RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.53 22.2568 0.824957
2 to 25 15.92 13.5147 0.298891
3 to 26 15.64 20.7368 0.761715
4 to 27 15.78 14.0380 0.335589
5 to 28 15.88 14.0221 0.334462
6 to 29 15.87 26.7117 0.937566
7 to 30 15.96 14.4444 0.364570
8 to 31 15.81 12.5766 0.235962
9 to 32 15.47 20.1726 0.734505
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.646661
Tough bday spacings test for dh-ranFile-2018-07-10_14:31: 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 37 77 91 102 88 56 22 12 5 3
(O-E)^2/E 0.5 0.0 0.2 0.5 0.2 1.2 0.3 2.0 0.6 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.147, p= 0.197
RESULTS OF GCD FOR dh-ranFile-2018-07-10_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.087311
p-value, dist. of gcd's: 0.366281
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.186 0.533 0.379 0.077 0.364 0.362 0.330 0.657
Bits 8 to 15---> 0.289 0.844 0.055 0.008 0.377 0.648 0.840 0.789
Bits 16 to 23---> 0.579 0.659 0.189 0.970 0.206 0.458 0.960 0.267
Bits 24 to 31---> 0.814 0.827 0.186 0.596 0.649 0.324 0.104 0.773
KS test for the above 32 p values: 0.061
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_14:31,
p-values for 5 runs: 0.2573, 0.7756, 0.3376, 0.6067, 0.4918
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5034 5134.0 1.948 1.949
r= 30 23315 23103.0 1.944 3.894
r= 31 11440 11551.5 1.077 4.970
chi-square = 4.970 with df = 3; p-value = 0.826
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 226 211.4 1.006 1.006
r= 30 5062 5134.0 1.010 2.016
r= 31 23166 23103.0 0.172 2.187
r= 32 11546 11551.5 0.003 2.190
chi-square = 2.190 with df = 3; p-value = 0.466
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_14:31
b-rank test for bits 1 to 8, p=0.75831
b-rank test for bits 2 to 9, p=0.78870
b-rank test for bits 3 to 10, p=0.96652
b-rank test for bits 4 to 11, p=0.00278
b-rank test for bits 5 to 12, p=0.22041
b-rank test for bits 6 to 13, p=0.35392
b-rank test for bits 7 to 14, p=0.30084
b-rank test for bits 8 to 15, p=0.80395
b-rank test for bits 9 to 16, p=0.83783
b-rank test for bits 10 to 17, p=0.08679
b-rank test for bits 11 to 18, p=0.42440
b-rank test for bits 12 to 19, p=0.30501
b-rank test for bits 13 to 20, p=0.01591
b-rank test for bits 14 to 21, p=0.24138
b-rank test for bits 15 to 22, p=0.31185
b-rank test for bits 16 to 23, p=0.81055
b-rank test for bits 17 to 24, p=0.83090
b-rank test for bits 18 to 25, p=0.84363
b-rank test for bits 19 to 26, p=0.90230
b-rank test for bits 20 to 27, p=0.64975
b-rank test for bits 21 to 28, p=0.56802
b-rank test for bits 22 to 29, p=0.62476
b-rank test for bits 23 to 30, p=0.92735
b-rank test for bits 24 to 31, p=0.47687
b-rank test for bits 25 to 32, p=0.85540
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 = 0.345972
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_14:31
(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 141655 -0.59 0.276180
2 141866 -0.10 0.459681
3 142706 1.86 0.968655
4 142104 0.45 0.675387
5 141900 -0.02 0.491304
6 141124 -1.83 0.033262
7 142018 0.25 0.600214
8 142088 0.42 0.661827
9 141571 -0.79 0.214621
10 141951 0.10 0.538780
11 142271 0.85 0.800951
12 141714 -0.46 0.324059
13 141919 0.02 0.509013
14 141091 -1.91 0.027939
15 142166 0.60 0.725646
16 142579 1.56 0.941167
17 141532 -0.88 0.188993
18 142893 2.30 0.989227
19 142273 0.85 0.802253
20 142066 0.37 0.642837
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_14:31
Bits used No. missing words z-score p-value
23 to 32 141745 -0.5667 0.285474
22 to 31 141468 -1.5218 0.064026
21 to 30 141730 -0.6184 0.268163
20 to 29 142483 1.9782 0.976045
19 to 28 141862 -0.1632 0.435178
18 to 27 141767 -0.4908 0.311786
17 to 26 142026 0.4023 0.656272
16 to 25 142195 0.9851 0.837705
15 to 24 142257 1.1989 0.884709
14 to 23 141753 -0.5391 0.294920
13 to 22 141747 -0.5598 0.287822
12 to 21 142463 1.9092 0.971882
11 to 20 141695 -0.7391 0.229933
10 to 19 141960 0.1747 0.569352
9 to 18 141679 -0.7942 0.213528
8 to 17 142027 0.4058 0.657540
7 to 16 141476 -1.4942 0.067556
6 to 15 142012 0.3540 0.638344
5 to 14 141654 -0.8804 0.189308
4 to 13 141804 -0.3632 0.358225
3 to 12 142502 2.0437 0.979508
2 to 11 141754 -0.5356 0.296110
1 to 10 141508 -1.3839 0.083195
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_14:31
Bits used No. missing words z-score p-value
28 to 32 141912 0.0091 0.503611
27 to 31 142191 0.9548 0.830164
26 to 30 141578 -1.1232 0.130686
25 to 29 141664 -0.8316 0.202810
24 to 28 142209 1.0158 0.845145
23 to 27 141906 -0.0113 0.495497
22 to 26 141933 0.0802 0.531976
21 to 25 142130 0.7480 0.772780
20 to 24 141374 -1.8147 0.034787
19 to 23 141573 -1.1401 0.127122
18 to 22 142332 1.4328 0.924040
17 to 21 141796 -0.3842 0.350426
16 to 20 141804 -0.3571 0.360527
15 to 19 142235 1.1040 0.865196
14 to 18 142398 1.6565 0.951191
13 to 17 142261 1.1921 0.883389
12 to 16 141884 -0.0859 0.465787
11 to 15 141711 -0.6723 0.250695
10 to 14 141747 -0.5503 0.291067
9 to 13 141566 -1.1638 0.122246
8 to 12 141890 -0.0655 0.473878
7 to 11 141873 -0.1232 0.450993
6 to 10 142083 0.5887 0.721973
5 to 9 142379 1.5921 0.944319
4 to 8 142009 0.3379 0.632267
3 to 7 141305 -2.0486 0.020252
2 to 6 141522 -1.3130 0.094594
1 to 5 141642 -0.9062 0.182414
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_14:31
Bits used No. missing words z-score p-value
31 to 32 141785 -0.3668 0.356901
30 to 31 141249 -1.9479 0.025715
29 to 30 142062 0.4504 0.673772
28 to 29 141874 -0.1042 0.458498
27 to 28 141777 -0.3904 0.348137
26 to 27 141751 -0.4671 0.320232
25 to 26 141874 -0.1042 0.458498
24 to 25 141693 -0.6381 0.261691
23 to 24 142422 1.5123 0.934771
22 to 23 142409 1.4740 0.929753
21 to 22 142408 1.4710 0.929355
20 to 21 142561 1.9223 0.972718
19 to 20 141644 -0.7827 0.216906
18 to 19 141850 -0.1750 0.430534
17 to 18 141888 -0.0629 0.474915
16 to 17 142432 1.5418 0.938439
15 to 16 141720 -0.5585 0.288253
14 to 15 141222 -2.0275 0.021305
13 to 14 141679 -0.6794 0.248430
12 to 13 142072 0.4799 0.684334
11 to 12 142007 0.2881 0.613370
10 to 11 142061 0.4474 0.672708
9 to 10 141942 0.0964 0.538387
8 to 9 141610 -0.8830 0.188624
7 to 8 141775 -0.3963 0.345959
6 to 7 142280 1.0934 0.862896
5 to 6 142391 1.4209 0.922321
4 to 5 141629 -0.8269 0.204138
3 to 4 141413 -1.4641 0.071583
2 to 3 142268 1.0580 0.854978
1 to 2 141395 -1.5172 0.064608
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2468.38 -0.447 0.327399
Test results for specific bytes for dh-ranFile-2018-07-10_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2382.70 -1.659 0.048565
2 to 9 2470.91 -0.411 0.340410
3 to 10 2548.04 0.679 0.751567
4 to 11 2532.31 0.457 0.676147
5 to 12 2545.17 0.639 0.738524
6 to 13 2593.10 1.317 0.906026
7 to 14 2491.62 -0.119 0.452819
8 to 15 2477.66 -0.316 0.376038
9 to 16 2462.33 -0.533 0.297115
10 to 17 2521.38 0.302 0.618828
11 to 18 2428.82 -1.007 0.157067
12 to 19 2453.68 -0.655 0.256222
13 to 20 2457.10 -0.607 0.272044
14 to 21 2617.00 1.655 0.950999
15 to 22 2585.26 1.206 0.886033
16 to 23 2651.77 2.146 0.984080
17 to 24 2503.20 0.045 0.518071
18 to 25 2606.31 1.503 0.933631
19 to 26 2435.14 -0.917 0.179487
20 to 27 2429.45 -0.998 0.159211
21 to 28 2571.25 1.008 0.843179
22 to 29 2571.38 1.009 0.843616
23 to 30 2358.66 -1.999 0.022811
24 to 31 2468.84 -0.441 0.329706
25 to 32 2433.14 -0.946 0.172199
CDPARK for dh-ranFile-2018-07-10_14:31: 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
3533 0.4566 0.676028
3509 -0.6393 0.261324
3501 -1.0046 0.157553
3537 0.6393 0.738676
3502 -0.9589 0.168804
3506 -0.7763 0.218799
3504 -0.8676 0.192812
3534 0.5023 0.692266
3543 0.9132 0.819442
3579 2.5571 0.994722
Square side=100, avg. no. parked=3524.80 sample std.=23.86
p-value of the KSTEST for those 10 p-values: 0.568370
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_14:31
0.8381,0.1464,0.6828,0.8975,0.5814,0.0580,0.4605,0.9205,0.2548,0.7066,
The KS test for those 10 p-values: 0.872438
The 3DSPHERES test for dh-ranFile-2018-07-10_14:31
sample no r^3 equiv. uni.
1 6.592 0.197268
2 51.541 0.820581
3 13.534 0.363087
4 17.551 0.442918
5 3.563 0.111978
6 0.481 0.015902
7 128.849 0.986363
8 7.454 0.220006
9 31.266 0.647316
10 21.741 0.515529
11 20.915 0.502002
12 9.378 0.268448
13 9.326 0.267186
14 44.896 0.776098
15 18.017 0.451504
16 64.492 0.883484
17 46.741 0.789448
18 52.450 0.825938
19 37.395 0.712489
20 15.593 0.405348
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.983095
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 1.3 -0.3 -1.3 0.3
-2.1 0.7 0.5 0.2 -2.1 1.4
-1.1 0.3 -0.6 1.1 -1.4 1.0
0.6 1.2 -0.4 -0.0 0.6 -0.6
-0.0 -0.1 -1.3 0.5 -0.1 0.3
2.5 -1.2 -0.6 -1.6 -0.6 -1.2
-0.7 -0.7 -0.4 -0.7 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:42.960299
z-score=0.104777, p-value=0.570117
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_14:31
Test no p-value
1 0.260162
2 0.755990
3 0.164116
4 0.693977
5 0.002711
6 0.001818
7 0.614850
8 0.689372
9 0.320715
10 0.033687
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.031105
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_14:31:
(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 66739 0.08 66616 0.04
3 25000.00 25022 0.02 25046 0.08
4 6666.67 6534 2.64 6716 0.37
5 1388.89 1407 0.24 1356 0.78
6 238.10 251 0.70 235 0.04
7 34.72 37 0.15 28 1.30
8 4.96 9 3.29 2 1.77
p=0.68957 p=0.37385
Number of rngs required: 687600, p-value: 0.176
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_14:31
No. of wins: Observed Expected
98800 98585.9
z-score= 0.958, pvalue=0.83091
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66542 66666.7 0.233 0.233
2 37501 37654.3 0.624 0.857
3 27071 26954.7 0.502 1.359
4 19178 19313.5 0.950 2.309
5 13956 13851.4 0.790 3.099
6 9944 9943.5 0.000 3.099
7 7156 7145.0 0.017 3.116
8 5180 5139.1 0.326 3.441
9 3760 3699.9 0.977 4.419
10 2727 2666.3 1.382 5.801
11 1922 1923.3 0.001 5.802
12 1459 1388.7 3.555 9.356
13 960 1003.7 1.904 11.260
14 723 726.1 0.014 11.274
15 530 525.8 0.033 11.307
16 381 381.2 0.000 11.307
17 291 276.5 0.756 12.063
18 193 200.8 0.305 12.368
19 147 146.0 0.007 12.375
20 100 106.2 0.364 12.739
21 279 287.1 0.229 12.968
Chisq= 12.97 for 20 degrees of freedom, p= 0.12126
SUMMARY of craptest
p-value for no. of wins: 0.830909
p-value for throws/game: 0.121265
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_14:31
No. of wins: Observed Expected
98684 98585.9
z-score= 0.439, pvalue=0.66965
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66522 66666.7 0.314 0.314
2 37541 37654.3 0.341 0.655
3 27087 26954.7 0.649 1.304
4 19258 19313.5 0.159 1.463
5 14183 13851.4 7.937 9.401
6 9984 9943.5 0.165 9.565
7 7213 7145.0 0.647 10.212
8 5126 5139.1 0.033 10.245
9 3548 3699.9 6.233 16.479
10 2645 2666.3 0.170 16.649
11 1994 1923.3 2.597 19.246
12 1331 1388.7 2.401 21.646
13 964 1003.7 1.571 23.218
14 687 726.1 2.110 25.328
15 535 525.8 0.160 25.487
16 396 381.2 0.579 26.066
17 291 276.5 0.756 26.822
18 197 200.8 0.073 26.895
19 145 146.0 0.007 26.902
20 87 106.2 3.476 30.378
21 266 287.1 1.553 31.930
Chisq= 31.93 for 20 degrees of freedom, p= 0.95596
SUMMARY of craptest
p-value for no. of wins: 0.669650
p-value for throws/game: 0.955955
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0027,0.0028,0.0081,0.0159,0.0159,0.0203,0.0213,0.0228,0.0257,
0.0279,0.0311,0.0333,0.0337,0.0348,0.0486,0.0546,0.0580,0.0614,0.0640,
0.0646,0.0676,0.0716,0.0773,0.0832,0.0868,0.0873,0.0946,0.1044,0.1120,
0.1213,0.1222,0.1271,0.1307,0.1464,0.1571,0.1576,0.1592,0.1641,0.1688,
0.1722,0.1763,0.1795,0.1824,0.1858,0.1864,0.1886,0.1889,0.1890,0.1893,
0.1928,0.1972,0.1973,0.2028,0.2041,0.2064,0.2135,0.2146,0.2169,0.2188,
0.2200,0.2204,0.2299,0.2360,0.2414,0.2484,0.2507,0.2548,0.2562,0.2573,
0.2602,0.2613,0.2617,0.2666,0.2672,0.2682,0.2684,0.2720,0.2762,0.2855,
0.2878,0.2883,0.2894,0.2911,0.2949,0.2961,0.2971,0.2989,0.3008,0.3050,
0.3118,0.3119,0.3202,0.3207,0.3241,0.3241,0.3274,0.3295,0.3297,0.3345,
0.3356,0.3376,0.3404,0.3460,0.3460,0.3481,0.3504,0.3539,0.3569,0.3582,
0.3605,0.3620,0.3631,0.3637,0.3646,0.3663,0.3738,0.3760,0.3773,0.3793,
0.4053,0.4244,0.4305,0.4352,0.4429,0.4510,0.4515,0.4528,0.4578,0.4585,
0.4585,0.4597,0.4605,0.4658,0.4661,0.4739,0.4749,0.4769,0.4913,0.4918,
0.4955,0.5020,0.5036,0.5090,0.5155,0.5181,0.5320,0.5335,0.5384,0.5388,
0.5680,0.5684,0.5694,0.5701,0.5787,0.5814,0.5964,0.6002,0.6067,0.6134,
0.6148,0.6188,0.6248,0.6323,0.6383,0.6428,0.6467,0.6473,0.6482,0.6489,
0.6498,0.6563,0.6568,0.6575,0.6589,0.6618,0.6696,0.6727,0.6738,0.6754,
0.6760,0.6761,0.6828,0.6843,0.6894,0.6896,0.6923,0.6940,0.7066,0.7125,
0.7220,0.7256,0.7345,0.7385,0.7387,0.7516,0.7560,0.7583,0.7617,0.7728,
0.7734,0.7756,0.7761,0.7887,0.7892,0.7894,0.8010,0.8023,0.8039,0.8106,
0.8142,0.8194,0.8206,0.8250,0.8259,0.8260,0.8267,0.8302,0.8309,0.8309,
0.8377,0.8378,0.8381,0.8399,0.8432,0.8436,0.8436,0.8442,0.8451,0.8550,
0.8554,0.8629,0.8652,0.8724,0.8834,0.8835,0.8847,0.8860,0.8975,0.9023,
0.9060,0.9205,0.9223,0.9240,0.9273,0.9294,0.9298,0.9336,0.9348,0.9376,
0.9384,0.9412,0.9443,0.9510,0.9512,0.9560,0.9599,0.9665,0.9687,0.9704,
0.9719,0.9727,0.9760,0.9795,0.9831,0.9841,0.9864,0.9892,0.9947,
Overall p-value after applying KStest on 269 p-values = 0.539897
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.