RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.89 18.3813 0.634822
2 to 25 15.49 26.8704 0.940004
3 to 26 15.79 20.1186 0.731790
4 to 27 16.03 10.4275 0.115268
5 to 28 15.91 9.7226 0.085163
6 to 29 15.69 16.0453 0.479374
7 to 30 15.78 14.9089 0.397960
8 to 31 16.05 23.6534 0.870837
9 to 32 15.92 10.3007 0.109469
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.907390
Tough bday spacings test for dh-ranFile-2018-06-26_23:31: 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 8 26 75 83 108 90 56 28 14 6 6
(O-E)^2/E 0.1 3.1 0.0 2.2 1.1 1.8 0.3 0.1 0.1 0.1 0.9
Birthday Spacings: Sum(O-E)^2/E= 9.795, p= 0.541
RESULTS OF GCD FOR dh-ranFile-2018-06-26_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.939332
p-value, dist. of gcd's: 0.188091
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.210 0.437 0.475 0.200 0.026 0.556 0.681 0.671
Bits 8 to 15---> 0.891 0.106 0.953 0.199 0.736 0.006 0.507 0.764
Bits 16 to 23---> 0.041 0.637 0.578 0.400 0.328 0.276 0.385 0.343
Bits 24 to 31---> 0.202 0.267 0.600 0.884 0.175 0.121 0.412 0.992
KS test for the above 32 p values: 0.566
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_23:31,
p-values for 5 runs: 0.9448, 0.3733, 0.0768, 0.8028, 0.5656
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5145 5134.0 0.024 0.079
r= 30 23051 23103.0 0.117 0.196
r= 31 11596 11551.5 0.171 0.367
chi-square = 0.367 with df = 3; p-value = 0.053
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5075 5134.0 0.678 0.706
r= 31 23097 23103.0 0.002 0.708
r= 32 11619 11551.5 0.394 1.102
chi-square = 1.102 with df = 3; p-value = 0.223
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_23:31
b-rank test for bits 1 to 8, p=0.70230
b-rank test for bits 2 to 9, p=0.39863
b-rank test for bits 3 to 10, p=0.74813
b-rank test for bits 4 to 11, p=0.59674
b-rank test for bits 5 to 12, p=0.53570
b-rank test for bits 6 to 13, p=0.05534
b-rank test for bits 7 to 14, p=0.10666
b-rank test for bits 8 to 15, p=0.25401
b-rank test for bits 9 to 16, p=0.27758
b-rank test for bits 10 to 17, p=0.59559
b-rank test for bits 11 to 18, p=0.36318
b-rank test for bits 12 to 19, p=0.95579
b-rank test for bits 13 to 20, p=0.21284
b-rank test for bits 14 to 21, p=0.62246
b-rank test for bits 15 to 22, p=0.91068
b-rank test for bits 16 to 23, p=0.52649
b-rank test for bits 17 to 24, p=0.71310
b-rank test for bits 18 to 25, p=0.26182
b-rank test for bits 19 to 26, p=0.83391
b-rank test for bits 20 to 27, p=0.30407
b-rank test for bits 21 to 28, p=0.13534
b-rank test for bits 22 to 29, p=0.78840
b-rank test for bits 23 to 30, p=0.82070
b-rank test for bits 24 to 31, p=0.55650
b-rank test for bits 25 to 32, p=0.91881
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 = 0.920201
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_23:31
(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 142020 0.26 0.602018
2 141946 0.09 0.534139
3 142076 0.39 0.651516
4 141286 -1.46 0.072644
5 142049 0.33 0.627913
6 141470 -1.03 0.152335
7 141704 -0.48 0.315705
8 142101 0.45 0.672861
9 142074 0.38 0.649786
10 142091 0.42 0.664386
11 142190 0.66 0.744014
12 142648 1.73 0.957814
13 142186 0.65 0.740998
14 141499 -0.96 0.168851
15 141469 -1.03 0.151785
16 141378 -1.24 0.107224
17 142159 0.58 0.720168
18 141603 -0.72 0.237081
19 142140 0.54 0.705039
20 142051 0.33 0.629680
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_23:31
Bits used No. missing words z-score p-value
23 to 32 142170 0.8989 0.815637
22 to 31 142301 1.3506 0.911586
21 to 30 142015 0.3644 0.642213
20 to 29 142140 0.7954 0.786814
19 to 28 142058 0.5127 0.695904
18 to 27 141722 -0.6460 0.259151
17 to 26 142041 0.4540 0.675098
16 to 25 142032 0.4230 0.663852
15 to 24 142321 1.4196 0.922131
14 to 23 141894 -0.0529 0.478921
13 to 22 141626 -0.9770 0.164285
12 to 21 141876 -0.1149 0.454250
11 to 20 141893 -0.0563 0.477547
10 to 19 141956 0.1609 0.563926
9 to 18 141774 -0.4667 0.320373
8 to 17 141754 -0.5356 0.296110
7 to 16 141969 0.2058 0.581510
6 to 15 141831 -0.2701 0.393540
5 to 14 141720 -0.6529 0.256923
4 to 13 142019 0.3782 0.647349
3 to 12 141659 -0.8632 0.194012
2 to 11 142295 1.3299 0.908224
1 to 10 141566 -1.1839 0.118227
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_23:31
Bits used No. missing words z-score p-value
28 to 32 141749 -0.5435 0.293396
27 to 31 141629 -0.9503 0.170987
26 to 30 141672 -0.8045 0.210552
25 to 29 141822 -0.2960 0.383602
24 to 28 141719 -0.6452 0.259403
23 to 27 141911 0.0057 0.502258
22 to 26 142230 1.0870 0.861485
21 to 25 141424 -1.6452 0.049966
20 to 24 141845 -0.2181 0.413688
19 to 23 141536 -1.2655 0.102842
18 to 22 141906 -0.0113 0.495497
17 to 21 141762 -0.4994 0.308741
16 to 20 142032 0.4158 0.661233
15 to 19 141858 -0.1740 0.430933
14 to 18 141773 -0.4621 0.321992
13 to 17 141387 -1.7706 0.038313
12 to 16 142046 0.4633 0.678421
11 to 15 141893 -0.0554 0.477928
10 to 14 141574 -1.1367 0.127829
9 to 13 141979 0.2362 0.593349
8 to 12 141911 0.0057 0.502258
7 to 11 142088 0.6057 0.727630
6 to 10 141673 -0.8011 0.211532
5 to 9 141804 -0.3571 0.360527
4 to 8 142251 1.1582 0.876610
3 to 7 142263 1.1989 0.884713
2 to 6 141931 0.0735 0.529279
1 to 5 141332 -1.9571 0.025171
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_23:31
Bits used No. missing words z-score p-value
31 to 32 142329 1.2380 0.892135
30 to 31 142069 0.4710 0.681181
29 to 30 141926 0.0492 0.519610
28 to 29 142231 0.9489 0.828659
27 to 28 142191 0.8309 0.796981
26 to 27 142185 0.8132 0.791944
25 to 26 141786 -0.3638 0.358002
24 to 25 141602 -0.9066 0.182315
23 to 24 141567 -1.0098 0.156290
22 to 23 141071 -2.4729 0.006700
21 to 22 141959 0.1465 0.558244
20 to 21 142135 0.6657 0.747196
19 to 20 142335 1.2557 0.895381
18 to 19 141839 -0.2075 0.417824
17 to 18 141525 -1.1337 0.128457
16 to 17 141739 -0.5024 0.307676
15 to 16 142119 0.6185 0.731876
14 to 15 141956 0.1377 0.554749
13 to 14 141074 -2.4641 0.006868
12 to 13 141327 -1.7178 0.042918
11 to 12 141655 -0.7502 0.226556
10 to 11 141941 0.0934 0.537216
9 to 10 142106 0.5801 0.719092
8 to 9 141511 -1.1750 0.119994
7 to 8 141403 -1.4936 0.067640
6 to 7 142023 0.3353 0.631304
5 to 6 141890 -0.0570 0.477264
4 to 5 141572 -0.9951 0.159850
3 to 4 141850 -0.1750 0.430534
2 to 3 141972 0.1849 0.573333
1 to 2 142318 1.2055 0.885998
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2413.02 -1.230 0.109323
Test results for specific bytes for dh-ranFile-2018-06-26_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2524.67 0.349 0.636400
2 to 9 2466.55 -0.473 0.318090
3 to 10 2513.57 0.192 0.576111
4 to 11 2488.34 -0.165 0.434509
5 to 12 2405.19 -1.341 0.089998
6 to 13 2525.43 0.360 0.640418
7 to 14 2553.38 0.755 0.774859
8 to 15 2545.74 0.647 0.741142
9 to 16 2383.13 -1.653 0.049180
10 to 17 2590.39 1.278 0.899441
11 to 18 2418.57 -1.152 0.124743
12 to 19 2436.91 -0.892 0.186124
13 to 20 2517.88 0.253 0.599798
14 to 21 2568.93 0.975 0.835171
15 to 22 2577.51 1.096 0.863488
16 to 23 2562.08 0.878 0.810027
17 to 24 2402.74 -1.375 0.084502
18 to 25 2552.68 0.745 0.771865
19 to 26 2490.87 -0.129 0.448613
20 to 27 2540.82 0.577 0.718108
21 to 28 2541.70 0.590 0.722308
22 to 29 2519.03 0.269 0.606105
23 to 30 2429.21 -1.001 0.158388
24 to 31 2392.84 -1.515 0.064835
25 to 32 2464.97 -0.495 0.310176
CDPARK for dh-ranFile-2018-06-26_23:31: 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
3535 0.5479 0.708135
3538 0.6849 0.753306
3545 1.0046 0.842447
3543 0.9132 0.819442
3546 1.0502 0.853193
3489 -1.5525 0.060270
3523 0.0000 0.500000
3531 0.3653 0.642555
3510 -0.5936 0.276387
3523 0.0000 0.500000
Square side=100, avg. no. parked=3528.30 sample std.=17.00
p-value of the KSTEST for those 10 p-values: 0.375028
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_23:31
0.3848,0.6397,0.4132,0.6899,0.3878,0.1547,0.6027,0.0279,0.5749,0.9610,
The KS test for those 10 p-values: 0.856322
The 3DSPHERES test for dh-ranFile-2018-06-26_23:31
sample no r^3 equiv. uni.
1 26.786 0.590520
2 29.994 0.632050
3 3.360 0.105944
4 36.491 0.703697
5 26.983 0.593196
6 13.169 0.355307
7 8.017 0.234513
8 0.232 0.007717
9 7.882 0.231042
10 13.927 0.371373
11 20.996 0.503351
12 13.551 0.363450
13 29.406 0.624767
14 11.971 0.329026
15 24.435 0.557138
16 48.369 0.800569
17 20.213 0.490207
18 65.236 0.886340
19 53.480 0.831808
20 22.026 0.520112
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.511774
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 -0.4 0.2 2.0 0.1
-0.9 -0.5 -0.3 2.1 0.6 0.4
-1.2 -0.7 -1.7 -1.1 0.8 -1.0
1.3 0.2 -1.0 1.7 0.6 1.8
-0.7 0.3 0.8 0.1 0.3 -1.9
-0.1 -1.7 -1.4 -0.9 0.6 1.7
1.4 -2.0 0.9 -0.1 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:49.021714
z-score=0.766132, p-value=0.787864
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_23:31
Test no p-value
1 0.178825
2 0.316279
3 0.394146
4 0.319950
5 0.210670
6 0.363112
7 0.355419
8 0.041913
9 0.000451
10 0.814975
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.024567
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_23:31:
(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 66547 0.21 66716 0.04
3 25000.00 25023 0.02 25057 0.13
4 6666.67 6693 0.10 6591 0.86
5 1388.89 1452 2.87 1378 0.09
6 238.10 241 0.04 224 0.83
7 34.72 38 0.31 31 0.40
8 4.96 5 0.00 2 1.77
p=0.26313 p=0.33823
Number of rngs required: 689545, p-value: 0.908
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_23:31
No. of wins: Observed Expected
99045 98585.9
z-score= 2.054, pvalue=0.97999
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66903 66666.7 0.838 0.838
2 37419 37654.3 1.471 2.308
3 26919 26954.7 0.047 2.356
4 19075 19313.5 2.944 5.300
5 13920 13851.4 0.340 5.640
6 10023 9943.5 0.635 6.275
7 7289 7145.0 2.901 9.176
8 5033 5139.1 2.189 11.365
9 3697 3699.9 0.002 11.367
10 2714 2666.3 0.853 12.221
11 1890 1923.3 0.578 12.798
12 1371 1388.7 0.227 13.025
13 1075 1003.7 5.063 18.088
14 785 726.1 4.771 22.859
15 520 525.8 0.065 22.923
16 357 381.2 1.530 24.454
17 284 276.5 0.201 24.655
18 189 200.8 0.697 25.352
19 132 146.0 1.340 26.691
20 109 106.2 0.073 26.764
21 296 287.1 0.275 27.039
Chisq= 27.04 for 20 degrees of freedom, p= 0.86584
SUMMARY of craptest
p-value for no. of wins: 0.979990
p-value for throws/game: 0.865841
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_23:31
No. of wins: Observed Expected
98682 98585.9
z-score= 0.430, pvalue=0.66640
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66801 66666.7 0.271 0.271
2 37939 37654.3 2.152 2.423
3 26807 26954.7 0.810 3.233
4 19203 19313.5 0.632 3.864
5 13802 13851.4 0.176 4.041
6 9810 9943.5 1.793 5.834
7 7150 7145.0 0.003 5.838
8 5222 5139.1 1.338 7.176
9 3673 3699.9 0.195 7.371
10 2615 2666.3 0.987 8.358
11 1975 1923.3 1.388 9.746
12 1375 1388.7 0.136 9.882
13 1030 1003.7 0.688 10.570
14 694 726.1 1.423 11.993
15 518 525.8 0.117 12.110
16 357 381.2 1.530 13.640
17 269 276.5 0.206 13.845
18 219 200.8 1.644 15.489
19 152 146.0 0.248 15.737
20 98 106.2 0.635 16.373
21 291 287.1 0.053 16.425
Chisq= 16.43 for 20 degrees of freedom, p= 0.31009
SUMMARY of craptest
p-value for no. of wins: 0.666402
p-value for throws/game: 0.310088
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0064,0.0067,0.0069,0.0077,0.0246,0.0252,0.0259,0.0279,0.0383,
0.0409,0.0419,0.0429,0.0492,0.0500,0.0531,0.0553,0.0603,0.0648,0.0676,
0.0726,0.0768,0.0845,0.0852,0.0900,0.1028,0.1059,0.1061,0.1067,0.1072,
0.1093,0.1095,0.1153,0.1182,0.1200,0.1214,0.1247,0.1278,0.1285,0.1353,
0.1518,0.1523,0.1547,0.1563,0.1584,0.1599,0.1643,0.1689,0.1710,0.1753,
0.1788,0.1823,0.1861,0.1881,0.1940,0.1988,0.2002,0.2019,0.2096,0.2106,
0.2107,0.2115,0.2128,0.2233,0.2266,0.2310,0.2345,0.2371,0.2540,0.2569,
0.2592,0.2594,0.2618,0.2631,0.2674,0.2756,0.2764,0.2776,0.2934,0.2961,
0.3041,0.3077,0.3087,0.3101,0.3102,0.3157,0.3163,0.3181,0.3200,0.3204,
0.3220,0.3281,0.3290,0.3382,0.3427,0.3553,0.3554,0.3580,0.3605,0.3631,
0.3632,0.3635,0.3714,0.3733,0.3750,0.3836,0.3848,0.3855,0.3878,0.3935,
0.3941,0.3980,0.3986,0.3997,0.4116,0.4132,0.4137,0.4178,0.4305,0.4309,
0.4345,0.4366,0.4486,0.4542,0.4751,0.4773,0.4775,0.4779,0.4789,0.4794,
0.4902,0.4955,0.5000,0.5000,0.5023,0.5023,0.5034,0.5067,0.5118,0.5196,
0.5201,0.5265,0.5293,0.5341,0.5357,0.5372,0.5413,0.5547,0.5559,0.5565,
0.5571,0.5582,0.5639,0.5656,0.5656,0.5733,0.5749,0.5761,0.5779,0.5815,
0.5905,0.5932,0.5933,0.5956,0.5967,0.5998,0.5998,0.6020,0.6027,0.6061,
0.6225,0.6248,0.6279,0.6297,0.6313,0.6320,0.6348,0.6364,0.6367,0.6397,
0.6404,0.6422,0.6426,0.6473,0.6498,0.6515,0.6612,0.6639,0.6644,0.6664,
0.6712,0.6729,0.6751,0.6784,0.6812,0.6812,0.6899,0.6959,0.7023,0.7037,
0.7050,0.7081,0.7131,0.7181,0.7191,0.7202,0.7223,0.7276,0.7318,0.7319,
0.7362,0.7410,0.7411,0.7440,0.7472,0.7481,0.7533,0.7640,0.7719,0.7749,
0.7868,0.7879,0.7884,0.7919,0.7970,0.8006,0.8028,0.8100,0.8150,0.8156,
0.8194,0.8207,0.8287,0.8318,0.8339,0.8352,0.8424,0.8532,0.8563,0.8615,
0.8635,0.8658,0.8708,0.8766,0.8838,0.8847,0.8860,0.8863,0.8910,0.8921,
0.8954,0.8994,0.9074,0.9082,0.9082,0.9107,0.9116,0.9188,0.9202,0.9221,
0.9393,0.9400,0.9448,0.9532,0.9558,0.9578,0.9610,0.9800,0.9918,
Overall p-value after applying KStest on 269 p-values = 0.286341
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.