RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_06:31
(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 22.8166 0.844682
2 to 25 15.84 12.7248 0.245593
3 to 26 15.95 22.7741 0.843249
4 to 27 16.08 18.5343 0.644090
5 to 28 15.77 18.7626 0.657673
6 to 29 15.68 19.5984 0.704716
7 to 30 15.67 12.8330 0.252710
8 to 31 15.76 25.4590 0.915103
9 to 32 15.62 24.4115 0.891323
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.107315
Tough bday spacings test for dh-ranFile-2018-06-20_06:31: 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 40 79 83 93 93 53 23 15 6 5
(O-E)^2/E 0.1 0.3 0.4 2.2 0.2 2.8 0.0 1.5 0.0 0.1 0.2
Birthday Spacings: Sum(O-E)^2/E= 7.919, p= 0.363
RESULTS OF GCD FOR dh-ranFile-2018-06-20_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.811284
p-value, dist. of gcd's: 0.579754
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.889 0.718 0.969 0.617 0.101 0.949 0.606 0.450
Bits 8 to 15---> 0.831 0.691 0.475 0.536 0.469 0.915 0.894 0.404
Bits 16 to 23---> 0.309 0.407 0.140 0.244 0.693 0.218 0.856 0.535
Bits 24 to 31---> 0.862 0.753 0.990 0.476 0.569 0.906 0.910 0.862
KS test for the above 32 p values: 0.986
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_06:31,
p-values for 5 runs: 0.8397, 0.7012, 0.9008, 0.2336, 0.4293
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 253 211.4 8.178 8.178
r= 29 5170 5134.0 0.252 8.431
r= 30 22965 23103.0 0.825 9.256
r= 31 11612 11551.5 0.317 9.572
chi-square = 9.572 with df = 3; p-value = 0.977
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5115 5134.0 0.070 0.080
r= 31 23163 23103.0 0.156 0.235
r= 32 11512 11551.5 0.135 0.371
chi-square = 0.371 with df = 3; p-value = 0.054
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_06:31
b-rank test for bits 1 to 8, p=0.12595
b-rank test for bits 2 to 9, p=0.20137
b-rank test for bits 3 to 10, p=0.62794
b-rank test for bits 4 to 11, p=0.71178
b-rank test for bits 5 to 12, p=0.38568
b-rank test for bits 6 to 13, p=0.57356
b-rank test for bits 7 to 14, p=0.59563
b-rank test for bits 8 to 15, p=0.53656
b-rank test for bits 9 to 16, p=0.79533
b-rank test for bits 10 to 17, p=0.73934
b-rank test for bits 11 to 18, p=0.95456
b-rank test for bits 12 to 19, p=0.28300
b-rank test for bits 13 to 20, p=0.30971
b-rank test for bits 14 to 21, p=0.88056
b-rank test for bits 15 to 22, p=0.08017
b-rank test for bits 16 to 23, p=0.83541
b-rank test for bits 17 to 24, p=0.56557
b-rank test for bits 18 to 25, p=0.00458
b-rank test for bits 19 to 26, p=0.95853
b-rank test for bits 20 to 27, p=0.48746
b-rank test for bits 21 to 28, p=0.89031
b-rank test for bits 22 to 29, p=0.97881
b-rank test for bits 23 to 30, p=0.68125
b-rank test for bits 24 to 31, p=0.37968
b-rank test for bits 25 to 32, p=0.51296
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 = 0.499285
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_06:31
(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 142102 0.45 0.673704
2 141504 -0.95 0.171811
3 141523 -0.90 0.183358
4 141597 -0.73 0.232774
5 141942 0.08 0.530422
6 141668 -0.56 0.286426
7 142198 0.67 0.749991
8 141548 -0.84 0.199271
9 142025 0.27 0.606519
10 141179 -1.71 0.043969
11 142084 0.41 0.658403
12 142870 2.24 0.987602
13 142754 1.97 0.975782
14 142328 0.98 0.836013
15 142042 0.31 0.621711
16 141460 -1.05 0.146897
17 141590 -0.75 0.227804
18 141654 -0.60 0.275399
19 141694 -0.50 0.307444
20 142585 1.58 0.942794
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_06:31
Bits used No. missing words z-score p-value
23 to 32 141942 0.1127 0.544848
22 to 31 141903 -0.0218 0.491293
21 to 30 141813 -0.3322 0.369880
20 to 29 141371 -1.8563 0.031705
19 to 28 141815 -0.3253 0.372486
18 to 27 141933 0.0816 0.532526
17 to 26 141580 -1.1356 0.128058
16 to 25 141464 -1.5356 0.062316
15 to 24 142217 1.0609 0.855639
14 to 23 141934 0.0851 0.533897
13 to 22 142277 1.2678 0.897570
12 to 21 141772 -0.4736 0.317910
11 to 20 141830 -0.2736 0.392215
10 to 19 141848 -0.2115 0.416255
9 to 18 142037 0.4402 0.670119
8 to 17 141567 -1.1804 0.118911
7 to 16 142126 0.7471 0.772510
6 to 15 141339 -1.9667 0.024611
5 to 14 142008 0.3402 0.633163
4 to 13 141924 0.0506 0.520172
3 to 12 141985 0.2609 0.602927
2 to 11 142164 0.8782 0.810075
1 to 10 141545 -1.2563 0.104502
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_06:31
Bits used No. missing words z-score p-value
28 to 32 141944 0.1175 0.546778
27 to 31 141989 0.2701 0.606446
26 to 30 141712 -0.6689 0.251775
25 to 29 141853 -0.1909 0.424283
24 to 28 142161 0.8531 0.803203
23 to 27 142044 0.4565 0.675988
22 to 26 141991 0.2768 0.609051
21 to 25 142207 1.0091 0.843525
20 to 24 141534 -1.2723 0.101632
19 to 23 142342 1.4667 0.928768
18 to 22 142082 0.5853 0.720834
17 to 21 142045 0.4599 0.677205
16 to 20 141640 -0.9130 0.180626
15 to 19 142155 0.8328 0.797516
14 to 18 141747 -0.5503 0.291067
13 to 17 141800 -0.3706 0.355464
12 to 16 141712 -0.6689 0.251775
11 to 15 141571 -1.1469 0.125715
10 to 14 141542 -1.2452 0.106532
9 to 13 142085 0.5955 0.724243
8 to 12 141650 -0.8791 0.189678
7 to 11 141839 -0.2384 0.405783
6 to 10 141878 -0.1062 0.457711
5 to 9 141651 -0.8757 0.190598
4 to 8 141773 -0.4621 0.321992
3 to 7 141886 -0.0791 0.468483
2 to 6 141489 -1.4248 0.077101
1 to 5 142024 0.3887 0.651255
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_06:31
Bits used No. missing words z-score p-value
31 to 32 141832 -0.2281 0.409780
30 to 31 141756 -0.4523 0.325526
29 to 30 141976 0.1967 0.577956
28 to 29 141466 -1.3078 0.095478
27 to 28 141797 -0.3314 0.370187
26 to 27 142169 0.7660 0.778158
25 to 26 141627 -0.8328 0.202470
24 to 25 142245 0.9902 0.838956
23 to 24 141843 -0.1957 0.422437
22 to 23 142048 0.4091 0.658751
21 to 22 142397 1.4386 0.924862
20 to 21 142117 0.6126 0.729928
19 to 20 141512 -1.1721 0.120586
18 to 19 141283 -1.8476 0.032331
17 to 18 142023 0.3353 0.631304
16 to 17 142162 0.7453 0.771967
15 to 16 141543 -1.0806 0.139933
14 to 15 142157 0.7306 0.767485
13 to 14 142113 0.6008 0.726012
12 to 13 142222 0.9223 0.821822
11 to 12 141773 -0.4022 0.343786
10 to 11 141329 -1.7119 0.043459
9 to 10 141323 -1.7296 0.041852
8 to 9 141776 -0.3933 0.347048
7 to 8 142018 0.3206 0.625728
6 to 7 141375 -1.5762 0.057490
5 to 6 141865 -0.1308 0.447980
4 to 5 142306 1.1701 0.879023
3 to 4 141851 -0.1721 0.431693
2 to 3 141802 -0.3166 0.375771
1 to 2 141740 -0.4995 0.308714
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2580.10 1.133 0.871360
Test results for specific bytes for dh-ranFile-2018-06-20_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2265.81 -3.312 0.000463
2 to 9 2586.54 1.224 0.889500
3 to 10 2490.64 -0.132 0.447330
4 to 11 2479.80 -0.286 0.387582
5 to 12 2372.93 -1.797 0.036165
6 to 13 2496.90 -0.044 0.482501
7 to 14 2462.04 -0.537 0.295677
8 to 15 2529.03 0.411 0.659320
9 to 16 2656.49 2.213 0.986555
10 to 17 2483.15 -0.238 0.405817
11 to 18 2438.88 -0.864 0.193674
12 to 19 2407.14 -1.313 0.094540
13 to 20 2583.53 1.181 0.881250
14 to 21 2459.97 -0.566 0.285652
15 to 22 2598.41 1.392 0.918008
16 to 23 2454.05 -0.650 0.257886
17 to 24 2506.22 0.088 0.535045
18 to 25 2646.61 2.073 0.980934
19 to 26 2477.13 -0.323 0.373196
20 to 27 2511.47 0.162 0.564438
21 to 28 2536.83 0.521 0.698755
22 to 29 2667.17 2.364 0.990965
23 to 30 2495.59 -0.062 0.475159
24 to 31 2415.13 -1.200 0.115022
25 to 32 2530.87 0.437 0.668785
CDPARK for dh-ranFile-2018-06-20_06:31: 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
3549 1.1872 0.882429
3533 0.4566 0.676028
3529 0.2740 0.607947
3542 0.8676 0.807188
3512 -0.5023 0.307734
3478 -2.0548 0.019949
3531 0.3653 0.642555
3557 1.5525 0.939730
3503 -0.9132 0.180558
3525 0.0913 0.536383
Square side=100, avg. no. parked=3525.90 sample std.=22.04
p-value of the KSTEST for those 10 p-values: 0.803713
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_06:31
0.8045,0.8032,0.3297,0.7184,0.8303,0.5075,0.4333,0.5130,0.0289,0.2121,
The KS test for those 10 p-values: 0.869084
The 3DSPHERES test for dh-ranFile-2018-06-20_06:31
sample no r^3 equiv. uni.
1 14.391 0.381036
2 72.828 0.911752
3 180.079 0.997528
4 46.282 0.786205
5 14.263 0.378380
6 84.467 0.940130
7 7.551 0.222525
8 10.505 0.295429
9 7.908 0.231728
10 10.847 0.303410
11 11.584 0.320329
12 39.265 0.729862
13 5.838 0.176847
14 0.141 0.004692
15 36.793 0.706659
16 19.195 0.472624
17 8.362 0.243260
18 41.512 0.749363
19 45.225 0.778535
20 14.896 0.391357
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.662743
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.3 0.1 -0.1 -1.6 -0.1
-1.7 -0.9 -0.7 0.3 1.0 0.1
-0.4 0.3 -1.2 0.0 -0.1 0.3
-0.1 0.8 0.2 0.0 0.5 1.2
1.9 -1.2 -1.5 -0.8 0.4 -1.1
-1.2 0.9 0.3 0.3 0.1 -0.3
-0.9 1.8 -1.6 0.4 -0.6 2.0
-0.1
Chi-square with 42 degrees of freedom:38.715224
z-score=-0.358398, p-value=0.384040
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_06:31
Test no p-value
1 0.039915
2 0.963967
3 0.025551
4 0.038704
5 0.733225
6 0.040521
7 0.462636
8 0.018306
9 0.434573
10 0.830317
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.011611
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_06:31:
(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 66572 0.13 66732 0.06
3 25000.00 25137 0.75 25056 0.13
4 6666.67 6660 0.01 6583 1.05
5 1388.89 1365 0.41 1368 0.31
6 238.10 233 0.11 225 0.72
7 34.72 26 2.19 33 0.09
8 4.96 6 0.22 2 1.77
p=0.29897 p=0.34032
Number of rngs required: 687631, p-value: 0.186
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_06:31
No. of wins: Observed Expected
98670 98585.9
z-score= 0.376, pvalue=0.64666
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66767 66666.7 0.151 0.151
2 37648 37654.3 0.001 0.152
3 26899 26954.7 0.115 0.267
4 19228 19313.5 0.378 0.645
5 13731 13851.4 1.047 1.692
6 10005 9943.5 0.380 2.072
7 7080 7145.0 0.592 2.664
8 5198 5139.1 0.676 3.340
9 3741 3699.9 0.457 3.797
10 2657 2666.3 0.032 3.829
11 1962 1923.3 0.778 4.607
12 1382 1388.7 0.033 4.640
13 1031 1003.7 0.742 5.381
14 721 726.1 0.036 5.418
15 517 525.8 0.148 5.566
16 382 381.2 0.002 5.568
17 295 276.5 1.232 6.801
18 209 200.8 0.332 7.133
19 158 146.0 0.989 8.122
20 101 106.2 0.256 8.378
21 288 287.1 0.003 8.381
Chisq= 8.38 for 20 degrees of freedom, p= 0.01097
SUMMARY of craptest
p-value for no. of wins: 0.646664
p-value for throws/game: 0.010965
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_06:31
No. of wins: Observed Expected
98178 98585.9
z-score=-1.824, pvalue=0.03406
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66400 66666.7 1.067 1.067
2 37775 37654.3 0.387 1.453
3 27087 26954.7 0.649 2.102
4 19399 19313.5 0.379 2.481
5 13829 13851.4 0.036 2.518
6 9879 9943.5 0.419 2.937
7 7124 7145.0 0.062 2.998
8 5042 5139.1 1.834 4.832
9 3739 3699.9 0.414 5.246
10 2691 2666.3 0.229 5.475
11 1979 1923.3 1.611 7.086
12 1406 1388.7 0.215 7.301
13 1009 1003.7 0.028 7.329
14 739 726.1 0.228 7.556
15 507 525.8 0.675 8.231
16 395 381.2 0.503 8.734
17 285 276.5 0.259 8.993
18 196 200.8 0.116 9.109
19 141 146.0 0.170 9.279
20 94 106.2 1.405 10.684
21 284 287.1 0.034 10.718
Chisq= 10.72 for 20 degrees of freedom, p= 0.04679
SUMMARY of craptest
p-value for no. of wins: 0.034062
p-value for throws/game: 0.046790
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0046,0.0047,0.0110,0.0116,0.0183,0.0199,0.0246,0.0256,0.0289,
0.0317,0.0323,0.0341,0.0362,0.0387,0.0399,0.0405,0.0419,0.0435,0.0440,
0.0468,0.0538,0.0575,0.0623,0.0771,0.0802,0.0945,0.0955,0.1008,0.1016,
0.1045,0.1065,0.1073,0.1150,0.1189,0.1206,0.1257,0.1260,0.1281,0.1398,
0.1399,0.1469,0.1718,0.1768,0.1806,0.1806,0.1834,0.1859,0.1897,0.1906,
0.1937,0.1993,0.2014,0.2025,0.2121,0.2183,0.2225,0.2278,0.2317,0.2328,
0.2336,0.2433,0.2444,0.2456,0.2518,0.2518,0.2527,0.2579,0.2754,0.2830,
0.2857,0.2864,0.2911,0.2954,0.2957,0.2990,0.3034,0.3074,0.3077,0.3087,
0.3088,0.3097,0.3179,0.3203,0.3220,0.3255,0.3297,0.3403,0.3438,0.3470,
0.3555,0.3633,0.3699,0.3702,0.3725,0.3732,0.3758,0.3784,0.3797,0.3810,
0.3840,0.3857,0.3876,0.3914,0.3922,0.4044,0.4058,0.4058,0.4068,0.4098,
0.4163,0.4224,0.4243,0.4293,0.4317,0.4333,0.4346,0.4473,0.4480,0.4503,
0.4577,0.4626,0.4685,0.4687,0.4726,0.4748,0.4752,0.4756,0.4825,0.4875,
0.4913,0.4993,0.5075,0.5130,0.5130,0.5202,0.5304,0.5325,0.5339,0.5349,
0.5350,0.5358,0.5364,0.5366,0.5448,0.5468,0.5644,0.5656,0.5694,0.5736,
0.5780,0.5798,0.5956,0.6029,0.6062,0.6064,0.6065,0.6079,0.6091,0.6174,
0.6217,0.6257,0.6279,0.6313,0.6332,0.6426,0.6441,0.6467,0.6513,0.6577,
0.6584,0.6588,0.6593,0.6627,0.6688,0.6701,0.6737,0.6760,0.6760,0.6772,
0.6812,0.6911,0.6931,0.6988,0.7012,0.7047,0.7067,0.7118,0.7181,0.7184,
0.7208,0.7242,0.7260,0.7299,0.7299,0.7332,0.7393,0.7494,0.7500,0.7529,
0.7675,0.7720,0.7725,0.7782,0.7785,0.7862,0.7953,0.7975,0.8032,0.8032,
0.8037,0.8045,0.8072,0.8101,0.8113,0.8218,0.8303,0.8303,0.8313,0.8354,
0.8360,0.8390,0.8397,0.8432,0.8435,0.8447,0.8556,0.8556,0.8617,0.8618,
0.8691,0.8714,0.8790,0.8806,0.8813,0.8824,0.8891,0.8895,0.8903,0.8913,
0.8940,0.8976,0.9008,0.9062,0.9104,0.9118,0.9151,0.9151,0.9180,0.9249,
0.9288,0.9397,0.9401,0.9428,0.9488,0.9546,0.9585,0.9640,0.9694,0.9758,
0.9774,0.9788,0.9809,0.9861,0.9866,0.9876,0.9898,0.9910,0.9975,
Overall p-value after applying KStest on 269 p-values = 0.811690
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.