RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_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 15.56 20.2636 0.739032
2 to 25 15.70 14.5153 0.369649
3 to 26 15.87 16.6164 0.519366
4 to 27 15.66 26.4003 0.932530
5 to 28 15.59 23.3025 0.860341
6 to 29 15.53 17.8758 0.603285
7 to 30 16.00 31.9501 0.984736
8 to 31 15.94 16.1649 0.487821
9 to 32 15.86 21.4720 0.794114
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.066528
Tough bday spacings test for dh-ranFile-2018-07-06_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 12 43 73 82 97 83 51 33 16 4 6
(O-E)^2/E 0.9 1.1 0.0 2.5 0.0 0.3 0.0 0.4 0.1 1.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.225, p= 0.296
RESULTS OF GCD FOR dh-ranFile-2018-07-06_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.832855
p-value, dist. of gcd's: 0.725537
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.247 0.948 0.970 0.829 0.450 0.475 0.644 0.301
Bits 8 to 15---> 0.938 0.516 0.038 0.977 0.475 0.214 0.713 0.163
Bits 16 to 23---> 0.993 0.930 0.424 0.736 0.524 0.524 0.353 0.104
Bits 24 to 31---> 0.928 0.230 0.399 0.756 0.220 0.773 0.492 0.080
KS test for the above 32 p values: 0.562
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_11:31,
p-values for 5 runs: 0.5355, 0.6776, 0.0722, 0.5450, 0.8766
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 223 211.4 0.634 0.634
r= 29 5006 5134.0 3.192 3.826
r= 30 23169 23103.0 0.188 4.015
r= 31 11602 11551.5 0.221 4.235
chi-square = 4.235 with df = 3; p-value = 0.763
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 189 211.4 2.377 2.377
r= 30 5201 5134.0 0.874 3.251
r= 31 23121 23103.0 0.014 3.265
r= 32 11489 11551.5 0.338 3.604
chi-square = 3.604 with df = 3; p-value = 0.692
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_11:31
b-rank test for bits 1 to 8, p=0.61369
b-rank test for bits 2 to 9, p=0.85391
b-rank test for bits 3 to 10, p=0.15720
b-rank test for bits 4 to 11, p=0.86593
b-rank test for bits 5 to 12, p=0.49731
b-rank test for bits 6 to 13, p=0.03720
b-rank test for bits 7 to 14, p=0.20333
b-rank test for bits 8 to 15, p=0.35067
b-rank test for bits 9 to 16, p=0.72370
b-rank test for bits 10 to 17, p=0.91741
b-rank test for bits 11 to 18, p=0.45627
b-rank test for bits 12 to 19, p=0.22642
b-rank test for bits 13 to 20, p=0.72531
b-rank test for bits 14 to 21, p=0.90170
b-rank test for bits 15 to 22, p=0.01270
b-rank test for bits 16 to 23, p=0.77443
b-rank test for bits 17 to 24, p=0.78286
b-rank test for bits 18 to 25, p=0.28599
b-rank test for bits 19 to 26, p=0.18439
b-rank test for bits 20 to 27, p=0.49962
b-rank test for bits 21 to 28, p=0.07704
b-rank test for bits 22 to 29, p=0.78404
b-rank test for bits 23 to 30, p=0.49692
b-rank test for bits 24 to 31, p=0.66364
b-rank test for bits 25 to 32, p=0.99017
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 = 0.928317
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_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 142753 1.97 0.975649
2 141603 -0.72 0.237081
3 141624 -0.67 0.252495
4 141784 -0.29 0.384827
5 142322 0.96 0.832523
6 142033 0.29 0.613690
7 142388 1.12 0.868299
8 141686 -0.52 0.300905
9 142225 0.74 0.769605
10 141537 -0.87 0.192169
11 141512 -0.93 0.176615
12 142614 1.65 0.950162
13 141227 -1.59 0.055442
14 141826 -0.19 0.422815
15 141746 -0.38 0.351375
16 141449 -1.08 0.141067
17 141985 0.18 0.570167
18 141959 0.12 0.546194
19 141901 -0.02 0.492236
20 142347 1.02 0.846750
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_11:31
Bits used No. missing words z-score p-value
23 to 32 141867 -0.1460 0.441974
22 to 31 141853 -0.1942 0.422994
21 to 30 141770 -0.4804 0.315454
20 to 29 141670 -0.8253 0.204608
19 to 28 141401 -1.7529 0.039813
18 to 27 141241 -2.3046 0.010595
17 to 26 141858 -0.1770 0.429754
16 to 25 142176 0.9196 0.821097
15 to 24 142247 1.1644 0.877865
14 to 23 141849 -0.2080 0.417601
13 to 22 142186 0.9540 0.829967
12 to 21 142221 1.0747 0.858751
11 to 20 141539 -1.2770 0.100801
10 to 19 141613 -1.0218 0.153431
9 to 18 141862 -0.1632 0.435178
8 to 17 141973 0.2196 0.586890
7 to 16 141705 -0.7046 0.240534
6 to 15 141831 -0.2701 0.393540
5 to 14 142057 0.5092 0.694696
4 to 13 141712 -0.6804 0.248110
3 to 12 141895 -0.0494 0.480295
2 to 11 142064 0.5333 0.703103
1 to 10 142146 0.8161 0.792780
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_11:31
Bits used No. missing words z-score p-value
28 to 32 141458 -1.5299 0.063017
27 to 31 141694 -0.7299 0.232716
26 to 30 141950 0.1379 0.554826
25 to 29 141814 -0.3232 0.373290
24 to 28 142715 2.7311 0.996844
23 to 27 142204 0.9989 0.841074
22 to 26 141389 -1.7638 0.038880
21 to 25 142173 0.8938 0.814285
20 to 24 142100 0.6463 0.740970
19 to 23 141473 -1.4791 0.069559
18 to 22 142449 1.8294 0.966329
17 to 21 142631 2.4463 0.992784
16 to 20 141866 -0.1469 0.441613
15 to 19 141736 -0.5876 0.278414
14 to 18 141892 -0.0587 0.476577
13 to 17 142198 0.9785 0.836097
12 to 16 141814 -0.3232 0.373290
11 to 15 141594 -1.0689 0.142554
10 to 14 141366 -1.8418 0.032752
9 to 13 141952 0.1446 0.557504
8 to 12 142314 1.3718 0.914931
7 to 11 141793 -0.3943 0.346665
6 to 10 141817 -0.3130 0.377147
5 to 9 141311 -2.0282 0.021268
4 to 8 141511 -1.3503 0.088465
3 to 7 142203 0.9955 0.840251
2 to 6 141677 -0.7876 0.215477
1 to 5 141932 0.0768 0.530628
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_11:31
Bits used No. missing words z-score p-value
31 to 32 141268 -1.8918 0.029257
30 to 31 142133 0.6598 0.745307
29 to 30 142557 1.9105 0.971968
28 to 29 141731 -0.5260 0.299428
27 to 28 141602 -0.9066 0.182315
26 to 27 141266 -1.8977 0.028866
25 to 26 141626 -0.8358 0.201639
24 to 25 142063 0.4533 0.674835
23 to 24 141842 -0.1986 0.421283
22 to 23 142478 1.6775 0.953277
21 to 22 142500 1.7424 0.959280
20 to 21 141637 -0.8033 0.210891
19 to 20 142462 1.6303 0.948480
18 to 19 141774 -0.3992 0.344872
17 to 18 141619 -0.8564 0.195880
16 to 17 141332 -1.7030 0.044280
15 to 16 141584 -0.9597 0.168609
14 to 15 141828 -0.2399 0.405199
13 to 14 142187 0.8191 0.793631
12 to 13 142288 1.1170 0.868007
11 to 12 142766 2.5271 0.994249
10 to 11 141989 0.2350 0.592901
9 to 10 141899 -0.0305 0.487845
8 to 9 141529 -1.1219 0.130949
7 to 8 142233 0.9548 0.830155
6 to 7 141327 -1.7178 0.042918
5 to 6 141845 -0.1898 0.424747
4 to 5 141407 -1.4818 0.069197
3 to 4 142055 0.4297 0.666295
2 to 3 142481 1.6863 0.954135
1 to 2 142327 1.2321 0.891038
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2532.00 0.453 0.674558
Test results for specific bytes for dh-ranFile-2018-07-06_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2547.15 0.667 0.747555
2 to 9 2497.39 -0.037 0.485297
3 to 10 2627.73 1.806 0.964572
4 to 11 2517.82 0.252 0.599486
5 to 12 2565.36 0.924 0.822351
6 to 13 2590.75 1.283 0.900332
7 to 14 2493.28 -0.095 0.462154
8 to 15 2599.19 1.403 0.919661
9 to 16 2560.02 0.849 0.801990
10 to 17 2444.58 -0.784 0.216596
11 to 18 2565.86 0.931 0.824183
12 to 19 2529.37 0.415 0.661069
13 to 20 2530.88 0.437 0.668824
14 to 21 2443.52 -0.799 0.212235
15 to 22 2616.90 1.653 0.950859
16 to 23 2514.99 0.212 0.583969
17 to 24 2590.89 1.285 0.900681
18 to 25 2519.43 0.275 0.608260
19 to 26 2467.68 -0.457 0.323821
20 to 27 2602.38 1.448 0.926183
21 to 28 2390.63 -1.547 0.060961
22 to 29 2525.79 0.365 0.642323
23 to 30 2518.99 0.269 0.605891
24 to 31 2562.39 0.882 0.811206
25 to 32 2539.78 0.563 0.713128
CDPARK for dh-ranFile-2018-07-06_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
3495 -1.2785 0.100530
3510 -0.5936 0.276387
3513 -0.4566 0.323972
3545 1.0046 0.842447
3538 0.6849 0.753306
3509 -0.6393 0.261324
3561 1.7352 0.958644
3522 -0.0457 0.481790
3496 -1.2329 0.108811
3549 1.1872 0.882429
Square side=100, avg. no. parked=3523.80 sample std.=21.91
p-value of the KSTEST for those 10 p-values: 0.886190
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_11:31
0.3310,0.8942,0.2503,0.2098,0.3224,0.5234,0.5009,0.2489,0.8023,0.9403,
The KS test for those 10 p-values: 0.728891
The 3DSPHERES test for dh-ranFile-2018-07-06_11:31
sample no r^3 equiv. uni.
1 27.512 0.600316
2 21.152 0.505923
3 31.497 0.650023
4 15.174 0.396975
5 25.220 0.568581
6 13.447 0.361249
7 43.475 0.765237
8 30.286 0.635613
9 23.468 0.542630
10 78.747 0.927554
11 7.252 0.214741
12 57.782 0.854278
13 16.519 0.423417
14 31.397 0.648853
15 15.950 0.412377
16 8.540 0.247735
17 16.489 0.422832
18 15.671 0.406883
19 40.099 0.737274
20 61.940 0.873139
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.165724
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -1.2 -0.1 -1.1 -0.1 -0.5
-0.2 0.8 0.2 0.6 0.0 0.4
0.2 -0.9 -0.6 2.8 -0.7 0.6
1.2 -0.2 -1.1 -0.5 0.6 0.5
-1.2 0.6 -1.2 -1.1 -2.3 -0.7
-0.8 -1.5 0.6 0.0 -0.9 -0.1
0.0 -0.4 1.7 0.4 2.4 1.0
-1.1
Chi-square with 42 degrees of freedom:44.565398
z-score=0.279908, p-value=0.635653
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_11:31
Test no p-value
1 0.320831
2 0.960357
3 0.968409
4 0.214159
5 0.086334
6 0.131318
7 0.260541
8 0.727954
9 0.128737
10 0.460939
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.339116
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_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 66750 0.10 66762 0.14
3 25000.00 25008 0.00 24780 1.94
4 6666.67 6612 0.45 6812 3.17
5 1388.89 1366 0.38 1384 0.02
6 238.10 237 0.01 224 0.83
7 34.72 19 7.12 33 0.09
8 4.96 7 0.84 4 0.19
p=0.82036 p=0.61623
Number of rngs required: 687686, p-value: 0.204
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_11:31
No. of wins: Observed Expected
98402 98585.9
z-score=-0.822, pvalue=0.20545
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66740 66666.7 0.081 0.081
2 37417 37654.3 1.496 1.576
3 27077 26954.7 0.555 2.131
4 19228 19313.5 0.378 2.509
5 13797 13851.4 0.214 2.723
6 9945 9943.5 0.000 2.723
7 7143 7145.0 0.001 2.724
8 5159 5139.1 0.077 2.801
9 3729 3699.9 0.229 3.030
10 2663 2666.3 0.004 3.035
11 1989 1923.3 2.242 5.277
12 1373 1388.7 0.178 5.455
13 996 1003.7 0.059 5.515
14 738 726.1 0.194 5.708
15 579 525.8 5.375 11.083
16 392 381.2 0.309 11.392
17 260 276.5 0.989 12.381
18 237 200.8 6.514 18.896
19 147 146.0 0.007 18.903
20 103 106.2 0.097 19.000
21 288 287.1 0.003 19.003
Chisq= 19.00 for 20 degrees of freedom, p= 0.47836
SUMMARY of craptest
p-value for no. of wins: 0.205447
p-value for throws/game: 0.478361
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_11:31
No. of wins: Observed Expected
98028 98585.9
z-score=-2.495, pvalue=0.00630
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66474 66666.7 0.557 0.557
2 37928 37654.3 1.989 2.546
3 27044 26954.7 0.296 2.842
4 19123 19313.5 1.878 4.720
5 13944 13851.4 0.619 5.339
6 9845 9943.5 0.977 6.315
7 7191 7145.0 0.296 6.611
8 5167 5139.1 0.152 6.763
9 3696 3699.9 0.004 6.767
10 2758 2666.3 3.154 9.921
11 1882 1923.3 0.888 10.809
12 1314 1388.7 4.022 14.831
13 1001 1003.7 0.007 14.839
14 726 726.1 0.000 14.839
15 474 525.8 5.110 19.949
16 409 381.2 2.035 21.983
17 283 276.5 0.151 22.134
18 199 200.8 0.017 22.151
19 148 146.0 0.028 22.179
20 115 106.2 0.727 22.905
21 279 287.1 0.229 23.135
Chisq= 23.13 for 20 degrees of freedom, p= 0.71777
SUMMARY of craptest
p-value for no. of wins: 0.006297
p-value for throws/game: 0.717774
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0063,0.0106,0.0127,0.0213,0.0289,0.0293,0.0328,0.0372,0.0380,0.0389,
0.0398,0.0429,0.0443,0.0554,0.0610,0.0630,0.0665,0.0692,0.0696,0.0722,
0.0770,0.0796,0.0863,0.0885,0.1005,0.1008,0.1035,0.1088,0.1287,0.1309,
0.1313,0.1411,0.1426,0.1534,0.1572,0.1626,0.1657,0.1686,0.1766,0.1823,
0.1844,0.1922,0.1959,0.2016,0.2033,0.2036,0.2046,0.2054,0.2098,0.2109,
0.2122,0.2139,0.2142,0.2147,0.2155,0.2166,0.2197,0.2264,0.2296,0.2327,
0.2371,0.2405,0.2467,0.2477,0.2481,0.2489,0.2503,0.2525,0.2605,0.2613,
0.2764,0.2784,0.2860,0.2960,0.2994,0.3009,0.3014,0.3155,0.3208,0.3224,
0.3238,0.3240,0.3310,0.3391,0.3449,0.3467,0.3507,0.3514,0.3530,0.3612,
0.3696,0.3733,0.3733,0.3771,0.3848,0.3935,0.3970,0.3988,0.4052,0.4069,
0.4124,0.4176,0.4213,0.4228,0.4228,0.4230,0.4234,0.4237,0.4247,0.4298,
0.4352,0.4416,0.4420,0.4499,0.4563,0.4609,0.4622,0.4748,0.4750,0.4766,
0.4784,0.4803,0.4818,0.4853,0.4878,0.4878,0.4921,0.4922,0.4969,0.4973,
0.4996,0.5009,0.5059,0.5156,0.5194,0.5234,0.5236,0.5244,0.5306,0.5355,
0.5426,0.5450,0.5462,0.5548,0.5575,0.5615,0.5686,0.5702,0.5840,0.5869,
0.5929,0.5995,0.6003,0.6033,0.6059,0.6083,0.6137,0.6137,0.6162,0.6356,
0.6357,0.6423,0.6442,0.6489,0.6500,0.6611,0.6636,0.6663,0.6688,0.6746,
0.6748,0.6776,0.6924,0.6947,0.7031,0.7131,0.7131,0.7178,0.7237,0.7253,
0.7255,0.7280,0.7289,0.7359,0.7373,0.7390,0.7410,0.7453,0.7476,0.7533,
0.7559,0.7628,0.7652,0.7696,0.7728,0.7744,0.7829,0.7840,0.7928,0.7936,
0.7941,0.8020,0.8023,0.8112,0.8143,0.8204,0.8211,0.8224,0.8242,0.8288,
0.8300,0.8302,0.8325,0.8329,0.8361,0.8403,0.8411,0.8424,0.8467,0.8539,
0.8543,0.8588,0.8603,0.8659,0.8680,0.8683,0.8731,0.8766,0.8779,0.8824,
0.8862,0.8910,0.8942,0.9003,0.9007,0.9017,0.9149,0.9174,0.9197,0.9262,
0.9276,0.9276,0.9283,0.9302,0.9325,0.9385,0.9403,0.9484,0.9485,0.9502,
0.9509,0.9533,0.9541,0.9586,0.9593,0.9604,0.9646,0.9663,0.9684,0.9704,
0.9720,0.9756,0.9766,0.9847,0.9902,0.9928,0.9931,0.9942,0.9968,
Overall p-value after applying KStest on 269 p-values = 0.153257
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.