RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_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 15.86 14.7955 0.389793
2 to 25 15.78 24.5743 0.895348
3 to 26 15.45 22.9704 0.849784
4 to 27 15.56 27.2991 0.946175
5 to 28 16.08 8.9700 0.058802
6 to 29 15.80 28.3813 0.959324
7 to 30 15.58 26.0277 0.926042
8 to 31 15.74 34.6354 0.993056
9 to 32 15.63 18.9140 0.666510
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.003938
Tough bday spacings test for dh-ranFile-2018-06-18_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 8 35 67 102 94 78 51 40 12 9 4
(O-E)^2/E 0.1 0.1 0.5 0.2 0.1 0.0 0.0 3.5 0.6 0.9 0.0
Birthday Spacings: Sum(O-E)^2/E= 6.042, p= 0.188
RESULTS OF GCD FOR dh-ranFile-2018-06-18_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.211411
p-value, dist. of gcd's: 0.325371
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.966 0.163 0.883 0.604 0.261 0.578 0.360 0.783
Bits 8 to 15---> 0.543 0.196 0.614 0.495 0.585 0.987 0.142 0.264
Bits 16 to 23---> 0.432 0.506 0.271 0.276 0.468 0.372 0.260 0.083
Bits 24 to 31---> 0.767 0.146 0.704 0.801 0.489 0.002 0.320 0.877
KS test for the above 32 p values: 0.249
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_01:31,
p-values for 5 runs: 0.0706, 0.0860, 0.8368, 0.5824, 0.6980
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 230 211.4 1.633 1.633
r= 29 4934 5134.0 7.792 9.425
r= 30 23158 23103.0 0.131 9.556
r= 31 11678 11551.5 1.385 10.941
chi-square = 10.941 with df = 3; p-value = 0.988
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 230 211.4 1.633 1.633
r= 30 5185 5134.0 0.506 2.140
r= 31 22928 23103.0 1.326 3.466
r= 32 11657 11551.5 0.963 4.429
chi-square = 4.429 with df = 3; p-value = 0.781
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_01:31
b-rank test for bits 1 to 8, p=0.49789
b-rank test for bits 2 to 9, p=0.60178
b-rank test for bits 3 to 10, p=0.20677
b-rank test for bits 4 to 11, p=0.39737
b-rank test for bits 5 to 12, p=0.75531
b-rank test for bits 6 to 13, p=0.43273
b-rank test for bits 7 to 14, p=0.80487
b-rank test for bits 8 to 15, p=0.87508
b-rank test for bits 9 to 16, p=0.56852
b-rank test for bits 10 to 17, p=0.79422
b-rank test for bits 11 to 18, p=0.73572
b-rank test for bits 12 to 19, p=0.61166
b-rank test for bits 13 to 20, p=0.99080
b-rank test for bits 14 to 21, p=0.46850
b-rank test for bits 15 to 22, p=0.29101
b-rank test for bits 16 to 23, p=0.57577
b-rank test for bits 17 to 24, p=0.35302
b-rank test for bits 18 to 25, p=0.09936
b-rank test for bits 19 to 26, p=0.30224
b-rank test for bits 20 to 27, p=0.45329
b-rank test for bits 21 to 28, p=0.61586
b-rank test for bits 22 to 29, p=0.43595
b-rank test for bits 23 to 30, p=0.23987
b-rank test for bits 24 to 31, p=0.69269
b-rank test for bits 25 to 32, p=0.93802
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 = 0.336998
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_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 141574 -0.78 0.216672
2 141971 0.14 0.557285
3 142795 2.07 0.980742
4 142323 0.97 0.833108
5 141527 -0.89 0.185850
6 142011 0.24 0.593884
7 142303 0.92 0.821159
8 142532 1.45 0.927143
9 141879 -0.07 0.471753
10 141943 0.08 0.531352
11 141770 -0.33 0.372387
12 142114 0.48 0.683746
13 142077 0.39 0.652379
14 142362 1.06 0.854890
15 142100 0.45 0.672017
16 142187 0.65 0.741754
17 141821 -0.21 0.418248
18 142122 0.50 0.690368
19 141817 -0.22 0.414601
20 141616 -0.69 0.246561
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_01:31
Bits used No. missing words z-score p-value
23 to 32 141992 0.2851 0.612204
22 to 31 142025 0.3989 0.655003
21 to 30 142153 0.8402 0.799614
20 to 29 141896 -0.0460 0.481669
19 to 28 141351 -1.9253 0.027097
18 to 27 142191 0.9713 0.834295
17 to 26 142357 1.5437 0.938668
16 to 25 141751 -0.5460 0.292545
15 to 24 142097 0.6471 0.741229
14 to 23 142269 1.2402 0.892557
13 to 22 142077 0.5782 0.718426
12 to 21 142169 0.8954 0.814717
11 to 20 141962 0.1816 0.572060
10 to 19 142121 0.7299 0.767273
9 to 18 142150 0.8299 0.796701
8 to 17 141937 0.0954 0.538007
7 to 16 142049 0.4816 0.684962
6 to 15 141950 0.1402 0.555765
5 to 14 141825 -0.2908 0.385605
4 to 13 142072 0.5609 0.712578
3 to 12 142097 0.6471 0.741229
2 to 11 142054 0.4989 0.691062
1 to 10 141884 -0.0873 0.465199
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_01:31
Bits used No. missing words z-score p-value
28 to 32 141773 -0.4621 0.321992
27 to 31 142114 0.6938 0.756095
26 to 30 141969 0.2023 0.580148
25 to 29 141523 -1.3096 0.095167
24 to 28 141865 -0.1503 0.440275
23 to 27 141821 -0.2994 0.382308
22 to 26 141833 -0.2587 0.397916
21 to 25 141799 -0.3740 0.354202
20 to 24 142129 0.7446 0.771757
19 to 23 142025 0.3921 0.652509
18 to 22 141893 -0.0554 0.477928
17 to 21 141643 -0.9028 0.183312
16 to 20 141418 -1.6655 0.047904
15 to 19 141532 -1.2791 0.100434
14 to 18 141888 -0.0723 0.471180
13 to 17 142207 1.0091 0.843525
12 to 16 141582 -1.1096 0.133587
11 to 15 141898 -0.0384 0.484682
10 to 14 141177 -2.4825 0.006524
9 to 13 141986 0.2599 0.602529
8 to 12 141965 0.1887 0.574841
7 to 11 141189 -2.4418 0.007307
6 to 10 141614 -1.0011 0.158385
5 to 9 141641 -0.9096 0.181519
4 to 8 142305 1.3413 0.910081
3 to 7 142227 1.0768 0.859226
2 to 6 142064 0.5243 0.699967
1 to 5 141514 -1.3401 0.090106
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_01:31
Bits used No. missing words z-score p-value
31 to 32 141383 -1.5526 0.060260
30 to 31 141756 -0.4523 0.325526
29 to 30 141584 -0.9597 0.168609
28 to 29 142047 0.4061 0.657668
27 to 28 141937 0.0816 0.532527
26 to 27 142133 0.6598 0.745307
25 to 26 142279 1.0905 0.862247
24 to 25 142153 0.7188 0.763865
23 to 24 142073 0.4828 0.685382
22 to 23 141978 0.2026 0.580263
21 to 22 142901 2.9253 0.998279
20 to 21 141930 0.0610 0.524310
19 to 20 142092 0.5388 0.705005
18 to 19 141553 -1.0511 0.146602
17 to 18 141758 -0.4464 0.327654
16 to 17 142068 0.4681 0.680127
15 to 16 141690 -0.6470 0.258819
14 to 15 142018 0.3206 0.625728
13 to 14 142029 0.3530 0.637959
12 to 13 141862 -0.1396 0.444482
11 to 12 142703 2.3412 0.990389
10 to 11 141752 -0.4641 0.321288
9 to 10 141639 -0.7974 0.212600
8 to 9 141681 -0.6735 0.250302
7 to 8 141880 -0.0865 0.465527
6 to 7 142284 1.1052 0.865468
5 to 6 141977 0.1996 0.579110
4 to 5 142082 0.5094 0.694747
3 to 4 142306 1.1701 0.879023
2 to 3 141798 -0.3284 0.371302
1 to 2 141587 -0.9508 0.170846
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2594.24 1.333 0.908684
Test results for specific bytes for dh-ranFile-2018-06-18_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2602.53 1.450 0.926478
2 to 9 2437.13 -0.889 0.186969
3 to 10 2517.26 0.244 0.596414
4 to 11 2447.73 -0.739 0.229897
5 to 12 2442.29 -0.816 0.207203
6 to 13 2537.54 0.531 0.702261
7 to 14 2447.91 -0.737 0.230674
8 to 15 2514.33 0.203 0.580276
9 to 16 2414.78 -1.205 0.114062
10 to 17 2528.14 0.398 0.654693
11 to 18 2490.75 -0.131 0.447957
12 to 19 2460.75 -0.555 0.289403
13 to 20 2431.09 -0.974 0.164911
14 to 21 2517.48 0.247 0.597623
15 to 22 2579.74 1.128 0.870281
16 to 23 2449.16 -0.719 0.236081
17 to 24 2461.35 -0.547 0.292332
18 to 25 2454.03 -0.650 0.257798
19 to 26 2573.83 1.044 0.851787
20 to 27 2498.63 -0.019 0.492284
21 to 28 2522.66 0.321 0.625709
22 to 29 2393.90 -1.500 0.066748
23 to 30 2587.18 1.233 0.891199
24 to 31 2649.11 2.109 0.982514
25 to 32 2399.78 -1.417 0.078201
CDPARK for dh-ranFile-2018-06-18_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
3528 0.2283 0.590298
3536 0.5936 0.723613
3571 2.1918 0.985802
3510 -0.5936 0.276387
3527 0.1826 0.572463
3498 -1.1416 0.126820
3534 0.5023 0.692266
3537 0.6393 0.738676
3528 0.2283 0.590298
3502 -0.9589 0.168804
Square side=100, avg. no. parked=3527.10 sample std.=19.81
p-value of the KSTEST for those 10 p-values: 0.671042
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_01:31
0.1457,0.1237,0.0150,0.1347,0.4314,0.9637,0.5148,0.1427,0.6400,0.3007,
The KS test for those 10 p-values: 0.098077
The 3DSPHERES test for dh-ranFile-2018-06-18_01:31
sample no r^3 equiv. uni.
1 21.615 0.513491
2 9.109 0.261863
3 17.774 0.447042
4 30.139 0.633819
5 4.303 0.133630
6 20.579 0.496390
7 40.533 0.741047
8 44.894 0.776082
9 86.252 0.943587
10 78.560 0.927099
11 50.234 0.812591
12 2.035 0.065598
13 97.660 0.961432
14 60.187 0.865507
15 38.839 0.726006
16 15.026 0.393986
17 56.107 0.845913
18 20.304 0.491767
19 25.384 0.570932
20 91.633 0.952851
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.077052
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.2 -0.8 -1.0 -0.9 -0.1
-0.0 1.4 0.6 0.7 1.1 0.7
-1.0 -1.8 0.8 1.0 0.4 0.2
-1.6 0.4 -0.8 -0.4 -0.6 -0.2
0.6 1.9 0.0 -0.0 -1.2 -0.1
-1.6 0.1 0.0 0.4 -1.0 2.4
1.0 0.8 0.5 2.1 -1.3 1.0
-1.1
Chi-square with 42 degrees of freedom:43.471534
z-score=0.160558, p-value=0.591471
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_01:31
Test no p-value
1 0.294374
2 0.095886
3 0.283965
4 0.516444
5 0.126741
6 0.028450
7 0.106453
8 0.063248
9 0.020991
10 0.359076
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000622
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_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 66646 0.01 66520 0.32
3 25000.00 25021 0.02 25132 0.70
4 6666.67 6708 0.26 6657 0.01
5 1388.89 1363 0.48 1398 0.06
6 238.10 223 0.96 251 0.70
7 34.72 34 0.01 36 0.05
8 4.96 4 0.19 5 0.00
p=0.07315 p=0.06622
Number of rngs required: 688714, p-value: 0.640
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_01:31
No. of wins: Observed Expected
98275 98585.9
z-score=-1.390, pvalue=0.08221
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66388 66666.7 1.165 1.165
2 37624 37654.3 0.024 1.189
3 27004 26954.7 0.090 1.279
4 19476 19313.5 1.368 2.647
5 13867 13851.4 0.018 2.665
6 9937 9943.5 0.004 2.669
7 7262 7145.0 1.915 4.584
8 5130 5139.1 0.016 4.600
9 3617 3699.9 1.856 6.456
10 2723 2666.3 1.206 7.662
11 1880 1923.3 0.976 8.638
12 1387 1388.7 0.002 8.640
13 1057 1003.7 2.829 11.469
14 766 726.1 2.188 13.657
15 531 525.8 0.051 13.708
16 374 381.2 0.134 13.842
17 269 276.5 0.206 14.047
18 187 200.8 0.952 15.000
19 138 146.0 0.437 15.436
20 95 106.2 1.184 16.621
21 288 287.1 0.003 16.623
Chisq= 16.62 for 20 degrees of freedom, p= 0.32272
SUMMARY of craptest
p-value for no. of wins: 0.082213
p-value for throws/game: 0.322719
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_01:31
No. of wins: Observed Expected
98629 98585.9
z-score= 0.193, pvalue=0.57650
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66664 66666.7 0.000 0.000
2 37913 37654.3 1.777 1.777
3 26810 26954.7 0.777 2.554
4 19429 19313.5 0.691 3.246
5 13781 13851.4 0.358 3.604
6 9887 9943.5 0.322 3.925
7 7061 7145.0 0.988 4.913
8 5067 5139.1 1.011 5.924
9 3699 3699.9 0.000 5.924
10 2700 2666.3 0.426 6.350
11 1930 1923.3 0.023 6.373
12 1444 1388.7 2.199 8.572
13 956 1003.7 2.268 10.840
14 718 726.1 0.091 10.932
15 542 525.8 0.497 11.429
16 372 381.2 0.220 11.648
17 260 276.5 0.989 12.637
18 229 200.8 3.951 16.589
19 144 146.0 0.027 16.616
20 110 106.2 0.135 16.751
21 284 287.1 0.034 16.784
Chisq= 16.78 for 20 degrees of freedom, p= 0.33308
SUMMARY of craptest
p-value for no. of wins: 0.576502
p-value for throws/game: 0.333079
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0024,0.0039,0.0065,0.0073,0.0150,0.0210,0.0271,0.0285,0.0479,
0.0588,0.0603,0.0632,0.0656,0.0662,0.0667,0.0706,0.0732,0.0771,0.0782,
0.0822,0.0831,0.0860,0.0901,0.0952,0.0959,0.0981,0.0994,0.1004,0.1065,
0.1141,0.1237,0.1267,0.1268,0.1336,0.1336,0.1347,0.1418,0.1427,0.1457,
0.1458,0.1466,0.1584,0.1628,0.1649,0.1686,0.1688,0.1708,0.1815,0.1833,
0.1858,0.1870,0.1883,0.1965,0.2068,0.2072,0.2114,0.2126,0.2167,0.2299,
0.2307,0.2361,0.2399,0.2466,0.2486,0.2503,0.2578,0.2588,0.2602,0.2611,
0.2619,0.2644,0.2705,0.2763,0.2764,0.2840,0.2894,0.2910,0.2923,0.2925,
0.2944,0.3007,0.3022,0.3197,0.3213,0.3220,0.3227,0.3254,0.3255,0.3277,
0.3331,0.3370,0.3530,0.3542,0.3591,0.3595,0.3713,0.3723,0.3724,0.3823,
0.3856,0.3898,0.3940,0.3974,0.3979,0.4146,0.4182,0.4314,0.4318,0.4327,
0.4359,0.4403,0.4445,0.4470,0.4480,0.4533,0.4652,0.4655,0.4679,0.4685,
0.4712,0.4718,0.4779,0.4817,0.4847,0.4893,0.4918,0.4923,0.4945,0.4964,
0.4979,0.5062,0.5135,0.5148,0.5164,0.5243,0.5314,0.5325,0.5380,0.5425,
0.5558,0.5573,0.5685,0.5709,0.5721,0.5725,0.5748,0.5758,0.5765,0.5779,
0.5791,0.5801,0.5803,0.5803,0.5824,0.5853,0.5903,0.5903,0.5915,0.5939,
0.5964,0.5976,0.6018,0.6025,0.6037,0.6117,0.6122,0.6141,0.6159,0.6257,
0.6257,0.6338,0.6380,0.6399,0.6400,0.6524,0.6525,0.6547,0.6550,0.6577,
0.6665,0.6710,0.6720,0.6801,0.6837,0.6850,0.6854,0.6904,0.6911,0.6923,
0.6927,0.6947,0.6980,0.7000,0.7023,0.7042,0.7050,0.7126,0.7184,0.7236,
0.7260,0.7357,0.7387,0.7410,0.7412,0.7412,0.7418,0.7453,0.7553,0.7561,
0.7639,0.7666,0.7673,0.7718,0.7761,0.7813,0.7834,0.7942,0.7967,0.7996,
0.8006,0.8049,0.8126,0.8147,0.8212,0.8331,0.8343,0.8368,0.8435,0.8459,
0.8498,0.8518,0.8549,0.8592,0.8622,0.8655,0.8655,0.8703,0.8751,0.8772,
0.8790,0.8825,0.8912,0.8926,0.8953,0.9087,0.9101,0.9260,0.9265,0.9271,
0.9271,0.9380,0.9387,0.9436,0.9462,0.9529,0.9593,0.9614,0.9637,0.9657,
0.9807,0.9825,0.9858,0.9874,0.9879,0.9904,0.9908,0.9931,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.913449
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.