RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_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 15.90 13.0356 0.266202
2 to 25 15.42 23.0327 0.851811
3 to 26 15.66 26.0263 0.926017
4 to 27 15.42 27.6129 0.950331
5 to 28 15.47 22.4646 0.832495
6 to 29 15.48 44.3175 0.999693
7 to 30 15.63 21.1165 0.778876
8 to 31 15.64 19.9197 0.721642
9 to 32 16.05 15.3665 0.430902
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.006872
Tough bday spacings test for dh-ranFile-2018-06-29_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 6 32 78 106 86 92 46 27 17 9 1
(O-E)^2/E 1.1 0.6 0.3 0.7 1.4 2.5 0.7 0.3 0.3 0.9 2.3
Birthday Spacings: Sum(O-E)^2/E= 10.985, p= 0.641
RESULTS OF GCD FOR dh-ranFile-2018-06-29_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.792210
p-value, dist. of gcd's: 0.175997
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.947 0.883 0.834 0.396 0.115 0.228 0.413 0.256
Bits 8 to 15---> 0.046 0.171 0.815 0.175 0.359 0.123 0.268 0.316
Bits 16 to 23---> 0.896 0.137 0.457 0.193 0.500 0.178 0.280 0.554
Bits 24 to 31---> 0.521 0.772 0.059 0.190 0.674 0.354 0.161 0.584
KS test for the above 32 p values: 0.939
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_12:31,
p-values for 5 runs: 0.8895, 0.2228, 0.7659, 0.4516, 0.2186
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 206 211.4 0.139 0.139
r= 29 5236 5134.0 2.026 2.165
r= 30 23116 23103.0 0.007 2.172
r= 31 11442 11551.5 1.038 3.211
chi-square = 3.211 with df = 3; p-value = 0.640
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 240 211.4 3.864 3.864
r= 30 5182 5134.0 0.449 4.313
r= 31 22971 23103.0 0.755 5.067
r= 32 11607 11551.5 0.266 5.334
chi-square = 5.334 with df = 3; p-value = 0.851
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_12:31
b-rank test for bits 1 to 8, p=0.89028
b-rank test for bits 2 to 9, p=0.63062
b-rank test for bits 3 to 10, p=0.76237
b-rank test for bits 4 to 11, p=0.04512
b-rank test for bits 5 to 12, p=0.35250
b-rank test for bits 6 to 13, p=0.82657
b-rank test for bits 7 to 14, p=0.24402
b-rank test for bits 8 to 15, p=0.73991
b-rank test for bits 9 to 16, p=0.54225
b-rank test for bits 10 to 17, p=0.96249
b-rank test for bits 11 to 18, p=0.87607
b-rank test for bits 12 to 19, p=0.09028
b-rank test for bits 13 to 20, p=0.76050
b-rank test for bits 14 to 21, p=0.38656
b-rank test for bits 15 to 22, p=0.44258
b-rank test for bits 16 to 23, p=0.80558
b-rank test for bits 17 to 24, p=0.79535
b-rank test for bits 18 to 25, p=0.18945
b-rank test for bits 19 to 26, p=0.53751
b-rank test for bits 20 to 27, p=0.16951
b-rank test for bits 21 to 28, p=0.83398
b-rank test for bits 22 to 29, p=0.63705
b-rank test for bits 23 to 30, p=0.68229
b-rank test for bits 24 to 31, p=0.19200
b-rank test for bits 25 to 32, p=0.76143
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 = 0.330816
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_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 141730 -0.42 0.337610
2 141867 -0.10 0.460608
3 142532 1.45 0.927143
4 141761 -0.35 0.364459
5 142374 1.09 0.861189
6 141989 0.19 0.573834
7 142003 0.22 0.586619
8 142194 0.67 0.747012
9 141962 0.12 0.548971
10 141976 0.16 0.561893
11 141634 -0.64 0.260017
12 141760 -0.35 0.363582
13 141007 -2.11 0.017505
14 141516 -0.92 0.179049
15 141723 -0.44 0.331654
16 141709 -0.47 0.319871
17 141434 -1.11 0.133374
18 142444 1.25 0.894209
19 142396 1.14 0.872247
20 141693 -0.51 0.306624
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_12:31
Bits used No. missing words z-score p-value
23 to 32 141608 -1.0391 0.149386
22 to 31 141643 -0.9184 0.179210
21 to 30 141934 0.0851 0.533897
20 to 29 142182 0.9402 0.826453
19 to 28 141945 0.1230 0.548947
18 to 27 141817 -0.3184 0.375099
17 to 26 142194 0.9816 0.836857
16 to 25 142329 1.4471 0.926071
15 to 24 142155 0.8471 0.801541
14 to 23 142806 3.0920 0.999006
13 to 22 141797 -0.3873 0.349251
12 to 21 141911 0.0058 0.502297
11 to 20 141649 -0.8977 0.184676
10 to 19 141946 0.1264 0.550312
9 to 18 141979 0.2402 0.594928
8 to 17 142223 1.0816 0.860289
7 to 16 142002 0.3196 0.625346
6 to 15 142189 0.9644 0.832572
5 to 14 142077 0.5782 0.718426
4 to 13 142143 0.8058 0.789809
3 to 12 141396 -1.7701 0.038355
2 to 11 141281 -2.1667 0.015131
1 to 10 141552 -1.2322 0.108942
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_12:31
Bits used No. missing words z-score p-value
28 to 32 142193 0.9616 0.831873
27 to 31 142456 1.8531 0.968067
26 to 30 141630 -0.9469 0.171850
25 to 29 142286 1.2768 0.899172
24 to 28 142286 1.2768 0.899172
23 to 27 141973 0.2158 0.585440
22 to 26 141950 0.1379 0.554826
21 to 25 141817 -0.3130 0.377147
20 to 24 141958 0.1650 0.565521
19 to 23 141885 -0.0825 0.467135
18 to 22 142105 0.6633 0.746427
17 to 21 142132 0.7548 0.774820
16 to 20 142088 0.6057 0.727630
15 to 19 141575 -1.1333 0.128540
14 to 18 141961 0.1752 0.569520
13 to 17 142173 0.8938 0.814285
12 to 16 141531 -1.2825 0.099838
11 to 15 142269 1.2192 0.888620
10 to 14 141616 -0.9943 0.160029
9 to 13 141478 -1.4621 0.071852
8 to 12 141692 -0.7367 0.230649
7 to 11 142164 0.8633 0.806011
6 to 10 142441 1.8023 0.964249
5 to 9 141445 -1.5740 0.057744
4 to 8 142114 0.6938 0.756095
3 to 7 141491 -1.4181 0.078086
2 to 6 141715 -0.6587 0.255030
1 to 5 141360 -1.8621 0.031292
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_12:31
Bits used No. missing words z-score p-value
31 to 32 141751 -0.4671 0.320232
30 to 31 142186 0.8161 0.792789
29 to 30 141556 -1.0423 0.148643
28 to 29 142202 0.8633 0.806023
27 to 28 142247 0.9961 0.840394
26 to 27 141917 0.0226 0.509025
25 to 26 141820 -0.2635 0.396079
24 to 25 142077 0.4946 0.689559
23 to 24 141598 -0.9184 0.179211
22 to 23 141970 0.1790 0.571018
21 to 22 141780 -0.3815 0.351415
20 to 21 141290 -1.8269 0.033855
19 to 20 141660 -0.7355 0.231022
18 to 19 141412 -1.4671 0.071181
17 to 18 142633 2.1347 0.983608
16 to 17 141517 -1.1573 0.123572
15 to 16 141742 -0.4936 0.310795
14 to 15 142179 0.7955 0.786835
13 to 14 142321 1.2144 0.887696
12 to 13 141822 -0.2576 0.398354
11 to 12 142069 0.4710 0.681181
10 to 11 141735 -0.5142 0.303539
9 to 10 141311 -1.7650 0.038783
8 to 9 142072 0.4799 0.684334
7 to 8 142144 0.6922 0.755607
6 to 7 142601 2.0403 0.979341
5 to 6 141947 0.1111 0.544240
4 to 5 142205 0.8722 0.808446
3 to 4 141987 0.2291 0.590610
2 to 3 141658 -0.7414 0.229230
1 to 2 142004 0.2793 0.609978
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2542.48 0.601 0.725998
Test results for specific bytes for dh-ranFile-2018-06-29_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2533.69 0.476 0.683121
2 to 9 2522.29 0.315 0.623688
3 to 10 2502.04 0.029 0.511489
4 to 11 2555.91 0.791 0.785453
5 to 12 2331.25 -2.386 0.008506
6 to 13 2408.94 -1.288 0.098904
7 to 14 2396.99 -1.457 0.072586
8 to 15 2576.41 1.081 0.860062
9 to 16 2471.30 -0.406 0.342406
10 to 17 2498.90 -0.016 0.493772
11 to 18 2542.99 0.608 0.728374
12 to 19 2615.73 1.637 0.949148
13 to 20 2464.17 -0.507 0.306185
14 to 21 2428.93 -1.005 0.157427
15 to 22 2429.40 -0.998 0.159026
16 to 23 2461.76 -0.541 0.294310
17 to 24 2502.74 0.039 0.515481
18 to 25 2483.37 -0.235 0.407029
19 to 26 2451.57 -0.685 0.246694
20 to 27 2487.51 -0.177 0.429907
21 to 28 2456.79 -0.611 0.270559
22 to 29 2496.57 -0.049 0.480649
23 to 30 2516.85 0.238 0.594154
24 to 31 2435.88 -0.907 0.182273
25 to 32 2426.37 -1.041 0.148858
CDPARK for dh-ranFile-2018-06-29_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
3501 -1.0046 0.157553
3522 -0.0457 0.481790
3510 -0.5936 0.276387
3543 0.9132 0.819442
3501 -1.0046 0.157553
3491 -1.4612 0.071982
3535 0.5479 0.708135
3492 -1.4155 0.078457
3480 -1.9635 0.024796
3538 0.6849 0.753306
Square side=100, avg. no. parked=3511.30 sample std.=20.91
p-value of the KSTEST for those 10 p-values: 0.118934
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_12:31
0.5703,0.8615,0.5503,0.9329,0.1050,0.5238,0.4644,0.3081,0.4365,0.0238,
The KS test for those 10 p-values: 0.890317
The 3DSPHERES test for dh-ranFile-2018-06-29_12:31
sample no r^3 equiv. uni.
1 3.355 0.105801
2 55.176 0.841057
3 94.934 0.957764
4 6.360 0.191037
5 97.889 0.961725
6 9.734 0.277098
7 119.644 0.981466
8 16.785 0.428504
9 40.695 0.742439
10 14.409 0.381397
11 40.755 0.742956
12 62.315 0.874716
13 8.634 0.250077
14 21.055 0.504333
15 77.651 0.924857
16 12.592 0.342781
17 4.909 0.150949
18 0.750 0.024689
19 8.811 0.254508
20 11.691 0.322734
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.544626
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 0.1 -1.1 1.0 0.4
0.9 -1.5 0.4 -0.2 -1.0 2.5
0.3 2.1 -0.3 -0.9 -1.4 -0.5
-0.1 1.5 -0.1 -1.5 -0.7 0.1
0.1 0.8 -0.2 1.5 -1.2 1.2
-2.3 -0.6 -0.1 -0.8 1.0 0.4
1.4 0.2 0.5 -1.3 1.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:47.013509
z-score=0.547019, p-value=0.725340
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_12:31
Test no p-value
1 0.128609
2 0.199704
3 0.190079
4 0.069927
5 0.334798
6 0.009937
7 0.224598
8 0.660474
9 0.015463
10 0.139828
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000731
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_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 66635 0.02 66794 0.24
3 25000.00 24976 0.02 24820 1.30
4 6666.67 6689 0.07 6709 0.27
5 1388.89 1406 0.21 1405 0.19
6 238.10 243 0.10 236 0.02
7 34.72 40 0.80 27 1.72
8 4.96 10 5.12 8 1.86
p=0.61474 p=0.52972
Number of rngs required: 687645, p-value: 0.190
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_12:31
No. of wins: Observed Expected
99029 98585.9
z-score= 1.982, pvalue=0.97626
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66852 66666.7 0.515 0.515
2 37908 37654.3 1.709 2.224
3 26691 26954.7 2.580 4.805
4 19180 19313.5 0.922 5.727
5 13973 13851.4 1.067 6.794
6 9960 9943.5 0.027 6.821
7 7164 7145.0 0.050 6.872
8 5055 5139.1 1.375 8.247
9 3614 3699.9 1.993 10.240
10 2599 2666.3 1.699 11.938
11 1885 1923.3 0.764 12.702
12 1433 1388.7 1.411 14.113
13 1002 1003.7 0.003 14.116
14 722 726.1 0.024 14.139
15 551 525.8 1.204 15.344
16 373 381.2 0.174 15.518
17 286 276.5 0.324 15.842
18 223 200.8 2.447 18.289
19 133 146.0 1.155 19.444
20 111 106.2 0.216 19.659
21 285 287.1 0.016 19.675
Chisq= 19.67 for 20 degrees of freedom, p= 0.52158
SUMMARY of craptest
p-value for no. of wins: 0.976260
p-value for throws/game: 0.521580
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_12:31
No. of wins: Observed Expected
98220 98585.9
z-score=-1.636, pvalue=0.05088
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66633 66666.7 0.017 0.017
2 37509 37654.3 0.561 0.578
3 27288 26954.7 4.121 4.698
4 19319 19313.5 0.002 4.700
5 13563 13851.4 6.006 10.706
6 10018 9943.5 0.558 11.263
7 7200 7145.0 0.423 11.686
8 5133 5139.1 0.007 11.693
9 3838 3699.9 5.157 16.851
10 2664 2666.3 0.002 16.853
11 1954 1923.3 0.489 17.342
12 1352 1388.7 0.972 18.314
13 980 1003.7 0.560 18.874
14 646 726.1 8.845 27.719
15 532 525.8 0.072 27.791
16 344 381.2 3.621 31.412
17 261 276.5 0.873 32.285
18 198 200.8 0.040 32.325
19 135 146.0 0.827 33.152
20 115 106.2 0.727 33.878
21 318 287.1 3.323 37.201
Chisq= 37.20 for 20 degrees of freedom, p= 0.98893
SUMMARY of craptest
p-value for no. of wins: 0.050885
p-value for throws/game: 0.988930
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0069,0.0085,0.0099,0.0151,0.0155,0.0175,0.0238,0.0247,0.0248,
0.0313,0.0339,0.0384,0.0388,0.0451,0.0458,0.0509,0.0577,0.0595,0.0699,
0.0712,0.0719,0.0720,0.0726,0.0781,0.0785,0.0903,0.0989,0.0998,0.1050,
0.1058,0.1089,0.1152,0.1189,0.1226,0.1236,0.1285,0.1286,0.1334,0.1372,
0.1398,0.1486,0.1489,0.1494,0.1509,0.1574,0.1576,0.1576,0.1590,0.1600,
0.1606,0.1695,0.1714,0.1718,0.1749,0.1760,0.1777,0.1790,0.1792,0.1792,
0.1823,0.1847,0.1895,0.1899,0.1901,0.1903,0.1910,0.1920,0.1927,0.1997,
0.2186,0.2228,0.2246,0.2277,0.2292,0.2306,0.2310,0.2440,0.2467,0.2501,
0.2545,0.2550,0.2558,0.2600,0.2662,0.2680,0.2706,0.2764,0.2771,0.2804,
0.2943,0.3035,0.3062,0.3066,0.3081,0.3108,0.3158,0.3199,0.3202,0.3227,
0.3308,0.3317,0.3348,0.3376,0.3424,0.3428,0.3493,0.3514,0.3525,0.3535,
0.3586,0.3636,0.3645,0.3751,0.3771,0.3814,0.3866,0.3958,0.3961,0.3984,
0.4070,0.4129,0.4285,0.4299,0.4309,0.4365,0.4426,0.4516,0.4572,0.4606,
0.4644,0.4671,0.4806,0.4818,0.4938,0.4995,0.5023,0.5043,0.5090,0.5115,
0.5155,0.5214,0.5216,0.5238,0.5297,0.5339,0.5375,0.5422,0.5442,0.5446,
0.5489,0.5490,0.5503,0.5503,0.5536,0.5548,0.5619,0.5655,0.5695,0.5703,
0.5710,0.5738,0.5840,0.5854,0.5866,0.5906,0.5942,0.5949,0.6100,0.6147,
0.6237,0.6253,0.6306,0.6370,0.6397,0.6413,0.6605,0.6743,0.6812,0.6823,
0.6831,0.6843,0.6896,0.7081,0.7184,0.7216,0.7253,0.7260,0.7276,0.7284,
0.7399,0.7424,0.7430,0.7464,0.7470,0.7533,0.7556,0.7561,0.7605,0.7614,
0.7624,0.7659,0.7723,0.7748,0.7789,0.7855,0.7868,0.7898,0.7922,0.7928,
0.7954,0.8015,0.8056,0.8060,0.8060,0.8084,0.8143,0.8151,0.8194,0.8265,
0.8266,0.8319,0.8325,0.8326,0.8339,0.8340,0.8369,0.8404,0.8411,0.8511,
0.8518,0.8601,0.8603,0.8612,0.8615,0.8722,0.8747,0.8761,0.8835,0.8877,
0.8886,0.8895,0.8903,0.8903,0.8942,0.8960,0.8992,0.8992,0.9249,0.9260,
0.9261,0.9271,0.9329,0.9386,0.9470,0.9491,0.9503,0.9578,0.9617,0.9625,
0.9642,0.9681,0.9763,0.9793,0.9815,0.9836,0.9889,0.9990,0.9997,
Overall p-value after applying KStest on 269 p-values = 0.338341
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.