RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_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 15.72 29.8659 0.972672
2 to 25 15.81 17.2552 0.562791
3 to 26 16.06 11.3751 0.163585
4 to 27 15.84 11.9934 0.199462
5 to 28 15.91 17.7927 0.597972
6 to 29 15.41 25.5718 0.917376
7 to 30 16.03 15.5696 0.445478
8 to 31 15.58 20.3238 0.741996
9 to 32 15.85 14.9686 0.402256
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.852805
Tough bday spacings test for dh-ranFile-2018-07-12_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 8 40 80 96 98 80 45 27 17 6 3
(O-E)^2/E 0.1 0.3 0.6 0.0 0.0 0.0 1.0 0.3 0.3 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 3.012, p= 0.019
RESULTS OF GCD FOR dh-ranFile-2018-07-12_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.488031
p-value, dist. of gcd's: 0.657032
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.686 0.836 0.531 0.643 0.001 0.158 0.030 0.676
Bits 8 to 15---> 0.724 0.982 0.619 0.394 0.511 0.579 0.112 0.437
Bits 16 to 23---> 0.777 0.296 0.547 0.112 0.218 0.438 0.566 0.934
Bits 24 to 31---> 0.796 0.824 0.715 0.808 0.730 0.606 0.778 0.242
KS test for the above 32 p values: 0.605
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_09:31,
p-values for 5 runs: 0.7405, 0.6702, 0.8116, 0.2480, 0.6967
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 187 211.4 2.820 2.820
r= 29 5130 5134.0 0.003 2.823
r= 30 23104 23103.0 0.000 2.823
r= 31 11579 11551.5 0.065 2.889
chi-square = 2.889 with df = 3; p-value = 0.591
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 207 211.4 0.092 0.092
r= 30 5210 5134.0 1.125 1.217
r= 31 23108 23103.0 0.001 1.218
r= 32 11475 11551.5 0.507 1.725
chi-square = 1.725 with df = 3; p-value = 0.369
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_09:31
b-rank test for bits 1 to 8, p=0.43013
b-rank test for bits 2 to 9, p=0.00767
b-rank test for bits 3 to 10, p=0.79358
b-rank test for bits 4 to 11, p=0.28737
b-rank test for bits 5 to 12, p=0.20502
b-rank test for bits 6 to 13, p=0.06529
b-rank test for bits 7 to 14, p=0.17129
b-rank test for bits 8 to 15, p=0.80553
b-rank test for bits 9 to 16, p=0.77078
b-rank test for bits 10 to 17, p=0.62384
b-rank test for bits 11 to 18, p=0.98641
b-rank test for bits 12 to 19, p=0.76290
b-rank test for bits 13 to 20, p=0.80817
b-rank test for bits 14 to 21, p=0.14987
b-rank test for bits 15 to 22, p=0.41029
b-rank test for bits 16 to 23, p=0.70725
b-rank test for bits 17 to 24, p=0.03846
b-rank test for bits 18 to 25, p=0.93331
b-rank test for bits 19 to 26, p=0.69657
b-rank test for bits 20 to 27, p=0.36656
b-rank test for bits 21 to 28, p=0.11746
b-rank test for bits 22 to 29, p=0.47712
b-rank test for bits 23 to 30, p=0.66096
b-rank test for bits 24 to 31, p=0.75304
b-rank test for bits 25 to 32, p=0.86002
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 = 0.785733
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_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 141707 -0.47 0.318202
2 142039 0.30 0.619043
3 141568 -0.80 0.212580
4 142249 0.79 0.786292
5 142074 0.38 0.649786
6 141833 -0.18 0.429228
7 141130 -1.82 0.034314
8 141377 -1.24 0.106794
9 141607 -0.71 0.239976
10 142615 1.65 0.950402
11 141664 -0.57 0.283254
12 142259 0.82 0.793032
13 141856 -0.12 0.450419
14 140923 -2.30 0.010597
15 141461 -1.05 0.147435
16 142010 0.24 0.592977
17 142425 1.20 0.885867
18 141115 -1.86 0.031733
19 142367 1.07 0.857538
20 141967 0.13 0.553593
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_09:31
Bits used No. missing words z-score p-value
23 to 32 141973 0.2196 0.586890
22 to 31 141998 0.3058 0.620106
21 to 30 141573 -1.1598 0.123074
20 to 29 141441 -1.6149 0.053163
19 to 28 141838 -0.2460 0.402855
18 to 27 142236 1.1264 0.870012
17 to 26 141971 0.2127 0.584202
16 to 25 141817 -0.3184 0.375099
15 to 24 141949 0.1368 0.554403
14 to 23 142053 0.4954 0.689846
13 to 22 142298 1.3402 0.909917
12 to 21 142124 0.7402 0.770423
11 to 20 141705 -0.7046 0.240534
10 to 19 141815 -0.3253 0.372486
9 to 18 141955 0.1575 0.562568
8 to 17 141959 0.1713 0.567997
7 to 16 141908 -0.0046 0.498170
6 to 15 141825 -0.2908 0.385605
5 to 14 141748 -0.5563 0.288999
4 to 13 141900 -0.0322 0.487167
3 to 12 141608 -1.0391 0.149386
2 to 11 141783 -0.4356 0.331556
1 to 10 141409 -1.7253 0.042239
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_09:31
Bits used No. missing words z-score p-value
28 to 32 141825 -0.2859 0.387491
27 to 31 142039 0.4396 0.669872
26 to 30 141142 -2.6011 0.004646
25 to 29 141527 -1.2960 0.097482
24 to 28 141899 -0.0350 0.486033
23 to 27 141216 -2.3503 0.009380
22 to 26 141894 -0.0520 0.479278
21 to 25 142044 0.4565 0.675988
20 to 24 142277 1.2463 0.893680
19 to 23 141558 -1.1909 0.116837
18 to 22 141785 -0.4215 0.336711
17 to 21 142199 0.9819 0.836933
16 to 20 142236 1.1074 0.865930
15 to 19 142110 0.6802 0.751823
14 to 18 142218 1.0463 0.852298
13 to 17 142096 0.6328 0.736561
12 to 16 142162 0.8565 0.804142
11 to 15 142178 0.9107 0.818785
10 to 14 141877 -0.1096 0.456366
9 to 13 141564 -1.1706 0.120878
8 to 12 142034 0.4226 0.663710
7 to 11 141944 0.1175 0.546778
6 to 10 141939 0.1006 0.540057
5 to 9 142164 0.8633 0.806011
4 to 8 142390 1.6294 0.948385
3 to 7 141520 -1.3198 0.093457
2 to 6 142085 0.5955 0.724243
1 to 5 141304 -2.0520 0.020086
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_09:31
Bits used No. missing words z-score p-value
31 to 32 141845 -0.1898 0.424747
30 to 31 141838 -0.2104 0.416673
29 to 30 142132 0.6568 0.744359
28 to 29 141736 -0.5113 0.304571
27 to 28 142551 1.8928 0.970810
26 to 27 141573 -0.9921 0.160569
25 to 26 142075 0.4887 0.687474
24 to 25 142070 0.4740 0.682233
23 to 24 141812 -0.2871 0.387014
22 to 23 142146 0.6981 0.757456
21 to 22 141552 -1.0541 0.145925
20 to 21 141896 -0.0393 0.484317
19 to 20 141964 0.1613 0.564059
18 to 19 141789 -0.3550 0.361311
17 to 18 141931 0.0639 0.525484
16 to 17 141372 -1.5850 0.056478
15 to 16 141667 -0.7148 0.237355
14 to 15 141753 -0.4612 0.322345
13 to 14 141424 -1.4317 0.076122
12 to 13 141945 0.1052 0.541900
11 to 12 142062 0.4504 0.673772
10 to 11 142274 1.0757 0.858974
9 to 10 142100 0.5624 0.713095
8 to 9 142203 0.8663 0.806833
7 to 8 142088 0.5271 0.700921
6 to 7 141971 0.1819 0.572176
5 to 6 141520 -1.1485 0.125388
4 to 5 141631 -0.8210 0.205814
3 to 4 142160 0.7394 0.770180
2 to 3 142346 1.2881 0.901147
1 to 2 141223 -2.0246 0.021456
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2507.03 0.099 0.539617
Test results for specific bytes for dh-ranFile-2018-07-12_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2459.86 -0.568 0.285119
2 to 9 2590.23 1.276 0.899041
3 to 10 2469.81 -0.427 0.334724
4 to 11 2447.21 -0.747 0.227683
5 to 12 2768.09 3.791 0.999925
6 to 13 2469.37 -0.433 0.332427
7 to 14 2541.08 0.581 0.719352
8 to 15 2434.56 -0.926 0.177351
9 to 16 2479.00 -0.297 0.383233
10 to 17 2445.61 -0.769 0.220895
11 to 18 2641.36 1.999 0.977206
12 to 19 2467.39 -0.461 0.322360
13 to 20 2516.68 0.236 0.593229
14 to 21 2697.79 2.797 0.997423
15 to 22 2476.84 -0.327 0.371647
16 to 23 2606.11 1.501 0.933273
17 to 24 2457.67 -0.599 0.274710
18 to 25 2465.72 -0.485 0.313936
19 to 26 2612.84 1.596 0.944735
20 to 27 2453.14 -0.663 0.253778
21 to 28 2607.30 1.517 0.935426
22 to 29 2471.45 -0.404 0.343220
23 to 30 2430.01 -0.990 0.161139
24 to 31 2277.56 -3.146 0.000828
25 to 32 2464.05 -0.508 0.305594
CDPARK for dh-ranFile-2018-07-12_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
3527 0.1826 0.572463
3513 -0.4566 0.323972
3536 0.5936 0.723613
3540 0.7763 0.781201
3511 -0.5479 0.291865
3496 -1.2329 0.108811
3537 0.6393 0.738676
3511 -0.5479 0.291865
3537 0.6393 0.738676
Square side=100, avg. no. parked=3525.80 sample std.=16.23
p-value of the KSTEST for those 10 p-values: 0.693477
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_09:31
0.4399,0.1798,0.3104,0.2167,0.4042,0.2728,0.0819,0.5088,0.7257,0.4638,
The KS test for those 10 p-values: 0.138484
The 3DSPHERES test for dh-ranFile-2018-07-12_09:31
sample no r^3 equiv. uni.
1 8.841 0.255243
2 15.022 0.393913
3 23.465 0.542586
4 15.584 0.405154
5 73.677 0.914213
6 18.149 0.453910
7 19.757 0.482403
8 26.694 0.589258
9 46.418 0.787171
10 3.035 0.096208
11 7.198 0.213315
12 47.357 0.793729
13 1.206 0.039390
14 58.575 0.858080
15 0.386 0.012772
16 60.275 0.865899
17 9.698 0.276221
18 12.285 0.336023
19 22.959 0.534804
20 18.735 0.464465
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.796370
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 2.2 -0.4 0.2 -2.4 -0.1
-0.9 1.1 -0.2 -0.5 1.8 -0.4
1.6 0.1 0.6 -0.3 -1.3 0.8
1.3 -1.2 0.6 -0.0 -0.7 -1.1
-0.8 0.6 -1.3 -0.9 -0.6 -0.1
0.9 0.5 0.7 0.7 -0.8 -0.8
0.0 0.5 -1.2 -1.3 1.6 0.0
1.8
Chi-square with 42 degrees of freedom:43.042211
z-score=0.113715, p-value=0.573566
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_09:31
Test no p-value
1 0.000289
2 0.679924
3 0.040934
4 0.442406
5 0.544538
6 0.039267
7 0.064590
8 0.625871
9 0.320550
10 0.051452
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004925
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_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 66751 0.11 66828 0.39
3 25000.00 24966 0.05 24996 0.00
4 6666.67 6691 0.09 6521 3.18
5 1388.89 1314 4.04 1384 0.02
6 238.10 230 0.28 234 0.07
7 34.72 39 0.53 33 0.09
8 4.96 8 1.86 3 0.77
p=0.67412 p=0.39351
Number of rngs required: 687260, p-value: 0.092
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_09:31
No. of wins: Observed Expected
98644 98585.9
z-score= 0.260, pvalue=0.60258
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66917 66666.7 0.940 0.940
2 37696 37654.3 0.046 0.986
3 26676 26954.7 2.882 3.868
4 19208 19313.5 0.576 4.444
5 13879 13851.4 0.055 4.499
6 9908 9943.5 0.127 4.626
7 7240 7145.0 1.262 5.889
8 5017 5139.1 2.900 8.788
9 3749 3699.9 0.653 9.441
10 2662 2666.3 0.007 9.448
11 1910 1923.3 0.092 9.540
12 1461 1388.7 3.760 13.300
13 1024 1003.7 0.410 13.710
14 768 726.1 2.413 16.123
15 518 525.8 0.117 16.240
16 404 381.2 1.370 17.610
17 276 276.5 0.001 17.611
18 182 200.8 1.765 19.376
19 135 146.0 0.827 20.203
20 95 106.2 1.184 21.387
21 275 287.1 0.511 21.898
Chisq= 21.90 for 20 degrees of freedom, p= 0.65393
SUMMARY of craptest
p-value for no. of wins: 0.602584
p-value for throws/game: 0.653929
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_09:31
No. of wins: Observed Expected
98542 98585.9
z-score=-0.196, pvalue=0.42224
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66669 66666.7 0.000 0.000
2 37498 37654.3 0.649 0.649
3 26907 26954.7 0.085 0.734
4 19432 19313.5 0.728 1.461
5 13828 13851.4 0.040 1.501
6 9864 9943.5 0.636 2.137
7 7109 7145.0 0.182 2.319
8 5230 5139.1 1.609 3.927
9 3687 3699.9 0.045 3.972
10 2734 2666.3 1.719 5.691
11 1987 1923.3 2.108 7.799
12 1404 1388.7 0.168 7.967
13 983 1003.7 0.428 8.394
14 716 726.1 0.142 8.536
15 520 525.8 0.065 8.601
16 389 381.2 0.162 8.762
17 262 276.5 0.764 9.527
18 208 200.8 0.256 9.783
19 150 146.0 0.110 9.893
20 118 106.2 1.308 11.201
21 305 287.1 1.114 12.315
Chisq= 12.31 for 20 degrees of freedom, p= 0.09519
SUMMARY of craptest
p-value for no. of wins: 0.422242
p-value for throws/game: 0.095192
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0008,0.0009,0.0046,0.0049,0.0077,0.0094,0.0106,0.0128,0.0189,
0.0201,0.0215,0.0296,0.0317,0.0343,0.0385,0.0393,0.0394,0.0409,0.0422,
0.0515,0.0532,0.0565,0.0646,0.0653,0.0761,0.0819,0.0916,0.0935,0.0952,
0.0962,0.0975,0.1068,0.1088,0.1115,0.1119,0.1168,0.1175,0.1209,0.1231,
0.1254,0.1385,0.1459,0.1474,0.1494,0.1499,0.1585,0.1606,0.1611,0.1636,
0.1713,0.1774,0.1798,0.1995,0.2050,0.2058,0.2126,0.2133,0.2167,0.2177,
0.2209,0.2277,0.2374,0.2400,0.2405,0.2417,0.2480,0.2538,0.2552,0.2728,
0.2747,0.2762,0.2833,0.2851,0.2874,0.2890,0.2919,0.2919,0.2959,0.3046,
0.3056,0.3104,0.3139,0.3182,0.3205,0.3223,0.3224,0.3240,0.3316,0.3324,
0.3347,0.3360,0.3367,0.3432,0.3613,0.3666,0.3686,0.3716,0.3725,0.3751,
0.3832,0.3856,0.3870,0.3875,0.3935,0.3938,0.3939,0.4023,0.4029,0.4042,
0.4052,0.4103,0.4167,0.4222,0.4247,0.4292,0.4301,0.4365,0.4376,0.4399,
0.4424,0.4455,0.4504,0.4539,0.4564,0.4638,0.4645,0.4771,0.4793,0.4824,
0.4843,0.4860,0.4872,0.4880,0.4982,0.5088,0.5112,0.5255,0.5312,0.5348,
0.5396,0.5401,0.5419,0.5426,0.5445,0.5468,0.5469,0.5536,0.5544,0.5626,
0.5628,0.5641,0.5659,0.5680,0.5722,0.5725,0.5736,0.5791,0.5842,0.5869,
0.5893,0.5909,0.5930,0.5932,0.5980,0.6026,0.6050,0.6064,0.6190,0.6191,
0.6201,0.6238,0.6259,0.6428,0.6498,0.6539,0.6570,0.6610,0.6637,0.6699,
0.6702,0.6738,0.6741,0.6759,0.6760,0.6799,0.6822,0.6865,0.6875,0.6898,
0.6935,0.6966,0.6967,0.7009,0.7073,0.7131,0.7148,0.7194,0.7236,0.7242,
0.7245,0.7257,0.7296,0.7366,0.7387,0.7387,0.7405,0.7420,0.7444,0.7518,
0.7530,0.7575,0.7629,0.7702,0.7704,0.7708,0.7774,0.7783,0.7812,0.7857,
0.7863,0.7872,0.7930,0.7936,0.7937,0.7960,0.7964,0.8041,0.8055,0.8060,
0.8068,0.8077,0.8082,0.8116,0.8188,0.8244,0.8362,0.8369,0.8523,0.8528,
0.8575,0.8581,0.8590,0.8600,0.8659,0.8659,0.8700,0.8859,0.8912,0.8937,
0.8990,0.9011,0.9099,0.9142,0.9174,0.9333,0.9333,0.9338,0.9354,0.9447,
0.9484,0.9504,0.9708,0.9727,0.9772,0.9819,0.9864,0.9974,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.294506
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.