0.253
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_12:31
b-rank test for bits 1 to 8, p=0.36632
b-rank test for bits 2 to 9, p=0.14382
b-rank test for bits 3 to 10, p=0.64887
b-rank test for bits 4 to 11, p=0.06885
b-rank test for bits 5 to 12, p=0.69274
b-rank test for bits 6 to 13, p=0.98655
b-rank test for bits 7 to 14, p=0.16393
b-rank test for bits 8 to 15, p=0.23529
b-rank test for bits 9 to 16, p=0.52442
b-rank test for bits 10 to 17, p=0.90046
b-rank test for bits 11 to 18, p=0.15923
b-rank test for bits 12 to 19, p=0.88704
b-rank test for bits 13 to 20, p=0.77990
b-rank test for bits 14 to 21, p=0.57976
b-rank test for bits 15 to 22, p=0.28801
b-rank test for bits 16 to 23, p=0.65232
b-rank test for bits 17 to 24, p=0.60531
b-rank test for bits 18 to 25, p=0.97212
b-rank test for bits 19 to 26, p=0.01346
b-rank test for bits 20 to 27, p=0.86863
b-rank test for bits 21 to 28, p=0.13389
b-rank test for bits 22 to 29, p=0.37262
b-rank test for bits 23 to 30, p=0.60940
b-rank test for bits 24 to 31, p=0.98133
b-rank test for bits 25 to 32, p=0.24098
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 = 0.757054
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_12:31
(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 142009 0.23 0.592070
2 142066 0.37 0.642837
3 141932 0.05 0.521121
4 141808 -0.24 0.406425
5 142121 0.49 0.689543
6 142199 0.68 0.750733
7 142407 1.16 0.877541
8 142717 1.89 0.970425
9 142783 2.04 0.979389
10 142477 1.33 0.907635
11 142086 0.41 0.660116
12 141281 -1.47 0.071044
13 141057 -1.99 0.023217
14 141325 -1.37 0.086086
15 141632 -0.65 0.258503
16 142519 1.42 0.922844
17 141213 -1.63 0.051875
18 142562 1.52 0.936362
19 142524 1.44 0.924519
20 142452 1.27 0.897587
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_12:31
Bits used No. missing words z-score p-value
23 to 32 141814 -0.3287 0.371182
22 to 31 141693 -0.7460 0.227844
21 to 30 141775 -0.4632 0.321608
20 to 29 142044 0.4644 0.678812
19 to 28 141944 0.1196 0.547581
18 to 27 142003 0.3230 0.626652
17 to 26 142035 0.4333 0.667618
16 to 25 142061 0.5230 0.699513
15 to 24 141328 -2.0046 0.022504
14 to 23 142055 0.5023 0.692275
13 to 22 141528 -1.3149 0.094267
12 to 21 141811 -0.3391 0.367279
11 to 20 141844 -0.2253 0.410882
10 to 19 141604 -1.0529 0.146202
9 to 18 142228 1.0989 0.864086
8 to 17 142071 0.5575 0.711401
7 to 16 141917 0.0264 0.510550
6 to 15 141685 -0.7736 0.219598
5 to 14 142015 0.3644 0.642213
4 to 13 141708 -0.6942 0.243765
3 to 12 142291 1.3161 0.905930
2 to 11 141646 -0.9080 0.181930
1 to 10 141776 -0.4598 0.322845
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_12:31
Bits used No. missing words z-score p-value
28 to 32 141963 0.1819 0.572182
27 to 31 142119 0.7107 0.761379
26 to 30 141820 -0.3028 0.381016
25 to 29 141722 -0.6350 0.262709
24 to 28 142035 0.4260 0.664946
23 to 27 141855 -0.1842 0.426940
22 to 26 141841 -0.2316 0.408414
21 to 25 141878 -0.1062 0.457711
20 to 24 142075 0.5616 0.712803
19 to 23 141872 -0.1265 0.449651
18 to 22 141972 0.2124 0.584118
17 to 21 141570 -1.1503 0.125016
16 to 20 141713 -0.6655 0.252857
15 to 19 141634 -0.9333 0.175327
14 to 18 141357 -1.8723 0.030582
13 to 17 142092 0.6192 0.732114
12 to 16 142000 0.3074 0.620714
11 to 15 141899 -0.0350 0.486033
10 to 14 142227 1.0768 0.859226
9 to 13 141723 -0.6316 0.263815
8 to 12 142098 0.6396 0.738770
7 to 11 142294 1.3040 0.903877
6 to 10 141588 -1.0893 0.138021
5 to 9 141247 -2.2452 0.012378
4 to 8 141871 -0.1299 0.448310
3 to 7 142473 1.9107 0.971981
2 to 6 142062 0.5175 0.697605
1 to 5 142301 1.3277 0.907861
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_12:31
Bits used No. missing words z-score p-value
31 to 32 141426 -1.4258 0.076970
30 to 31 142294 1.1347 0.871754
29 to 30 141845 -0.1898 0.424747
28 to 29 141130 -2.2989 0.010755
27 to 28 141829 -0.2370 0.406343
26 to 27 141981 0.2114 0.583719
25 to 26 142046 0.4032 0.656583
24 to 25 141866 -0.1278 0.449147
23 to 24 141998 0.2616 0.603171
22 to 23 141706 -0.5998 0.274322
21 to 22 141588 -0.9479 0.171596
20 to 21 141907 -0.0069 0.497258
19 to 20 141867 -0.1249 0.450314
18 to 19 142020 0.3265 0.627962
17 to 18 142132 0.6568 0.744359
16 to 17 142742 2.4563 0.992980
15 to 16 142019 0.3235 0.626846
14 to 15 141894 -0.0452 0.481966
13 to 14 141999 0.2645 0.604308
12 to 13 141902 -0.0216 0.491375
11 to 12 142007 0.2881 0.613370
10 to 11 142276 1.0816 0.860290
9 to 10 142155 0.7247 0.765679
8 to 9 142170 0.7689 0.779035
7 to 8 141770 -0.4110 0.340535
6 to 7 142042 0.3914 0.652233
5 to 6 141576 -0.9833 0.162736
4 to 5 142195 0.8427 0.800298
3 to 4 142497 1.7335 0.958500
2 to 3 141991 0.2409 0.595189
1 to 2 141467 -1.3048 0.095979
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2428.02 -1.018 0.154336
Test results for specific bytes for dh-ranFile-2018-07-10_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2701.62 2.851 0.997823
2 to 9 2431.85 -0.964 0.167584
3 to 10 2405.94 -1.330 0.091728
4 to 11 2422.21 -1.100 0.135642
5 to 12 2356.19 -2.034 0.020983
6 to 13 2525.95 0.367 0.643193
7 to 14 2380.76 -1.686 0.045862
8 to 15 2373.28 -1.792 0.036559
9 to 16 2421.19 -1.114 0.132533
10 to 17 2578.90 1.116 0.867761
11 to 18 2597.63 1.381 0.916316
12 to 19 2657.10 2.222 0.986849
13 to 20 2594.27 1.333 0.908770
14 to 21 2498.94 -0.015 0.494010
15 to 22 2407.93 -1.302 0.096454
16 to 23 2384.80 -1.629 0.051634
17 to 24 2391.04 -1.541 0.061662
18 to 25 2577.88 1.101 0.864646
19 to 26 2441.49 -0.827 0.203978
20 to 27 2418.33 -1.155 0.124048
21 to 28 2440.46 -0.842 0.199906
22 to 29 2487.47 -0.177 0.429654
23 to 30 2551.22 0.724 0.765557
24 to 31 2562.85 0.889 0.812943
25 to 32 2418.47 -1.153 0.124447
CDPARK for dh-ranFile-2018-07-10_12:31: 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
3490 -1.5068 0.065925
3538 0.6849 0.753306
3537 0.6393 0.738676
3545 1.0046 0.842447
3527 0.1826 0.572463
3520 -0.1370 0.445521
3496 -1.2329 0.108811
3499 -1.0959 0.136563
3503 -0.9132 0.180558
3527 0.1826 0.572463
Square side=100, avg. no. parked=3518.20 sample std.=18.73
p-value of the KSTEST for those 10 p-values: 0.698812
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_12:31
0.5150,0.2720,0.5618,0.7242,0.1276,0.6073,0.0117,0.3088,0.9193,0.0118,
The KS test for those 10 p-values: 0.303393
The 3DSPHERES test for dh-ranFile-2018-07-10_12:31
sample no r^3 equiv. uni.
1 30.997 0.644142
2 27.105 0.594854
3 20.249 0.490827
4 6.007 0.181457
5 19.978 0.486199
6 42.556 0.757931
7 13.531 0.363028
8 2.114 0.068029
9 9.802 0.278734
10 11.795 0.325074
11 38.373 0.721716
12 38.749 0.725174
13 21.505 0.511696
14 13.037 0.352452
15 84.854 0.940897
16 54.122 0.835369
17 3.057 0.096886
18 6.997 0.208043
19 63.295 0.878742
20 3.398 0.107086
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.974524
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 0.6 -0.5 -0.3 0.3
1.5 -0.2 1.0 -0.2 0.2 -0.5
1.0 0.9 0.6 -0.2 1.6 -1.4
-0.5 -0.9 -0.9 -0.1 -0.3 -0.9
0.1 0.4 0.2 1.0 -0.6 -0.2
-0.1 0.8 -1.7 0.5 0.8 0.6
0.3 -0.4 -0.4 -0.7 0.1 1.0
-0.1
Chi-square with 42 degrees of freedom:23.861175
z-score=-1.979108, p-value=0.010941
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_12:31
Test no p-value
1 0.352810
2 0.058740
3 0.902367
4 0.035068
5 0.332203
6 0.006731
7 0.363994
8 0.912503
9 0.607372
10 0.383838
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.200019
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_12:31:
(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 66690 0.01 66788 0.22
3 25000.00 24945 0.12 24981 0.01
4 6666.67 6707 0.24 6614 0.42
5 1388.89 1345 1.39 1367 0.35
6 238.10 274 5.41 223 0.96
7 34.72 32 0.21 24 3.31
8 4.96 6 0.22 2 1.77
p=0.73156 p=0.68189
Number of rngs required: 688247, p-value: 0.429
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_12:31
No. of wins: Observed Expected
98701 98585.9
z-score= 0.515, pvalue=0.69672
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66756 66666.7 0.120 0.120
2 37551 37654.3 0.284 0.403
3 26696 26954.7 2.484 2.887
4 19315 19313.5 0.000 2.887
5 14019 13851.4 2.027 4.914
6 9876 9943.5 0.459 5.373
7 7219 7145.0 0.766 6.139
8 5168 5139.1 0.163 6.302
9 3669 3699.9 0.257 6.559
10 2567 2666.3 3.698 10.257
11 1981 1923.3 1.729 11.987
12 1442 1388.7 2.043 14.029
13 1024 1003.7 0.410 14.439
14 693 726.1 1.513 15.952
15 529 525.8 0.019 15.971
16 419 381.2 3.759 19.729
17 307 276.5 3.355 23.084
18 219 200.8 1.644 24.728
19 138 146.0 0.437 25.165
20 109 106.2 0.073 25.238
21 303 287.1 0.879 26.117
Chisq= 26.12 for 20 degrees of freedom, p= 0.83802
SUMMARY of craptest
p-value for no. of wins: 0.696716
p-value for throws/game: 0.838017
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_12:31
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 66825 66666.7 0.376 0.376
2 37489 37654.3 0.726 1.102
3 26849 26954.7 0.415 1.517
4 19557 19313.5 3.071 4.588
5 13687 13851.4 1.952 6.539
6 9967 9943.5 0.055 6.595
7 7126 7145.0 0.051 6.645
8 5127 5139.1 0.028 6.674
9 3725 3699.9 0.171 6.844
10 2632 2666.3 0.441 7.286
11 1906 1923.3 0.156 7.442
12 1416 1388.7 0.535 7.977
13 962 1003.7 1.734 9.710
14 795 726.1 6.530 16.240
15 542 525.8 0.497 16.737
16 377 381.2 0.045 16.782
17 254 276.5 1.837 18.620
18 197 200.8 0.073 18.693
19 173 146.0 4.999 23.692
20 125 106.2 3.322 27.014
21 269 287.1 1.143 28.157
Chisq= 28.16 for 20 degrees of freedom, p= 0.89427
SUMMARY of craptest
p-value for no. of wins: 0.649983
p-value for throws/game: 0.894267
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0067,0.0108,0.0109,0.0117,0.0118,0.0124,0.0135,0.0210,0.0225,0.0232,
0.0306,0.0351,0.0366,0.0418,0.0459,0.0516,0.0519,0.0555,0.0587,0.0617,
0.0659,0.0680,0.0689,0.0710,0.0713,0.0766,0.0770,0.0832,0.0861,0.0917,
0.0943,0.0960,0.0965,0.0969,0.1002,0.1071,0.1088,0.1101,0.1209,0.1235,
0.1240,0.1244,0.1250,0.1276,0.1325,0.1339,0.1356,0.1366,0.1380,0.1438,
0.1462,0.1543,0.1592,0.1616,0.1627,0.1639,0.1676,0.1716,0.1753,0.1806,
0.1815,0.1819,0.1999,0.2000,0.2019,0.2027,0.2040,0.2080,0.2125,0.2196,
0.2278,0.2353,0.2410,0.2438,0.2529,0.2529,0.2585,0.2604,0.2627,0.2638,
0.2720,0.2743,0.2787,0.2880,0.3034,0.3037,0.3088,0.3114,0.3216,0.3228,
0.3251,0.3322,0.3405,0.3525,0.3528,0.3630,0.3640,0.3663,0.3673,0.3707,
0.3712,0.3726,0.3735,0.3772,0.3810,0.3822,0.3836,0.3838,0.3857,0.4063,
0.4064,0.4084,0.4109,0.4112,0.4247,0.4269,0.4288,0.4297,0.4351,0.4455,
0.4483,0.4491,0.4497,0.4503,0.4577,0.4616,0.4640,0.4820,0.4860,0.4862,
0.4908,0.4914,0.4940,0.4962,0.4973,0.5106,0.5117,0.5150,0.5165,0.5211,
0.5244,0.5387,0.5476,0.5618,0.5657,0.5669,0.5722,0.5725,0.5725,0.5726,
0.5798,0.5837,0.5841,0.5921,0.5949,0.5952,0.6026,0.6032,0.6043,0.6053,
0.6073,0.6074,0.6094,0.6134,0.6207,0.6267,0.6268,0.6280,0.6358,0.6422,
0.6428,0.6432,0.6441,0.6489,0.6500,0.6501,0.6522,0.6523,0.6566,0.6594,
0.6601,0.6649,0.6676,0.6721,0.6788,0.6819,0.6895,0.6923,0.6923,0.6927,
0.6967,0.6976,0.6988,0.6995,0.7114,0.7128,0.7217,0.7242,0.7252,0.7289,
0.7316,0.7321,0.7375,0.7386,0.7387,0.7388,0.7444,0.7507,0.7533,0.7571,
0.7579,0.7614,0.7656,0.7657,0.7688,0.7790,0.7799,0.8003,0.8129,0.8223,
0.8354,0.8364,0.8380,0.8424,0.8447,0.8579,0.8592,0.8603,0.8641,0.8646,
0.8678,0.8686,0.8718,0.8723,0.8775,0.8787,0.8843,0.8870,0.8943,0.8969,
0.8976,0.9005,0.9024,0.9039,0.9059,0.9076,0.9079,0.9088,0.9125,0.9163,
0.9193,0.9228,0.9245,0.9364,0.9409,0.9489,0.9585,0.9704,0.9704,0.9720,
0.9721,0.9745,0.9794,0.9813,0.9865,0.9868,0.9928,0.9930,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.570647
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.