RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 21.7823 0.806763
2 to 25 15.94 7.5773 0.025231
3 to 26 15.72 17.6715 0.590155
4 to 27 15.76 20.0728 0.729477
5 to 28 15.55 24.1339 0.884158
6 to 29 15.74 20.6262 0.756540
7 to 30 15.52 19.2991 0.688361
8 to 31 15.56 16.9635 0.543160
9 to 32 15.84 9.7543 0.086404
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.412582
Tough bday spacings test for dh-ranFile-2018-07-07_18:31: 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 32 65 101 107 68 64 27 14 4 6
(O-E)^2/E 0.9 0.6 0.9 0.1 0.9 1.3 2.7 0.3 0.1 1.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 9.702, p= 0.533
RESULTS OF GCD FOR dh-ranFile-2018-07-07_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.948384
p-value, dist. of gcd's: 0.614854
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.468 0.664 0.782 0.454 0.796 0.951 0.908 0.216
Bits 8 to 15---> 0.434 0.919 0.142 0.065 0.860 0.615 0.957 0.375
Bits 16 to 23---> 0.344 0.839 0.193 0.411 0.953 0.445 0.168 0.271
Bits 24 to 31---> 0.760 0.387 0.588 0.378 0.762 0.607 0.491 0.853
KS test for the above 32 p values: 0.700
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_18:31,
p-values for 5 runs: 0.2686, 0.6980, 0.5118, 0.2687, 0.6808
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 235 211.4 2.630 2.630
r= 29 5186 5134.0 0.526 3.157
r= 30 23057 23103.0 0.092 3.249
r= 31 11522 11551.5 0.075 3.324
chi-square = 3.324 with df = 3; p-value = 0.656
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 212 211.4 0.002 0.002
r= 30 5198 5134.0 0.798 0.799
r= 31 23247 23103.0 0.897 1.696
r= 32 11343 11551.5 3.764 5.460
chi-square = 5.460 with df = 3; p-value = 0.859
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_18:31
b-rank test for bits 1 to 8, p=0.47467
b-rank test for bits 2 to 9, p=0.58533
b-rank test for bits 3 to 10, p=0.09914
b-rank test for bits 4 to 11, p=0.96560
b-rank test for bits 5 to 12, p=0.94970
b-rank test for bits 6 to 13, p=0.04503
b-rank test for bits 7 to 14, p=0.86926
b-rank test for bits 8 to 15, p=0.55815
b-rank test for bits 9 to 16, p=0.69681
b-rank test for bits 10 to 17, p=0.53265
b-rank test for bits 11 to 18, p=0.17124
b-rank test for bits 12 to 19, p=0.83423
b-rank test for bits 13 to 20, p=0.27915
b-rank test for bits 14 to 21, p=0.83685
b-rank test for bits 15 to 22, p=0.25315
b-rank test for bits 16 to 23, p=0.46243
b-rank test for bits 17 to 24, p=0.47307
b-rank test for bits 18 to 25, p=0.47748
b-rank test for bits 19 to 26, p=0.26614
b-rank test for bits 20 to 27, p=0.21472
b-rank test for bits 21 to 28, p=0.55907
b-rank test for bits 22 to 29, p=0.38479
b-rank test for bits 23 to 30, p=0.68661
b-rank test for bits 24 to 31, p=0.26803
b-rank test for bits 25 to 32, p=0.52764
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 = 0.805174
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_18:31
(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 141731 -0.42 0.338464
2 142665 1.77 0.961267
3 141864 -0.11 0.457826
4 141988 0.18 0.572918
5 142061 0.35 0.638469
6 142154 0.57 0.716223
7 141474 -1.02 0.154547
8 141539 -0.87 0.193449
9 142428 1.21 0.887214
10 141921 0.03 0.510876
11 141620 -0.68 0.249519
12 141874 -0.08 0.467106
13 142107 0.46 0.677904
14 140933 -2.28 0.011270
15 141763 -0.34 0.366216
16 142708 1.87 0.968983
17 142090 0.42 0.663534
18 142383 1.11 0.865789
19 141327 -1.36 0.086823
20 141335 -1.34 0.089815
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_18:31
Bits used No. missing words z-score p-value
23 to 32 141683 -0.7804 0.217564
22 to 31 141681 -0.7873 0.215540
21 to 30 142031 0.4196 0.662594
20 to 29 141437 -1.6287 0.051686
19 to 28 142193 0.9782 0.836006
18 to 27 142122 0.7333 0.768326
17 to 26 141841 -0.2356 0.406864
16 to 25 142298 1.3402 0.909917
15 to 24 142468 1.9264 0.972976
14 to 23 141704 -0.7080 0.239462
13 to 22 141420 -1.6873 0.045769
12 to 21 141679 -0.7942 0.213528
11 to 20 141890 -0.0667 0.473428
10 to 19 142483 1.9782 0.976045
9 to 18 141675 -0.8080 0.209535
8 to 17 141988 0.2713 0.606911
7 to 16 142231 1.1092 0.866330
6 to 15 142428 1.7885 0.963154
5 to 14 141586 -1.1149 0.132440
4 to 13 141528 -1.3149 0.094267
3 to 12 141670 -0.8253 0.204608
2 to 11 141850 -0.2046 0.418948
1 to 10 141592 -1.0942 0.136925
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_18:31
Bits used No. missing words z-score p-value
28 to 32 142423 1.7413 0.959181
27 to 31 141710 -0.6757 0.249617
26 to 30 141954 0.1514 0.560179
25 to 29 141872 -0.1265 0.449651
24 to 28 142133 0.7582 0.775835
23 to 27 141869 -0.1367 0.445629
22 to 26 142377 1.5853 0.943553
21 to 25 141635 -0.9299 0.176203
20 to 24 141554 -1.2045 0.114197
19 to 23 141905 -0.0147 0.494145
18 to 22 142285 1.2735 0.898572
17 to 21 141654 -0.8655 0.193375
16 to 20 142187 0.9413 0.826713
15 to 19 142340 1.4599 0.927841
14 to 18 142080 0.5785 0.718551
13 to 17 141793 -0.3943 0.346665
12 to 16 141883 -0.0893 0.464440
11 to 15 141965 0.1887 0.574841
10 to 14 141866 -0.1469 0.441613
9 to 13 141565 -1.1672 0.121561
8 to 12 142318 1.3853 0.917023
7 to 11 142520 2.0701 0.980777
6 to 10 142293 1.3006 0.903298
5 to 9 141955 0.1548 0.561516
4 to 8 141473 -1.4791 0.069559
3 to 7 141745 -0.5571 0.288746
2 to 6 142159 0.8463 0.801318
1 to 5 142187 0.9413 0.826713
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_18:31
Bits used No. missing words z-score p-value
31 to 32 142378 1.3825 0.916592
30 to 31 141850 -0.1750 0.430534
29 to 30 142499 1.7394 0.959021
28 to 29 141854 -0.1632 0.435174
27 to 28 141306 -1.7797 0.037560
26 to 27 141968 0.1731 0.568701
25 to 26 141799 -0.3255 0.372418
24 to 25 141772 -0.4051 0.342701
23 to 24 142331 1.2439 0.893225
22 to 23 141203 -2.0836 0.018600
21 to 22 141901 -0.0246 0.490198
20 to 21 141858 -0.1514 0.439824
19 to 20 142217 0.9076 0.817950
18 to 19 141641 -0.7915 0.214316
17 to 18 141726 -0.5408 0.294324
16 to 17 142091 0.5359 0.703986
15 to 16 142154 0.7217 0.764773
14 to 15 141779 -0.3845 0.350321
13 to 14 142380 1.3884 0.917493
12 to 13 142145 0.6952 0.756532
11 to 12 141634 -0.8122 0.208343
10 to 11 141442 -1.3786 0.084016
9 to 10 141558 -1.0364 0.150014
8 to 9 142587 1.9990 0.977197
7 to 8 141901 -0.0246 0.490198
6 to 7 141810 -0.2930 0.384758
5 to 6 142253 1.0138 0.844655
4 to 5 142196 0.8456 0.801122
3 to 4 142313 1.1908 0.883127
2 to 3 141340 -1.6794 0.046533
1 to 2 141464 -1.3137 0.094481
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2572.07 1.019 0.845965
Test results for specific bytes for dh-ranFile-2018-07-07_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2488.57 -0.162 0.435798
2 to 9 2471.01 -0.410 0.340930
3 to 10 2351.37 -2.102 0.017780
4 to 11 2516.01 0.226 0.589541
5 to 12 2491.37 -0.122 0.451458
6 to 13 2780.85 3.972 0.999964
7 to 14 2509.41 0.133 0.552952
8 to 15 2561.01 0.863 0.805864
9 to 16 2438.28 -0.873 0.191379
10 to 17 2506.07 0.086 0.534191
11 to 18 2533.03 0.467 0.679794
12 to 19 2627.28 1.800 0.964066
13 to 20 2495.35 -0.066 0.473805
14 to 21 2346.16 -2.176 0.014792
15 to 22 2481.58 -0.260 0.397262
16 to 23 2464.27 -0.505 0.306656
17 to 24 2566.86 0.946 0.827821
18 to 25 2415.25 -1.198 0.115363
19 to 26 2494.74 -0.074 0.470336
20 to 27 2548.22 0.682 0.752359
21 to 28 2408.35 -1.296 0.097457
22 to 29 2540.10 0.567 0.714682
23 to 30 2433.90 -0.935 0.174942
24 to 31 2501.06 0.015 0.505955
25 to 32 2404.00 -1.358 0.087279
CDPARK for dh-ranFile-2018-07-07_18:31: 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
3543 0.9132 0.819442
3511 -0.5479 0.291865
3550 1.2329 0.891189
3517 -0.2740 0.392053
3520 -0.1370 0.445521
3508 -0.6849 0.246694
3531 0.3653 0.642555
3518 -0.2283 0.409702
3546 1.0502 0.853193
3502 -0.9589 0.168804
Square side=100, avg. no. parked=3524.60 sample std.=16.05
p-value of the KSTEST for those 10 p-values: 0.843323
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_18:31
0.2078,0.8797,0.7256,0.4026,0.0944,0.2480,0.6330,0.5832,0.3982,0.9875,
The KS test for those 10 p-values: 0.981249
The 3DSPHERES test for dh-ranFile-2018-07-07_18:31
sample no r^3 equiv. uni.
1 9.217 0.264529
2 92.746 0.954567
3 41.059 0.745543
4 28.443 0.612525
5 43.589 0.766125
6 6.706 0.200300
7 40.320 0.739202
8 74.466 0.916439
9 101.801 0.966405
10 4.064 0.126706
11 37.713 0.715523
12 18.902 0.467449
13 9.084 0.261243
14 0.529 0.017481
15 48.093 0.798732
16 4.906 0.150870
17 7.862 0.230543
18 30.267 0.635377
19 89.246 0.948945
20 62.994 0.877518
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.313953
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.3 -0.1 0.0 -1.8 1.4
0.2 -1.2 -0.4 -0.3 -1.4 0.0
1.7 -0.4 0.7 -0.3 0.8 0.1
-0.9 0.1 -0.6 1.1 -1.1 0.5
-0.3 -0.6 -0.2 2.2 -0.3 -1.0
0.0 0.1 1.4 0.8 -0.5 -0.3
-1.2 -1.7 -0.8 -1.3 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:36.943399
z-score=-0.551720, p-value=0.307839
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_18:31
Test no p-value
1 0.000133
2 0.687363
3 0.059115
4 0.929147
5 0.949479
6 0.017983
7 0.388143
8 0.002381
9 0.059225
10 0.209387
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001895
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_18:31:
(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 66447 0.72 66555 0.19
3 25000.00 25263 2.77 25092 0.34
4 6666.67 6700 0.17 6707 0.24
5 1388.89 1278 8.85 1359 0.64
6 238.10 267 3.51 244 0.15
7 34.72 42 1.53 38 0.31
8 4.96 2 1.77 4 0.19
p=0.99633 p=0.08542
Number of rngs required: 689595, p-value: 0.918
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_18:31
No. of wins: Observed Expected
98543 98585.9
z-score=-0.192, pvalue=0.42399
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66494 66666.7 0.447 0.447
2 37703 37654.3 0.063 0.510
3 26751 26954.7 1.540 2.050
4 19435 19313.5 0.765 2.815
5 13904 13851.4 0.200 3.014
6 10141 9943.5 3.921 6.935
7 7054 7145.0 1.160 8.095
8 5175 5139.1 0.251 8.346
9 3667 3699.9 0.292 8.638
10 2670 2666.3 0.005 8.643
11 1871 1923.3 1.424 10.067
12 1447 1388.7 2.444 12.511
13 1019 1003.7 0.233 12.744
14 763 726.1 1.871 14.615
15 505 525.8 0.826 15.441
16 388 381.2 0.123 15.564
17 267 276.5 0.329 15.893
18 199 200.8 0.017 15.909
19 156 146.0 0.687 16.597
20 93 106.2 1.644 18.241
21 298 287.1 0.413 18.654
Chisq= 18.65 for 20 degrees of freedom, p= 0.45556
SUMMARY of craptest
p-value for no. of wins: 0.423993
p-value for throws/game: 0.455562
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_18:31
No. of wins: Observed Expected
98447 98585.9
z-score=-0.621, pvalue=0.26728
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66591 66666.7 0.086 0.086
2 37689 37654.3 0.032 0.118
3 26960 26954.7 0.001 0.119
4 19290 19313.5 0.029 0.147
5 13822 13851.4 0.062 0.210
6 9797 9943.5 2.160 2.370
7 7200 7145.0 0.423 2.792
8 5115 5139.1 0.113 2.905
9 3813 3699.9 3.459 6.365
10 2686 2666.3 0.146 6.510
11 1960 1923.3 0.699 7.209
12 1358 1388.7 0.680 7.890
13 1055 1003.7 2.620 10.510
14 733 726.1 0.065 10.575
15 532 525.8 0.072 10.647
16 382 381.2 0.002 10.649
17 264 276.5 0.569 11.218
18 212 200.8 0.621 11.839
19 149 146.0 0.062 11.901
20 102 106.2 0.167 12.069
21 290 287.1 0.029 12.098
Chisq= 12.10 for 20 degrees of freedom, p= 0.08733
SUMMARY of craptest
p-value for no. of wins: 0.267281
p-value for throws/game: 0.087330
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0019,0.0024,0.0113,0.0148,0.0175,0.0178,0.0180,0.0186,0.0252,
0.0376,0.0450,0.0458,0.0465,0.0517,0.0591,0.0592,0.0655,0.0696,0.0840,
0.0854,0.0864,0.0868,0.0873,0.0873,0.0898,0.0943,0.0944,0.0945,0.0975,
0.0991,0.1142,0.1154,0.1216,0.1267,0.1324,0.1369,0.1422,0.1500,0.1509,
0.1545,0.1684,0.1688,0.1712,0.1749,0.1762,0.1914,0.1926,0.1934,0.1934,
0.2003,0.2046,0.2078,0.2083,0.2094,0.2095,0.2135,0.2143,0.2147,0.2155,
0.2159,0.2176,0.2305,0.2395,0.2467,0.2480,0.2495,0.2496,0.2531,0.2612,
0.2645,0.2661,0.2673,0.2680,0.2686,0.2687,0.2711,0.2791,0.2887,0.2919,
0.2943,0.3067,0.3078,0.3140,0.3385,0.3409,0.3427,0.3441,0.3467,0.3503,
0.3662,0.3724,0.3748,0.3782,0.3848,0.3848,0.3875,0.3881,0.3921,0.3973,
0.3982,0.4026,0.4069,0.4097,0.4113,0.4126,0.4189,0.4240,0.4305,0.4335,
0.4352,0.4358,0.4398,0.4416,0.4448,0.4455,0.4456,0.4497,0.4515,0.4535,
0.4556,0.4578,0.4624,0.4644,0.4671,0.4674,0.4685,0.4703,0.4731,0.4734,
0.4738,0.4747,0.4775,0.4902,0.4902,0.4915,0.4941,0.5060,0.5109,0.5118,
0.5276,0.5326,0.5329,0.5342,0.5432,0.5530,0.5581,0.5591,0.5602,0.5615,
0.5687,0.5729,0.5748,0.5832,0.5853,0.5882,0.5895,0.5902,0.6069,0.6071,
0.6125,0.6149,0.6153,0.6330,0.6354,0.6385,0.6426,0.6557,0.6626,0.6635,
0.6638,0.6779,0.6798,0.6808,0.6866,0.6874,0.6884,0.6968,0.6980,0.6997,
0.7040,0.7147,0.7155,0.7162,0.7186,0.7256,0.7295,0.7392,0.7455,0.7524,
0.7565,0.7565,0.7600,0.7617,0.7648,0.7661,0.7683,0.7758,0.7822,0.7956,
0.7987,0.8011,0.8013,0.8052,0.8059,0.8068,0.8180,0.8194,0.8267,0.8267,
0.8278,0.8342,0.8360,0.8369,0.8389,0.8433,0.8447,0.8460,0.8532,0.8535,
0.8590,0.8604,0.8658,0.8663,0.8693,0.8775,0.8797,0.8831,0.8842,0.8872,
0.8912,0.8932,0.8986,0.9033,0.9077,0.9099,0.9164,0.9166,0.9170,0.9175,
0.9177,0.9194,0.9278,0.9291,0.9436,0.9484,0.9489,0.9495,0.9497,0.9513,
0.9525,0.9546,0.9569,0.9590,0.9592,0.9613,0.9632,0.9641,0.9656,0.9664,
0.9690,0.9730,0.9760,0.9772,0.9808,0.9812,0.9875,0.9963,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.293004
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.