RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.68 17.2212 0.560517
2 to 25 15.78 16.1565 0.487231
3 to 26 15.84 16.2400 0.493114
4 to 27 15.81 16.9073 0.539334
5 to 28 15.74 15.8635 0.466469
6 to 29 15.99 12.2909 0.217788
7 to 30 15.96 16.1386 0.485971
8 to 31 15.66 24.2275 0.886615
9 to 32 15.61 20.5689 0.753831
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.301394
Tough bday spacings test for dh-ranFile-2018-06-20_08:31: 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 42 71 79 97 88 59 27 13 8 6
(O-E)^2/E 0.1 0.8 0.1 3.6 0.0 1.2 0.9 0.3 0.2 0.3 0.9
Birthday Spacings: Sum(O-E)^2/E= 8.375, p= 0.408
RESULTS OF GCD FOR dh-ranFile-2018-06-20_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.913013
p-value, dist. of gcd's: 0.429757
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.949 0.268 0.266 0.783 0.329 0.708 0.383 0.034
Bits 8 to 15---> 0.268 0.383 0.369 0.892 0.430 0.253 0.537 0.846
Bits 16 to 23---> 0.025 0.099 0.404 0.651 0.686 0.803 0.043 0.587
Bits 24 to 31---> 0.773 0.223 0.460 0.362 0.699 0.430 0.569 0.864
KS test for the above 32 p values: 0.250
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_08:31,
p-values for 5 runs: 0.7063, 0.4508, 0.8147, 0.7230, 0.4174
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5120 5134.0 0.038 0.066
r= 30 23135 23103.0 0.044 0.110
r= 31 11536 11551.5 0.021 0.131
chi-square = 0.131 with df = 3; p-value = 0.012
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 208 211.4 0.055 0.055
r= 30 4990 5134.0 4.040 4.095
r= 31 23255 23103.0 0.999 5.094
r= 32 11547 11551.5 0.002 5.096
chi-square = 5.096 with df = 3; p-value = 0.835
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_08:31
b-rank test for bits 1 to 8, p=0.08423
b-rank test for bits 2 to 9, p=0.17131
b-rank test for bits 3 to 10, p=0.26662
b-rank test for bits 4 to 11, p=0.62274
b-rank test for bits 5 to 12, p=0.81554
b-rank test for bits 6 to 13, p=0.81558
b-rank test for bits 7 to 14, p=0.31263
b-rank test for bits 8 to 15, p=0.35492
b-rank test for bits 9 to 16, p=0.30356
b-rank test for bits 10 to 17, p=0.02861
b-rank test for bits 11 to 18, p=0.99627
b-rank test for bits 12 to 19, p=0.94455
b-rank test for bits 13 to 20, p=0.16643
b-rank test for bits 14 to 21, p=0.78899
b-rank test for bits 15 to 22, p=0.93955
b-rank test for bits 16 to 23, p=0.51682
b-rank test for bits 17 to 24, p=0.68117
b-rank test for bits 18 to 25, p=0.94077
b-rank test for bits 19 to 26, p=0.91307
b-rank test for bits 20 to 27, p=0.62787
b-rank test for bits 21 to 28, p=0.94306
b-rank test for bits 22 to 29, p=0.40131
b-rank test for bits 23 to 30, p=0.65256
b-rank test for bits 24 to 31, p=0.35619
b-rank test for bits 25 to 32, p=0.41678
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 = 0.342409
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_08:31
(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 141181 -1.70 0.044405
2 141899 -0.02 0.490372
3 142644 1.72 0.956966
4 142001 0.21 0.584798
5 141871 -0.09 0.464320
6 142329 0.98 0.836590
7 141073 -1.95 0.025348
8 141858 -0.12 0.452269
9 141818 -0.21 0.415512
10 141121 -1.84 0.032745
11 141981 0.17 0.566493
12 142030 0.28 0.611005
13 142372 1.08 0.860153
14 141848 -0.14 0.443029
15 141207 -1.64 0.050403
16 142330 0.98 0.837165
17 140960 -2.22 0.013275
18 141932 0.05 0.521121
19 141902 -0.02 0.493168
20 140753 -2.70 0.003449
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_08:31
Bits used No. missing words z-score p-value
23 to 32 142175 0.9161 0.820194
22 to 31 142339 1.4816 0.930779
21 to 30 141963 0.1851 0.573413
20 to 29 142158 0.8575 0.804411
19 to 28 141643 -0.9184 0.179210
18 to 27 141765 -0.4977 0.309351
17 to 26 141827 -0.2839 0.388245
16 to 25 141670 -0.8253 0.204608
15 to 24 141791 -0.4080 0.341624
14 to 23 141378 -1.8322 0.033463
13 to 22 141952 0.1471 0.558488
12 to 21 141993 0.2885 0.613525
11 to 20 142242 1.1471 0.874338
10 to 19 141821 -0.3046 0.380341
9 to 18 141758 -0.5218 0.300895
8 to 17 142026 0.4023 0.656272
7 to 16 141723 -0.6425 0.260269
6 to 15 141790 -0.4115 0.340359
5 to 14 142237 1.1299 0.870740
4 to 13 142150 0.8299 0.796701
3 to 12 142016 0.3678 0.643499
2 to 11 141685 -0.7736 0.219598
1 to 10 141337 -1.9736 0.024216
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_08:31
Bits used No. missing words z-score p-value
28 to 32 142272 1.2294 0.890537
27 to 31 141558 -1.1909 0.116837
26 to 30 142065 0.5277 0.701145
25 to 29 141580 -1.1164 0.132131
24 to 28 141878 -0.1062 0.457711
23 to 27 141996 0.2938 0.615543
22 to 26 142047 0.4667 0.679635
21 to 25 141510 -1.3537 0.087922
20 to 24 141728 -0.6147 0.269384
19 to 23 142371 1.5650 0.941207
18 to 22 142307 1.3480 0.911176
17 to 21 142579 2.2701 0.988398
16 to 20 141835 -0.2520 0.400534
15 to 19 142243 1.1311 0.870990
14 to 18 142402 1.6701 0.952547
13 to 17 141953 0.1480 0.558842
12 to 16 141971 0.2091 0.582796
11 to 15 141728 -0.6147 0.269384
10 to 14 141781 -0.4350 0.331775
9 to 13 142276 1.2429 0.893057
8 to 12 142234 1.1006 0.864459
7 to 11 142184 0.9311 0.824095
6 to 10 142168 0.8768 0.809715
5 to 9 141468 -1.4960 0.067322
4 to 8 141956 0.1582 0.562852
3 to 7 141723 -0.6316 0.263815
2 to 6 142218 1.0463 0.852298
1 to 5 142254 1.1684 0.878672
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_08:31
Bits used No. missing words z-score p-value
31 to 32 141348 -1.6558 0.048877
30 to 31 141951 0.1229 0.548915
29 to 30 142017 0.3176 0.624610
28 to 29 142117 0.6126 0.729928
27 to 28 141316 -1.7502 0.040039
26 to 27 141969 0.1760 0.569860
25 to 26 141156 -2.2222 0.013134
24 to 25 142865 2.8191 0.997592
23 to 24 142190 0.8279 0.796146
22 to 23 141723 -0.5496 0.291281
21 to 22 141686 -0.6588 0.255015
20 to 21 141594 -0.9302 0.176140
19 to 20 141826 -0.2458 0.402914
18 to 19 141491 -1.2340 0.108599
17 to 18 142332 1.2468 0.893767
16 to 17 141654 -0.7532 0.225669
15 to 16 141845 -0.1898 0.424747
14 to 15 141652 -0.7591 0.223901
13 to 14 142356 1.3176 0.906183
12 to 13 142485 1.6981 0.955259
11 to 12 141815 -0.2783 0.390407
10 to 11 141711 -0.5850 0.279259
9 to 10 142390 1.4179 0.921891
8 to 9 142216 0.9046 0.817170
7 to 8 141807 -0.3019 0.381380
6 to 7 142027 0.3471 0.635745
5 to 6 141739 -0.5024 0.307676
4 to 5 141822 -0.2576 0.398354
3 to 4 142194 0.8397 0.799471
2 to 3 142282 1.0993 0.864186
1 to 2 141523 -1.1396 0.127223
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2524.98 0.353 0.638076
Test results for specific bytes for dh-ranFile-2018-06-20_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2547.88 0.677 0.750849
2 to 9 2420.91 -1.119 0.131673
3 to 10 2562.98 0.891 0.813451
4 to 11 2459.73 -0.569 0.284530
5 to 12 2524.86 0.352 0.637406
6 to 13 2508.14 0.115 0.545822
7 to 14 2507.78 0.110 0.543786
8 to 15 2464.81 -0.498 0.309352
9 to 16 2411.31 -1.254 0.104869
10 to 17 2384.32 -1.636 0.050917
11 to 18 2329.29 -2.414 0.007884
12 to 19 2528.99 0.410 0.659099
13 to 20 2538.43 0.544 0.706612
14 to 21 2475.42 -0.348 0.364057
15 to 22 2488.98 -0.156 0.438050
16 to 23 2573.64 1.041 0.851160
17 to 24 2648.63 2.102 0.982219
18 to 25 2468.57 -0.444 0.328358
19 to 26 2519.03 0.269 0.606098
20 to 27 2708.03 2.942 0.998369
21 to 28 2587.40 1.236 0.891780
22 to 29 2566.90 0.946 0.827962
23 to 30 2526.38 0.373 0.645471
24 to 31 2556.88 0.804 0.789432
25 to 32 2465.65 -0.486 0.313586
CDPARK for dh-ranFile-2018-06-20_08:31: 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
3486 -1.6895 0.045562
3515 -0.3653 0.357445
3536 0.5936 0.723613
3499 -1.0959 0.136563
3521 -0.0913 0.463617
3503 -0.9132 0.180558
3521 -0.0913 0.463617
3524 0.0457 0.518210
3530 0.3196 0.625377
3552 1.3242 0.907282
Square side=100, avg. no. parked=3518.70 sample std.=18.14
p-value of the KSTEST for those 10 p-values: 0.852201
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_08:31
0.3229,0.6171,0.5338,0.3553,0.1182,0.8734,0.2665,0.9253,0.7382,0.1691,
The KS test for those 10 p-values: 0.990813
The 3DSPHERES test for dh-ranFile-2018-06-20_08:31
sample no r^3 equiv. uni.
1 38.759 0.725273
2 13.537 0.363155
3 27.205 0.596200
4 52.465 0.826024
5 48.402 0.800791
6 10.034 0.284281
7 24.209 0.553786
8 1.885 0.060913
9 17.827 0.448023
10 9.005 0.259302
11 48.561 0.801841
12 65.035 0.885574
13 27.636 0.601964
14 4.774 0.147117
15 26.252 0.583164
16 28.345 0.611262
17 81.079 0.932971
18 1.500 0.048786
19 11.410 0.316373
20 12.042 0.330611
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.955497
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.3 1.3 0.8 0.2 -1.1
-3.0 -0.9 -0.6 -2.0 0.5 -0.3
-0.3 -0.8 -0.9 2.4 1.3 0.3
-1.1 -1.9 0.3 -0.3 -0.3 -0.0
1.9 1.5 1.3 -0.3 1.2 1.6
-0.1 -0.3 -1.5 2.2 -0.4 -0.8
0.3 0.8 1.7 1.0 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:60.184240
z-score=1.984063, p-value=0.965932
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_08:31
Test no p-value
1 0.027132
2 0.022497
3 0.007441
4 0.029161
5 0.187344
6 0.601412
7 0.063763
8 0.637376
9 0.642289
10 0.075927
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000311
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_08:31:
(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 66593 0.08 66905 0.85
3 25000.00 25074 0.22 24803 1.55
4 6666.67 6677 0.02 6649 0.05
5 1388.89 1406 0.21 1358 0.69
6 238.10 210 3.32 242 0.06
7 34.72 32 0.21 36 0.05
8 4.96 7 0.84 6 0.22
p=0.44260 p=0.25171
Number of rngs required: 688911, p-value: 0.721
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_08:31
No. of wins: Observed Expected
98902 98585.9
z-score= 1.414, pvalue=0.92131
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66505 66666.7 0.392 0.392
2 37510 37654.3 0.553 0.945
3 27145 26954.7 1.343 2.288
4 19150 19313.5 1.383 3.672
5 14067 13851.4 3.355 7.027
6 10072 9943.5 1.659 8.686
7 7058 7145.0 1.060 9.746
8 5067 5139.1 1.011 10.757
9 3682 3699.9 0.086 10.843
10 2694 2666.3 0.288 11.131
11 1931 1923.3 0.031 11.162
12 1472 1388.7 4.992 16.154
13 1015 1003.7 0.127 16.280
14 746 726.1 0.543 16.824
15 499 525.8 1.370 18.193
16 376 381.2 0.070 18.263
17 269 276.5 0.206 18.468
18 206 200.8 0.133 18.601
19 141 146.0 0.170 18.772
20 114 106.2 0.571 19.342
21 281 287.1 0.130 19.472
Chisq= 19.47 for 20 degrees of freedom, p= 0.50866
SUMMARY of craptest
p-value for no. of wins: 0.921314
p-value for throws/game: 0.508659
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_08:31
No. of wins: Observed Expected
98602 98585.9
z-score= 0.072, pvalue=0.52878
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67229 66666.7 4.743 4.743
2 37685 37654.3 0.025 4.768
3 26770 26954.7 1.266 6.034
4 19293 19313.5 0.022 6.056
5 13835 13851.4 0.019 6.075
6 9907 9943.5 0.134 6.210
7 7014 7145.0 2.403 8.613
8 5036 5139.1 2.067 10.680
9 3707 3699.9 0.014 10.694
10 2545 2666.3 5.518 16.212
11 1973 1923.3 1.283 17.494
12 1400 1388.7 0.091 17.586
13 972 1003.7 1.002 18.588
14 731 726.1 0.033 18.620
15 500 525.8 1.269 19.890
16 390 381.2 0.205 20.095
17 276 276.5 0.001 20.096
18 218 200.8 1.468 21.564
19 131 146.0 1.538 23.102
20 101 106.2 0.256 23.358
21 287 287.1 0.000 23.358
Chisq= 23.36 for 20 degrees of freedom, p= 0.72846
SUMMARY of craptest
p-value for no. of wins: 0.528776
p-value for throws/game: 0.728462
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0034,0.0074,0.0079,0.0121,0.0131,0.0133,0.0225,0.0242,0.0250,
0.0253,0.0271,0.0286,0.0292,0.0327,0.0335,0.0338,0.0400,0.0427,0.0444,
0.0456,0.0488,0.0489,0.0504,0.0509,0.0609,0.0638,0.0673,0.0759,0.0842,
0.0879,0.0992,0.1049,0.1086,0.1168,0.1182,0.1272,0.1317,0.1321,0.1366,
0.1471,0.1664,0.1691,0.1713,0.1761,0.1792,0.1806,0.1873,0.2046,0.2178,
0.2196,0.2231,0.2239,0.2257,0.2501,0.2517,0.2533,0.2550,0.2593,0.2603,
0.2638,0.2663,0.2665,0.2666,0.2682,0.2684,0.2694,0.2694,0.2793,0.2843,
0.2845,0.2913,0.3009,0.3014,0.3036,0.3077,0.3094,0.3094,0.3126,0.3136,
0.3164,0.3229,0.3284,0.3287,0.3306,0.3318,0.3404,0.3416,0.3424,0.3549,
0.3553,0.3562,0.3574,0.3619,0.3632,0.3641,0.3694,0.3803,0.3814,0.3827,
0.3835,0.3882,0.3904,0.3984,0.4005,0.4013,0.4029,0.4043,0.4078,0.4155,
0.4168,0.4174,0.4247,0.4298,0.4298,0.4298,0.4381,0.4426,0.4430,0.4480,
0.4508,0.4523,0.4577,0.4599,0.4636,0.4636,0.4643,0.4665,0.4860,0.4872,
0.4904,0.4931,0.4932,0.5087,0.5168,0.5182,0.5211,0.5288,0.5338,0.5368,
0.5393,0.5438,0.5458,0.5489,0.5538,0.5585,0.5588,0.5605,0.5629,0.5665,
0.5687,0.5699,0.5734,0.5828,0.5832,0.5848,0.5871,0.5962,0.6014,0.6020,
0.6061,0.6110,0.6113,0.6135,0.6155,0.6171,0.6227,0.6246,0.6254,0.6279,
0.6357,0.6374,0.6374,0.6381,0.6423,0.6435,0.6455,0.6511,0.6526,0.6563,
0.6591,0.6796,0.6812,0.6863,0.6990,0.7011,0.7063,0.7066,0.7084,0.7210,
0.7230,0.7236,0.7253,0.7285,0.7299,0.7382,0.7508,0.7538,0.7726,0.7828,
0.7890,0.7894,0.7961,0.7967,0.7995,0.8008,0.8018,0.8033,0.8044,0.8097,
0.8135,0.8147,0.8155,0.8156,0.8172,0.8202,0.8241,0.8260,0.8280,0.8351,
0.8366,0.8372,0.8461,0.8512,0.8522,0.8523,0.8602,0.8642,0.8642,0.8645,
0.8707,0.8710,0.8734,0.8743,0.8787,0.8856,0.8866,0.8905,0.8916,0.8918,
0.8931,0.8938,0.9062,0.9073,0.9112,0.9130,0.9131,0.9213,0.9219,0.9253,
0.9308,0.9330,0.9395,0.9408,0.9412,0.9431,0.9445,0.9485,0.9525,0.9553,
0.9555,0.9570,0.9659,0.9822,0.9884,0.9908,0.9963,0.9976,0.9984,
Overall p-value after applying KStest on 269 p-values = 0.484410
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.