RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2019-04-24_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.58 21.1650 0.781004
2 to 25 15.78 14.1109 0.340767
3 to 26 15.54 18.9728 0.669906
4 to 27 15.81 13.6620 0.309136
5 to 28 15.85 25.7401 0.920672
6 to 29 15.73 22.1370 0.820494
7 to 30 15.87 11.4820 0.169560
8 to 31 15.73 11.0010 0.143488
9 to 32 16.13 15.2626 0.423425
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.973020
Tough bday spacings test for dh-ranFile-2019-04-24_11:31: 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 40 93 99 95 67 42 34 16 2 5
(O-E)^2/E 0.5 0.3 5.3 0.0 0.1 1.6 2.0 0.6 0.1 3.2 0.2
Birthday Spacings: Sum(O-E)^2/E= 13.893, p= 0.822
RESULTS OF GCD FOR dh-ranFile-2019-04-24_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.915930
p-value, dist. of gcd's: 0.030747
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2019-04-24_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.593 0.699 0.272 0.858 0.747 0.307 0.594 0.030
Bits 8 to 15---> 0.861 0.060 0.106 0.476 0.265 0.971 0.637 0.867
Bits 16 to 23---> 0.418 0.069 0.017 0.383 0.070 0.001 0.797 0.478
Bits 24 to 31---> 0.907 0.746 0.569 0.874 0.079 0.870 0.045 0.160
KS test for the above 32 p values: 0.807
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2019-04-24_11:31,
p-values for 5 runs: 0.5518, 0.3524, 0.0772, 0.8695, 0.7467
Rank test for binary matrices (31x31) for dh-ranFile-2019-04-24_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 213 211.4 0.012 0.012
r= 29 5095 5134.0 0.296 0.308
r= 30 23090 23103.0 0.007 0.316
r= 31 11602 11551.5 0.221 0.536
chi-square = 0.536 with df = 3; p-value = 0.089
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2019-04-24_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 224 211.4 0.749 0.749
r= 30 5034 5134.0 1.948 2.697
r= 31 23004 23103.0 0.425 3.122
r= 32 11738 11551.5 3.010 6.132
chi-square = 6.132 with df = 3; p-value = 0.895
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2019-04-24_11:31
b-rank test for bits 1 to 8, p=0.33090
b-rank test for bits 2 to 9, p=0.84101
b-rank test for bits 3 to 10, p=0.61755
b-rank test for bits 4 to 11, p=0.82132
b-rank test for bits 5 to 12, p=0.09396
b-rank test for bits 6 to 13, p=0.63826
b-rank test for bits 7 to 14, p=0.30512
b-rank test for bits 8 to 15, p=0.32992
b-rank test for bits 9 to 16, p=0.69830
b-rank test for bits 10 to 17, p=0.67088
b-rank test for bits 11 to 18, p=0.06268
b-rank test for bits 12 to 19, p=0.34826
b-rank test for bits 13 to 20, p=0.38281
b-rank test for bits 14 to 21, p=0.57500
b-rank test for bits 15 to 22, p=0.28219
b-rank test for bits 16 to 23, p=0.54178
b-rank test for bits 17 to 24, p=0.30755
b-rank test for bits 18 to 25, p=0.88318
b-rank test for bits 19 to 26, p=0.89441
b-rank test for bits 20 to 27, p=0.44200
b-rank test for bits 21 to 28, p=0.51370
b-rank test for bits 22 to 29, p=0.41476
b-rank test for bits 23 to 30, p=0.68581
b-rank test for bits 24 to 31, p=0.99807
b-rank test for bits 25 to 32, p=0.65667
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 = 0.476869
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2019-04-24_11:31
(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 141477 -1.01 0.156220
2 141894 -0.04 0.485714
3 141851 -0.14 0.445798
4 142203 0.69 0.753689
5 142038 0.30 0.618152
6 142004 0.22 0.587528
7 141725 -0.43 0.333351
8 142552 1.50 0.933395
9 141719 -0.44 0.328270
10 141306 -1.41 0.079322
11 142482 1.34 0.909554
12 141212 -1.63 0.051627
13 142123 0.50 0.691191
14 142584 1.58 0.942525
15 141695 -0.50 0.308266
16 142195 0.67 0.747759
17 141039 -2.03 0.021002
18 142292 0.89 0.814363
19 141399 -1.19 0.116560
20 142253 0.80 0.789003
----------------------------------------------------------------
OPSO test for dh-ranFile-2019-04-24_11:31
Bits used No. missing words z-score p-value
23 to 32 142043 0.4609 0.677576
22 to 31 141622 -0.9908 0.160893
21 to 30 141389 -1.7942 0.036387
20 to 29 142117 0.7161 0.763036
19 to 28 141918 0.0299 0.511925
18 to 27 141934 0.0851 0.533897
17 to 26 141350 -1.9287 0.026883
16 to 25 141845 -0.2218 0.412224
15 to 24 142317 1.4058 0.920102
14 to 23 141727 -0.6287 0.264765
13 to 22 141972 0.2161 0.585547
12 to 21 142171 0.9023 0.816554
11 to 20 142082 0.5954 0.724217
10 to 19 141553 -1.2287 0.109588
9 to 18 141652 -0.8873 0.187447
8 to 17 141033 -3.0218 0.001256
7 to 16 141240 -2.3080 0.010499
6 to 15 140815 -3.7736 0.000080
5 to 14 142271 1.2471 0.893827
4 to 13 141677 -0.8011 0.211526
3 to 12 141307 -2.0770 0.018901
2 to 11 141611 -1.0287 0.151805
1 to 10 141903 -0.0218 0.491293
-----------------------------------------------------------------
OQSO test for dh-ranFile-2019-04-24_11:31
Bits used No. missing words z-score p-value
28 to 32 141522 -1.3130 0.094594
27 to 31 141787 -0.4147 0.339189
26 to 30 141869 -0.1367 0.445629
25 to 29 142188 0.9446 0.827580
24 to 28 141754 -0.5265 0.299256
23 to 27 141685 -0.7604 0.223496
22 to 26 141678 -0.7842 0.216470
21 to 25 142148 0.8091 0.790757
20 to 24 142299 1.3209 0.906735
19 to 23 141311 -2.0282 0.021268
18 to 22 141852 -0.1943 0.422955
17 to 21 141854 -0.1876 0.425611
16 to 20 142088 0.6057 0.727630
15 to 19 142182 0.9243 0.822336
14 to 18 141756 -0.5198 0.301615
13 to 17 142143 0.7921 0.785849
12 to 16 141525 -1.3028 0.096319
11 to 15 142258 1.1819 0.881384
10 to 14 142126 0.7345 0.768670
9 to 13 141206 -2.3842 0.008559
8 to 12 141574 -1.1367 0.127829
7 to 11 141794 -0.3909 0.347917
6 to 10 141742 -0.5672 0.285282
5 to 9 142526 2.0904 0.981709
4 to 8 141455 -1.5401 0.061768
3 to 7 141725 -0.6248 0.266036
2 to 6 142880 3.2904 0.999500
1 to 5 142293 1.3006 0.903298
-----------------------------------------------------------------
DNA test for dh-ranFile-2019-04-24_11:31
Bits used No. missing words z-score p-value
31 to 32 141836 -0.2163 0.414372
30 to 31 142635 2.1406 0.983848
29 to 30 142388 1.4120 0.921026
28 to 29 141297 -1.8063 0.035437
27 to 28 142233 0.9548 0.830155
26 to 27 141551 -1.0570 0.145251
25 to 26 141990 0.2380 0.594046
24 to 25 142585 1.9931 0.976876
23 to 24 141329 -1.7119 0.043459
22 to 23 142062 0.4504 0.673772
21 to 22 141515 -1.1632 0.122371
20 to 21 142450 1.5949 0.944632
19 to 20 142147 0.7011 0.758377
18 to 19 142313 1.1908 0.883127
17 to 18 142706 2.3501 0.990615
16 to 17 141808 -0.2989 0.382505
15 to 16 141546 -1.0718 0.141912
14 to 15 142547 1.8810 0.970016
13 to 14 141876 -0.0983 0.460840
12 to 13 141810 -0.2930 0.384758
11 to 12 141492 -1.2311 0.109150
10 to 11 141543 -1.0806 0.139933
9 to 10 141904 -0.0157 0.493728
8 to 9 141806 -0.3048 0.380256
7 to 8 142288 1.1170 0.868007
6 to 7 142366 1.3471 0.911027
5 to 6 141754 -0.4582 0.323404
4 to 5 141679 -0.6794 0.248430
3 to 4 142100 0.5624 0.713095
2 to 3 142031 0.3589 0.640168
1 to 2 141759 -0.4435 0.328720
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2019-04-24_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2518.05 0.255 0.600756
Test results for specific bytes for dh-ranFile-2019-04-24_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2548.21 0.682 0.752307
2 to 9 2466.75 -0.470 0.319113
3 to 10 2545.05 0.637 0.737950
4 to 11 2704.20 2.888 0.998060
5 to 12 2621.52 1.719 0.957149
6 to 13 2455.94 -0.623 0.266623
7 to 14 2594.56 1.337 0.909438
8 to 15 2586.41 1.222 0.889156
9 to 16 2512.89 0.182 0.572343
10 to 17 2426.20 -1.044 0.148315
11 to 18 2642.72 2.018 0.978222
12 to 19 2513.68 0.193 0.576700
13 to 20 2520.14 0.285 0.612099
14 to 21 2628.76 1.821 0.965690
15 to 22 2460.99 -0.552 0.290559
16 to 23 2510.44 0.148 0.558710
17 to 24 2561.76 0.873 0.808764
18 to 25 2435.88 -0.907 0.182270
19 to 26 2475.01 -0.353 0.361889
20 to 27 2545.59 0.645 0.740454
21 to 28 2545.55 0.644 0.740280
22 to 29 2401.81 -1.389 0.082468
23 to 30 2545.73 0.647 0.741105
24 to 31 2587.18 1.233 0.891196
25 to 32 2413.03 -1.230 0.109357
CDPARK for dh-ranFile-2019-04-24_11:31: 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
3535 0.5479 0.708135
3516 -0.3196 0.374623
3491 -1.4612 0.071982
3531 0.3653 0.642555
3576 2.4201 0.992242
3545 1.0046 0.842447
3508 -0.6849 0.246694
3523 0.0000 0.500000
3536 0.5936 0.723613
3527 0.1826 0.572463
Square side=100, avg. no. parked=3528.80 sample std.=21.56
p-value of the KSTEST for those 10 p-values: 0.723974
Results for the MINIMUM DISTANCE test for dh-ranFile-2019-04-24_11:31
0.0915,0.7593,0.0133,0.9371,0.7347,0.4193,0.7544,0.6141,0.0740,0.0811,
The KS test for those 10 p-values: 0.320537
The 3DSPHERES test for dh-ranFile-2019-04-24_11:31
sample no r^3 equiv. uni.
1 7.756 0.227808
2 44.156 0.770500
3 43.454 0.765067
4 6.100 0.183983
5 50.225 0.812538
6 26.958 0.592863
7 4.990 0.153244
8 29.587 0.627022
9 54.094 0.835221
10 26.566 0.587510
11 1.439 0.046832
12 29.813 0.629820
13 8.957 0.258129
14 1.522 0.049484
15 81.702 0.934350
16 70.346 0.904139
17 18.591 0.461892
18 27.614 0.601664
19 7.102 0.210810
20 66.947 0.892639
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.801283
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2019-04-24_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 -0.1 -0.4 -1.7 -0.4
-1.3 0.7 -1.0 -0.8 -0.3 1.6
1.3 0.3 0.1 0.3 0.0 -0.3
1.6 0.4 -0.6 -1.1 0.9 0.5
-1.4 -1.7 -1.7 -1.3 0.2 0.8
-0.8 -0.2 -0.5 1.7 1.2 -0.8
1.0 1.5 -0.8 -0.1 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:39.123256
z-score=-0.313878, p-value=0.402027
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2019-04-24_11:31
Test no p-value
1 0.097714
2 0.487539
3 0.522794
4 0.181950
5 0.212294
6 0.489780
7 0.066470
8 0.438103
9 0.096421
10 0.417416
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.036243
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2019-04-24_11:31:
(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 66396 1.10 66560 0.17
3 25000.00 25238 2.27 25085 0.29
4 6666.67 6669 0.00 6677 0.02
5 1388.89 1399 0.07 1402 0.12
6 238.10 261 2.20 232 0.16
7 34.72 31 0.40 39 0.53
8 4.96 5 0.00 4 0.19
p=0.58144 p=0.03846
Number of rngs required: 689485, p-value: 0.896
RESULTS OF CRAPS TEST for dh-ranFile-2019-04-24_11:31
No. of wins: Observed Expected
98707 98585.9
z-score= 0.542, pvalue=0.70603
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66927 66666.7 1.017 1.017
2 37767 37654.3 0.337 1.354
3 26776 26954.7 1.185 2.539
4 19249 19313.5 0.215 2.754
5 13786 13851.4 0.309 3.063
6 9996 9943.5 0.277 3.340
7 7014 7145.0 2.403 5.743
8 5061 5139.1 1.186 6.929
9 3659 3699.9 0.451 7.380
10 2714 2666.3 0.853 8.233
11 1982 1923.3 1.790 10.023
12 1381 1388.7 0.043 10.066
13 1025 1003.7 0.451 10.518
14 704 726.1 0.675 11.193
15 515 525.8 0.223 11.416
16 370 381.2 0.326 11.742
17 303 276.5 2.532 14.274
18 233 200.8 5.153 19.427
19 142 146.0 0.109 19.536
20 111 106.2 0.216 19.752
21 285 287.1 0.016 19.767
Chisq= 19.77 for 20 degrees of freedom, p= 0.52742
SUMMARY of craptest
p-value for no. of wins: 0.706027
p-value for throws/game: 0.527424
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2019-04-24_11:31
No. of wins: Observed Expected
98741 98585.9
z-score= 0.694, pvalue=0.75612
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66323 66666.7 1.772 1.772
2 37576 37654.3 0.163 1.935
3 27139 26954.7 1.260 3.194
4 19507 19313.5 1.939 5.134
5 13862 13851.4 0.008 5.142
6 9950 9943.5 0.004 5.146
7 7209 7145.0 0.573 5.719
8 5040 5139.1 1.910 7.629
9 3742 3699.9 0.480 8.108
10 2645 2666.3 0.170 8.279
11 1938 1923.3 0.112 8.391
12 1384 1388.7 0.016 8.407
13 968 1003.7 1.271 9.678
14 722 726.1 0.024 9.701
15 514 525.8 0.266 9.968
16 384 381.2 0.021 9.989
17 275 276.5 0.009 9.997
18 229 200.8 3.951 13.949
19 148 146.0 0.028 13.977
20 140 106.2 10.746 24.723
21 305 287.1 1.114 25.837
Chisq= 25.84 for 20 degrees of freedom, p= 0.82874
SUMMARY of craptest
p-value for no. of wins: 0.756122
p-value for throws/game: 0.828739
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0006,0.0013,0.0086,0.0105,0.0133,0.0175,0.0189,0.0210,0.0213,
0.0269,0.0297,0.0307,0.0354,0.0362,0.0364,0.0385,0.0435,0.0451,0.0468,
0.0495,0.0516,0.0596,0.0618,0.0627,0.0665,0.0692,0.0697,0.0720,0.0740,
0.0772,0.0789,0.0793,0.0811,0.0825,0.0891,0.0915,0.0940,0.0946,0.0963,
0.0964,0.0977,0.1059,0.1091,0.1094,0.1096,0.1166,0.1224,0.1278,0.1399,
0.1419,0.1435,0.1453,0.1483,0.1518,0.1532,0.1562,0.1597,0.1609,0.1696,
0.1820,0.1823,0.1840,0.1874,0.2108,0.2115,0.2123,0.2165,0.2235,0.2278,
0.2467,0.2484,0.2581,0.2645,0.2648,0.2660,0.2666,0.2720,0.2822,0.2853,
0.2906,0.2993,0.3016,0.3051,0.3075,0.3075,0.3083,0.3091,0.3191,0.3205,
0.3234,0.3283,0.3287,0.3299,0.3309,0.3334,0.3392,0.3408,0.3479,0.3483,
0.3524,0.3619,0.3746,0.3803,0.3825,0.3828,0.3834,0.3848,0.4020,0.4122,
0.4144,0.4148,0.4174,0.4184,0.4193,0.4230,0.4234,0.4256,0.4381,0.4420,
0.4456,0.4458,0.4608,0.4619,0.4763,0.4769,0.4776,0.4857,0.4875,0.4898,
0.4913,0.4937,0.5000,0.5119,0.5137,0.5228,0.5274,0.5339,0.5418,0.5518,
0.5587,0.5691,0.5723,0.5725,0.5750,0.5767,0.5814,0.5855,0.5875,0.5875,
0.5929,0.5931,0.5938,0.5940,0.6008,0.6017,0.6121,0.6141,0.6176,0.6182,
0.6270,0.6298,0.6372,0.6383,0.6402,0.6426,0.6567,0.6699,0.6709,0.6738,
0.6776,0.6858,0.6912,0.6983,0.6990,0.7060,0.7081,0.7131,0.7236,0.7240,
0.7242,0.7276,0.7347,0.7380,0.7403,0.7405,0.7411,0.7463,0.7467,0.7467,
0.7478,0.7523,0.7537,0.7544,0.7561,0.7584,0.7593,0.7630,0.7651,0.7687,
0.7705,0.7810,0.7858,0.7890,0.7908,0.7971,0.8013,0.8071,0.8088,0.8125,
0.8144,0.8166,0.8205,0.8213,0.8221,0.8223,0.8276,0.8287,0.8302,0.8352,
0.8410,0.8424,0.8577,0.8613,0.8668,0.8680,0.8695,0.8704,0.8742,0.8814,
0.8831,0.8832,0.8892,0.8912,0.8926,0.8938,0.8944,0.8946,0.8959,0.9033,
0.9041,0.9067,0.9073,0.9094,0.9096,0.9110,0.9159,0.9201,0.9207,0.9210,
0.9334,0.9343,0.9371,0.9425,0.9446,0.9571,0.9657,0.9700,0.9711,0.9730,
0.9769,0.9782,0.9817,0.9838,0.9906,0.9922,0.9981,0.9981,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.116045
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.