RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-02-28_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 15.76 17.2610 0.563176
2 to 25 15.88 21.2210 0.783438
3 to 26 15.84 17.1488 0.555673
4 to 27 15.73 16.1888 0.489510
5 to 28 15.50 22.5861 0.836784
6 to 29 15.79 18.9193 0.666814
7 to 30 15.63 18.0319 0.613170
8 to 31 15.71 13.0397 0.266477
9 to 32 15.65 18.8031 0.660048
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.180095
Tough bday spacings test for dh-ranFile-2018-02-28_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 9 50 61 114 78 86 47 22 20 8 5
(O-E)^2/E 0.0 4.9 2.1 2.7 4.0 0.8 0.5 2.0 1.8 0.3 0.2
Birthday Spacings: Sum(O-E)^2/E= 19.204, p= 0.962
RESULTS OF GCD FOR dh-ranFile-2018-02-28_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.589958
p-value, dist. of gcd's: 0.650059
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-02-28_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.914 0.695 0.192 0.541 0.928 0.449 0.701 0.914
Bits 8 to 15---> 0.849 0.821 0.341 0.649 0.246 0.787 0.870 0.097
Bits 16 to 23---> 0.604 0.971 0.904 0.077 0.153 0.128 0.507 0.423
Bits 24 to 31---> 0.162 0.836 0.345 0.406 0.226 0.248 0.547 0.732
KS test for the above 32 p values: 0.306
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-02-28_09:31,
p-values for 5 runs: 0.1467, 0.8304, 0.7902, 0.5896, 0.2944
Rank test for binary matrices (31x31) for dh-ranFile-2018-02-28_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5041 5134.0 1.685 1.880
r= 30 23148 23103.0 0.087 1.967
r= 31 11606 11551.5 0.257 2.224
chi-square = 2.224 with df = 3; p-value = 0.473
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-02-28_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5169 5134.0 0.238 2.210
r= 31 23130 23103.0 0.031 2.242
r= 32 11510 11551.5 0.149 2.391
chi-square = 2.391 with df = 3; p-value = 0.505
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-02-28_09:31
b-rank test for bits 1 to 8, p=0.76032
b-rank test for bits 2 to 9, p=0.60865
b-rank test for bits 3 to 10, p=0.86215
b-rank test for bits 4 to 11, p=0.76828
b-rank test for bits 5 to 12, p=0.67569
b-rank test for bits 6 to 13, p=0.73859
b-rank test for bits 7 to 14, p=0.38299
b-rank test for bits 8 to 15, p=0.25156
b-rank test for bits 9 to 16, p=0.43555
b-rank test for bits 10 to 17, p=0.08047
b-rank test for bits 11 to 18, p=0.33559
b-rank test for bits 12 to 19, p=0.53895
b-rank test for bits 13 to 20, p=0.01291
b-rank test for bits 14 to 21, p=0.47197
b-rank test for bits 15 to 22, p=0.38787
b-rank test for bits 16 to 23, p=0.16673
b-rank test for bits 17 to 24, p=0.83208
b-rank test for bits 18 to 25, p=0.99566
b-rank test for bits 19 to 26, p=0.23047
b-rank test for bits 20 to 27, p=0.43099
b-rank test for bits 21 to 28, p=0.63503
b-rank test for bits 22 to 29, p=0.51598
b-rank test for bits 23 to 30, p=0.51395
b-rank test for bits 24 to 31, p=0.05943
b-rank test for bits 25 to 32, p=0.94144
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 = 0.978629
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-02-28_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 141446 -1.08 0.139505
2 142073 0.38 0.648920
3 141713 -0.46 0.323219
4 142051 0.33 0.629680
5 142420 1.19 0.883596
6 142376 1.09 0.862221
7 142150 0.56 0.713049
8 141601 -0.72 0.235640
9 142461 1.29 0.901292
10 141365 -1.27 0.101722
11 142103 0.45 0.674546
12 142421 1.20 0.884052
13 141783 -0.30 0.383935
14 141490 -0.98 0.163607
15 142608 1.63 0.948703
16 142228 0.74 0.771730
17 141958 0.11 0.545268
18 141976 0.16 0.561893
19 142369 1.07 0.858588
20 142293 0.90 0.814987
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-02-28_09:31
Bits used No. missing words z-score p-value
23 to 32 141703 -0.7115 0.238393
22 to 31 142196 0.9885 0.838550
21 to 30 141771 -0.4770 0.316681
20 to 29 141950 0.1402 0.555765
19 to 28 142238 1.1333 0.871465
18 to 27 142282 1.2851 0.900616
17 to 26 141969 0.2058 0.581510
16 to 25 141389 -1.7942 0.036387
15 to 24 141898 -0.0391 0.484418
14 to 23 142047 0.4747 0.682508
13 to 22 142193 0.9782 0.836006
12 to 21 142011 0.3506 0.637051
11 to 20 142067 0.5437 0.706673
10 to 19 142084 0.6023 0.726516
9 to 18 142004 0.3264 0.627957
8 to 17 141426 -1.6667 0.047792
7 to 16 141359 -1.8977 0.028868
6 to 15 141551 -1.2356 0.108300
5 to 14 142048 0.4782 0.683736
4 to 13 142057 0.5092 0.694696
3 to 12 142214 1.0506 0.853276
2 to 11 141817 -0.3184 0.375099
1 to 10 141475 -1.4977 0.067107
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-02-28_09:31
Bits used No. missing words z-score p-value
28 to 32 141630 -0.9469 0.171850
27 to 31 141880 -0.0994 0.460401
26 to 30 141628 -0.9537 0.170128
25 to 29 141994 0.2870 0.612950
24 to 28 141754 -0.5265 0.299256
23 to 27 141941 0.1074 0.542747
22 to 26 141521 -1.3164 0.094024
21 to 25 141356 -1.8757 0.030349
20 to 24 142146 0.8023 0.788802
19 to 23 141831 -0.2655 0.395302
18 to 22 141851 -0.1977 0.421629
17 to 21 142000 0.3074 0.620714
16 to 20 142188 0.9446 0.827580
15 to 19 142351 1.4972 0.932828
14 to 18 141975 0.2226 0.588081
13 to 17 141702 -0.7028 0.241086
12 to 16 142280 1.2565 0.895534
11 to 15 142298 1.3175 0.906169
10 to 14 142005 0.3243 0.627147
9 to 13 141746 -0.5537 0.289905
8 to 12 141573 -1.1401 0.127122
7 to 11 141685 -0.7604 0.223496
6 to 10 142008 0.3345 0.630989
5 to 9 141734 -0.5943 0.276143
4 to 8 141838 -0.2418 0.404469
3 to 7 141492 -1.4147 0.078581
2 to 6 141725 -0.6248 0.266036
1 to 5 141441 -1.5876 0.056193
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-02-28_09:31
Bits used No. missing words z-score p-value
31 to 32 142185 0.8132 0.791944
30 to 31 141581 -0.9685 0.166391
29 to 30 141325 -1.7237 0.042382
28 to 29 141858 -0.1514 0.439824
27 to 28 142552 1.8958 0.971006
26 to 27 142287 1.1141 0.867376
25 to 26 141622 -0.8476 0.198336
24 to 25 142086 0.5212 0.698869
23 to 24 142444 1.5772 0.942625
22 to 23 142058 0.4386 0.669508
21 to 22 141911 0.0049 0.501965
20 to 21 141878 -0.0924 0.463183
19 to 20 141589 -0.9449 0.172348
18 to 19 142051 0.4179 0.661992
17 to 18 142417 1.4976 0.932875
16 to 17 142419 1.5035 0.933639
15 to 16 142533 1.8397 0.967096
14 to 15 142010 0.2970 0.616752
13 to 14 141904 -0.0157 0.493728
12 to 13 142397 1.4386 0.924862
11 to 12 142022 0.3324 0.630191
10 to 11 141784 -0.3697 0.355801
9 to 10 142097 0.5536 0.710073
8 to 9 142162 0.7453 0.771967
7 to 8 141881 -0.0836 0.466699
6 to 7 141887 -0.0659 0.473741
5 to 6 141508 -1.1839 0.118233
4 to 5 141875 -0.1013 0.459669
3 to 4 141911 0.0049 0.501965
2 to 3 141738 -0.5054 0.306640
1 to 2 142366 1.3471 0.911027
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-02-28_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2447.10 -0.748 0.227207
Test results for specific bytes for dh-ranFile-2018-02-28_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2488.43 -0.164 0.435008
2 to 9 2567.41 0.953 0.829798
3 to 10 2327.71 -2.436 0.007415
4 to 11 2487.63 -0.175 0.430539
5 to 12 2461.46 -0.545 0.292863
6 to 13 2415.20 -1.199 0.115225
7 to 14 2473.55 -0.374 0.354188
8 to 15 2489.75 -0.145 0.442393
9 to 16 2451.58 -0.685 0.246741
10 to 17 2449.21 -0.718 0.236278
11 to 18 2426.41 -1.041 0.148989
12 to 19 2574.43 1.053 0.853735
13 to 20 2557.14 0.808 0.790479
14 to 21 2570.17 0.992 0.839494
15 to 22 2598.79 1.397 0.918804
16 to 23 2508.93 0.126 0.550224
17 to 24 2442.98 -0.806 0.209999
18 to 25 2511.38 0.161 0.563953
19 to 26 2472.35 -0.391 0.347882
20 to 27 2586.43 1.222 0.889208
21 to 28 2520.78 0.294 0.615548
22 to 29 2416.46 -1.181 0.118706
23 to 30 2544.87 0.635 0.737149
24 to 31 2434.22 -0.930 0.176118
25 to 32 2557.99 0.820 0.793936
CDPARK for dh-ranFile-2018-02-28_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
3537 0.6393 0.738676
3523 0.0000 0.500000
3550 1.2329 0.891189
3531 0.3653 0.642555
3570 2.1461 0.984068
3506 -0.7763 0.218799
3537 0.6393 0.738676
3537 0.6393 0.738676
3481 -1.9178 0.027568
Square side=100, avg. no. parked=3532.20 sample std.=23.51
p-value of the KSTEST for those 10 p-values: 0.168952
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-02-28_09:31
0.9823,0.1989,0.3576,0.7031,0.1544,0.0307,0.8812,0.4877,0.8668,0.5711,
The KS test for those 10 p-values: 0.958724
The 3DSPHERES test for dh-ranFile-2018-02-28_09:31
sample no r^3 equiv. uni.
1 0.672 0.022163
2 0.244 0.008111
3 66.258 0.890144
4 4.856 0.149454
5 0.478 0.015819
6 17.493 0.441843
7 44.393 0.772310
8 8.729 0.252467
9 17.359 0.439341
10 32.885 0.665850
11 2.081 0.067021
12 2.614 0.083455
13 55.736 0.843996
14 23.161 0.537934
15 41.336 0.747881
16 14.775 0.388900
17 2.216 0.071217
18 29.202 0.622208
19 38.650 0.724273
20 13.628 0.365081
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.109498
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-02-28_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 0.6 -0.3 0.3 -1.4
-2.1 -0.0 -1.7 0.4 0.7 0.6
1.2 -0.9 -0.2 2.3 -0.6 -1.5
-1.0 -0.2 -0.4 0.4 2.0 -1.7
-0.6 1.3 1.1 -0.1 1.1 -0.6
1.1 0.8 1.2 -0.2 -1.0 -0.5
0.3 -2.0 -1.6 -1.3 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:48.116052
z-score=0.667316, p-value=0.760963
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-02-28_09:31
Test no p-value
1 0.723706
2 0.147818
3 0.004655
4 0.114346
5 0.666486
6 0.176324
7 0.189224
8 0.637844
9 0.642233
10 0.103154
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.066715
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-02-28_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 66493 0.45 66840 0.45
3 25000.00 25037 0.05 24815 1.37
4 6666.67 6833 4.15 6650 0.04
5 1388.89 1384 0.02 1436 1.60
6 238.10 215 2.24 220 1.38
7 34.72 33 0.09 34 0.01
8 4.96 4 0.19 4 0.19
p=0.69597 p=0.46070
Number of rngs required: 688205, p-value: 0.410
RESULTS OF CRAPS TEST for dh-ranFile-2018-02-28_09:31
No. of wins: Observed Expected
98827 98585.9
z-score= 1.079, pvalue=0.85960
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66726 66666.7 0.053 0.053
2 37543 37654.3 0.329 0.382
3 27042 26954.7 0.283 0.664
4 19476 19313.5 1.368 2.032
5 13767 13851.4 0.515 2.547
6 10007 9943.5 0.405 2.952
7 7050 7145.0 1.264 4.216
8 5128 5139.1 0.024 4.239
9 3767 3699.9 1.218 5.458
10 2642 2666.3 0.221 5.679
11 1867 1923.3 1.650 7.329
12 1356 1388.7 0.772 8.101
13 1020 1003.7 0.264 8.365
14 720 726.1 0.052 8.417
15 527 525.8 0.003 8.419
16 347 381.2 3.060 11.479
17 280 276.5 0.043 11.523
18 210 200.8 0.419 11.941
19 148 146.0 0.028 11.969
20 110 106.2 0.135 12.104
21 267 287.1 1.409 13.513
Chisq= 13.51 for 20 degrees of freedom, p= 0.14570
SUMMARY of craptest
p-value for no. of wins: 0.859600
p-value for throws/game: 0.145697
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-02-28_09:31
No. of wins: Observed Expected
98688 98585.9
z-score= 0.457, pvalue=0.67611
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66357 66666.7 1.438 1.438
2 37825 37654.3 0.774 2.212
3 27137 26954.7 1.232 3.445
4 19442 19313.5 0.855 4.300
5 13795 13851.4 0.230 4.530
6 9826 9943.5 1.389 5.919
7 7044 7145.0 1.428 7.348
8 5197 5139.1 0.653 8.001
9 3653 3699.9 0.594 8.594
10 2687 2666.3 0.161 8.755
11 1965 1923.3 0.903 9.658
12 1370 1388.7 0.253 9.911
13 1040 1003.7 1.312 11.223
14 697 726.1 1.169 12.392
15 533 525.8 0.098 12.490
16 410 381.2 2.184 14.673
17 266 276.5 0.402 15.075
18 219 200.8 1.644 16.719
19 152 146.0 0.248 16.967
20 99 106.2 0.490 17.457
21 286 287.1 0.004 17.461
Chisq= 17.46 for 20 degrees of freedom, p= 0.37714
SUMMARY of craptest
p-value for no. of wins: 0.676106
p-value for throws/game: 0.377142
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0047,0.0074,0.0081,0.0129,0.0158,0.0222,0.0276,0.0289,0.0303,0.0307,
0.0364,0.0424,0.0478,0.0562,0.0594,0.0667,0.0670,0.0671,0.0712,0.0769,
0.0786,0.0805,0.0835,0.0940,0.0975,0.1017,0.1032,0.1083,0.1095,0.1143,
0.1152,0.1182,0.1187,0.1271,0.1281,0.1395,0.1457,0.1467,0.1478,0.1490,
0.1495,0.1534,0.1544,0.1620,0.1636,0.1664,0.1667,0.1690,0.1701,0.1718,
0.1723,0.1761,0.1763,0.1801,0.1892,0.1923,0.1983,0.1989,0.2100,0.2188,
0.2235,0.2263,0.2272,0.2305,0.2356,0.2363,0.2384,0.2411,0.2459,0.2467,
0.2481,0.2516,0.2525,0.2660,0.2665,0.2761,0.2899,0.2929,0.2944,0.2993,
0.3058,0.3066,0.3167,0.3232,0.3356,0.3413,0.3453,0.3479,0.3542,0.3558,
0.3576,0.3651,0.3751,0.3771,0.3830,0.3839,0.3879,0.3889,0.3953,0.4045,
0.4057,0.4099,0.4216,0.4235,0.4305,0.4310,0.4350,0.4355,0.4393,0.4398,
0.4418,0.4424,0.4489,0.4597,0.4604,0.4607,0.4632,0.4667,0.4720,0.4728,
0.4737,0.4844,0.4877,0.4895,0.4937,0.5000,0.5020,0.5020,0.5047,0.5067,
0.5140,0.5160,0.5379,0.5390,0.5415,0.5427,0.5453,0.5471,0.5502,0.5557,
0.5558,0.5619,0.5632,0.5640,0.5711,0.5815,0.5881,0.5896,0.5900,0.6039,
0.6086,0.6130,0.6132,0.6155,0.6168,0.6207,0.6222,0.6271,0.6280,0.6297,
0.6302,0.6310,0.6350,0.6371,0.6378,0.6422,0.6426,0.6489,0.6493,0.6501,
0.6600,0.6620,0.6659,0.6665,0.6668,0.6695,0.6745,0.6757,0.6761,0.6825,
0.6837,0.6947,0.6947,0.6960,0.6989,0.7007,0.7031,0.7067,0.7101,0.7130,
0.7237,0.7243,0.7265,0.7324,0.7371,0.7386,0.7387,0.7387,0.7387,0.7479,
0.7603,0.7610,0.7683,0.7717,0.7720,0.7723,0.7834,0.7872,0.7888,0.7902,
0.7905,0.7919,0.7939,0.8150,0.8206,0.8276,0.8298,0.8304,0.8321,0.8359,
0.8360,0.8368,0.8386,0.8395,0.8440,0.8494,0.8533,0.8537,0.8586,0.8596,
0.8621,0.8622,0.8668,0.8674,0.8703,0.8715,0.8812,0.8836,0.8841,0.8892,
0.8901,0.8912,0.8912,0.8955,0.9006,0.9013,0.9043,0.9062,0.9110,0.9142,
0.9145,0.9188,0.9249,0.9279,0.9328,0.9329,0.9336,0.9414,0.9426,0.9487,
0.9587,0.9623,0.9671,0.9710,0.9710,0.9786,0.9823,0.9841,0.9957,
Overall p-value after applying KStest on 269 p-values = 0.624232
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.