RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.43 29.7804 0.972027
2 to 25 15.78 16.5938 0.517803
3 to 26 15.59 19.4036 0.694135
4 to 27 15.59 31.8648 0.984359
5 to 28 15.60 26.0000 0.925539
6 to 29 15.56 32.5450 0.987136
7 to 30 15.90 14.3815 0.360059
8 to 31 15.59 23.5788 0.868660
9 to 32 15.44 24.3829 0.890600
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000709
Tough bday spacings test for dh-ranFile-2018-07-06_01:31: 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 35 78 109 92 73 52 35 8 7 2
(O-E)^2/E 0.0 0.1 0.3 1.3 0.3 0.3 0.0 0.9 3.2 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 7.538, p= 0.326
RESULTS OF GCD FOR dh-ranFile-2018-07-06_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.637211
p-value, dist. of gcd's: 0.848641
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.129 0.743 0.777 0.407 0.904 0.003 0.258 0.133
Bits 8 to 15---> 0.673 0.250 0.996 0.155 0.370 0.750 0.669 0.334
Bits 16 to 23---> 0.414 0.204 0.044 0.071 0.940 0.124 0.889 0.037
Bits 24 to 31---> 0.380 0.721 0.844 0.605 0.539 0.790 0.222 0.886
KS test for the above 32 p values: 0.280
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_01:31,
p-values for 5 runs: 0.7534, 0.0421, 0.7197, 0.3151, 0.6200
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5111 5134.0 0.103 0.308
r= 30 23141 23103.0 0.062 0.370
r= 31 11530 11551.5 0.040 0.410
chi-square = 0.410 with df = 3; p-value = 0.062
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5113 5134.0 0.086 0.434
r= 31 23252 23103.0 0.960 1.395
r= 32 11415 11551.5 1.614 3.008
chi-square = 3.008 with df = 3; p-value = 0.610
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_01:31
b-rank test for bits 1 to 8, p=0.81774
b-rank test for bits 2 to 9, p=0.91783
b-rank test for bits 3 to 10, p=0.76427
b-rank test for bits 4 to 11, p=0.65225
b-rank test for bits 5 to 12, p=0.14247
b-rank test for bits 6 to 13, p=0.31134
b-rank test for bits 7 to 14, p=0.53716
b-rank test for bits 8 to 15, p=0.33480
b-rank test for bits 9 to 16, p=0.47449
b-rank test for bits 10 to 17, p=0.79142
b-rank test for bits 11 to 18, p=0.92049
b-rank test for bits 12 to 19, p=0.02310
b-rank test for bits 13 to 20, p=0.38603
b-rank test for bits 14 to 21, p=0.85525
b-rank test for bits 15 to 22, p=0.13021
b-rank test for bits 16 to 23, p=0.23404
b-rank test for bits 17 to 24, p=0.88579
b-rank test for bits 18 to 25, p=0.79962
b-rank test for bits 19 to 26, p=0.24556
b-rank test for bits 20 to 27, p=0.42967
b-rank test for bits 21 to 28, p=0.44200
b-rank test for bits 22 to 29, p=0.75412
b-rank test for bits 23 to 30, p=0.39537
b-rank test for bits 24 to 31, p=0.01052
b-rank test for bits 25 to 32, p=0.40052
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 = 0.894359
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_01:31
(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 141055 -2.00 0.022962
2 141591 -0.74 0.228510
3 141799 -0.26 0.398288
4 141768 -0.33 0.370621
5 141490 -0.98 0.163607
6 142014 0.24 0.596600
7 142191 0.66 0.744765
8 142261 0.82 0.794364
9 142680 1.80 0.964119
10 141624 -0.67 0.252495
11 142229 0.75 0.772436
12 141364 -1.27 0.101308
13 141230 -1.59 0.056231
14 141192 -1.68 0.046869
15 142140 0.54 0.705039
16 142511 1.41 0.920104
17 141691 -0.51 0.304985
18 142075 0.39 0.650651
19 142149 0.56 0.712252
20 142248 0.79 0.785611
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_01:31
Bits used No. missing words z-score p-value
23 to 32 141928 0.0644 0.525666
22 to 31 142325 1.4333 0.924120
21 to 30 141806 -0.3563 0.360804
20 to 29 141711 -0.6839 0.247020
19 to 28 141963 0.1851 0.573413
18 to 27 142066 0.5402 0.705485
17 to 26 141569 -1.1736 0.120287
16 to 25 141668 -0.8322 0.202656
15 to 24 141571 -1.1667 0.121675
14 to 23 141715 -0.6701 0.251396
13 to 22 142432 1.8023 0.964252
12 to 21 141869 -0.1391 0.444698
11 to 20 142432 1.8023 0.964252
10 to 19 142100 0.6575 0.744565
9 to 18 141586 -1.1149 0.132440
8 to 17 141782 -0.4391 0.330306
7 to 16 141977 0.2333 0.592253
6 to 15 141572 -1.1632 0.122373
5 to 14 142301 1.3506 0.911586
4 to 13 141830 -0.2736 0.392215
3 to 12 141821 -0.3046 0.380341
2 to 11 141903 -0.0218 0.491293
1 to 10 141930 0.0713 0.528411
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_01:31
Bits used No. missing words z-score p-value
28 to 32 142106 0.6667 0.747511
27 to 31 142068 0.5379 0.704665
26 to 30 141842 -0.2282 0.409731
25 to 29 142289 1.2870 0.900956
24 to 28 141852 -0.1943 0.422955
23 to 27 141821 -0.2994 0.382308
22 to 26 141566 -1.1638 0.122246
21 to 25 142079 0.5752 0.717406
20 to 24 141846 -0.2147 0.415009
19 to 23 142125 0.7311 0.767636
18 to 22 142013 0.3514 0.637365
17 to 21 142100 0.6463 0.740970
16 to 20 142111 0.6836 0.752895
15 to 19 142132 0.7548 0.774820
14 to 18 142327 1.4158 0.921587
13 to 17 141799 -0.3740 0.354202
12 to 16 141957 0.1616 0.564187
11 to 15 141981 0.2429 0.595978
10 to 14 142476 1.9209 0.972629
9 to 13 141529 -1.2893 0.098655
8 to 12 141779 -0.4418 0.329318
7 to 11 142064 0.5243 0.699967
6 to 10 141895 -0.0486 0.480629
5 to 9 141625 -0.9638 0.167565
4 to 8 141895 -0.0486 0.480629
3 to 7 141469 -1.4926 0.067765
2 to 6 141945 0.1209 0.548121
1 to 5 142132 0.7548 0.774820
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_01:31
Bits used No. missing words z-score p-value
31 to 32 141679 -0.6794 0.248430
30 to 31 141892 -0.0511 0.479615
29 to 30 142070 0.4740 0.682233
28 to 29 141960 0.1495 0.559408
27 to 28 142361 1.3324 0.908629
26 to 27 141590 -0.9420 0.173102
25 to 26 141448 -1.3609 0.086780
24 to 25 141577 -0.9803 0.163463
23 to 24 142147 0.7011 0.758377
22 to 23 141677 -0.6853 0.246565
21 to 22 142131 0.6539 0.743410
20 to 21 142187 0.8191 0.793631
19 to 20 141654 -0.7532 0.225669
18 to 19 141608 -0.8889 0.187034
17 to 18 141661 -0.7325 0.231921
16 to 17 142543 1.8692 0.969205
15 to 16 142144 0.6922 0.755607
14 to 15 142131 0.6539 0.743410
13 to 14 141857 -0.1544 0.438661
12 to 13 141668 -0.7119 0.238267
11 to 12 141664 -0.7237 0.234629
10 to 11 141647 -0.7738 0.219514
9 to 10 141495 -1.2222 0.110814
8 to 9 141574 -0.9892 0.161289
7 to 8 141760 -0.4405 0.329787
6 to 7 142162 0.7453 0.771967
5 to 6 141857 -0.1544 0.438661
4 to 5 141601 -0.9095 0.181536
3 to 4 142173 0.7778 0.781653
2 to 3 141571 -0.9980 0.159134
1 to 2 142138 0.6745 0.750017
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2474.82 -0.356 0.360883
Test results for specific bytes for dh-ranFile-2018-07-06_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2381.77 -1.672 0.047260
2 to 9 2382.59 -1.660 0.048420
3 to 10 2660.57 2.271 0.988422
4 to 11 2547.61 0.673 0.749609
5 to 12 2612.81 1.595 0.944693
6 to 13 2555.48 0.785 0.783678
7 to 14 2388.59 -1.576 0.057565
8 to 15 2478.07 -0.310 0.378226
9 to 16 2520.76 0.294 0.615446
10 to 17 2444.27 -0.788 0.215317
11 to 18 2627.68 1.806 0.964520
12 to 19 2459.81 -0.568 0.284903
13 to 20 2576.96 1.088 0.861789
14 to 21 2582.43 1.166 0.878133
15 to 22 2604.51 1.478 0.930287
16 to 23 2473.35 -0.377 0.353105
17 to 24 2377.32 -1.735 0.041375
18 to 25 2505.18 0.073 0.529176
19 to 26 2424.31 -1.070 0.142209
20 to 27 2471.41 -0.404 0.342986
21 to 28 2460.38 -0.560 0.287622
22 to 29 2514.99 0.212 0.583938
23 to 30 2491.68 -0.118 0.453181
24 to 31 2435.76 -0.908 0.181810
25 to 32 2444.31 -0.788 0.215478
CDPARK for dh-ranFile-2018-07-06_01:31: 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
3513 -0.4566 0.323972
3552 1.3242 0.907282
3561 1.7352 0.958644
3565 1.9178 0.972432
3547 1.0959 0.863437
3539 0.7306 0.767486
3508 -0.6849 0.246694
3541 0.8219 0.794438
3565 1.9178 0.972432
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3540.90 sample std.=20.29
p-value of the KSTEST for those 10 p-values: 0.009917
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_01:31
0.9783,0.3418,0.7227,0.8470,0.3544,0.0419,0.0266,0.2192,0.4037,0.3682,
The KS test for those 10 p-values: 0.533786
The 3DSPHERES test for dh-ranFile-2018-07-06_01:31
sample no r^3 equiv. uni.
1 10.409 0.293166
2 7.314 0.216363
3 4.392 0.136178
4 14.291 0.378963
5 16.131 0.415916
6 6.603 0.197559
7 29.960 0.631636
8 36.214 0.700944
9 0.291 0.009668
10 7.462 0.220224
11 7.710 0.226629
12 2.200 0.070713
13 9.696 0.276162
14 8.144 0.237731
15 9.766 0.277848
16 39.467 0.731674
17 8.421 0.244741
18 37.924 0.717514
19 65.023 0.885528
20 1.383 0.045052
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.019463
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.8 1.5 -0.6 0.5
-0.1 -0.3 -0.5 1.6 1.6 -1.3
0.9 2.5 1.6 -0.4 -3.0 1.1
-0.4 0.6 -0.9 0.2 -2.6 -0.2
0.3 0.8 -1.5 1.4 -1.5 -2.1
0.7 0.4 -0.7 0.7 0.2 0.2
1.2 1.8 1.3 0.4 0.1 -1.0
0.8
Chi-square with 42 degrees of freedom:60.802679
z-score=2.051540, p-value=0.969750
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_01:31
Test no p-value
1 0.411693
2 0.094916
3 0.359806
4 0.150751
5 0.158725
6 0.351608
7 0.645570
8 0.231167
9 0.195811
10 0.340411
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.025415
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_01:31:
(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 66724 0.05 66557 0.18
3 25000.00 24942 0.13 25125 0.62
4 6666.67 6651 0.04 6680 0.03
5 1388.89 1399 0.07 1373 0.18
6 238.10 244 0.15 234 0.07
7 34.72 35 0.00 27 1.72
8 4.96 4 0.19 3 0.77
p=0.00410 p=0.26608
Number of rngs required: 688152, p-value: 0.386
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_01:31
No. of wins: Observed Expected
98691 98585.9
z-score= 0.470, pvalue=0.68091
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67109 66666.7 2.935 2.935
2 37800 37654.3 0.564 3.498
3 26754 26954.7 1.495 4.993
4 19355 19313.5 0.089 5.083
5 13819 13851.4 0.076 5.159
6 9858 9943.5 0.736 5.894
7 7095 7145.0 0.350 6.245
8 5142 5139.1 0.002 6.246
9 3717 3699.9 0.079 6.326
10 2557 2666.3 4.480 10.806
11 1937 1923.3 0.097 10.903
12 1314 1388.7 4.022 14.926
13 998 1003.7 0.033 14.958
14 731 726.1 0.033 14.991
15 493 525.8 2.050 17.041
16 359 381.2 1.287 18.328
17 265 276.5 0.482 18.810
18 198 200.8 0.040 18.850
19 140 146.0 0.245 19.095
20 103 106.2 0.097 19.193
21 256 287.1 3.372 22.564
Chisq= 22.56 for 20 degrees of freedom, p= 0.68931
SUMMARY of craptest
p-value for no. of wins: 0.680913
p-value for throws/game: 0.689309
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_01:31
No. of wins: Observed Expected
98692 98585.9
z-score= 0.475, pvalue=0.68251
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66692 66666.7 0.010 0.010
2 37881 37654.3 1.365 1.374
3 26875 26954.7 0.236 1.610
4 19206 19313.5 0.598 2.208
5 13640 13851.4 3.227 5.435
6 9883 9943.5 0.369 5.804
7 7196 7145.0 0.364 6.167
8 5196 5139.1 0.631 6.798
9 3728 3699.9 0.214 7.012
10 2666 2666.3 0.000 7.012
11 1937 1923.3 0.097 7.109
12 1442 1388.7 2.043 9.152
13 1008 1003.7 0.018 9.170
14 714 726.1 0.203 9.373
15 512 525.8 0.364 9.737
16 386 381.2 0.062 9.799
17 286 276.5 0.324 10.122
18 195 200.8 0.169 10.292
19 157 146.0 0.831 11.123
20 102 106.2 0.167 11.290
21 298 287.1 0.413 11.703
Chisq= 11.70 for 20 degrees of freedom, p= 0.07407
SUMMARY of craptest
p-value for no. of wins: 0.682509
p-value for throws/game: 0.074074
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0030,0.0041,0.0097,0.0099,0.0105,0.0195,0.0230,0.0231,0.0254,
0.0266,0.0375,0.0414,0.0419,0.0421,0.0442,0.0451,0.0469,0.0473,0.0484,
0.0562,0.0576,0.0619,0.0678,0.0707,0.0711,0.0741,0.0868,0.0949,0.0987,
0.1013,0.1108,0.1203,0.1217,0.1222,0.1224,0.1240,0.1289,0.1302,0.1324,
0.1328,0.1362,0.1422,0.1425,0.1508,0.1550,0.1587,0.1591,0.1613,0.1635,
0.1636,0.1676,0.1731,0.1815,0.1818,0.1870,0.1958,0.1976,0.2027,0.2035,
0.2153,0.2155,0.2164,0.2192,0.2195,0.2202,0.2224,0.2257,0.2266,0.2285,
0.2312,0.2319,0.2340,0.2346,0.2377,0.2383,0.2447,0.2456,0.2466,0.2467,
0.2470,0.2484,0.2503,0.2514,0.2525,0.2579,0.2661,0.2762,0.2778,0.2801,
0.2849,0.2876,0.2932,0.3050,0.3113,0.3151,0.3240,0.3262,0.3293,0.3298,
0.3303,0.3343,0.3348,0.3404,0.3418,0.3430,0.3516,0.3531,0.3542,0.3544,
0.3598,0.3601,0.3608,0.3609,0.3682,0.3701,0.3706,0.3782,0.3790,0.3799,
0.3803,0.3823,0.3860,0.3863,0.3922,0.3954,0.3983,0.4005,0.4037,0.4075,
0.4097,0.4097,0.4117,0.4144,0.4150,0.4159,0.4230,0.4297,0.4387,0.4387,
0.4420,0.4447,0.4532,0.4745,0.4796,0.4806,0.4806,0.4913,0.5178,0.5257,
0.5284,0.5292,0.5338,0.5372,0.5385,0.5481,0.5594,0.5642,0.5734,0.5839,
0.5923,0.5960,0.5966,0.6049,0.6096,0.6154,0.6200,0.6316,0.6372,0.6374,
0.6456,0.6507,0.6522,0.6694,0.6726,0.6809,0.6822,0.6825,0.6893,0.6941,
0.7000,0.7009,0.7047,0.7050,0.7055,0.7123,0.7174,0.7175,0.7197,0.7211,
0.7227,0.7317,0.7410,0.7428,0.7434,0.7434,0.7446,0.7448,0.7475,0.7496,
0.7500,0.7501,0.7529,0.7534,0.7541,0.7556,0.7584,0.7643,0.7675,0.7676,
0.7720,0.7724,0.7748,0.7748,0.7772,0.7817,0.7837,0.7856,0.7896,0.7914,
0.7936,0.7944,0.7944,0.7996,0.8177,0.8440,0.8470,0.8486,0.8552,0.8618,
0.8634,0.8687,0.8781,0.8855,0.8858,0.8861,0.8887,0.8906,0.8944,0.9010,
0.9036,0.9073,0.9086,0.9116,0.9178,0.9201,0.9205,0.9216,0.9241,0.9255,
0.9303,0.9398,0.9447,0.9586,0.9641,0.9643,0.9643,0.9645,0.9692,0.9698,
0.9720,0.9724,0.9724,0.9726,0.9783,0.9844,0.9871,0.9884,0.9959,
Overall p-value after applying KStest on 269 p-values = 0.150292
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.