RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-08-17_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 15.75 24.6719 0.897703
2 to 25 15.74 24.1307 0.884074
3 to 26 16.06 9.7243 0.085227
4 to 27 15.97 18.3045 0.630122
5 to 28 15.55 19.2021 0.682946
6 to 29 15.86 22.7405 0.842110
7 to 30 15.53 16.7697 0.529929
8 to 31 15.46 43.5453 0.999600
9 to 32 15.47 30.7553 0.978615
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.011428
Tough bday spacings test for dh-ranFile-2018-08-17_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 9 34 90 96 98 72 49 29 16 4 3
(O-E)^2/E 0.0 0.2 3.8 0.0 0.0 0.5 0.2 0.0 0.1 1.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.130, p= 0.196
RESULTS OF GCD FOR dh-ranFile-2018-08-17_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.098191
p-value, dist. of gcd's: 0.906368
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-08-17_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.781 0.962 0.780 0.511 0.638 0.263 0.037 0.185
Bits 8 to 15---> 0.799 0.246 0.837 0.110 0.985 0.421 0.767 0.261
Bits 16 to 23---> 0.635 0.274 0.580 0.399 0.513 0.511 0.841 0.669
Bits 24 to 31---> 0.588 0.865 0.830 0.195 0.770 0.355 0.502 0.501
KS test for the above 32 p values: 0.565
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-08-17_11:31,
p-values for 5 runs: 0.5619, 0.8339, 0.3273, 0.8066, 0.0244
Rank test for binary matrices (31x31) for dh-ranFile-2018-08-17_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 227 211.4 1.148 1.148
r= 29 5147 5134.0 0.033 1.181
r= 30 22946 23103.0 1.068 2.249
r= 31 11680 11551.5 1.429 3.678
chi-square = 3.678 with df = 3; p-value = 0.702
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-08-17_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5174 5134.0 0.311 0.459
r= 31 22960 23103.0 0.886 1.345
r= 32 11649 11551.5 0.823 2.167
chi-square = 2.167 with df = 3; p-value = 0.462
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-08-17_11:31
b-rank test for bits 1 to 8, p=0.88122
b-rank test for bits 2 to 9, p=0.10787
b-rank test for bits 3 to 10, p=0.71919
b-rank test for bits 4 to 11, p=0.19661
b-rank test for bits 5 to 12, p=0.51957
b-rank test for bits 6 to 13, p=0.14694
b-rank test for bits 7 to 14, p=0.24595
b-rank test for bits 8 to 15, p=0.89976
b-rank test for bits 9 to 16, p=0.82995
b-rank test for bits 10 to 17, p=0.07371
b-rank test for bits 11 to 18, p=0.39921
b-rank test for bits 12 to 19, p=0.76523
b-rank test for bits 13 to 20, p=0.10751
b-rank test for bits 14 to 21, p=0.25595
b-rank test for bits 15 to 22, p=0.34561
b-rank test for bits 16 to 23, p=0.88396
b-rank test for bits 17 to 24, p=0.70230
b-rank test for bits 18 to 25, p=0.06984
b-rank test for bits 19 to 26, p=0.41149
b-rank test for bits 20 to 27, p=0.98287
b-rank test for bits 21 to 28, p=0.94195
b-rank test for bits 22 to 29, p=0.55317
b-rank test for bits 23 to 30, p=0.14763
b-rank test for bits 24 to 31, p=0.58187
b-rank test for bits 25 to 32, p=0.40836
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 = 0.897119
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-08-17_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 141581 -0.77 0.221503
2 141570 -0.79 0.213939
3 141628 -0.66 0.255490
4 141611 -0.70 0.242891
5 141398 -1.19 0.116103
6 142102 0.45 0.673704
7 141679 -0.54 0.295235
8 141414 -1.16 0.123572
9 142287 0.88 0.811222
10 141701 -0.49 0.313217
11 141091 -1.91 0.027939
12 142000 0.21 0.583886
13 141365 -1.27 0.101722
14 141889 -0.05 0.481057
15 141914 0.01 0.504353
16 141466 -1.04 0.150144
17 141716 -0.45 0.325741
18 141367 -1.27 0.102555
19 141620 -0.68 0.249519
20 142607 1.63 0.948457
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-08-17_11:31
Bits used No. missing words z-score p-value
23 to 32 141942 0.1127 0.544848
22 to 31 142357 1.5437 0.938668
21 to 30 141828 -0.2804 0.389567
20 to 29 141537 -1.2839 0.099589
19 to 28 141493 -1.4356 0.075555
18 to 27 142082 0.5954 0.724217
17 to 26 142206 1.0230 0.846846
16 to 25 141988 0.2713 0.606911
15 to 24 142159 0.8609 0.805362
14 to 23 142100 0.6575 0.744565
13 to 22 142207 1.0264 0.847660
12 to 21 141611 -1.0287 0.151805
11 to 20 142015 0.3644 0.642213
10 to 19 141743 -0.5736 0.283136
9 to 18 141855 -0.1873 0.425695
8 to 17 142148 0.8230 0.794746
7 to 16 141972 0.2161 0.585547
6 to 15 142251 1.1782 0.880636
5 to 14 141982 0.2506 0.598933
4 to 13 141587 -1.1115 0.133180
3 to 12 141702 -0.7149 0.237326
2 to 11 141548 -1.2460 0.106389
1 to 10 141944 0.1196 0.547581
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-08-17_11:31
Bits used No. missing words z-score p-value
28 to 32 142550 2.1718 0.985063
27 to 31 141891 -0.0621 0.475227
26 to 30 142033 0.4192 0.662473
25 to 29 141654 -0.8655 0.193375
24 to 28 141963 0.1819 0.572182
23 to 27 142395 1.6463 0.950153
22 to 26 142202 0.9921 0.839426
21 to 25 142267 1.2124 0.887328
20 to 24 141828 -0.2757 0.391391
19 to 23 142230 1.0870 0.861485
18 to 22 142219 1.0497 0.853079
17 to 21 142328 1.4192 0.922083
16 to 20 142010 0.3413 0.633544
15 to 19 141996 0.2938 0.615543
14 to 18 141705 -0.6926 0.244267
13 to 17 141840 -0.2350 0.407098
12 to 16 142105 0.6633 0.746427
11 to 15 142137 0.7718 0.779873
10 to 14 141917 0.0260 0.510371
9 to 13 142141 0.7853 0.783868
8 to 12 142014 0.3548 0.638635
7 to 11 142258 1.1819 0.881384
6 to 10 142315 1.3752 0.915458
5 to 9 142108 0.6735 0.749672
4 to 8 142024 0.3887 0.651255
3 to 7 141612 -1.0079 0.156752
2 to 6 142128 0.7413 0.770730
1 to 5 141886 -0.0791 0.468483
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-08-17_11:31
Bits used No. missing words z-score p-value
31 to 32 142077 0.4946 0.689559
30 to 31 142137 0.6716 0.749079
29 to 30 142303 1.1613 0.877234
28 to 29 141184 -2.1396 0.016193
27 to 28 141763 -0.4317 0.332997
26 to 27 141772 -0.4051 0.342701
25 to 26 142052 0.4209 0.663070
24 to 25 142034 0.3678 0.643473
23 to 24 141650 -0.7650 0.222140
22 to 23 141776 -0.3933 0.347048
21 to 22 142008 0.2911 0.614498
20 to 21 141807 -0.3019 0.381380
19 to 20 141787 -0.3609 0.359104
18 to 19 141700 -0.6175 0.268455
17 to 18 142493 1.7217 0.957442
16 to 17 142034 0.3678 0.643473
15 to 16 141705 -0.6027 0.273340
14 to 15 142002 0.2734 0.607713
13 to 14 141919 0.0285 0.511378
12 to 13 142197 0.8486 0.801944
11 to 12 141708 -0.5939 0.276292
10 to 11 141627 -0.8328 0.202470
9 to 10 142739 2.4474 0.992806
8 to 9 141744 -0.4877 0.312882
7 to 8 142135 0.6657 0.747196
6 to 7 141827 -0.2429 0.404056
5 to 6 141978 0.2026 0.580263
4 to 5 142499 1.7394 0.959021
3 to 4 141779 -0.3845 0.350321
2 to 3 141832 -0.2281 0.409780
1 to 2 142051 0.4179 0.661992
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-08-17_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2502.77 0.039 0.515643
Test results for specific bytes for dh-ranFile-2018-08-17_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2477.52 -0.318 0.375276
2 to 9 2492.40 -0.107 0.457215
3 to 10 2504.41 0.062 0.524880
4 to 11 2524.61 0.348 0.636117
5 to 12 2387.17 -1.596 0.055282
6 to 13 2385.87 -1.614 0.053256
7 to 14 2457.61 -0.600 0.274401
8 to 15 2641.25 1.998 0.977123
9 to 16 2596.10 1.359 0.912945
10 to 17 2411.25 -1.255 0.104709
11 to 18 2452.49 -0.672 0.250822
12 to 19 2319.54 -2.552 0.005354
13 to 20 2535.41 0.501 0.691733
14 to 21 2555.72 0.788 0.784654
15 to 22 2512.35 0.175 0.569331
16 to 23 2336.27 -2.316 0.010292
17 to 24 2581.00 1.145 0.873988
18 to 25 2446.48 -0.757 0.224565
19 to 26 2547.69 0.674 0.749996
20 to 27 2536.86 0.521 0.698929
21 to 28 2501.57 0.022 0.508856
22 to 29 2495.65 -0.062 0.475467
23 to 30 2478.90 -0.298 0.382719
24 to 31 2591.21 1.290 0.901465
25 to 32 2437.51 -0.884 0.188409
CDPARK for dh-ranFile-2018-08-17_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
3505 -0.8219 0.205562
3495 -1.2785 0.100530
3493 -1.3699 0.085365
3507 -0.7306 0.232514
3484 -1.7808 0.037471
3488 -1.5982 0.055002
3575 2.3744 0.991212
3479 -2.0091 0.022262
3570 2.1461 0.984068
3476 -2.1461 0.015932
Square side=100, avg. no. parked=3507.20 sample std.=34.02
p-value of the KSTEST for those 10 p-values: 0.000475
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-08-17_11:31
0.5912,0.2947,0.5515,0.2344,0.5503,0.6403,0.7482,0.0035,0.2932,0.2851,
The KS test for those 10 p-values: 0.314733
The 3DSPHERES test for dh-ranFile-2018-08-17_11:31
sample no r^3 equiv. uni.
1 11.630 0.321364
2 31.170 0.646196
3 36.036 0.699166
4 33.268 0.670084
5 7.893 0.231330
6 42.131 0.754474
7 21.438 0.510608
8 26.484 0.586382
9 38.623 0.724019
10 50.021 0.811257
11 33.508 0.672723
12 60.402 0.866465
13 4.404 0.136533
14 0.418 0.013823
15 99.727 0.964000
16 54.023 0.834829
17 106.707 0.971473
18 29.891 0.630777
19 6.878 0.204887
20 24.155 0.552993
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.222455
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-08-17_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 -0.4 -1.4 -1.4 -0.6
-2.0 -0.4 1.4 1.2 -0.9 -0.8
2.2 0.6 1.9 -2.2 -2.2 -0.0
0.3 1.2 0.7 -1.7 -1.3 1.6
0.3 0.6 0.5 -0.9 0.4 -0.2
-1.0 0.1 0.4 0.4 -0.2 0.6
0.3 1.8 -1.6 0.4 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:53.478064
z-score=1.252360, p-value=0.889692
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-08-17_11:31
Test no p-value
1 0.922384
2 0.677940
3 0.099853
4 0.273754
5 0.517424
6 0.208437
7 0.143773
8 0.000236
9 0.071318
10 0.217755
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.032261
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-08-17_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 66791 0.23 66621 0.03
3 25000.00 24999 0.00 25064 0.16
4 6666.67 6560 1.71 6640 0.11
5 1388.89 1384 0.02 1382 0.03
6 238.10 223 0.96 245 0.20
7 34.72 39 0.53 38 0.31
8 4.96 3 0.77 9 3.29
p=0.35240 p=0.34182
Number of rngs required: 688020, p-value: 0.330
RESULTS OF CRAPS TEST for dh-ranFile-2018-08-17_11:31
No. of wins: Observed Expected
98461 98585.9
z-score=-0.558, pvalue=0.28827
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66518 66666.7 0.332 0.332
2 37495 37654.3 0.674 1.006
3 26927 26954.7 0.029 1.034
4 19314 19313.5 0.000 1.034
5 13888 13851.4 0.097 1.131
6 9993 9943.5 0.246 1.377
7 7114 7145.0 0.135 1.511
8 5167 5139.1 0.152 1.663
9 3795 3699.9 2.446 4.109
10 2791 2666.3 5.832 9.942
11 1962 1923.3 0.778 10.719
12 1359 1388.7 0.637 11.356
13 1026 1003.7 0.495 11.851
14 706 726.1 0.559 12.410
15 512 525.8 0.364 12.774
16 414 381.2 2.831 15.605
17 281 276.5 0.072 15.677
18 199 200.8 0.017 15.693
19 150 146.0 0.110 15.804
20 122 106.2 2.346 18.150
21 267 287.1 1.409 19.559
Chisq= 19.56 for 20 degrees of freedom, p= 0.51419
SUMMARY of craptest
p-value for no. of wins: 0.288272
p-value for throws/game: 0.514186
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-08-17_11:31
No. of wins: Observed Expected
98365 98585.9
z-score=-0.988, pvalue=0.16162
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67013 66666.7 1.799 1.799
2 37536 37654.3 0.372 2.171
3 27093 26954.7 0.709 2.880
4 19151 19313.5 1.367 4.247
5 13680 13851.4 2.121 6.368
6 10075 9943.5 1.738 8.106
7 7085 7145.0 0.504 8.610
8 5099 5139.1 0.312 8.923
9 3582 3699.9 3.755 12.678
10 2645 2666.3 0.170 12.848
11 1957 1923.3 0.589 13.437
12 1373 1388.7 0.178 13.616
13 1057 1003.7 2.829 16.444
14 730 726.1 0.021 16.465
15 509 525.8 0.539 17.004
16 382 381.2 0.002 17.006
17 265 276.5 0.482 17.487
18 205 200.8 0.087 17.574
19 144 146.0 0.027 17.601
20 106 106.2 0.000 17.601
21 313 287.1 2.334 19.935
Chisq= 19.94 for 20 degrees of freedom, p= 0.53802
SUMMARY of craptest
p-value for no. of wins: 0.161623
p-value for throws/game: 0.538017
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0005,0.0035,0.0054,0.0103,0.0114,0.0138,0.0159,0.0162,0.0223,
0.0244,0.0279,0.0323,0.0368,0.0375,0.0533,0.0550,0.0553,0.0698,0.0713,
0.0737,0.0756,0.0852,0.0854,0.0982,0.0996,0.0999,0.1005,0.1017,0.1026,
0.1047,0.1064,0.1075,0.1079,0.1102,0.1161,0.1236,0.1332,0.1365,0.1438,
0.1469,0.1476,0.1501,0.1518,0.1568,0.1616,0.1851,0.1884,0.1934,0.1949,
0.1958,0.1966,0.2025,0.2049,0.2056,0.2084,0.2139,0.2178,0.2215,0.2221,
0.2225,0.2246,0.2313,0.2325,0.2344,0.2373,0.2429,0.2443,0.2456,0.2460,
0.2495,0.2508,0.2555,0.2559,0.2608,0.2626,0.2685,0.2733,0.2738,0.2742,
0.2744,0.2763,0.2831,0.2851,0.2883,0.2932,0.2947,0.2952,0.3129,0.3132,
0.3147,0.3214,0.3257,0.3273,0.3295,0.3330,0.3418,0.3427,0.3456,0.3470,
0.3503,0.3524,0.3551,0.3591,0.3753,0.3814,0.3827,0.3896,0.3914,0.3987,
0.3992,0.4041,0.4071,0.4084,0.4098,0.4115,0.4211,0.4257,0.4572,0.4615,
0.4685,0.4752,0.4755,0.4811,0.5010,0.5020,0.5044,0.5089,0.5104,0.5105,
0.5106,0.5107,0.5114,0.5125,0.5142,0.5156,0.5174,0.5196,0.5249,0.5299,
0.5380,0.5448,0.5476,0.5503,0.5515,0.5530,0.5532,0.5619,0.5655,0.5693,
0.5722,0.5803,0.5804,0.5819,0.5839,0.5855,0.5864,0.5879,0.5912,0.5989,
0.6069,0.6077,0.6145,0.6155,0.6301,0.6308,0.6335,0.6353,0.6361,0.6378,
0.6386,0.6403,0.6422,0.6435,0.6435,0.6462,0.6513,0.6620,0.6625,0.6631,
0.6694,0.6701,0.6727,0.6737,0.6779,0.6829,0.6896,0.6917,0.6989,0.6992,
0.7016,0.7023,0.7192,0.7240,0.7242,0.7446,0.7464,0.7472,0.7482,0.7491,
0.7497,0.7500,0.7545,0.7652,0.7674,0.7698,0.7707,0.7799,0.7799,0.7809,
0.7839,0.7847,0.7947,0.7990,0.8019,0.8054,0.8066,0.8112,0.8113,0.8300,
0.8304,0.8339,0.8348,0.8366,0.8394,0.8410,0.8421,0.8468,0.8477,0.8531,
0.8615,0.8652,0.8665,0.8740,0.8772,0.8806,0.8812,0.8814,0.8840,0.8841,
0.8873,0.8897,0.8971,0.8977,0.8998,0.9015,0.9064,0.9129,0.9155,0.9221,
0.9224,0.9387,0.9419,0.9485,0.9502,0.9574,0.9590,0.9618,0.9640,0.9715,
0.9771,0.9786,0.9829,0.9841,0.9851,0.9854,0.9912,0.9928,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.911003
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.