RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_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 15.77 12.4590 0.228417
2 to 25 15.79 22.5293 0.834789
3 to 26 15.29 37.7393 0.997331
4 to 27 15.56 15.1835 0.417735
5 to 28 15.75 19.1834 0.681891
6 to 29 15.81 15.8936 0.468608
7 to 30 15.79 9.6459 0.082202
8 to 31 15.76 30.1617 0.974798
9 to 32 15.58 19.6748 0.708800
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.310921
Tough bday spacings test for dh-ranFile-2018-06-24_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 7 39 70 101 95 88 42 28 19 4 7
(O-E)^2/E 0.5 0.2 0.1 0.1 0.1 1.2 2.0 0.1 1.1 1.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 8.587, p= 0.428
RESULTS OF GCD FOR dh-ranFile-2018-06-24_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.121154
p-value, dist. of gcd's: 0.743995
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.563 0.994 0.551 0.660 0.746 0.113 0.294 0.887
Bits 8 to 15---> 0.011 0.123 0.567 0.462 0.681 0.177 0.871 0.956
Bits 16 to 23---> 0.518 0.365 0.181 0.095 0.503 0.663 0.528 0.446
Bits 24 to 31---> 0.600 0.180 0.570 0.675 0.085 0.595 0.224 0.251
KS test for the above 32 p values: 0.361
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_20:31,
p-values for 5 runs: 0.4015, 0.8908, 0.3423, 0.2660, 0.2443
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 190 211.4 2.170 2.170
r= 29 5207 5134.0 1.038 3.207
r= 30 23012 23103.0 0.359 3.566
r= 31 11591 11551.5 0.135 3.701
chi-square = 3.701 with df = 3; p-value = 0.704
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 223 211.4 0.634 0.634
r= 30 5173 5134.0 0.296 0.931
r= 31 23193 23103.0 0.350 1.281
r= 32 11411 11551.5 1.709 2.990
chi-square = 2.990 with df = 3; p-value = 0.607
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_20:31
b-rank test for bits 1 to 8, p=0.72680
b-rank test for bits 2 to 9, p=0.99555
b-rank test for bits 3 to 10, p=0.97686
b-rank test for bits 4 to 11, p=0.93698
b-rank test for bits 5 to 12, p=0.70098
b-rank test for bits 6 to 13, p=0.78434
b-rank test for bits 7 to 14, p=0.07851
b-rank test for bits 8 to 15, p=0.91989
b-rank test for bits 9 to 16, p=0.03124
b-rank test for bits 10 to 17, p=0.06693
b-rank test for bits 11 to 18, p=0.08263
b-rank test for bits 12 to 19, p=0.50068
b-rank test for bits 13 to 20, p=0.46437
b-rank test for bits 14 to 21, p=0.22411
b-rank test for bits 15 to 22, p=0.80595
b-rank test for bits 16 to 23, p=0.76903
b-rank test for bits 17 to 24, p=0.81108
b-rank test for bits 18 to 25, p=0.44324
b-rank test for bits 19 to 26, p=0.54513
b-rank test for bits 20 to 27, p=0.29765
b-rank test for bits 21 to 28, p=0.73895
b-rank test for bits 22 to 29, p=0.47906
b-rank test for bits 23 to 30, p=0.21311
b-rank test for bits 24 to 31, p=0.92066
b-rank test for bits 25 to 32, p=0.72124
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 = 0.266353
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_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 140722 -2.77 0.002767
2 141764 -0.34 0.367095
3 142225 0.74 0.769605
4 141368 -1.26 0.102973
5 141361 -1.28 0.100071
6 141945 0.08 0.533210
7 142075 0.39 0.650651
8 141927 0.04 0.516466
9 141743 -0.39 0.348778
10 141847 -0.15 0.442106
11 141174 -1.72 0.042893
12 141526 -0.90 0.185225
13 141539 -0.87 0.193449
14 142382 1.10 0.865284
15 141355 -1.30 0.097632
16 142734 1.93 0.972998
17 141354 -1.30 0.097230
18 142323 0.97 0.833108
19 142120 0.49 0.688718
20 141718 -0.45 0.327426
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_20:31
Bits used No. missing words z-score p-value
23 to 32 141644 -0.9149 0.180114
22 to 31 142143 0.8058 0.789809
21 to 30 142286 1.2989 0.903004
20 to 29 142140 0.7954 0.786814
19 to 28 142047 0.4747 0.682508
18 to 27 141205 -2.4287 0.007576
17 to 26 141845 -0.2218 0.412224
16 to 25 142431 1.7989 0.963980
15 to 24 142312 1.3885 0.917510
14 to 23 141498 -1.4184 0.078040
13 to 22 142108 0.6851 0.753350
12 to 21 142139 0.7920 0.785810
11 to 20 142335 1.4678 0.928924
10 to 19 141901 -0.0287 0.488542
9 to 18 141779 -0.4494 0.326567
8 to 17 142261 1.2127 0.887369
7 to 16 142055 0.5023 0.692275
6 to 15 142230 1.1058 0.865585
5 to 14 142477 1.9575 0.974855
4 to 13 142165 0.8816 0.811009
3 to 12 141676 -0.8046 0.210529
2 to 11 141834 -0.2598 0.397525
1 to 10 141622 -0.9908 0.160893
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_20:31
Bits used No. missing words z-score p-value
28 to 32 142127 0.7379 0.769702
27 to 31 141576 -1.1299 0.129252
26 to 30 141724 -0.6282 0.264924
25 to 29 141664 -0.8316 0.202810
24 to 28 141630 -0.9469 0.171850
23 to 27 141802 -0.3638 0.357992
22 to 26 142243 1.1311 0.870990
21 to 25 141626 -0.9604 0.168417
20 to 24 141838 -0.2418 0.404469
19 to 23 142319 1.3887 0.917540
18 to 22 142028 0.4023 0.656258
17 to 21 141564 -1.1706 0.120878
16 to 20 141526 -1.2994 0.096899
15 to 19 142054 0.4904 0.688077
14 to 18 141473 -1.4791 0.069559
13 to 17 142178 0.9107 0.818785
12 to 16 141871 -0.1299 0.448310
11 to 15 141962 0.1785 0.570852
10 to 14 142001 0.3107 0.622003
9 to 13 142084 0.5921 0.723109
8 to 12 141488 -1.4282 0.076612
7 to 11 142304 1.3379 0.909530
6 to 10 141845 -0.2181 0.413688
5 to 9 142178 0.9107 0.818785
4 to 8 141883 -0.0893 0.464440
3 to 7 142334 1.4396 0.925004
2 to 6 141891 -0.0621 0.475227
1 to 5 142045 0.4599 0.677205
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_20:31
Bits used No. missing words z-score p-value
31 to 32 141448 -1.3609 0.086780
30 to 31 141492 -1.2311 0.109150
29 to 30 142534 1.8427 0.967312
28 to 29 141619 -0.8564 0.195880
27 to 28 141752 -0.4641 0.321288
26 to 27 141537 -1.0983 0.136033
25 to 26 142054 0.4268 0.665221
24 to 25 141871 -0.1131 0.454988
23 to 24 141921 0.0344 0.513731
22 to 23 142373 1.3678 0.914306
21 to 22 142470 1.6539 0.950925
20 to 21 142023 0.3353 0.631304
19 to 20 141253 -1.9361 0.026429
18 to 19 142100 0.5624 0.713095
17 to 18 141946 0.1082 0.543070
16 to 17 142393 1.4268 0.923175
15 to 16 142374 1.3707 0.914767
14 to 15 141570 -1.0010 0.158420
13 to 14 142103 0.5713 0.716101
12 to 13 141425 -1.4287 0.076545
11 to 12 141503 -1.1986 0.115339
10 to 11 141651 -0.7620 0.223019
9 to 10 141817 -0.2724 0.392673
8 to 9 141708 -0.5939 0.276292
7 to 8 141710 -0.5880 0.278268
6 to 7 141917 0.0226 0.509025
5 to 6 141981 0.2114 0.583719
4 to 5 142136 0.6686 0.748138
3 to 4 142146 0.6981 0.757456
2 to 3 141775 -0.3963 0.345959
1 to 2 141751 -0.4671 0.320232
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2458.37 -0.589 0.278016
Test results for specific bytes for dh-ranFile-2018-06-24_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2508.97 0.127 0.550494
2 to 9 2492.16 -0.111 0.455833
3 to 10 2489.48 -0.149 0.440867
4 to 11 2360.77 -1.969 0.024472
5 to 12 2558.52 0.828 0.796058
6 to 13 2557.18 0.809 0.790626
7 to 14 2543.15 0.610 0.729141
8 to 15 2479.23 -0.294 0.384471
9 to 16 2552.37 0.741 0.770535
10 to 17 2468.06 -0.452 0.325748
11 to 18 2495.11 -0.069 0.472448
12 to 19 2473.76 -0.371 0.355293
13 to 20 2384.44 -1.634 0.051101
14 to 21 2501.65 0.023 0.509308
15 to 22 2497.45 -0.036 0.485615
16 to 23 2552.72 0.746 0.772032
17 to 24 2558.60 0.829 0.796381
18 to 25 2432.65 -0.952 0.170427
19 to 26 2582.15 1.162 0.877347
20 to 27 2501.96 0.028 0.511070
21 to 28 2555.72 0.788 0.784671
22 to 29 2482.86 -0.242 0.404254
23 to 30 2477.63 -0.316 0.375890
24 to 31 2499.23 -0.011 0.495680
25 to 32 2462.89 -0.525 0.299872
CDPARK for dh-ranFile-2018-06-24_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
3516 -0.3196 0.374623
3526 0.1370 0.554479
3547 1.0959 0.863437
3581 2.6484 0.995956
3527 0.1826 0.572463
3519 -0.1826 0.427537
3524 0.0457 0.518210
3546 1.0502 0.853193
3558 1.5982 0.944998
3498 -1.1416 0.126820
Square side=100, avg. no. parked=3534.20 sample std.=22.71
p-value of the KSTEST for those 10 p-values: 0.226991
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_20:31
0.0404,0.2829,0.2355,0.7958,0.8389,0.4714,0.5659,0.9146,0.6018,0.8765,
The KS test for those 10 p-values: 0.802796
The 3DSPHERES test for dh-ranFile-2018-06-24_20:31
sample no r^3 equiv. uni.
1 82.985 0.937097
2 8.270 0.240932
3 8.963 0.258265
4 1.790 0.057912
5 0.890 0.029238
6 38.193 0.720037
7 12.781 0.346899
8 29.436 0.625143
9 19.570 0.479164
10 8.113 0.236955
11 22.237 0.523476
12 123.977 0.983958
13 7.524 0.221826
14 50.966 0.817107
15 11.469 0.317709
16 107.605 0.972314
17 25.879 0.577956
18 4.129 0.128576
19 29.346 0.624016
20 13.570 0.363866
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.850570
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.1 0.1 -1.1 -0.1 -1.2
0.0 0.7 -0.6 0.0 0.0 -0.2
0.6 0.5 1.9 -1.3 -0.4 0.2
0.5 0.5 -0.3 -0.5 -0.7 -0.3
-1.6 -0.3 -0.1 -1.0 1.0 -0.4
1.8 2.9 1.2 0.5 -0.6 0.2
0.0 0.8 -2.0 -0.7 0.1 -1.0
0.8
Chi-square with 42 degrees of freedom:40.420891
z-score=-0.172295, p-value=0.459596
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_20:31
Test no p-value
1 0.353668
2 0.640134
3 0.150265
4 0.294205
5 0.655766
6 0.940683
7 0.051414
8 0.072815
9 0.068659
10 0.307136
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.140607
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_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 66489 0.47 66583 0.11
3 25000.00 24991 0.00 25112 0.50
4 6666.67 6802 2.75 6622 0.30
5 1388.89 1421 0.74 1410 0.32
6 238.10 252 0.81 224 0.83
7 34.72 40 0.80 42 1.53
8 4.96 4 0.19 6 0.22
p=0.55021 p=0.29707
Number of rngs required: 688490, p-value: 0.540
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_20:31
No. of wins: Observed Expected
98224 98585.9
z-score=-1.618, pvalue=0.05278
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66751 66666.7 0.107 0.107
2 37898 37654.3 1.577 1.684
3 26871 26954.7 0.260 1.944
4 19049 19313.5 3.621 5.565
5 13851 13851.4 0.000 5.565
6 10028 9943.5 0.717 6.282
7 7101 7145.0 0.271 6.554
8 5107 5139.1 0.200 6.754
9 3679 3699.9 0.118 6.872
10 2660 2666.3 0.015 6.886
11 1900 1923.3 0.283 7.169
12 1411 1388.7 0.357 7.526
13 978 1003.7 0.659 8.185
14 736 726.1 0.134 8.319
15 566 525.8 3.068 11.387
16 429 381.2 6.007 17.394
17 249 276.5 2.743 20.136
18 211 200.8 0.515 20.651
19 130 146.0 1.750 22.401
20 110 106.2 0.135 22.536
21 285 287.1 0.016 22.552
Chisq= 22.55 for 20 degrees of freedom, p= 0.68867
SUMMARY of craptest
p-value for no. of wins: 0.052784
p-value for throws/game: 0.688667
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_20:31
No. of wins: Observed Expected
98663 98585.9
z-score= 0.345, pvalue=0.63496
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66681 66666.7 0.003 0.003
2 37719 37654.3 0.111 0.114
3 26889 26954.7 0.160 0.274
4 19276 19313.5 0.073 0.347
5 13969 13851.4 0.998 1.345
6 9819 9943.5 1.560 2.905
7 7200 7145.0 0.423 3.328
8 5229 5139.1 1.574 4.902
9 3640 3699.9 0.969 5.870
10 2636 2666.3 0.344 6.215
11 1895 1923.3 0.417 6.632
12 1376 1388.7 0.117 6.749
13 997 1003.7 0.045 6.794
14 756 726.1 1.228 8.022
15 510 525.8 0.477 8.498
16 351 381.2 2.385 10.884
17 299 276.5 1.824 12.708
18 227 200.8 3.410 16.118
19 156 146.0 0.687 16.805
20 114 106.2 0.571 17.376
21 261 287.1 2.375 19.751
Chisq= 19.75 for 20 degrees of freedom, p= 0.52639
SUMMARY of craptest
p-value for no. of wins: 0.634961
p-value for throws/game: 0.526390
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0028,0.0076,0.0106,0.0245,0.0264,0.0292,0.0312,0.0404,0.0429,0.0511,
0.0514,0.0528,0.0579,0.0669,0.0687,0.0696,0.0728,0.0765,0.0766,0.0780,
0.0785,0.0822,0.0826,0.0845,0.0868,0.0949,0.0969,0.0972,0.0976,0.1001,
0.1030,0.1091,0.1130,0.1153,0.1209,0.1212,0.1227,0.1268,0.1286,0.1293,
0.1360,0.1406,0.1503,0.1584,0.1609,0.1684,0.1704,0.1718,0.1769,0.1801,
0.1801,0.1808,0.1852,0.1934,0.1959,0.2028,0.2105,0.2131,0.2218,0.2230,
0.2238,0.2241,0.2270,0.2284,0.2355,0.2370,0.2409,0.2443,0.2505,0.2583,
0.2649,0.2660,0.2664,0.2763,0.2780,0.2783,0.2829,0.2935,0.2942,0.2971,
0.2976,0.2999,0.3071,0.3109,0.3177,0.3202,0.3213,0.3257,0.3266,0.3274,
0.3423,0.3460,0.3469,0.3488,0.3537,0.3553,0.3580,0.3608,0.3639,0.3654,
0.3671,0.3746,0.3759,0.3845,0.3927,0.3975,0.4015,0.4043,0.4045,0.4122,
0.4137,0.4177,0.4275,0.4283,0.4409,0.4421,0.4432,0.4457,0.4483,0.4550,
0.4558,0.4596,0.4622,0.4644,0.4644,0.4686,0.4714,0.4724,0.4752,0.4791,
0.4792,0.4856,0.4885,0.4957,0.5007,0.5027,0.5090,0.5093,0.5111,0.5137,
0.5165,0.5182,0.5183,0.5235,0.5264,0.5280,0.5332,0.5399,0.5431,0.5451,
0.5502,0.5505,0.5512,0.5545,0.5626,0.5659,0.5674,0.5704,0.5709,0.5725,
0.5780,0.5837,0.5949,0.6001,0.6018,0.6069,0.6220,0.6240,0.6251,0.6313,
0.6350,0.6401,0.6507,0.6558,0.6563,0.6600,0.6626,0.6652,0.6749,0.6772,
0.6811,0.6819,0.6825,0.6881,0.6887,0.6887,0.6923,0.7010,0.7044,0.7088,
0.7131,0.7161,0.7200,0.7212,0.7231,0.7268,0.7291,0.7390,0.7440,0.7463,
0.7481,0.7533,0.7575,0.7690,0.7696,0.7697,0.7705,0.7720,0.7843,0.7847,
0.7858,0.7868,0.7898,0.7906,0.7958,0.7961,0.7964,0.8028,0.8059,0.8110,
0.8111,0.8171,0.8188,0.8188,0.8331,0.8348,0.8389,0.8506,0.8532,0.8634,
0.8653,0.8656,0.8710,0.8713,0.8765,0.8773,0.8873,0.8874,0.8908,0.9030,
0.9095,0.9143,0.9146,0.9148,0.9175,0.9175,0.9199,0.9207,0.9232,0.9250,
0.9289,0.9370,0.9371,0.9407,0.9450,0.9509,0.9560,0.9640,0.9673,0.9723,
0.9730,0.9748,0.9749,0.9769,0.9840,0.9941,0.9955,0.9960,0.9973,
Overall p-value after applying KStest on 269 p-values = 0.998458
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.