RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_11:31
(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 22.2347 0.824139
2 to 25 15.95 14.5055 0.368946
3 to 26 15.79 15.9956 0.475852
4 to 27 15.80 9.7395 0.085822
5 to 28 15.89 13.4594 0.295067
6 to 29 16.06 11.9081 0.194333
7 to 30 15.70 16.6495 0.521654
8 to 31 16.01 16.4704 0.509232
9 to 32 15.59 36.7268 0.996336
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.728009
Tough bday spacings test for dh-ranFile-2018-07-07_11:31: 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 42 84 94 86 80 51 25 18 9 1
(O-E)^2/E 0.1 0.8 1.6 0.1 1.4 0.0 0.0 0.8 0.7 0.9 2.3
Birthday Spacings: Sum(O-E)^2/E= 8.629, p= 0.432
RESULTS OF GCD FOR dh-ranFile-2018-07-07_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.363546
p-value, dist. of gcd's: 0.209087
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.476 0.328 0.582 0.803 0.731 0.975 0.714 0.770
Bits 8 to 15---> 0.766 0.601 0.923 0.798 0.934 0.764 0.151 0.419
Bits 16 to 23---> 0.590 0.189 0.566 0.912 0.154 0.302 0.201 0.842
Bits 24 to 31---> 0.730 0.808 0.629 0.352 0.326 0.449 0.188 0.320
KS test for the above 32 p values: 0.801
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_11:31,
p-values for 5 runs: 0.1523, 0.2452, 0.8750, 0.6253, 0.7883
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5117 5134.0 0.056 0.261
r= 30 23043 23103.0 0.156 0.417
r= 31 11622 11551.5 0.430 0.847
chi-square = 0.847 with df = 3; p-value = 0.162
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 193 211.4 1.605 1.605
r= 30 5165 5134.0 0.187 1.792
r= 31 23238 23103.0 0.788 2.580
r= 32 11404 11551.5 1.884 4.464
chi-square = 4.464 with df = 3; p-value = 0.784
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_11:31
b-rank test for bits 1 to 8, p=0.96017
b-rank test for bits 2 to 9, p=0.38758
b-rank test for bits 3 to 10, p=0.11834
b-rank test for bits 4 to 11, p=0.36243
b-rank test for bits 5 to 12, p=0.16795
b-rank test for bits 6 to 13, p=0.22689
b-rank test for bits 7 to 14, p=0.73170
b-rank test for bits 8 to 15, p=0.06391
b-rank test for bits 9 to 16, p=0.56890
b-rank test for bits 10 to 17, p=0.97845
b-rank test for bits 11 to 18, p=0.44733
b-rank test for bits 12 to 19, p=0.58383
b-rank test for bits 13 to 20, p=0.58546
b-rank test for bits 14 to 21, p=0.29662
b-rank test for bits 15 to 22, p=0.93989
b-rank test for bits 16 to 23, p=0.69571
b-rank test for bits 17 to 24, p=0.58137
b-rank test for bits 18 to 25, p=0.36577
b-rank test for bits 19 to 26, p=0.44762
b-rank test for bits 20 to 27, p=0.31341
b-rank test for bits 21 to 28, p=0.24405
b-rank test for bits 22 to 29, p=0.84168
b-rank test for bits 23 to 30, p=0.15857
b-rank test for bits 24 to 31, p=0.30112
b-rank test for bits 25 to 32, p=0.61970
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 = 0.718761
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_11:31
(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 142031 0.28 0.611900
2 142227 0.74 0.771023
3 142291 0.89 0.813737
4 141153 -1.77 0.038604
5 141834 -0.18 0.430145
6 141489 -0.98 0.163030
7 142006 0.23 0.589347
8 141526 -0.90 0.185225
9 141981 0.17 0.566493
10 142270 0.84 0.800298
11 142116 0.48 0.685407
12 142263 0.83 0.795692
13 141826 -0.19 0.422815
14 141968 0.14 0.554516
15 142328 0.98 0.836013
16 141375 -1.25 0.105936
17 142366 1.07 0.857011
18 142460 1.29 0.900885
19 141411 -1.16 0.122147
20 141181 -1.70 0.044405
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_11:31
Bits used No. missing words z-score p-value
23 to 32 141801 -0.3736 0.354369
22 to 31 141618 -1.0046 0.157548
21 to 30 142379 1.6196 0.947336
20 to 29 141422 -1.6804 0.046435
19 to 28 141828 -0.2804 0.389567
18 to 27 142566 2.2644 0.988225
17 to 26 141781 -0.4425 0.329058
16 to 25 141790 -0.4115 0.340359
15 to 24 142031 0.4196 0.662594
14 to 23 142244 1.1540 0.875757
13 to 22 141377 -1.8356 0.033207
12 to 21 142192 0.9747 0.835151
11 to 20 142039 0.4471 0.672612
10 to 19 141420 -1.6873 0.045769
9 to 18 141872 -0.1287 0.448788
8 to 17 141557 -1.2149 0.112196
7 to 16 142200 1.0023 0.841903
6 to 15 141724 -0.6391 0.261389
5 to 14 142130 0.7609 0.776651
4 to 13 142181 0.9368 0.825568
3 to 12 141635 -0.9460 0.172083
2 to 11 142541 2.1782 0.985303
1 to 10 142122 0.7333 0.768326
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_11:31
Bits used No. missing words z-score p-value
28 to 32 141836 -0.2486 0.401844
27 to 31 141900 -0.0316 0.487385
26 to 30 141824 -0.2893 0.386193
25 to 29 141712 -0.6689 0.251775
24 to 28 142101 0.6497 0.742066
23 to 27 141966 0.1921 0.576169
22 to 26 142099 0.6429 0.739872
21 to 25 141954 0.1514 0.560179
20 to 24 142344 1.4735 0.929686
19 to 23 142251 1.1582 0.876610
18 to 22 141742 -0.5672 0.285282
17 to 21 141919 0.0328 0.513075
16 to 20 141587 -1.0926 0.137275
15 to 19 141531 -1.2825 0.099838
14 to 18 142092 0.6192 0.732114
13 to 17 142147 0.8057 0.789781
12 to 16 142127 0.7379 0.769702
11 to 15 142288 1.2836 0.900364
10 to 14 141332 -1.9571 0.025171
9 to 13 141991 0.2768 0.609051
8 to 12 141506 -1.3672 0.085778
7 to 11 141376 -1.8079 0.035311
6 to 10 141371 -1.8248 0.034012
5 to 9 141714 -0.6621 0.253942
4 to 8 141449 -1.5604 0.059328
3 to 7 141713 -0.6655 0.252857
2 to 6 141417 -1.6689 0.047567
1 to 5 141350 -1.8960 0.028978
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_11:31
Bits used No. missing words z-score p-value
31 to 32 142191 0.8309 0.796981
30 to 31 141737 -0.5083 0.305605
29 to 30 141624 -0.8417 0.199983
28 to 29 142252 1.0108 0.843950
27 to 28 141834 -0.2222 0.412074
26 to 27 141729 -0.5319 0.297381
25 to 26 141768 -0.4169 0.338375
24 to 25 141871 -0.1131 0.454988
23 to 24 142068 0.4681 0.680127
22 to 23 141557 -1.0393 0.149328
21 to 22 141842 -0.1986 0.421283
20 to 21 141786 -0.3638 0.358002
19 to 20 142193 0.8368 0.798643
18 to 19 141791 -0.3491 0.363524
17 to 18 141459 -1.3284 0.092022
16 to 17 141713 -0.5791 0.281246
15 to 16 141450 -1.3550 0.087716
14 to 15 142500 1.7424 0.959280
13 to 14 142274 1.0757 0.858974
12 to 13 141732 -0.5231 0.300453
11 to 12 142162 0.7453 0.771967
10 to 11 141647 -0.7738 0.219514
9 to 10 142312 1.1878 0.882547
8 to 9 142484 1.6952 0.954980
7 to 8 142050 0.4150 0.660913
6 to 7 142044 0.3973 0.654411
5 to 6 141881 -0.0836 0.466699
4 to 5 141964 0.1613 0.564059
3 to 4 142188 0.8220 0.794472
2 to 3 142017 0.3176 0.624610
1 to 2 141760 -0.4405 0.329787
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2545.53 0.644 0.740157
Test results for specific bytes for dh-ranFile-2018-07-07_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2466.28 -0.477 0.316717
2 to 9 2321.95 -2.518 0.005902
3 to 10 2588.35 1.249 0.894247
4 to 11 2533.38 0.472 0.681551
5 to 12 2294.38 -2.908 0.001819
6 to 13 2608.36 1.532 0.937299
7 to 14 2552.70 0.745 0.771931
8 to 15 2715.58 3.049 0.998851
9 to 16 2520.01 0.283 0.611419
10 to 17 2438.20 -0.874 0.191058
11 to 18 2368.84 -1.855 0.031802
12 to 19 2391.37 -1.536 0.062246
13 to 20 2497.88 -0.030 0.488015
14 to 21 2498.44 -0.022 0.491227
15 to 22 2581.66 1.155 0.875915
16 to 23 2390.58 -1.547 0.060886
17 to 24 2649.37 2.112 0.982675
18 to 25 2591.75 1.298 0.902786
19 to 26 2508.54 0.121 0.548065
20 to 27 2604.15 1.473 0.929616
21 to 28 2566.74 0.944 0.827392
22 to 29 2487.00 -0.184 0.427075
23 to 30 2480.19 -0.280 0.389679
24 to 31 2411.19 -1.256 0.104577
25 to 32 2535.72 0.505 0.693261
CDPARK for dh-ranFile-2018-07-07_11:31: 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
3545 1.0046 0.842447
3494 -1.3242 0.092718
3508 -0.6849 0.246694
3499 -1.0959 0.136563
3495 -1.2785 0.100530
3531 0.3653 0.642555
3514 -0.4110 0.340551
3524 0.0457 0.518210
3540 0.7763 0.781201
3520 -0.1370 0.445521
Square side=100, avg. no. parked=3517.00 sample std.=17.30
p-value of the KSTEST for those 10 p-values: 0.617206
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_11:31
0.6620,0.1889,0.0363,0.8740,0.9755,0.5164,0.0149,0.5049,0.0845,0.3940,
The KS test for those 10 p-values: 0.423942
The 3DSPHERES test for dh-ranFile-2018-07-07_11:31
sample no r^3 equiv. uni.
1 8.869 0.255939
2 51.948 0.822999
3 0.564 0.018609
4 9.310 0.266797
5 2.160 0.069478
6 45.160 0.778058
7 99.998 0.964323
8 7.895 0.231390
9 33.931 0.677300
10 62.405 0.875092
11 15.213 0.397759
12 19.988 0.486380
13 28.994 0.619581
14 32.571 0.662334
15 5.465 0.166533
16 16.013 0.413617
17 71.135 0.906627
18 39.557 0.732483
19 3.081 0.097587
20 19.703 0.481480
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.999949
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 -1.8 0.0 0.4 0.6
1.2 1.0 1.4 -0.3 0.3 -0.3
-0.5 0.6 -0.0 -0.1 0.2 -1.6
0.7 -0.4 -1.4 0.3 1.1 -0.3
-0.0 -0.1 1.4 -1.1 0.3 0.2
-0.9 -0.3 2.1 0.9 -0.9 -0.1
0.3 1.5 -1.2 1.0 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:31.090199
z-score=-1.190357, p-value=0.107851
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_11:31
Test no p-value
1 0.870081
2 0.052750
3 0.004680
4 0.240123
5 0.274384
6 0.001122
7 0.471034
8 0.461475
9 0.406636
10 0.541746
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.034055
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_11:31:
(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 66459 0.65 66727 0.05
3 25000.00 25077 0.24 25026 0.03
4 6666.67 6776 1.79 6557 1.80
5 1388.89 1383 0.02 1381 0.04
6 238.10 247 0.33 278 6.69
7 34.72 50 6.72 25 2.72
8 4.96 7 0.84 5 0.00
p=0.89840 p=0.92158
Number of rngs required: 688002, p-value: 0.322
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_11:31
No. of wins: Observed Expected
98597 98585.9
z-score= 0.050, pvalue=0.51987
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67004 66666.7 1.707 1.707
2 37487 37654.3 0.744 2.450
3 26828 26954.7 0.596 3.046
4 19310 19313.5 0.001 3.047
5 13811 13851.4 0.118 3.165
6 9932 9943.5 0.013 3.178
7 7114 7145.0 0.135 3.313
8 5198 5139.1 0.676 3.989
9 3844 3699.9 5.615 9.604
10 2549 2666.3 5.160 14.764
11 1924 1923.3 0.000 14.764
12 1364 1388.7 0.441 15.205
13 1014 1003.7 0.105 15.310
14 757 726.1 1.311 16.622
15 497 525.8 1.581 18.203
16 347 381.2 3.060 21.263
17 275 276.5 0.009 21.271
18 195 200.8 0.169 21.441
19 144 146.0 0.027 21.468
20 99 106.2 0.490 21.958
21 307 287.1 1.377 23.335
Chisq= 23.34 for 20 degrees of freedom, p= 0.72736
SUMMARY of craptest
p-value for no. of wins: 0.519871
p-value for throws/game: 0.727362
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_11:31
No. of wins: Observed Expected
98750 98585.9
z-score= 0.734, pvalue=0.76857
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66458 66666.7 0.653 0.653
2 37858 37654.3 1.102 1.755
3 26858 26954.7 0.347 2.102
4 19276 19313.5 0.073 2.175
5 14084 13851.4 3.905 6.080
6 9980 9943.5 0.134 6.214
7 7116 7145.0 0.118 6.332
8 5097 5139.1 0.344 6.676
9 3669 3699.9 0.257 6.933
10 2719 2666.3 1.042 7.975
11 1888 1923.3 0.649 8.624
12 1342 1388.7 1.573 10.197
13 975 1003.7 0.822 11.019
14 759 726.1 1.487 12.506
15 509 525.8 0.539 13.045
16 390 381.2 0.205 13.250
17 283 276.5 0.151 13.401
18 207 200.8 0.190 13.591
19 152 146.0 0.248 13.839
20 101 106.2 0.256 14.095
21 279 287.1 0.229 14.324
Chisq= 14.32 for 20 degrees of freedom, p= 0.18630
SUMMARY of craptest
p-value for no. of wins: 0.768567
p-value for throws/game: 0.186302
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0018,0.0047,0.0059,0.0149,0.0186,0.0252,0.0290,0.0318,0.0332,
0.0340,0.0341,0.0353,0.0363,0.0386,0.0444,0.0458,0.0464,0.0476,0.0527,
0.0593,0.0609,0.0622,0.0639,0.0695,0.0845,0.0858,0.0858,0.0877,0.0920,
0.0927,0.0976,0.0998,0.1005,0.1046,0.1059,0.1079,0.1122,0.1183,0.1221,
0.1366,0.1373,0.1493,0.1514,0.1523,0.1542,0.1575,0.1586,0.1619,0.1630,
0.1665,0.1679,0.1721,0.1852,0.1863,0.1877,0.1888,0.1889,0.1911,0.1943,
0.2000,0.2015,0.2091,0.2195,0.2269,0.2314,0.2401,0.2440,0.2452,0.2467,
0.2518,0.2529,0.2539,0.2559,0.2614,0.2668,0.2744,0.2812,0.2853,0.2951,
0.2966,0.2974,0.3005,0.3011,0.3025,0.3056,0.3134,0.3167,0.3202,0.3220,
0.3260,0.3279,0.3291,0.3298,0.3384,0.3404,0.3406,0.3520,0.3544,0.3580,
0.3624,0.3635,0.3635,0.3658,0.3689,0.3862,0.3876,0.3896,0.3897,0.3940,
0.3978,0.4018,0.4066,0.4121,0.4136,0.4193,0.4213,0.4228,0.4239,0.4271,
0.4301,0.4324,0.4455,0.4473,0.4476,0.4488,0.4492,0.4550,0.4615,0.4667,
0.4710,0.4759,0.4761,0.4815,0.4864,0.4874,0.4880,0.4912,0.5049,0.5092,
0.5131,0.5164,0.5182,0.5199,0.5217,0.5417,0.5481,0.5545,0.5602,0.5641,
0.5661,0.5665,0.5689,0.5762,0.5814,0.5822,0.5838,0.5855,0.5893,0.5902,
0.6007,0.6091,0.6114,0.6119,0.6172,0.6196,0.6197,0.6246,0.6253,0.6286,
0.6426,0.6544,0.6609,0.6620,0.6623,0.6626,0.6726,0.6773,0.6801,0.6816,
0.6854,0.6933,0.6957,0.7135,0.7188,0.7274,0.7280,0.7302,0.7305,0.7317,
0.7321,0.7325,0.7399,0.7402,0.7421,0.7638,0.7656,0.7683,0.7686,0.7697,
0.7700,0.7710,0.7719,0.7720,0.7767,0.7781,0.7812,0.7845,0.7883,0.7898,
0.7945,0.7957,0.7970,0.7984,0.7986,0.8003,0.8005,0.8032,0.8079,0.8137,
0.8230,0.8241,0.8256,0.8274,0.8352,0.8360,0.8417,0.8419,0.8419,0.8424,
0.8440,0.8570,0.8590,0.8701,0.8740,0.8750,0.8751,0.8758,0.8759,0.8766,
0.8825,0.8942,0.8984,0.9004,0.9009,0.9028,0.9066,0.9115,0.9216,0.9233,
0.9296,0.9297,0.9335,0.9373,0.9399,0.9473,0.9550,0.9593,0.9602,0.9643,
0.9751,0.9755,0.9784,0.9827,0.9853,0.9882,0.9963,0.9989,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.794555
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.