RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.99 18.2976 0.629698
2 to 25 15.76 26.7780 0.938595
3 to 26 15.64 30.7183 0.978394
4 to 27 15.61 20.4156 0.746476
5 to 28 15.49 22.0797 0.818327
6 to 29 15.66 20.2788 0.739780
7 to 30 15.52 20.6140 0.755968
8 to 31 15.45 29.8609 0.972634
9 to 32 15.65 30.6650 0.978071
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000232
Tough bday spacings test for dh-ranFile-2018-07-12_15:31: 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 7 33 65 99 104 86 60 29 11 5 1
(O-E)^2/E 0.5 0.4 0.9 0.0 0.4 0.8 1.2 0.0 1.0 0.4 2.3
Birthday Spacings: Sum(O-E)^2/E= 7.955, p= 0.367
RESULTS OF GCD FOR dh-ranFile-2018-07-12_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.864183
p-value, dist. of gcd's: 0.017430
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.924 0.738 0.598 0.457 0.763 0.847 0.378 0.591
Bits 8 to 15---> 0.825 0.799 0.687 0.874 0.857 0.357 0.700 0.103
Bits 16 to 23---> 0.389 0.862 0.364 0.754 0.514 0.203 0.314 0.952
Bits 24 to 31---> 0.984 0.194 0.871 0.641 0.152 0.175 0.379 0.532
KS test for the above 32 p values: 0.862
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_15:31,
p-values for 5 runs: 0.3718, 0.5696, 0.7855, 0.5863, 0.6442
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 5057 5134.0 1.155 1.575
r= 30 23329 23103.0 2.210 3.785
r= 31 11412 11551.5 1.685 5.470
chi-square = 5.470 with df = 3; p-value = 0.860
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5116 5134.0 0.063 0.211
r= 31 23137 23103.0 0.050 0.260
r= 32 11530 11551.5 0.040 0.301
chi-square = 0.301 with df = 3; p-value = 0.040
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_15:31
b-rank test for bits 1 to 8, p=0.28272
b-rank test for bits 2 to 9, p=0.57877
b-rank test for bits 3 to 10, p=0.37908
b-rank test for bits 4 to 11, p=0.14323
b-rank test for bits 5 to 12, p=0.44633
b-rank test for bits 6 to 13, p=0.25891
b-rank test for bits 7 to 14, p=0.13330
b-rank test for bits 8 to 15, p=0.34817
b-rank test for bits 9 to 16, p=0.87251
b-rank test for bits 10 to 17, p=0.20804
b-rank test for bits 11 to 18, p=0.09315
b-rank test for bits 12 to 19, p=0.83954
b-rank test for bits 13 to 20, p=0.25820
b-rank test for bits 14 to 21, p=0.38534
b-rank test for bits 15 to 22, p=0.55352
b-rank test for bits 16 to 23, p=0.84767
b-rank test for bits 17 to 24, p=0.08874
b-rank test for bits 18 to 25, p=0.01112
b-rank test for bits 19 to 26, p=0.35458
b-rank test for bits 20 to 27, p=0.47219
b-rank test for bits 21 to 28, p=0.00242
b-rank test for bits 22 to 29, p=0.28829
b-rank test for bits 23 to 30, p=0.41876
b-rank test for bits 24 to 31, p=0.68089
b-rank test for bits 25 to 32, p=0.85195
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 = 0.080669
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_15:31
(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 141901 -0.02 0.492236
2 142278 0.86 0.805485
3 141672 -0.55 0.289615
4 141959 0.12 0.546194
5 141099 -1.89 0.029159
6 142287 0.88 0.811222
7 141795 -0.27 0.394686
8 142464 1.30 0.902505
9 141938 0.07 0.526704
10 141157 -1.76 0.039392
11 141485 -0.99 0.160739
12 142303 0.92 0.821159
13 142279 0.86 0.806128
14 142379 1.10 0.863758
15 141369 -1.26 0.103393
16 140840 -2.50 0.006237
17 142017 0.25 0.599312
18 142508 1.40 0.919058
19 141986 0.18 0.571084
20 141573 -0.79 0.215987
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_15:31
Bits used No. missing words z-score p-value
23 to 32 141298 -2.1080 0.017514
22 to 31 141829 -0.2770 0.390890
21 to 30 141950 0.1402 0.555765
20 to 29 141993 0.2885 0.613525
19 to 28 141934 0.0851 0.533897
18 to 27 141912 0.0092 0.503673
17 to 26 141999 0.3092 0.621418
16 to 25 142409 1.7230 0.957556
15 to 24 141926 0.0575 0.522920
14 to 23 141860 -0.1701 0.432464
13 to 22 142134 0.7747 0.780749
12 to 21 142093 0.6333 0.736746
11 to 20 141595 -1.0839 0.139205
10 to 19 141719 -0.6563 0.255812
9 to 18 142080 0.5885 0.721907
8 to 17 142080 0.5885 0.721907
7 to 16 142537 2.1644 0.984782
6 to 15 142025 0.3989 0.655003
5 to 14 141930 0.0713 0.528411
4 to 13 141503 -1.4011 0.080586
3 to 12 141969 0.2058 0.581510
2 to 11 142245 1.1575 0.876462
1 to 10 141518 -1.3494 0.088602
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_15:31
Bits used No. missing words z-score p-value
28 to 32 141861 -0.1638 0.434932
27 to 31 142475 1.9175 0.972414
26 to 30 141894 -0.0520 0.479278
25 to 29 141639 -0.9164 0.179736
24 to 28 141803 -0.3604 0.359259
23 to 27 142169 0.8802 0.810635
22 to 26 142007 0.3311 0.629710
21 to 25 142246 1.1413 0.873118
20 to 24 142009 0.3379 0.632267
19 to 23 141473 -1.4791 0.069559
18 to 22 142039 0.4396 0.669872
17 to 21 141645 -0.8960 0.185117
16 to 20 141896 -0.0452 0.481979
15 to 19 142591 2.3107 0.989577
14 to 18 141750 -0.5401 0.294564
13 to 17 141769 -0.4757 0.317146
12 to 16 142155 0.8328 0.797516
11 to 15 142186 0.9379 0.825843
10 to 14 141700 -0.7096 0.238978
9 to 13 141560 -1.1842 0.118173
8 to 12 141752 -0.5333 0.296905
7 to 11 141964 0.1853 0.573512
6 to 10 141715 -0.6587 0.255030
5 to 9 141956 0.1582 0.562852
4 to 8 142082 0.5853 0.720834
3 to 7 141878 -0.1062 0.457711
2 to 6 142040 0.4429 0.671099
1 to 5 141423 -1.6486 0.049617
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_15:31
Bits used No. missing words z-score p-value
31 to 32 142028 0.3501 0.636853
30 to 31 141794 -0.3402 0.366851
29 to 30 142228 0.9400 0.826399
28 to 29 142102 0.5683 0.715101
27 to 28 142028 0.3501 0.636853
26 to 27 142146 0.6981 0.757456
25 to 26 142036 0.3737 0.645671
24 to 25 141707 -0.5968 0.275306
23 to 24 141767 -0.4199 0.337297
22 to 23 141338 -1.6853 0.045962
21 to 22 142198 0.8515 0.802764
20 to 21 142614 2.0787 0.981176
19 to 20 142090 0.5329 0.702966
18 to 19 141975 0.1937 0.576801
17 to 18 141614 -0.8712 0.191828
16 to 17 141733 -0.5201 0.301480
15 to 16 142502 1.7483 0.959793
14 to 15 141563 -1.0216 0.153480
13 to 14 141388 -1.5378 0.062043
12 to 13 142287 1.1141 0.867376
11 to 12 141954 0.1318 0.552417
10 to 11 141907 -0.0069 0.497258
9 to 10 142113 0.6008 0.726012
8 to 9 141524 -1.1367 0.127839
7 to 8 141711 -0.5850 0.279259
6 to 7 142581 1.9813 0.976223
5 to 6 141925 0.0462 0.518434
4 to 5 142451 1.5978 0.944961
3 to 4 141570 -1.0010 0.158420
2 to 3 142156 0.7276 0.766583
1 to 2 141784 -0.3697 0.355801
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2459.89 -0.567 0.285253
Test results for specific bytes for dh-ranFile-2018-07-12_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2453.40 -0.659 0.254921
2 to 9 2585.07 1.203 0.885535
3 to 10 2464.72 -0.499 0.308899
4 to 11 2392.60 -1.519 0.064391
5 to 12 2574.16 1.049 0.852865
6 to 13 2575.25 1.064 0.856365
7 to 14 2587.12 1.232 0.891045
8 to 15 2418.58 -1.151 0.124778
9 to 16 2467.54 -0.459 0.323092
10 to 17 2578.92 1.116 0.867814
11 to 18 2517.82 0.252 0.599483
12 to 19 2415.35 -1.197 0.115629
13 to 20 2429.78 -0.993 0.160356
14 to 21 2653.32 2.168 0.984931
15 to 22 2569.18 0.978 0.836054
16 to 23 2579.70 1.127 0.870156
17 to 24 2502.67 0.038 0.515064
18 to 25 2445.22 -0.775 0.219276
19 to 26 2393.02 -1.513 0.065149
20 to 27 2474.33 -0.363 0.358275
21 to 28 2644.41 2.042 0.979439
22 to 29 2428.41 -1.012 0.155666
23 to 30 2402.05 -1.385 0.083002
24 to 31 2517.00 0.240 0.594975
25 to 32 2411.69 -1.249 0.105844
CDPARK for dh-ranFile-2018-07-12_15:31: 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
3515 -0.3653 0.357445
3488 -1.5982 0.055002
3529 0.2740 0.607947
3536 0.5936 0.723613
3490 -1.5068 0.065925
3511 -0.5479 0.291865
3523 0.0000 0.500000
3530 0.3196 0.625377
3528 0.2283 0.590298
3546 1.0502 0.853193
Square side=100, avg. no. parked=3519.60 sample std.=17.93
p-value of the KSTEST for those 10 p-values: 0.794259
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_15:31
0.8504,0.8878,0.7396,0.6614,0.0726,0.2650,0.7493,0.4337,0.9207,0.1385,
The KS test for those 10 p-values: 0.635281
The 3DSPHERES test for dh-ranFile-2018-07-12_15:31
sample no r^3 equiv. uni.
1 0.595 0.019636
2 13.241 0.356833
3 3.235 0.102218
4 1.010 0.033117
5 57.042 0.850642
6 31.982 0.655634
7 45.594 0.781242
8 0.486 0.016060
9 17.116 0.434782
10 3.940 0.123073
11 57.959 0.855139
12 1.977 0.063774
13 1.975 0.063705
14 33.267 0.670077
15 5.210 0.159428
16 20.852 0.500962
17 108.726 0.973329
18 75.932 0.920427
19 5.789 0.175504
20 28.516 0.613460
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.094201
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.8 -0.6 -0.5 0.4 0.6
-1.1 0.6 0.8 -2.8 1.2 -0.1
-2.0 0.3 1.4 -0.1 0.8 -0.6
-1.5 -0.2 1.4 0.6 0.3 -0.7
-0.1 0.8 1.5 -0.7 -0.3 -0.6
0.6 0.0 0.2 0.2 0.1 -0.5
-0.7 0.8 0.5 -0.1 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:35.308618
z-score=-0.730090, p-value=0.242249
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_15:31
Test no p-value
1 0.007376
2 0.448852
3 0.990286
4 0.582803
5 0.256723
6 0.284594
7 0.013476
8 0.048926
9 0.063080
10 0.545015
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.024876
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_15:31:
(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 66776 0.18 66441 0.76
3 25000.00 24898 0.42 25278 3.09
4 6666.67 6708 0.26 6603 0.61
5 1388.89 1367 0.35 1412 0.38
6 238.10 212 2.86 228 0.43
7 34.72 30 0.64 29 0.94
8 4.96 8 1.86 8 1.86
p=0.63670 p=0.76781
Number of rngs required: 688260, p-value: 0.435
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_15:31
No. of wins: Observed Expected
98689 98585.9
z-score= 0.461, pvalue=0.67771
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67034 66666.7 2.024 2.024
2 37532 37654.3 0.397 2.421
3 27023 26954.7 0.173 2.594
4 19328 19313.5 0.011 2.605
5 13868 13851.4 0.020 2.625
6 9801 9943.5 2.043 4.668
7 7165 7145.0 0.056 4.724
8 5067 5139.1 1.011 5.735
9 3628 3699.9 1.396 7.131
10 2658 2666.3 0.026 7.157
11 1918 1923.3 0.015 7.172
12 1335 1388.7 2.080 9.251
13 1005 1003.7 0.002 9.253
14 757 726.1 1.311 10.564
15 541 525.8 0.437 11.002
16 378 381.2 0.026 11.028
17 259 276.5 1.112 12.140
18 186 200.8 1.095 13.235
19 126 146.0 2.736 15.971
20 92 106.2 1.902 17.873
21 299 287.1 0.492 18.365
Chisq= 18.37 for 20 degrees of freedom, p= 0.43665
SUMMARY of craptest
p-value for no. of wins: 0.677711
p-value for throws/game: 0.436647
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_15:31
No. of wins: Observed Expected
98613 98585.9
z-score= 0.121, pvalue=0.54831
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66502 66666.7 0.407 0.407
2 37676 37654.3 0.012 0.419
3 27083 26954.7 0.610 1.030
4 19360 19313.5 0.112 1.142
5 13832 13851.4 0.027 1.169
6 9836 9943.5 1.163 2.332
7 7223 7145.0 0.851 3.183
8 5090 5139.1 0.469 3.652
9 3674 3699.9 0.181 3.832
10 2679 2666.3 0.061 3.893
11 1887 1923.3 0.686 4.579
12 1450 1388.7 2.702 7.281
13 1020 1003.7 0.264 7.546
14 721 726.1 0.036 7.582
15 543 525.8 0.560 8.142
16 382 381.2 0.002 8.144
17 284 276.5 0.201 8.345
18 205 200.8 0.087 8.432
19 154 146.0 0.440 8.872
20 123 106.2 2.652 11.525
21 276 287.1 0.430 11.955
Chisq= 11.95 for 20 degrees of freedom, p= 0.08238
SUMMARY of craptest
p-value for no. of wins: 0.548310
p-value for throws/game: 0.082377
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0024,0.0062,0.0074,0.0111,0.0135,0.0161,0.0174,0.0175,0.0196,
0.0249,0.0292,0.0331,0.0394,0.0401,0.0460,0.0489,0.0496,0.0550,0.0620,
0.0631,0.0637,0.0638,0.0644,0.0651,0.0659,0.0696,0.0726,0.0806,0.0807,
0.0824,0.0830,0.0886,0.0887,0.0932,0.0942,0.1022,0.1028,0.1034,0.1058,
0.1156,0.1182,0.1231,0.1248,0.1278,0.1333,0.1385,0.1392,0.1432,0.1521,
0.1535,0.1557,0.1584,0.1594,0.1604,0.1607,0.1748,0.1755,0.1797,0.1851,
0.1918,0.1939,0.2030,0.2080,0.2160,0.2193,0.2390,0.2422,0.2549,0.2550,
0.2558,0.2567,0.2582,0.2589,0.2650,0.2753,0.2793,0.2827,0.2846,0.2853,
0.2883,0.2896,0.2919,0.2946,0.2969,0.3015,0.3089,0.3140,0.3171,0.3231,
0.3373,0.3482,0.3546,0.3558,0.3566,0.3568,0.3574,0.3583,0.3593,0.3645,
0.3668,0.3669,0.3718,0.3779,0.3786,0.3791,0.3853,0.3886,0.3909,0.3947,
0.4188,0.4325,0.4337,0.4347,0.4348,0.4349,0.4366,0.4463,0.4489,0.4569,
0.4577,0.4722,0.4793,0.4820,0.4922,0.4973,0.5000,0.5010,0.5037,0.5137,
0.5151,0.5184,0.5229,0.5267,0.5284,0.5324,0.5339,0.5450,0.5462,0.5483,
0.5524,0.5535,0.5558,0.5629,0.5696,0.5711,0.5735,0.5768,0.5788,0.5815,
0.5828,0.5863,0.5903,0.5906,0.5950,0.5982,0.5993,0.5995,0.6079,0.6135,
0.6135,0.6214,0.6254,0.6297,0.6297,0.6323,0.6353,0.6367,0.6369,0.6369,
0.6413,0.6442,0.6457,0.6550,0.6556,0.6614,0.6699,0.6701,0.6711,0.6777,
0.6809,0.6865,0.6996,0.7030,0.7151,0.7208,0.7219,0.7219,0.7236,0.7260,
0.7367,0.7376,0.7396,0.7398,0.7465,0.7493,0.7540,0.7560,0.7575,0.7627,
0.7666,0.7678,0.7807,0.7812,0.7855,0.7943,0.7975,0.7992,0.8028,0.8055,
0.8061,0.8106,0.8112,0.8183,0.8212,0.8247,0.8258,0.8264,0.8361,0.8395,
0.8470,0.8477,0.8504,0.8506,0.8519,0.8529,0.8532,0.8551,0.8564,0.8567,
0.8595,0.8622,0.8625,0.8638,0.8642,0.8674,0.8678,0.8702,0.8708,0.8725,
0.8731,0.8737,0.8765,0.8855,0.8878,0.8910,0.9025,0.9191,0.9204,0.9207,
0.9242,0.9386,0.9450,0.9518,0.9576,0.9598,0.9724,0.9726,0.9733,0.9762,
0.9781,0.9784,0.9794,0.9812,0.9842,0.9848,0.9849,0.9896,0.9903,
Overall p-value after applying KStest on 269 p-values = 0.381409
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.