RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.09 17.8997 0.604804
2 to 25 15.82 3.5171 0.000214
3 to 26 15.94 20.8360 0.766287
4 to 27 15.81 14.0067 0.333370
5 to 28 15.81 20.3286 0.742234
6 to 29 15.89 18.2044 0.623940
7 to 30 15.83 31.7801 0.983977
8 to 31 15.81 15.5475 0.443891
9 to 32 15.86 18.5331 0.644021
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.268027
Tough bday spacings test for dh-ranFile-2018-06-24_09:31: 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 6 31 73 108 100 83 57 20 13 4 5
(O-E)^2/E 1.1 0.9 0.0 1.1 0.1 0.3 0.5 3.2 0.2 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 8.556, p= 0.425
RESULTS OF GCD FOR dh-ranFile-2018-06-24_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.045444
p-value, dist. of gcd's: 0.433410
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.500 0.797 0.681 0.617 0.548 0.947 0.580 0.344
Bits 8 to 15---> 0.597 0.244 0.212 0.497 0.132 0.990 0.522 0.040
Bits 16 to 23---> 0.811 0.975 0.894 0.255 0.052 0.858 0.731 0.547
Bits 24 to 31---> 0.908 0.755 0.206 0.073 0.156 1.000 0.793 0.507
KS test for the above 32 p values: 0.670
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_09:31,
p-values for 5 runs: 0.6984, 0.4262, 0.2357, 0.7845, 0.8188
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5258 5134.0 2.994 3.611
r= 30 22974 23103.0 0.721 4.332
r= 31 11568 11551.5 0.024 4.355
chi-square = 4.355 with df = 3; p-value = 0.774
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 5135 5134.0 0.000 0.260
r= 31 23122 23103.0 0.016 0.276
r= 32 11539 11551.5 0.014 0.290
chi-square = 0.290 with df = 3; p-value = 0.038
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_09:31
b-rank test for bits 1 to 8, p=0.72117
b-rank test for bits 2 to 9, p=0.02790
b-rank test for bits 3 to 10, p=0.41809
b-rank test for bits 4 to 11, p=0.98034
b-rank test for bits 5 to 12, p=0.26736
b-rank test for bits 6 to 13, p=0.32856
b-rank test for bits 7 to 14, p=0.06196
b-rank test for bits 8 to 15, p=0.05507
b-rank test for bits 9 to 16, p=0.63382
b-rank test for bits 10 to 17, p=0.75817
b-rank test for bits 11 to 18, p=0.05141
b-rank test for bits 12 to 19, p=0.21332
b-rank test for bits 13 to 20, p=0.28057
b-rank test for bits 14 to 21, p=0.77694
b-rank test for bits 15 to 22, p=0.80695
b-rank test for bits 16 to 23, p=0.42672
b-rank test for bits 17 to 24, p=0.72942
b-rank test for bits 18 to 25, p=0.14081
b-rank test for bits 19 to 26, p=0.12624
b-rank test for bits 20 to 27, p=0.89743
b-rank test for bits 21 to 28, p=0.38288
b-rank test for bits 22 to 29, p=0.23224
b-rank test for bits 23 to 30, p=0.15346
b-rank test for bits 24 to 31, p=0.97619
b-rank test for bits 25 to 32, p=0.68871
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 = 0.407122
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_09:31
(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 142175 0.62 0.732610
2 141182 -1.70 0.044625
3 142256 0.81 0.791023
4 141782 -0.30 0.383042
5 141979 0.16 0.564654
6 141956 0.11 0.543415
7 141377 -1.24 0.106794
8 141610 -0.70 0.242161
9 141007 -2.11 0.017505
10 141610 -0.70 0.242161
11 141271 -1.49 0.067925
12 141664 -0.57 0.283254
13 141882 -0.06 0.474543
14 141450 -1.07 0.141591
15 141779 -0.30 0.380370
16 142301 0.92 0.819935
17 141668 -0.56 0.286426
18 141768 -0.33 0.370621
19 141621 -0.67 0.250261
20 142332 0.99 0.838313
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_09:31
Bits used No. missing words z-score p-value
23 to 32 141942 0.1127 0.544848
22 to 31 141840 -0.2391 0.405526
21 to 30 142022 0.3885 0.651183
20 to 29 141366 -1.8736 0.030496
19 to 28 141814 -0.3287 0.371182
18 to 27 141852 -0.1977 0.421644
17 to 26 141515 -1.3598 0.086953
16 to 25 142344 1.4989 0.933045
15 to 24 142359 1.5506 0.939500
14 to 23 141528 -1.3149 0.094267
13 to 22 141255 -2.2563 0.012026
12 to 21 141964 0.1885 0.574764
11 to 20 142174 0.9127 0.819288
10 to 19 141876 -0.1149 0.454250
9 to 18 142297 1.3368 0.909355
8 to 17 142128 0.7540 0.774586
7 to 16 142377 1.6127 0.946590
6 to 15 142109 0.6885 0.754436
5 to 14 141788 -0.4184 0.337835
4 to 13 141672 -0.8184 0.206570
3 to 12 141801 -0.3736 0.354369
2 to 11 142065 0.5368 0.704295
1 to 10 141791 -0.4080 0.341624
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_09:31
Bits used No. missing words z-score p-value
28 to 32 142416 1.7175 0.957058
27 to 31 142353 1.5040 0.933705
26 to 30 141738 -0.5808 0.280695
25 to 29 141942 0.1107 0.544091
24 to 28 141775 -0.4554 0.324427
23 to 27 141423 -1.6486 0.049617
22 to 26 142198 0.9785 0.836097
21 to 25 141592 -1.0757 0.141032
20 to 24 141868 -0.1401 0.444290
19 to 23 141813 -0.3265 0.372007
18 to 22 141839 -0.2384 0.405783
17 to 21 142592 2.3141 0.989670
16 to 20 141759 -0.5096 0.305168
15 to 19 141702 -0.7028 0.241086
14 to 18 142058 0.5040 0.692857
13 to 17 141614 -1.0011 0.158385
12 to 16 141585 -1.0994 0.135792
11 to 15 141817 -0.3130 0.377147
10 to 14 142263 1.1989 0.884713
9 to 13 141399 -1.7299 0.041821
8 to 12 141943 0.1141 0.545435
7 to 11 142268 1.2158 0.887975
6 to 10 141923 0.0463 0.518480
5 to 9 142293 1.3006 0.903298
4 to 8 141712 -0.6689 0.251775
3 to 7 142407 1.6870 0.954200
2 to 6 141969 0.2023 0.580148
1 to 5 141925 0.0531 0.521181
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_09:31
Bits used No. missing words z-score p-value
31 to 32 141947 0.1111 0.544240
30 to 31 142167 0.7601 0.776399
29 to 30 141674 -0.6942 0.243782
28 to 29 141978 0.2026 0.580263
27 to 28 141787 -0.3609 0.359104
26 to 27 141506 -1.1898 0.117070
25 to 26 141282 -1.8505 0.032119
24 to 25 141964 0.1613 0.564059
23 to 24 141722 -0.5526 0.290270
22 to 23 141797 -0.3314 0.370187
21 to 22 141632 -0.8181 0.206655
20 to 21 141872 -0.1101 0.456158
19 to 20 142185 0.8132 0.791944
18 to 19 141260 -1.9154 0.027719
17 to 18 141647 -0.7738 0.219514
16 to 17 141842 -0.1986 0.421283
15 to 16 141941 0.0934 0.537216
14 to 15 142442 1.5713 0.941943
13 to 14 142003 0.2763 0.608846
12 to 13 141924 0.0433 0.517259
11 to 12 142246 0.9931 0.839676
10 to 11 142100 0.5624 0.713095
9 to 10 142087 0.5241 0.699896
8 to 9 142132 0.6568 0.744359
7 to 8 141874 -0.1042 0.458498
6 to 7 141977 0.1996 0.579110
5 to 6 142280 1.0934 0.862896
4 to 5 141793 -0.3432 0.365740
3 to 4 142094 0.5447 0.707037
2 to 3 142498 1.7365 0.958761
1 to 2 142148 0.7040 0.759297
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2514.94 0.211 0.583658
Test results for specific bytes for dh-ranFile-2018-06-24_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2557.07 0.807 0.790174
2 to 9 2452.82 -0.667 0.252325
3 to 10 2613.80 1.609 0.946227
4 to 11 2522.47 0.318 0.624691
5 to 12 2565.27 0.923 0.822004
6 to 13 2458.29 -0.590 0.277621
7 to 14 2428.46 -1.012 0.155827
8 to 15 2640.39 1.985 0.976450
9 to 16 2612.44 1.590 0.944101
10 to 17 2562.93 0.890 0.813273
11 to 18 2445.97 -0.764 0.222416
12 to 19 2423.70 -1.079 0.140289
13 to 20 2505.39 0.076 0.530393
14 to 21 2357.04 -2.022 0.021601
15 to 22 2464.18 -0.507 0.306207
16 to 23 2447.61 -0.741 0.229392
17 to 24 2519.74 0.279 0.609935
18 to 25 2506.62 0.094 0.537287
19 to 26 2479.99 -0.283 0.388605
20 to 27 2582.83 1.171 0.879290
21 to 28 2453.65 -0.655 0.256081
22 to 29 2530.76 0.435 0.668224
23 to 30 2565.12 0.921 0.821441
24 to 31 2639.55 1.974 0.975782
25 to 32 2486.39 -0.192 0.423708
CDPARK for dh-ranFile-2018-06-24_09:31: 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
3550 1.2329 0.891189
3495 -1.2785 0.100530
3509 -0.6393 0.261324
3525 0.0913 0.536383
3538 0.6849 0.753306
3478 -2.0548 0.019949
3564 1.8721 0.969407
3513 -0.4566 0.323972
3493 -1.3699 0.085365
3506 -0.7763 0.218799
Square side=100, avg. no. parked=3517.10 sample std.=25.66
p-value of the KSTEST for those 10 p-values: 0.422415
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_09:31
0.6066,0.6975,0.1274,0.4758,0.1443,0.4913,0.4110,0.5563,0.2352,0.1847,
The KS test for those 10 p-values: 0.259769
The 3DSPHERES test for dh-ranFile-2018-06-24_09:31
sample no r^3 equiv. uni.
1 100.859 0.965333
2 24.242 0.554274
3 28.075 0.607742
4 17.376 0.439645
5 37.055 0.709216
6 2.494 0.079763
7 26.412 0.585385
8 18.271 0.456124
9 52.653 0.827107
10 22.943 0.534557
11 2.174 0.069910
12 18.736 0.464486
13 41.361 0.748097
14 16.152 0.416319
15 5.998 0.181211
16 40.299 0.739016
17 20.899 0.501738
18 2.962 0.094002
19 27.718 0.603044
20 76.676 0.922376
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.644767
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.5 -1.1 -0.5 0.4 0.9
-0.6 -1.3 3.4 0.8 1.1 2.7
0.1 0.8 -0.3 -0.8 -0.8 -1.6
-0.1 -1.5 0.8 -1.0 1.8 0.1
-1.4 1.1 0.2 -1.2 -1.3 0.3
0.6 0.6 -1.1 0.0 0.6 1.1
0.7 -1.7 -0.8 -0.1 0.9 0.0
0.8
Chi-square with 42 degrees of freedom:53.089856
z-score=1.210003, p-value=0.882729
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_09:31
Test no p-value
1 0.430740
2 0.404139
3 0.115957
4 0.200059
5 0.822955
6 0.041873
7 0.306020
8 0.067490
9 0.589808
10 0.415698
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.134033
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_09:31:
(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 66676 0.00 66835 0.43
3 25000.00 24969 0.04 24855 0.84
4 6666.67 6706 0.23 6663 0.00
5 1388.89 1355 0.83 1377 0.10
6 238.10 251 0.70 233 0.11
7 34.72 39 0.53 34 0.01
8 4.96 3 0.77 2 1.77
p=0.20384 p=0.22446
Number of rngs required: 688814, p-value: 0.682
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_09:31
No. of wins: Observed Expected
98681 98585.9
z-score= 0.426, pvalue=0.66477
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66716 66666.7 0.037 0.037
2 37647 37654.3 0.001 0.038
3 26880 26954.7 0.207 0.245
4 19439 19313.5 0.816 1.061
5 13792 13851.4 0.255 1.316
6 9945 9943.5 0.000 1.316
7 7210 7145.0 0.591 1.907
8 5123 5139.1 0.050 1.957
9 3708 3699.9 0.018 1.975
10 2686 2666.3 0.146 2.121
11 1915 1923.3 0.036 2.157
12 1366 1388.7 0.372 2.529
13 971 1003.7 1.066 3.596
14 693 726.1 1.513 5.108
15 509 525.8 0.539 5.647
16 411 381.2 2.338 7.985
17 276 276.5 0.001 7.986
18 194 200.8 0.232 8.218
19 149 146.0 0.062 8.280
20 99 106.2 0.490 8.771
21 271 287.1 0.904 9.675
Chisq= 9.67 for 20 degrees of freedom, p= 0.02631
SUMMARY of craptest
p-value for no. of wins: 0.664774
p-value for throws/game: 0.026309
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_09:31
No. of wins: Observed Expected
98400 98585.9
z-score=-0.831, pvalue=0.20291
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66490 66666.7 0.468 0.468
2 37641 37654.3 0.005 0.473
3 27069 26954.7 0.484 0.957
4 19293 19313.5 0.022 0.979
5 13861 13851.4 0.007 0.986
6 10107 9943.5 2.687 3.673
7 7115 7145.0 0.126 3.799
8 5080 5139.1 0.679 4.478
9 3749 3699.9 0.653 5.130
10 2682 2666.3 0.092 5.223
11 1940 1923.3 0.144 5.367
12 1354 1388.7 0.869 6.236
13 984 1003.7 0.387 6.624
14 735 726.1 0.108 6.732
15 551 525.8 1.204 7.936
16 385 381.2 0.039 7.975
17 283 276.5 0.151 8.126
18 179 200.8 2.373 10.499
19 145 146.0 0.007 10.505
20 91 106.2 2.180 12.685
21 266 287.1 1.553 14.237
Chisq= 14.24 for 20 degrees of freedom, p= 0.18175
SUMMARY of craptest
p-value for no. of wins: 0.202911
p-value for throws/game: 0.181747
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0120,0.0175,0.0199,0.0216,0.0263,0.0277,0.0279,0.0305,0.0321,
0.0380,0.0397,0.0418,0.0419,0.0446,0.0454,0.0496,0.0514,0.0516,0.0551,
0.0620,0.0675,0.0679,0.0699,0.0728,0.0798,0.0854,0.0870,0.0940,0.0943,
0.1005,0.1068,0.1160,0.1171,0.1262,0.1274,0.1321,0.1340,0.1358,0.1403,
0.1408,0.1410,0.1416,0.1443,0.1535,0.1558,0.1562,0.1584,0.1812,0.1817,
0.1847,0.2001,0.2029,0.2038,0.2060,0.2066,0.2067,0.2124,0.2133,0.2188,
0.2195,0.2224,0.2245,0.2294,0.2322,0.2352,0.2357,0.2411,0.2422,0.2422,
0.2438,0.2443,0.2503,0.2518,0.2523,0.2551,0.2561,0.2598,0.2613,0.2674,
0.2680,0.2776,0.2806,0.2807,0.2833,0.2864,0.2903,0.3052,0.3060,0.3062,
0.3240,0.3244,0.3286,0.3334,0.3378,0.3416,0.3441,0.3544,0.3591,0.3657,
0.3702,0.3706,0.3712,0.3720,0.3771,0.3804,0.3829,0.3830,0.3886,0.4041,
0.4055,0.4058,0.4071,0.4110,0.4157,0.4163,0.4181,0.4213,0.4216,0.4224,
0.4237,0.4254,0.4262,0.4267,0.4307,0.4334,0.4396,0.4439,0.4443,0.4542,
0.4561,0.4562,0.4585,0.4645,0.4745,0.4758,0.4913,0.4972,0.4995,0.5017,
0.5075,0.5173,0.5185,0.5212,0.5221,0.5304,0.5346,0.5364,0.5372,0.5373,
0.5434,0.5441,0.5442,0.5448,0.5454,0.5466,0.5480,0.5543,0.5563,0.5641,
0.5647,0.5748,0.5791,0.5801,0.5803,0.5804,0.5837,0.5854,0.5898,0.5967,
0.6030,0.6048,0.6066,0.6077,0.6088,0.6099,0.6170,0.6239,0.6247,0.6338,
0.6440,0.6448,0.6512,0.6648,0.6682,0.6697,0.6809,0.6821,0.6887,0.6929,
0.6975,0.6984,0.6999,0.7043,0.7070,0.7092,0.7131,0.7212,0.7294,0.7313,
0.7326,0.7390,0.7422,0.7444,0.7481,0.7533,0.7544,0.7554,0.7582,0.7593,
0.7663,0.7744,0.7746,0.7764,0.7769,0.7845,0.7902,0.7910,0.7919,0.7932,
0.7966,0.8069,0.8112,0.8133,0.8188,0.8193,0.8199,0.8214,0.8220,0.8230,
0.8271,0.8361,0.8383,0.8397,0.8579,0.8629,0.8793,0.8827,0.8847,0.8880,
0.8912,0.8938,0.8974,0.9033,0.9076,0.9094,0.9224,0.9330,0.9337,0.9395,
0.9419,0.9441,0.9462,0.9466,0.9471,0.9542,0.9571,0.9588,0.9653,0.9694,
0.9754,0.9758,0.9762,0.9765,0.9803,0.9840,0.9897,0.9903,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.708793
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.