RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_04:31
(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 25.3285 0.912405
2 to 25 15.64 20.1002 0.730861
3 to 26 15.68 14.4374 0.364067
4 to 27 15.56 17.7996 0.598413
5 to 28 15.76 16.9359 0.541282
6 to 29 15.78 11.9688 0.197976
7 to 30 15.75 16.8760 0.537200
8 to 31 15.77 15.1859 0.417909
9 to 32 15.62 16.3112 0.498112
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.526726
Tough bday spacings test for dh-ranFile-2018-06-24_04:31: 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 11 30 72 103 98 75 61 31 11 3 5
(O-E)^2/E 0.4 1.2 0.0 0.3 0.0 0.1 1.5 0.1 1.0 2.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 6.786, p= 0.255
RESULTS OF GCD FOR dh-ranFile-2018-06-24_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.399534
p-value, dist. of gcd's: 0.782496
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.413 0.046 0.092 0.184 0.217 0.230 0.748 0.818
Bits 8 to 15---> 0.476 0.695 0.569 0.121 0.152 0.433 0.623 0.351
Bits 16 to 23---> 0.619 0.046 0.650 0.277 0.207 0.406 0.775 0.057
Bits 24 to 31---> 0.787 0.133 0.307 0.009 0.624 0.037 0.218 0.299
KS test for the above 32 p values: 0.989
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_04:31,
p-values for 5 runs: 0.5579, 0.1516, 0.9077, 0.1053, 0.2692
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5201 5134.0 0.874 0.973
r= 30 22983 23103.0 0.624 1.597
r= 31 11600 11551.5 0.203 1.801
chi-square = 1.801 with df = 3; p-value = 0.385
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 5201 5134.0 0.874 1.134
r= 31 23000 23103.0 0.460 1.594
r= 32 11595 11551.5 0.164 1.758
chi-square = 1.758 with df = 3; p-value = 0.376
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_04:31
b-rank test for bits 1 to 8, p=0.95888
b-rank test for bits 2 to 9, p=0.18945
b-rank test for bits 3 to 10, p=0.68557
b-rank test for bits 4 to 11, p=0.24851
b-rank test for bits 5 to 12, p=0.22431
b-rank test for bits 6 to 13, p=0.09875
b-rank test for bits 7 to 14, p=0.42642
b-rank test for bits 8 to 15, p=0.98746
b-rank test for bits 9 to 16, p=0.03433
b-rank test for bits 10 to 17, p=0.88289
b-rank test for bits 11 to 18, p=0.93637
b-rank test for bits 12 to 19, p=0.47030
b-rank test for bits 13 to 20, p=0.40876
b-rank test for bits 14 to 21, p=0.46729
b-rank test for bits 15 to 22, p=0.88253
b-rank test for bits 16 to 23, p=0.33368
b-rank test for bits 17 to 24, p=0.31721
b-rank test for bits 18 to 25, p=0.30335
b-rank test for bits 19 to 26, p=0.97321
b-rank test for bits 20 to 27, p=0.81318
b-rank test for bits 21 to 28, p=0.36277
b-rank test for bits 22 to 29, p=0.10357
b-rank test for bits 23 to 30, p=0.93265
b-rank test for bits 24 to 31, p=0.68857
b-rank test for bits 25 to 32, p=0.85842
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 = 0.328320
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_04:31
(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 142235 0.76 0.776645
2 141585 -0.76 0.224291
3 142351 1.03 0.848950
4 142244 0.78 0.782875
5 141628 -0.66 0.255490
6 141402 -1.19 0.117939
7 141301 -1.42 0.077610
8 141789 -0.28 0.389300
9 142081 0.40 0.655826
10 141994 0.20 0.578410
11 142291 0.89 0.813737
12 141839 -0.16 0.434739
13 141845 -0.15 0.440263
14 141468 -1.03 0.151236
15 141579 -0.77 0.220117
16 141915 0.01 0.505285
17 141946 0.09 0.534139
18 142553 1.50 0.933697
19 142051 0.33 0.629680
20 141121 -1.84 0.032745
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_04:31
Bits used No. missing words z-score p-value
23 to 32 142150 0.8299 0.796701
22 to 31 141777 -0.4563 0.324083
21 to 30 142112 0.6989 0.757681
20 to 29 141432 -1.6460 0.049885
19 to 28 141745 -0.5667 0.285474
18 to 27 142213 1.0471 0.852482
17 to 26 141530 -1.3080 0.095431
16 to 25 142193 0.9782 0.836006
15 to 24 142094 0.6368 0.737870
14 to 23 142284 1.2920 0.901815
13 to 22 142505 2.0540 0.980014
12 to 21 142318 1.4092 0.920613
11 to 20 141446 -1.5977 0.055056
10 to 19 141669 -0.8287 0.203630
9 to 18 141981 0.2471 0.597599
8 to 17 141194 -2.4667 0.006819
7 to 16 141819 -0.3115 0.377717
6 to 15 141868 -0.1425 0.443336
5 to 14 141690 -0.7563 0.224732
4 to 13 142192 0.9747 0.835151
3 to 12 141832 -0.2667 0.394867
2 to 11 141812 -0.3356 0.368579
1 to 10 142163 0.8747 0.809138
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_04:31
Bits used No. missing words z-score p-value
28 to 32 142051 0.4802 0.684471
27 to 31 142266 1.2091 0.886678
26 to 30 141707 -0.6859 0.246399
25 to 29 141676 -0.7909 0.214487
24 to 28 141703 -0.6994 0.242144
23 to 27 141684 -0.7638 0.222484
22 to 26 141579 -1.1198 0.131407
21 to 25 141376 -1.8079 0.035311
20 to 24 142011 0.3446 0.634819
19 to 23 141410 -1.6926 0.045262
18 to 22 141850 -0.2011 0.420303
17 to 21 142464 1.8802 0.969962
16 to 20 141650 -0.8791 0.189678
15 to 19 141721 -0.6384 0.261605
14 to 18 142226 1.0735 0.858467
13 to 17 141959 0.1684 0.566855
12 to 16 142189 0.9480 0.828444
11 to 15 141620 -0.9808 0.163351
10 to 14 142076 0.5650 0.713957
9 to 13 142260 1.1887 0.882723
8 to 12 141988 0.2667 0.605141
7 to 11 141682 -0.7706 0.220469
6 to 10 141827 -0.2791 0.390090
5 to 9 142258 1.1819 0.881384
4 to 8 142033 0.4192 0.662473
3 to 7 141788 -0.4113 0.340431
2 to 6 141819 -0.3062 0.379725
1 to 5 141830 -0.2689 0.393998
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_04:31
Bits used No. missing words z-score p-value
31 to 32 142137 0.6716 0.749079
30 to 31 141710 -0.5880 0.278268
29 to 30 141742 -0.4936 0.310795
28 to 29 142746 2.4681 0.993207
27 to 28 141882 -0.0806 0.467872
26 to 27 142227 0.9371 0.825641
25 to 26 142119 0.6185 0.731876
24 to 25 141657 -0.7443 0.228337
23 to 24 141781 -0.3786 0.352509
22 to 23 142072 0.4799 0.684334
21 to 22 141940 0.0905 0.536044
20 to 21 142016 0.3147 0.623490
19 to 20 141744 -0.4877 0.312882
18 to 19 141258 -1.9213 0.027345
17 to 18 141632 -0.8181 0.206655
16 to 17 141985 0.2232 0.588316
15 to 16 141811 -0.2901 0.385886
14 to 15 142086 0.5212 0.698869
13 to 14 142042 0.3914 0.652233
12 to 13 141915 0.0167 0.506672
11 to 12 142195 0.8427 0.800298
10 to 11 141261 -1.9125 0.027907
9 to 10 141715 -0.5732 0.283240
8 to 9 141935 0.0757 0.530180
7 to 8 141997 0.2586 0.602033
6 to 7 142601 2.0403 0.979341
5 to 6 141774 -0.3992 0.344872
4 to 5 141640 -0.7945 0.213457
3 to 4 142104 0.5742 0.717100
2 to 3 142332 1.2468 0.893767
1 to 2 142016 0.3147 0.623490
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2561.52 0.870 0.807862
Test results for specific bytes for dh-ranFile-2018-06-24_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2438.14 -0.875 0.190845
2 to 9 2517.57 0.248 0.598105
3 to 10 2559.84 0.846 0.801300
4 to 11 2492.73 -0.103 0.459081
5 to 12 2471.93 -0.397 0.345686
6 to 13 2408.33 -1.296 0.097422
7 to 14 2474.95 -0.354 0.361565
8 to 15 2496.28 -0.053 0.479021
9 to 16 2395.91 -1.472 0.070512
10 to 17 2527.91 0.395 0.653486
11 to 18 2487.46 -0.177 0.429602
12 to 19 2560.70 0.858 0.804655
13 to 20 2540.40 0.571 0.716113
14 to 21 2593.47 1.322 0.906898
15 to 22 2530.39 0.430 0.666346
16 to 23 2504.61 0.065 0.526008
17 to 24 2484.29 -0.222 0.412068
18 to 25 2574.56 1.054 0.854148
19 to 26 2548.36 0.684 0.752996
20 to 27 2638.75 1.962 0.975132
21 to 28 2541.47 0.586 0.721207
22 to 29 2632.07 1.868 0.969104
23 to 30 2430.52 -0.983 0.162914
24 to 31 2545.35 0.641 0.739334
25 to 32 2440.85 -0.836 0.201444
CDPARK for dh-ranFile-2018-06-24_04:31: 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
3537 0.6393 0.738676
3538 0.6849 0.753306
3516 -0.3196 0.374623
3572 2.2374 0.987371
3527 0.1826 0.572463
3508 -0.6849 0.246694
3517 -0.2740 0.392053
3496 -1.2329 0.108811
3543 0.9132 0.819442
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3527.00 sample std.=20.41
p-value of the KSTEST for those 10 p-values: 0.873666
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_04:31
0.7584,0.5226,0.3992,0.3577,0.6773,0.9058,0.4909,0.5703,0.8104,0.1702,
The KS test for those 10 p-values: 0.583698
The 3DSPHERES test for dh-ranFile-2018-06-24_04:31
sample no r^3 equiv. uni.
1 11.377 0.315605
2 6.273 0.188698
3 26.370 0.584807
4 112.692 0.976632
5 48.909 0.804127
6 34.313 0.681383
7 0.050 0.001657
8 43.665 0.766717
9 13.611 0.364736
10 15.619 0.405858
11 6.154 0.185460
12 34.005 0.678092
13 62.930 0.877259
14 52.248 0.824760
15 90.864 0.951627
16 23.211 0.538691
17 29.279 0.623171
18 38.462 0.722539
19 38.053 0.718727
20 14.606 0.385451
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.323015
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -2.0 -0.6 1.8 -0.8 -0.9
-0.3 -0.9 -0.1 0.5 -0.9 -1.0
0.2 0.9 0.5 -0.5 -0.2 0.5
-0.5 -0.9 0.8 -0.1 1.0 1.0
-0.3 -0.6 0.1 0.5 0.2 0.4
-0.3 0.6 -0.5 -2.3 -0.2 -0.3
-0.2 -1.0 0.9 1.0 0.9 -1.0
-0.1
Chi-square with 42 degrees of freedom:29.729242
z-score=-1.338849, p-value=0.077438
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_04:31
Test no p-value
1 0.017994
2 0.012126
3 0.903047
4 0.037140
5 0.185072
6 0.155379
7 0.897335
8 0.368296
9 0.854424
10 0.315908
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.056407
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_04:31:
(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 66537 0.25 66655 0.00
3 25000.00 25122 0.60 25110 0.48
4 6666.67 6683 0.04 6547 2.15
5 1388.89 1380 0.06 1451 2.78
6 238.10 234 0.07 197 7.09
7 34.72 39 0.53 35 0.00
8 4.96 4 0.19 4 0.19
p=0.05709 p=0.95182
Number of rngs required: 688368, p-value: 0.484
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_04:31
No. of wins: Observed Expected
98417 98585.9
z-score=-0.755, pvalue=0.22505
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66808 66666.7 0.300 0.300
2 37709 37654.3 0.079 0.379
3 26838 26954.7 0.506 0.885
4 19167 19313.5 1.111 1.995
5 13895 13851.4 0.137 2.132
6 9883 9943.5 0.369 2.501
7 7225 7145.0 0.895 3.396
8 5080 5139.1 0.679 4.075
9 3694 3699.9 0.009 4.084
10 2600 2666.3 1.648 5.733
11 1869 1923.3 1.535 7.268
12 1448 1388.7 2.529 9.796
13 1064 1003.7 3.621 13.417
14 720 726.1 0.052 13.469
15 536 525.8 0.196 13.666
16 425 381.2 5.045 18.710
17 266 276.5 0.402 19.112
18 208 200.8 0.256 19.368
19 148 146.0 0.028 19.396
20 133 106.2 6.754 26.150
21 284 287.1 0.034 26.184
Chisq= 26.18 for 20 degrees of freedom, p= 0.84018
SUMMARY of craptest
p-value for no. of wins: 0.225054
p-value for throws/game: 0.840175
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_04:31
No. of wins: Observed Expected
98800 98585.9
z-score= 0.958, pvalue=0.83091
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66784 66666.7 0.207 0.207
2 37602 37654.3 0.073 0.279
3 27000 26954.7 0.076 0.355
4 19440 19313.5 0.829 1.184
5 13892 13851.4 0.119 1.303
6 9748 9943.5 3.845 5.149
7 7027 7145.0 1.950 7.098
8 5153 5139.1 0.038 7.136
9 3788 3699.9 2.099 9.235
10 2599 2666.3 1.699 10.934
11 1863 1923.3 1.892 12.826
12 1379 1388.7 0.068 12.895
13 1034 1003.7 0.914 13.808
14 706 726.1 0.559 14.367
15 550 525.8 1.110 15.478
16 387 381.2 0.090 15.567
17 282 276.5 0.108 15.675
18 219 200.8 1.644 17.319
19 150 146.0 0.110 17.430
20 114 106.2 0.571 18.000
21 283 287.1 0.059 18.059
Chisq= 18.06 for 20 degrees of freedom, p= 0.41648
SUMMARY of craptest
p-value for no. of wins: 0.830909
p-value for throws/game: 0.416480
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0068,0.0093,0.0121,0.0180,0.0273,0.0279,0.0327,0.0343,0.0353,
0.0371,0.0371,0.0453,0.0456,0.0460,0.0499,0.0551,0.0564,0.0571,0.0571,
0.0705,0.0774,0.0776,0.0916,0.0954,0.0974,0.0987,0.1036,0.1053,0.1088,
0.1179,0.1215,0.1314,0.1329,0.1512,0.1516,0.1519,0.1554,0.1629,0.1634,
0.1702,0.1842,0.1851,0.1855,0.1887,0.1895,0.1897,0.1908,0.1980,0.2014,
0.2036,0.2065,0.2067,0.2135,0.2145,0.2170,0.2176,0.2201,0.2205,0.2225,
0.2243,0.2243,0.2247,0.2251,0.2283,0.2298,0.2421,0.2464,0.2467,0.2485,
0.2546,0.2555,0.2616,0.2692,0.2767,0.2783,0.2832,0.2855,0.2993,0.3033,
0.3067,0.3108,0.3129,0.3156,0.3159,0.3172,0.3230,0.3241,0.3283,0.3337,
0.3404,0.3449,0.3457,0.3511,0.3525,0.3577,0.3616,0.3628,0.3641,0.3647,
0.3683,0.3686,0.3746,0.3746,0.3758,0.3777,0.3797,0.3852,0.3855,0.3859,
0.3893,0.3901,0.3921,0.3940,0.3949,0.3992,0.3995,0.4058,0.4059,0.4088,
0.4121,0.4132,0.4165,0.4179,0.4203,0.4264,0.4296,0.4329,0.4347,0.4403,
0.4433,0.4591,0.4673,0.4679,0.4703,0.4756,0.4790,0.4839,0.4909,0.4981,
0.5053,0.5067,0.5226,0.5260,0.5267,0.5302,0.5341,0.5360,0.5372,0.5387,
0.5413,0.5579,0.5669,0.5686,0.5703,0.5725,0.5784,0.5837,0.5848,0.5883,
0.5976,0.5981,0.5984,0.6020,0.6051,0.6191,0.6227,0.6232,0.6235,0.6235,
0.6242,0.6297,0.6348,0.6501,0.6522,0.6535,0.6558,0.6625,0.6663,0.6773,
0.6781,0.6814,0.6843,0.6845,0.6856,0.6886,0.6952,0.6989,0.7140,0.7161,
0.7171,0.7187,0.7212,0.7225,0.7309,0.7319,0.7379,0.7387,0.7393,0.7476,
0.7491,0.7530,0.7533,0.7577,0.7584,0.7667,0.7751,0.7766,0.7825,0.7829,
0.7874,0.7967,0.8003,0.8013,0.8041,0.8047,0.8079,0.8091,0.8104,0.8132,
0.8137,0.8183,0.8194,0.8248,0.8256,0.8284,0.8309,0.8352,0.8360,0.8402,
0.8489,0.8525,0.8541,0.8544,0.8584,0.8585,0.8737,0.8773,0.8814,0.8825,
0.8827,0.8829,0.8867,0.8938,0.8973,0.9018,0.9030,0.9058,0.9069,0.9077,
0.9124,0.9206,0.9326,0.9337,0.9364,0.9516,0.9518,0.9589,0.9691,0.9700,
0.9732,0.9751,0.9766,0.9793,0.9800,0.9874,0.9875,0.9889,0.9932,
Overall p-value after applying KStest on 269 p-values = 0.926402
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.