RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 12.7173 0.245105
2 to 25 15.90 21.8582 0.809766
3 to 26 15.76 18.4072 0.636403
4 to 27 15.76 18.4358 0.638138
5 to 28 15.93 12.3953 0.224367
6 to 29 15.49 25.6627 0.919171
7 to 30 16.11 19.8443 0.717728
8 to 31 15.74 29.3924 0.968926
9 to 32 15.83 10.3783 0.112999
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.582967
Tough bday spacings test for dh-ranFile-2018-06-19_03:31: 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 38 65 102 100 76 60 32 10 7 4
(O-E)^2/E 1.1 0.1 0.9 0.2 0.1 0.1 1.2 0.2 1.6 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.369, p= 0.135
RESULTS OF GCD FOR dh-ranFile-2018-06-19_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.380643
p-value, dist. of gcd's: 0.290876
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.104 0.584 0.313 0.384 0.399 0.427 0.161 0.764
Bits 8 to 15---> 0.446 0.351 0.797 0.921 0.291 0.368 0.818 0.974
Bits 16 to 23---> 0.362 0.308 0.572 0.404 0.741 0.802 0.551 0.502
Bits 24 to 31---> 0.794 0.224 0.968 0.787 0.936 0.320 0.835 0.318
KS test for the above 32 p values: 0.753
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_03:31,
p-values for 5 runs: 0.5074, 0.5399, 0.2780, 0.1288, 0.6751
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5147 5134.0 0.033 0.064
r= 30 23179 23103.0 0.250 0.314
r= 31 11460 11551.5 0.725 1.039
chi-square = 1.039 with df = 3; p-value = 0.208
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5062 5134.0 1.010 1.011
r= 31 23030 23103.0 0.231 1.242
r= 32 11697 11551.5 1.832 3.074
chi-square = 3.074 with df = 3; p-value = 0.620
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_03:31
b-rank test for bits 1 to 8, p=0.51418
b-rank test for bits 2 to 9, p=0.55887
b-rank test for bits 3 to 10, p=0.48769
b-rank test for bits 4 to 11, p=0.86735
b-rank test for bits 5 to 12, p=0.80015
b-rank test for bits 6 to 13, p=0.05514
b-rank test for bits 7 to 14, p=0.06259
b-rank test for bits 8 to 15, p=0.90252
b-rank test for bits 9 to 16, p=0.49824
b-rank test for bits 10 to 17, p=0.92477
b-rank test for bits 11 to 18, p=0.91441
b-rank test for bits 12 to 19, p=0.15716
b-rank test for bits 13 to 20, p=0.45474
b-rank test for bits 14 to 21, p=0.31656
b-rank test for bits 15 to 22, p=0.14705
b-rank test for bits 16 to 23, p=0.36803
b-rank test for bits 17 to 24, p=0.35791
b-rank test for bits 18 to 25, p=0.86972
b-rank test for bits 19 to 26, p=0.38856
b-rank test for bits 20 to 27, p=0.00244
b-rank test for bits 21 to 28, p=0.36492
b-rank test for bits 22 to 29, p=0.71506
b-rank test for bits 23 to 30, p=0.70255
b-rank test for bits 24 to 31, p=0.10948
b-rank test for bits 25 to 32, p=0.96875
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 = 0.881559
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_03:31
(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 142172 0.61 0.730298
2 141326 -1.36 0.086454
3 142042 0.31 0.621711
4 142277 0.86 0.804841
5 142124 0.50 0.692013
6 142598 1.61 0.946196
7 141145 -1.79 0.037064
8 141743 -0.39 0.348778
9 141554 -0.83 0.203210
10 142086 0.41 0.660116
11 141690 -0.51 0.304167
12 141925 0.04 0.514603
13 141789 -0.28 0.389300
14 142710 1.87 0.969308
15 141805 -0.24 0.403708
16 141451 -1.07 0.142115
17 141168 -1.73 0.041630
18 141444 -1.09 0.138470
19 142513 1.41 0.920796
20 141396 -1.20 0.115192
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_03:31
Bits used No. missing words z-score p-value
23 to 32 142131 0.7644 0.777679
22 to 31 142230 1.1058 0.865585
21 to 30 142006 0.3333 0.630563
20 to 29 142111 0.6954 0.756602
19 to 28 142304 1.3609 0.913232
18 to 27 142258 1.2023 0.885378
17 to 26 142278 1.2713 0.898185
16 to 25 141720 -0.6529 0.256923
15 to 24 141986 0.2644 0.604256
14 to 23 142110 0.6920 0.755521
13 to 22 142580 2.3127 0.989629
12 to 21 142002 0.3196 0.625346
11 to 20 141772 -0.4736 0.317910
10 to 19 142030 0.4161 0.661333
9 to 18 141865 -0.1529 0.439254
8 to 17 142153 0.8402 0.799614
7 to 16 142099 0.6540 0.743455
6 to 15 141944 0.1196 0.547581
5 to 14 141588 -1.1080 0.133923
4 to 13 141655 -0.8770 0.190243
3 to 12 141491 -1.4425 0.074578
2 to 11 142016 0.3678 0.643499
1 to 10 141891 -0.0632 0.474801
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_03:31
Bits used No. missing words z-score p-value
28 to 32 142026 0.3955 0.653760
27 to 31 141769 -0.4757 0.317146
26 to 30 141933 0.0802 0.531976
25 to 29 141602 -1.0418 0.148753
24 to 28 142004 0.3209 0.625863
23 to 27 142037 0.4328 0.667413
22 to 26 142035 0.4260 0.664946
21 to 25 142276 1.2429 0.893057
20 to 24 141849 -0.2045 0.418978
19 to 23 141777 -0.4486 0.326869
18 to 22 142198 0.9785 0.836097
17 to 21 141924 0.0497 0.519831
16 to 20 141925 0.0531 0.521181
15 to 19 141782 -0.4316 0.333006
14 to 18 141891 -0.0621 0.475227
13 to 17 141917 0.0260 0.510371
12 to 16 142054 0.4904 0.688077
11 to 15 141591 -1.0791 0.140275
10 to 14 141885 -0.0825 0.467135
9 to 13 141737 -0.5842 0.279553
8 to 12 142311 1.3616 0.913337
7 to 11 141774 -0.4587 0.323208
6 to 10 141922 0.0429 0.517129
5 to 9 142027 0.3989 0.655010
4 to 8 141742 -0.5672 0.285282
3 to 7 142096 0.6328 0.736561
2 to 6 141787 -0.4147 0.339189
1 to 5 141891 -0.0621 0.475227
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_03:31
Bits used No. missing words z-score p-value
31 to 32 142362 1.3353 0.909113
30 to 31 141681 -0.6735 0.250302
29 to 30 142362 1.3353 0.909113
28 to 29 141727 -0.5378 0.295342
27 to 28 141216 -2.0452 0.020417
26 to 27 142098 0.5565 0.711082
25 to 26 141556 -1.0423 0.148643
24 to 25 141695 -0.6322 0.263614
23 to 24 142233 0.9548 0.830155
22 to 23 142095 0.5477 0.708051
21 to 22 141769 -0.4140 0.339454
20 to 21 141998 0.2616 0.603171
19 to 20 142532 1.8368 0.966879
18 to 19 142171 0.7719 0.779910
17 to 18 142116 0.6096 0.728952
16 to 17 141580 -0.9715 0.165656
15 to 16 141563 -1.0216 0.153480
14 to 15 142253 1.0138 0.844655
13 to 14 142072 0.4799 0.684334
12 to 13 141531 -1.1160 0.132207
11 to 12 142077 0.4946 0.689559
10 to 11 141758 -0.4464 0.327654
9 to 10 142093 0.5418 0.706022
8 to 9 141968 0.1731 0.568701
7 to 8 142382 1.3943 0.918388
6 to 7 141658 -0.7414 0.229230
5 to 6 141620 -0.8535 0.196696
4 to 5 141445 -1.3697 0.085390
3 to 4 141683 -0.6676 0.252182
2 to 3 141013 -2.6440 0.004096
1 to 2 141662 -0.7296 0.232821
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2490.60 -0.133 0.447105
Test results for specific bytes for dh-ranFile-2018-06-19_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2414.69 -1.206 0.113813
2 to 9 2474.05 -0.367 0.356805
3 to 10 2448.55 -0.728 0.233438
4 to 11 2563.57 0.899 0.815672
5 to 12 2502.69 0.038 0.515146
6 to 13 2467.22 -0.464 0.321465
7 to 14 2325.98 -2.461 0.006927
8 to 15 2622.46 1.732 0.958347
9 to 16 2514.18 0.201 0.579466
10 to 17 2653.33 2.168 0.984936
11 to 18 2572.12 1.020 0.846115
12 to 19 2552.03 0.736 0.769062
13 to 20 2398.98 -1.429 0.076553
14 to 21 2542.41 0.600 0.725690
15 to 22 2522.31 0.316 0.623821
16 to 23 2564.03 0.906 0.817415
17 to 24 2556.41 0.798 0.787497
18 to 25 2555.59 0.786 0.784096
19 to 26 2433.40 -0.942 0.173143
20 to 27 2574.24 1.050 0.853114
21 to 28 2537.46 0.530 0.701841
22 to 29 2504.13 0.058 0.523263
23 to 30 2389.72 -1.560 0.059428
24 to 31 2486.24 -0.195 0.422842
25 to 32 2339.00 -2.277 0.011396
CDPARK for dh-ranFile-2018-06-19_03:31: 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
3531 0.3653 0.642555
3543 0.9132 0.819442
3570 2.1461 0.984068
3504 -0.8676 0.192812
3562 1.7808 0.962529
3506 -0.7763 0.218799
3533 0.4566 0.676028
3531 0.3653 0.642555
3533 0.4566 0.676028
3529 0.2740 0.607947
Square side=100, avg. no. parked=3534.20 sample std.=19.72
p-value of the KSTEST for those 10 p-values: 0.140550
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_03:31
0.4774,0.4982,0.5526,0.6583,0.0485,0.3894,0.0773,0.2785,0.9491,0.6155,
The KS test for those 10 p-values: 0.779146
The 3DSPHERES test for dh-ranFile-2018-06-19_03:31
sample no r^3 equiv. uni.
1 8.117 0.237055
2 6.595 0.197355
3 51.609 0.820985
4 10.604 0.297755
5 33.254 0.669931
6 65.557 0.887547
7 41.183 0.746599
8 57.418 0.852502
9 32.353 0.659873
10 9.417 0.269396
11 49.940 0.810749
12 10.865 0.303833
13 30.986 0.644015
14 17.139 0.435217
15 3.404 0.107275
16 21.566 0.512697
17 23.064 0.536438
18 38.817 0.725802
19 34.050 0.678581
20 4.506 0.139465
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.644261
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 -1.3 1.1 -0.4 0.2
0.0 0.3 -1.2 0.2 1.3 -0.8
-0.8 -0.5 -1.0 1.1 -0.4 0.4
1.0 -0.2 -0.0 -0.8 0.7 0.9
0.2 -0.3 0.3 -2.1 0.3 0.8
0.5 0.4 -1.3 -0.1 -0.1 -0.8
-0.2 1.1 2.5 2.6 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:37.948407
z-score=-0.442065, p-value=0.350594
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_03:31
Test no p-value
1 0.001166
2 0.197458
3 0.167687
4 0.428546
5 0.639056
6 0.031226
7 0.989860
8 0.398827
9 0.489146
10 0.006669
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.024933
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_03:31:
(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 66633 0.02 66618 0.04
3 25000.00 25079 0.25 25045 0.08
4 6666.67 6666 0.00 6722 0.46
5 1388.89 1341 1.65 1315 3.93
6 238.10 240 0.02 256 1.35
7 34.72 37 0.15 35 0.00
8 4.96 3 0.77 8 1.86
p=0.17349 p=0.74055
Number of rngs required: 688419, p-value: 0.507
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_03:31
No. of wins: Observed Expected
99200 98585.9
z-score= 2.747, pvalue=0.99699
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66723 66666.7 0.048 0.048
2 37945 37654.3 2.244 2.292
3 26855 26954.7 0.369 2.661
4 19371 19313.5 0.171 2.832
5 13716 13851.4 1.324 4.156
6 9788 9943.5 2.433 6.589
7 7199 7145.0 0.408 6.997
8 5144 5139.1 0.005 7.001
9 3770 3699.9 1.329 8.331
10 2581 2666.3 2.729 11.060
11 1929 1923.3 0.017 11.076
12 1394 1388.7 0.020 11.096
13 959 1003.7 1.992 13.088
14 732 726.1 0.047 13.136
15 523 525.8 0.015 13.151
16 384 381.2 0.021 13.172
17 268 276.5 0.264 13.436
18 204 200.8 0.050 13.486
19 143 146.0 0.061 13.547
20 100 106.2 0.364 13.911
21 272 287.1 0.796 14.706
Chisq= 14.71 for 20 degrees of freedom, p= 0.20704
SUMMARY of craptest
p-value for no. of wins: 0.996991
p-value for throws/game: 0.207042
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_03:31
No. of wins: Observed Expected
98476 98585.9
z-score=-0.491, pvalue=0.31159
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66503 66666.7 0.402 0.402
2 37606 37654.3 0.062 0.464
3 26782 26954.7 1.107 1.571
4 19408 19313.5 0.463 2.033
5 13951 13851.4 0.716 2.749
6 9973 9943.5 0.087 2.837
7 7081 7145.0 0.574 3.410
8 5179 5139.1 0.310 3.721
9 3729 3699.9 0.229 3.950
10 2701 2666.3 0.452 4.402
11 1950 1923.3 0.370 4.772
12 1399 1388.7 0.076 4.847
13 1020 1003.7 0.264 5.112
14 764 726.1 1.974 7.085
15 546 525.8 0.773 7.859
16 400 381.2 0.932 8.791
17 300 276.5 1.990 10.781
18 190 200.8 0.584 11.365
19 128 146.0 2.216 13.581
20 112 106.2 0.315 13.896
21 278 287.1 0.289 14.185
Chisq= 14.19 for 20 degrees of freedom, p= 0.17901
SUMMARY of craptest
p-value for no. of wins: 0.311589
p-value for throws/game: 0.179011
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0024,0.0041,0.0067,0.0069,0.0114,0.0204,0.0249,0.0312,0.0371,
0.0416,0.0485,0.0551,0.0594,0.0626,0.0746,0.0766,0.0773,0.0854,0.0865,
0.1035,0.1073,0.1095,0.1130,0.1138,0.1152,0.1288,0.1322,0.1339,0.1348,
0.1385,0.1395,0.1403,0.1406,0.1421,0.1471,0.1486,0.1488,0.1535,0.1572,
0.1613,0.1657,0.1677,0.1731,0.1735,0.1790,0.1902,0.1928,0.1967,0.1974,
0.1975,0.2032,0.2070,0.2082,0.2188,0.2243,0.2244,0.2292,0.2328,0.2334,
0.2371,0.2451,0.2503,0.2522,0.2569,0.2636,0.2694,0.2780,0.2785,0.2796,
0.2853,0.2909,0.2910,0.2953,0.2978,0.3038,0.3042,0.3083,0.3116,0.3134,
0.3166,0.3171,0.3179,0.3181,0.3200,0.3215,0.3232,0.3269,0.3277,0.3330,
0.3392,0.3395,0.3488,0.3505,0.3506,0.3568,0.3579,0.3622,0.3649,0.3675,
0.3680,0.3806,0.3840,0.3886,0.3893,0.3894,0.3986,0.3988,0.4037,0.4040,
0.4190,0.4228,0.4271,0.4285,0.4352,0.4393,0.4460,0.4471,0.4547,0.4671,
0.4748,0.4752,0.4752,0.4774,0.4877,0.4891,0.4982,0.4982,0.5021,0.5073,
0.5074,0.5104,0.5127,0.5142,0.5146,0.5151,0.5171,0.5198,0.5212,0.5233,
0.5320,0.5364,0.5399,0.5476,0.5514,0.5526,0.5589,0.5687,0.5724,0.5795,
0.5830,0.5840,0.6032,0.6043,0.6079,0.6155,0.6196,0.6217,0.6238,0.6253,
0.6259,0.6306,0.6364,0.6381,0.6391,0.6426,0.6426,0.6435,0.6440,0.6443,
0.6538,0.6550,0.6583,0.6599,0.6601,0.6613,0.6649,0.6674,0.6699,0.6751,
0.6760,0.6760,0.6786,0.6843,0.6881,0.6896,0.6920,0.7018,0.7025,0.7060,
0.7081,0.7111,0.7151,0.7177,0.7257,0.7258,0.7290,0.7303,0.7366,0.7406,
0.7415,0.7435,0.7466,0.7533,0.7555,0.7566,0.7645,0.7691,0.7777,0.7791,
0.7799,0.7841,0.7874,0.7875,0.7942,0.7971,0.7996,0.8002,0.8016,0.8048,
0.8098,0.8107,0.8157,0.8174,0.8176,0.8194,0.8210,0.8302,0.8347,0.8361,
0.8447,0.8461,0.8525,0.8531,0.8656,0.8673,0.8697,0.8816,0.8854,0.8875,
0.8931,0.8982,0.9025,0.9091,0.9091,0.9132,0.9133,0.9144,0.9184,0.9192,
0.9208,0.9208,0.9248,0.9362,0.9462,0.9491,0.9583,0.9625,0.9669,0.9680,
0.9687,0.9689,0.9693,0.9744,0.9841,0.9849,0.9896,0.9899,0.9970,
Overall p-value after applying KStest on 269 p-values = 0.850679
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.