RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.87 13.6165 0.305965
2 to 25 15.91 11.4488 0.167692
3 to 26 15.79 18.2020 0.623796
4 to 27 15.80 23.0773 0.853248
5 to 28 15.44 22.1524 0.821072
6 to 29 15.76 21.6857 0.802891
7 to 30 15.74 15.5815 0.446330
8 to 31 15.83 11.3669 0.163131
9 to 32 15.69 15.9334 0.471435
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.909115
Tough bday spacings test for dh-ranFile-2018-06-19_20:31: 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 10 39 59 99 108 82 53 21 20 4 5
(O-E)^2/E 0.1 0.2 2.8 0.0 1.1 0.2 0.0 2.6 1.8 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 9.910, p= 0.552
RESULTS OF GCD FOR dh-ranFile-2018-06-19_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.340401
p-value, dist. of gcd's: 0.280324
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.535 0.769 0.631 0.677 0.202 0.050 0.302 0.524
Bits 8 to 15---> 0.630 0.382 0.354 0.769 0.921 0.756 0.270 0.763
Bits 16 to 23---> 0.533 0.622 0.338 0.446 0.715 0.891 0.796 0.471
Bits 24 to 31---> 0.412 0.388 0.777 0.098 0.980 0.311 0.759 0.863
KS test for the above 32 p values: 0.771
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_20:31,
p-values for 5 runs: 0.5279, 0.9891, 0.3394, 0.4254, 0.6765
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5139 5134.0 0.005 0.353
r= 30 22989 23103.0 0.563 0.916
r= 31 11652 11551.5 0.874 1.790
chi-square = 1.790 with df = 3; p-value = 0.383
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 223 211.4 0.634 0.634
r= 30 5132 5134.0 0.001 0.635
r= 31 22832 23103.0 3.180 3.815
r= 32 11813 11551.5 5.919 9.734
chi-square = 9.734 with df = 3; p-value = 0.979
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_20:31
b-rank test for bits 1 to 8, p=0.69904
b-rank test for bits 2 to 9, p=0.97217
b-rank test for bits 3 to 10, p=0.90361
b-rank test for bits 4 to 11, p=0.10899
b-rank test for bits 5 to 12, p=0.17256
b-rank test for bits 6 to 13, p=0.49177
b-rank test for bits 7 to 14, p=0.78106
b-rank test for bits 8 to 15, p=0.03251
b-rank test for bits 9 to 16, p=0.69986
b-rank test for bits 10 to 17, p=0.64596
b-rank test for bits 11 to 18, p=0.19782
b-rank test for bits 12 to 19, p=0.71163
b-rank test for bits 13 to 20, p=0.31325
b-rank test for bits 14 to 21, p=0.21960
b-rank test for bits 15 to 22, p=0.85439
b-rank test for bits 16 to 23, p=0.62282
b-rank test for bits 17 to 24, p=0.86694
b-rank test for bits 18 to 25, p=0.27229
b-rank test for bits 19 to 26, p=0.70646
b-rank test for bits 20 to 27, p=0.99950
b-rank test for bits 21 to 28, p=0.99443
b-rank test for bits 22 to 29, p=0.03397
b-rank test for bits 23 to 30, p=0.90025
b-rank test for bits 24 to 31, p=0.68115
b-rank test for bits 25 to 32, p=0.93646
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 = 0.068331
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_20:31
(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 141505 -0.94 0.172407
2 142115 0.48 0.684577
3 141797 -0.26 0.396486
4 142096 0.44 0.668634
5 142197 0.67 0.749248
6 142039 0.30 0.619043
7 142032 0.29 0.612795
8 141005 -2.11 0.017304
9 141308 -1.40 0.080014
10 142486 1.35 0.911068
11 142037 0.30 0.617261
12 142169 0.61 0.727977
13 142334 0.99 0.839455
14 141660 -0.58 0.280099
15 142381 1.10 0.864776
16 141759 -0.35 0.362705
17 142115 0.48 0.684577
18 142050 0.33 0.628797
19 142276 0.86 0.804196
20 142532 1.45 0.927143
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_20:31
Bits used No. missing words z-score p-value
23 to 32 142203 1.0127 0.844388
22 to 31 141947 0.1299 0.551676
21 to 30 141568 -1.1770 0.119598
20 to 29 141527 -1.3184 0.093688
19 to 28 141848 -0.2115 0.416255
18 to 27 142325 1.4333 0.924120
17 to 26 141693 -0.7460 0.227844
16 to 25 142080 0.5885 0.721907
15 to 24 141850 -0.2046 0.418948
14 to 23 141129 -2.6908 0.003564
13 to 22 141869 -0.1391 0.444698
12 to 21 142232 1.1127 0.867072
11 to 20 142031 0.4196 0.662594
10 to 19 142119 0.7230 0.765160
9 to 18 141676 -0.8046 0.210529
8 to 17 141762 -0.5080 0.305715
7 to 16 141576 -1.1494 0.125193
6 to 15 141649 -0.8977 0.184676
5 to 14 142026 0.4023 0.656272
4 to 13 142396 1.6782 0.953343
3 to 12 141560 -1.2046 0.114182
2 to 11 142103 0.6678 0.747878
1 to 10 141702 -0.7149 0.237326
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_20:31
Bits used No. missing words z-score p-value
28 to 32 141753 -0.5299 0.298080
27 to 31 142251 1.1582 0.876610
26 to 30 141942 0.1107 0.544091
25 to 29 141520 -1.3198 0.093457
24 to 28 142226 1.0735 0.858467
23 to 27 141797 -0.3808 0.351683
22 to 26 142430 1.7650 0.961217
21 to 25 142280 1.2565 0.895534
20 to 24 142114 0.6938 0.756095
19 to 23 142283 1.2667 0.897365
18 to 22 142366 1.5480 0.939193
17 to 21 141663 -0.8350 0.201854
16 to 20 142102 0.6531 0.743160
15 to 19 142244 1.1345 0.871702
14 to 18 142447 1.8226 0.965819
13 to 17 141864 -0.1537 0.438939
12 to 16 142419 1.7277 0.957979
11 to 15 141926 0.0565 0.522532
10 to 14 141991 0.2768 0.609051
9 to 13 142194 0.9650 0.832723
8 to 12 141361 -1.8587 0.031532
7 to 11 142057 0.5006 0.691665
6 to 10 141946 0.1243 0.549463
5 to 9 141748 -0.5469 0.292230
4 to 8 141539 -1.2554 0.104675
3 to 7 142433 1.7752 0.962064
2 to 6 141987 0.2633 0.603836
1 to 5 142184 0.9311 0.824095
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_20:31
Bits used No. missing words z-score p-value
31 to 32 141725 -0.5437 0.293308
30 to 31 141946 0.1082 0.543070
29 to 30 142172 0.7748 0.780782
28 to 29 142189 0.8250 0.795310
27 to 28 142579 1.9754 0.975890
26 to 27 142015 0.3117 0.622370
25 to 26 141844 -0.1927 0.423592
24 to 25 141973 0.1878 0.574490
23 to 24 141729 -0.5319 0.297381
22 to 23 141788 -0.3579 0.360207
21 to 22 141867 -0.1249 0.450314
20 to 21 142620 2.0964 0.981975
19 to 20 141707 -0.5968 0.275306
18 to 19 140598 -3.8682 0.000055
17 to 18 141972 0.1849 0.573333
16 to 17 141689 -0.6499 0.257865
15 to 16 141340 -1.6794 0.046533
14 to 15 141552 -1.0541 0.145925
13 to 14 141797 -0.3314 0.370187
12 to 13 141783 -0.3727 0.354703
11 to 12 141917 0.0226 0.509025
10 to 11 141640 -0.7945 0.213457
9 to 10 142364 1.3412 0.910074
8 to 9 142374 1.3707 0.914767
7 to 8 142243 0.9843 0.837510
6 to 7 141844 -0.1927 0.423592
5 to 6 141892 -0.0511 0.479615
4 to 5 141096 -2.3992 0.008215
3 to 4 141988 0.2321 0.591756
2 to 3 142139 0.6775 0.750953
1 to 2 141817 -0.2724 0.392673
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2499.62 -0.005 0.497847
Test results for specific bytes for dh-ranFile-2018-06-19_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2529.42 0.416 0.661330
2 to 9 2513.43 0.190 0.575311
3 to 10 2484.96 -0.213 0.415799
4 to 11 2530.21 0.427 0.665378
5 to 12 2509.95 0.141 0.555978
6 to 13 2423.67 -1.079 0.140203
7 to 14 2415.77 -1.191 0.116790
8 to 15 2449.13 -0.719 0.235928
9 to 16 2435.05 -0.919 0.179157
10 to 17 2489.49 -0.149 0.440937
11 to 18 2469.62 -0.430 0.333718
12 to 19 2553.50 0.757 0.775358
13 to 20 2652.68 2.159 0.984582
14 to 21 2505.31 0.075 0.529903
15 to 22 2529.09 0.411 0.659611
16 to 23 2494.62 -0.076 0.469687
17 to 24 2460.71 -0.556 0.289217
18 to 25 2470.22 -0.421 0.336836
19 to 26 2655.58 2.200 0.986104
20 to 27 2402.36 -1.381 0.083654
21 to 28 2479.77 -0.286 0.387385
22 to 29 2522.54 0.319 0.625056
23 to 30 2522.00 0.311 0.622138
24 to 31 2598.39 1.391 0.917963
25 to 32 2521.86 0.309 0.621372
CDPARK for dh-ranFile-2018-06-19_20:31: 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
3541 0.8219 0.794438
3495 -1.2785 0.100530
3564 1.8721 0.969407
3536 0.5936 0.723613
3516 -0.3196 0.374623
3478 -2.0548 0.019949
3557 1.5525 0.939730
3509 -0.6393 0.261324
3513 -0.4566 0.323972
3521 -0.0913 0.463617
Square side=100, avg. no. parked=3523.00 sample std.=25.47
p-value of the KSTEST for those 10 p-values: 0.904041
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_20:31
0.7093,0.0072,0.0533,0.5661,0.6894,0.2660,0.1695,0.9637,0.2108,0.5986,
The KS test for those 10 p-values: 0.512848
The 3DSPHERES test for dh-ranFile-2018-06-19_20:31
sample no r^3 equiv. uni.
1 28.771 0.616734
2 6.830 0.203614
3 35.517 0.693916
4 39.962 0.736067
5 26.350 0.584528
6 36.627 0.705035
7 14.774 0.388884
8 56.109 0.845923
9 1.717 0.055612
10 37.711 0.715507
11 5.011 0.153839
12 67.713 0.895347
13 54.102 0.835264
14 17.721 0.446059
15 4.995 0.153370
16 37.786 0.716210
17 16.463 0.422337
18 25.922 0.578553
19 30.338 0.636244
20 12.320 0.336801
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.511018
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -1.2 -0.6 -0.8 0.4 -0.4
-0.0 -0.6 0.8 0.4 0.0 1.0
1.0 1.4 -0.8 -0.6 -1.1 -1.5
0.4 0.7 -0.9 1.5 -1.0 -0.5
-0.8 -0.0 0.8 0.6 -1.3 0.4
-0.1 1.4 2.0 0.8 2.6 -0.5
1.0 -0.7 -0.4 -1.8 0.9 0.0
0.8
Chi-square with 42 degrees of freedom:44.453229
z-score=0.267669, p-value=0.631226
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_20:31
Test no p-value
1 0.052018
2 0.182585
3 0.245511
4 0.033391
5 0.104934
6 0.000434
7 0.025387
8 0.104288
9 0.309741
10 0.286034
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000020
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_20:31:
(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 66709 0.03 66597 0.07
3 25000.00 25068 0.18 25040 0.06
4 6666.67 6558 1.77 6779 1.89
5 1388.89 1393 0.01 1342 1.58
6 238.10 243 0.10 207 4.06
7 34.72 24 3.31 30 0.64
8 4.96 4 0.19 4 0.19
p=0.52960 p=0.79636
Number of rngs required: 688950, p-value: 0.736
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_20:31
No. of wins: Observed Expected
98679 98585.9
z-score= 0.417, pvalue=0.66151
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66818 66666.7 0.344 0.344
2 37867 37654.3 1.201 1.545
3 26809 26954.7 0.788 2.333
4 19233 19313.5 0.335 2.668
5 13911 13851.4 0.256 2.924
6 9883 9943.5 0.369 3.293
7 7173 7145.0 0.110 3.402
8 5209 5139.1 0.952 4.354
9 3535 3699.9 7.346 11.700
10 2643 2666.3 0.204 11.904
11 1845 1923.3 3.190 15.094
12 1436 1388.7 1.608 16.702
13 1019 1003.7 0.233 16.935
14 735 726.1 0.108 17.043
15 571 525.8 3.879 20.922
16 362 381.2 0.962 21.884
17 295 276.5 1.232 23.117
18 193 200.8 0.305 23.422
19 134 146.0 0.984 24.406
20 93 106.2 1.644 26.050
21 236 287.1 9.100 35.150
Chisq= 35.15 for 20 degrees of freedom, p= 0.98068
SUMMARY of craptest
p-value for no. of wins: 0.661508
p-value for throws/game: 0.980678
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_20:31
No. of wins: Observed Expected
98616 98585.9
z-score= 0.135, pvalue=0.55362
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67089 66666.7 2.675 2.675
2 37533 37654.3 0.391 3.066
3 26829 26954.7 0.586 3.653
4 19297 19313.5 0.014 3.667
5 13805 13851.4 0.156 3.822
6 10220 9943.5 7.686 11.509
7 6995 7145.0 3.150 14.659
8 4911 5139.1 10.122 24.781
9 3640 3699.9 0.969 25.749
10 2617 2666.3 0.911 26.661
11 1911 1923.3 0.079 26.740
12 1459 1388.7 3.555 30.294
13 1021 1003.7 0.298 30.592
14 740 726.1 0.265 30.857
15 500 525.8 1.269 32.126
16 399 381.2 0.836 32.962
17 254 276.5 1.837 34.799
18 203 200.8 0.023 34.822
19 140 146.0 0.245 35.068
20 131 106.2 5.783 40.851
21 306 287.1 1.242 42.093
Chisq= 42.09 for 20 degrees of freedom, p= 0.99731
SUMMARY of craptest
p-value for no. of wins: 0.553619
p-value for throws/game: 0.997311
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0001,0.0004,0.0036,0.0072,0.0082,0.0173,0.0199,0.0254,0.0315,
0.0325,0.0334,0.0340,0.0465,0.0498,0.0520,0.0533,0.0556,0.0683,0.0800,
0.0837,0.0935,0.0937,0.0979,0.1005,0.1043,0.1047,0.1049,0.1090,0.1142,
0.1168,0.1196,0.1252,0.1402,0.1459,0.1534,0.1538,0.1631,0.1677,0.1695,
0.1724,0.1726,0.1792,0.1826,0.1847,0.1978,0.2019,0.2019,0.2036,0.2105,
0.2108,0.2135,0.2196,0.2278,0.2359,0.2373,0.2455,0.2579,0.2613,0.2660,
0.2698,0.2723,0.2753,0.2801,0.2803,0.2860,0.2892,0.2922,0.2933,0.2974,
0.2981,0.3022,0.3057,0.3060,0.3097,0.3108,0.3132,0.3240,0.3337,0.3368,
0.3368,0.3378,0.3394,0.3404,0.3517,0.3539,0.3547,0.3602,0.3627,0.3702,
0.3746,0.3820,0.3829,0.3874,0.3882,0.3889,0.3927,0.3965,0.4117,0.4158,
0.4163,0.4189,0.4223,0.4236,0.4236,0.4254,0.4389,0.4409,0.4447,0.4461,
0.4463,0.4463,0.4503,0.4636,0.4697,0.4714,0.4714,0.4796,0.4918,0.4978,
0.5090,0.5110,0.5128,0.5225,0.5237,0.5279,0.5296,0.5299,0.5327,0.5352,
0.5431,0.5441,0.5495,0.5516,0.5517,0.5536,0.5560,0.5661,0.5733,0.5745,
0.5753,0.5786,0.5845,0.5918,0.5986,0.6038,0.6091,0.6128,0.6167,0.6173,
0.6190,0.6214,0.6221,0.6224,0.6225,0.6228,0.6238,0.6251,0.6288,0.6296,
0.6312,0.6313,0.6362,0.6460,0.6563,0.6596,0.6613,0.6615,0.6626,0.6654,
0.6686,0.6765,0.6770,0.6811,0.6846,0.6846,0.6894,0.6917,0.6939,0.6990,
0.6999,0.7050,0.7065,0.7093,0.7116,0.7147,0.7155,0.7162,0.7219,0.7236,
0.7280,0.7360,0.7361,0.7432,0.7479,0.7492,0.7510,0.7561,0.7561,0.7586,
0.7630,0.7652,0.7693,0.7694,0.7712,0.7754,0.7766,0.7808,0.7811,0.7944,
0.7953,0.7958,0.7964,0.8029,0.8042,0.8211,0.8241,0.8327,0.8353,0.8375,
0.8395,0.8444,0.8459,0.8532,0.8544,0.8585,0.8626,0.8648,0.8669,0.8671,
0.8717,0.8766,0.8906,0.8953,0.8955,0.8974,0.9003,0.9036,0.9040,0.9091,
0.9101,0.9111,0.9148,0.9180,0.9205,0.9241,0.9271,0.9365,0.9392,0.9397,
0.9533,0.9580,0.9612,0.9621,0.9637,0.9658,0.9694,0.9722,0.9759,0.9790,
0.9796,0.9807,0.9820,0.9846,0.9861,0.9891,0.9944,0.9973,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.153344
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.