RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.66 13.4865 0.296939
2 to 25 15.67 33.0472 0.988883
3 to 26 15.99 12.5880 0.236702
4 to 27 15.84 25.6102 0.918139
5 to 28 15.61 21.1078 0.778494
6 to 29 15.65 15.4626 0.437800
7 to 30 15.64 25.2993 0.911792
8 to 31 15.93 19.4359 0.695907
9 to 32 16.12 12.2089 0.212674
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.310868
Tough bday spacings test for dh-ranFile-2018-06-16_20:31: 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 6 29 87 84 95 92 57 33 11 3 3
(O-E)^2/E 1.1 1.6 2.6 1.9 0.1 2.5 0.5 0.4 1.0 2.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 13.782, p= 0.817
RESULTS OF GCD FOR dh-ranFile-2018-06-16_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.106371
p-value, dist. of gcd's: 0.224095
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.543 0.905 0.626 0.403 0.491 0.893 0.958 0.619
Bits 8 to 15---> 0.798 0.475 0.911 0.222 0.815 0.011 0.792 0.592
Bits 16 to 23---> 0.844 0.566 0.190 0.593 0.608 0.482 0.539 0.560
Bits 24 to 31---> 0.502 0.037 0.596 0.306 0.729 0.580 0.168 0.925
KS test for the above 32 p values: 0.866
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_20:31,
p-values for 5 runs: 0.6277, 0.5985, 0.5814, 0.5165, 0.5071
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 197 211.4 0.983 0.983
r= 29 5172 5134.0 0.281 1.264
r= 30 22896 23103.0 1.856 3.120
r= 31 11735 11551.5 2.914 6.034
chi-square = 6.034 with df = 3; p-value = 0.890
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 212 211.4 0.002 0.002
r= 30 5063 5134.0 0.982 0.984
r= 31 23126 23103.0 0.023 1.007
r= 32 11599 11551.5 0.195 1.202
chi-square = 1.202 with df = 3; p-value = 0.247
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_20:31
b-rank test for bits 1 to 8, p=0.26422
b-rank test for bits 2 to 9, p=0.45986
b-rank test for bits 3 to 10, p=0.64142
b-rank test for bits 4 to 11, p=0.43763
b-rank test for bits 5 to 12, p=0.30676
b-rank test for bits 6 to 13, p=0.96459
b-rank test for bits 7 to 14, p=0.03158
b-rank test for bits 8 to 15, p=0.92290
b-rank test for bits 9 to 16, p=0.58112
b-rank test for bits 10 to 17, p=0.76090
b-rank test for bits 11 to 18, p=0.75356
b-rank test for bits 12 to 19, p=0.52599
b-rank test for bits 13 to 20, p=0.69232
b-rank test for bits 14 to 21, p=0.80130
b-rank test for bits 15 to 22, p=0.08294
b-rank test for bits 16 to 23, p=0.39673
b-rank test for bits 17 to 24, p=0.04406
b-rank test for bits 18 to 25, p=0.60344
b-rank test for bits 19 to 26, p=0.68980
b-rank test for bits 20 to 27, p=0.09375
b-rank test for bits 21 to 28, p=0.87187
b-rank test for bits 22 to 29, p=0.25824
b-rank test for bits 23 to 30, p=0.23344
b-rank test for bits 24 to 31, p=0.94680
b-rank test for bits 25 to 32, p=0.65263
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 = 0.975404
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_20:31
(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 141769 -0.33 0.371504
2 141802 -0.25 0.400996
3 141765 -0.34 0.367976
4 142472 1.31 0.905686
5 141672 -0.55 0.289615
6 141149 -1.78 0.037828
7 141767 -0.33 0.369738
8 141425 -1.13 0.128899
9 141619 -0.68 0.248778
10 142294 0.90 0.815610
11 141234 -1.58 0.057297
12 141960 0.12 0.547120
13 141616 -0.69 0.246561
14 141741 -0.39 0.347051
15 142393 1.13 0.870777
16 142075 0.39 0.650651
17 141620 -0.68 0.249519
18 141995 0.20 0.579324
19 143218 3.06 0.998885
20 141289 -1.45 0.073617
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_20:31
Bits used No. missing words z-score p-value
23 to 32 141704 -0.7080 0.239462
22 to 31 142253 1.1851 0.882005
21 to 30 141569 -1.1736 0.120287
20 to 29 141824 -0.2942 0.384287
19 to 28 141879 -0.1046 0.458352
18 to 27 141787 -0.4218 0.336575
17 to 26 141674 -0.8115 0.208544
16 to 25 141894 -0.0529 0.478921
15 to 24 141730 -0.6184 0.268163
14 to 23 141959 0.1713 0.567997
13 to 22 141797 -0.3873 0.349251
12 to 21 141775 -0.4632 0.321608
11 to 20 141990 0.2782 0.609560
10 to 19 141537 -1.2839 0.099589
9 to 18 141982 0.2506 0.598933
8 to 17 141905 -0.0149 0.494044
7 to 16 141390 -1.7908 0.036663
6 to 15 141479 -1.4839 0.068918
5 to 14 142134 0.7747 0.780749
4 to 13 142262 1.2161 0.888027
3 to 12 142002 0.3196 0.625346
2 to 11 141659 -0.8632 0.194012
1 to 10 142055 0.5023 0.692275
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_20:31
Bits used No. missing words z-score p-value
28 to 32 141936 0.0904 0.536018
27 to 31 141621 -0.9774 0.164188
26 to 30 141575 -1.1333 0.128540
25 to 29 141464 -1.5096 0.065574
24 to 28 141568 -1.1571 0.123626
23 to 27 142068 0.5379 0.704665
22 to 26 141693 -0.7333 0.231681
21 to 25 141919 0.0328 0.513075
20 to 24 141563 -1.1740 0.120198
19 to 23 142132 0.7548 0.774820
18 to 22 141406 -1.7062 0.043985
17 to 21 142098 0.6396 0.738770
16 to 20 142372 1.5684 0.941603
15 to 19 141678 -0.7842 0.216470
14 to 18 141695 -0.7265 0.233753
13 to 17 141696 -0.7232 0.234793
12 to 16 141842 -0.2282 0.409731
11 to 15 141775 -0.4554 0.324427
10 to 14 142040 0.4429 0.671099
9 to 13 141844 -0.2215 0.412368
8 to 12 141770 -0.4723 0.318355
7 to 11 141720 -0.6418 0.260503
6 to 10 141924 0.0497 0.519831
5 to 9 141703 -0.6994 0.242144
4 to 8 141994 0.2870 0.612950
3 to 7 141900 -0.0316 0.487385
2 to 6 142293 1.3006 0.903298
1 to 5 142258 1.1819 0.881384
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_20:31
Bits used No. missing words z-score p-value
31 to 32 141290 -1.8269 0.033855
30 to 31 141855 -0.1603 0.436336
29 to 30 141692 -0.6411 0.260732
28 to 29 141683 -0.6676 0.252182
27 to 28 141279 -1.8594 0.031487
26 to 27 141480 -1.2665 0.102674
25 to 26 142081 0.5064 0.693713
24 to 25 141758 -0.4464 0.327654
23 to 24 142415 1.4917 0.932105
22 to 23 141749 -0.4729 0.318125
21 to 22 141866 -0.1278 0.449147
20 to 21 141800 -0.3225 0.373534
19 to 20 141568 -1.0069 0.156998
18 to 19 141694 -0.6352 0.262652
17 to 18 142171 0.7719 0.779910
16 to 17 142425 1.5212 0.935889
15 to 16 141993 0.2468 0.597474
14 to 15 141990 0.2380 0.594046
13 to 14 141849 -0.1780 0.429375
12 to 13 141704 -0.6057 0.272359
11 to 12 141349 -1.6529 0.049177
10 to 11 141815 -0.2783 0.390407
9 to 10 141357 -1.6293 0.051626
8 to 9 141443 -1.3756 0.084472
7 to 8 141997 0.2586 0.602033
6 to 7 142330 1.2409 0.892681
5 to 6 142215 0.9017 0.816387
4 to 5 141636 -0.8063 0.210040
3 to 4 141460 -1.3255 0.092510
2 to 3 142671 2.2468 0.987674
1 to 2 141545 -1.0747 0.141250
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2572.07 1.019 0.845956
Test results for specific bytes for dh-ranFile-2018-06-16_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2569.23 0.979 0.836217
2 to 9 2536.15 0.511 0.695411
3 to 10 2534.71 0.491 0.688223
4 to 11 2398.36 -1.437 0.075311
5 to 12 2560.99 0.863 0.805801
6 to 13 2439.21 -0.860 0.194966
7 to 14 2390.34 -1.551 0.060470
8 to 15 2557.08 0.807 0.790242
9 to 16 2520.18 0.285 0.612344
10 to 17 2547.88 0.677 0.750844
11 to 18 2581.34 1.150 0.874989
12 to 19 2463.22 -0.520 0.301478
13 to 20 2443.81 -0.795 0.213397
14 to 21 2507.91 0.112 0.544525
15 to 22 2416.35 -1.183 0.118415
16 to 23 2467.60 -0.458 0.323383
17 to 24 2534.01 0.481 0.684720
18 to 25 2522.51 0.318 0.624895
19 to 26 2558.12 0.822 0.794453
20 to 27 2518.61 0.263 0.603805
21 to 28 2605.91 1.498 0.932915
22 to 29 2424.07 -1.074 0.141456
23 to 30 2467.73 -0.456 0.324081
24 to 31 2551.10 0.723 0.765043
25 to 32 2371.59 -1.816 0.034680
CDPARK for dh-ranFile-2018-06-16_20:31: 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
3523 0.0000 0.500000
3548 1.1416 0.873180
3537 0.6393 0.738676
3500 -1.0502 0.146807
3525 0.0913 0.536383
3495 -1.2785 0.100530
3516 -0.3196 0.374623
3579 2.5571 0.994722
3502 -0.9589 0.168804
3510 -0.5936 0.276387
Square side=100, avg. no. parked=3523.50 sample std.=24.35
p-value of the KSTEST for those 10 p-values: 0.840630
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_20:31
0.8074,0.3065,0.4199,0.8880,0.4826,0.5059,0.3495,0.8932,0.8589,0.8732,
The KS test for those 10 p-values: 0.137705
The 3DSPHERES test for dh-ranFile-2018-06-16_20:31
sample no r^3 equiv. uni.
1 0.667 0.021983
2 7.156 0.212213
3 10.070 0.285128
4 0.141 0.004680
5 14.595 0.385216
6 9.165 0.263251
7 59.801 0.863763
8 20.671 0.497946
9 0.069 0.002309
10 0.625 0.020618
11 27.598 0.601450
12 2.107 0.067836
13 11.178 0.311051
14 1.666 0.054031
15 69.037 0.899865
16 14.465 0.382546
17 26.848 0.591359
18 35.906 0.697864
19 48.554 0.801798
20 49.869 0.810298
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.036762
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -0.7 0.3 0.0 -0.7 1.1
-0.6 0.7 0.5 1.7 2.3 -1.5
-1.9 -1.2 0.2 0.5 1.1 0.4
-1.3 -0.2 0.1 1.1 0.3 2.0
-0.2 -0.8 -2.3 -0.6 -1.7 0.2
-0.2 -2.0 -0.3 3.7 -0.8 0.6
0.0 -2.0 -0.8 1.0 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:64.652139
z-score=2.471551, p-value=0.986084
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_20:31
Test no p-value
1 0.601753
2 0.466968
3 0.056348
4 0.030078
5 0.405583
6 0.494427
7 0.036192
8 0.613665
9 0.259837
10 0.040750
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.021354
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_20:31:
(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 66805 0.29 66503 0.40
3 25000.00 25021 0.02 25207 1.71
4 6666.67 6522 3.14 6670 0.00
5 1388.89 1374 0.16 1346 1.32
6 238.10 239 0.00 242 0.06
7 34.72 36 0.05 26 2.19
8 4.96 2 1.77 5 0.00
p=0.50892 p=0.54195
Number of rngs required: 688561, p-value: 0.572
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_20:31
No. of wins: Observed Expected
98803 98585.9
z-score= 0.971, pvalue=0.83427
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66668 66666.7 0.000 0.000
2 37783 37654.3 0.440 0.440
3 26772 26954.7 1.239 1.679
4 19092 19313.5 2.539 4.218
5 13921 13851.4 0.350 4.568
6 9979 9943.5 0.126 4.694
7 7301 7145.0 3.405 8.099
8 5123 5139.1 0.050 8.149
9 3709 3699.9 0.023 8.172
10 2677 2666.3 0.043 8.215
11 1887 1923.3 0.686 8.901
12 1453 1388.7 2.973 11.874
13 1017 1003.7 0.176 12.050
14 734 726.1 0.085 12.135
15 526 525.8 0.000 12.135
16 382 381.2 0.002 12.137
17 261 276.5 0.873 13.010
18 194 200.8 0.232 13.243
19 134 146.0 0.984 14.226
20 96 106.2 0.982 15.209
21 291 287.1 0.053 15.261
Chisq= 15.26 for 20 degrees of freedom, p= 0.23874
SUMMARY of craptest
p-value for no. of wins: 0.834271
p-value for throws/game: 0.238744
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_20:31
No. of wins: Observed Expected
98996 98585.9
z-score= 1.834, pvalue=0.96670
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67073 66666.7 2.477 2.477
2 37861 37654.3 1.134 3.611
3 26614 26954.7 4.307 7.918
4 19248 19313.5 0.222 8.140
5 13701 13851.4 1.633 9.774
6 9890 9943.5 0.288 10.062
7 7152 7145.0 0.007 10.069
8 5040 5139.1 1.910 11.979
9 3721 3699.9 0.121 12.099
10 2698 2666.3 0.377 12.476
11 1899 1923.3 0.308 12.784
12 1392 1388.7 0.008 12.792
13 1064 1003.7 3.621 16.413
14 772 726.1 2.896 19.309
15 522 525.8 0.028 19.337
16 375 381.2 0.099 19.436
17 268 276.5 0.264 19.700
18 172 200.8 4.139 23.838
19 170 146.0 3.951 27.789
20 104 106.2 0.046 27.835
21 264 287.1 1.861 29.696
Chisq= 29.70 for 20 degrees of freedom, p= 0.92507
SUMMARY of craptest
p-value for no. of wins: 0.966702
p-value for throws/game: 0.925070
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0023,0.0047,0.0115,0.0206,0.0214,0.0220,0.0301,0.0315,0.0316,0.0339,
0.0347,0.0362,0.0367,0.0368,0.0374,0.0378,0.0407,0.0440,0.0441,0.0492,
0.0516,0.0540,0.0563,0.0573,0.0605,0.0656,0.0678,0.0689,0.0736,0.0753,
0.0829,0.0845,0.0925,0.0937,0.0996,0.1005,0.1027,0.1064,0.1184,0.1202,
0.1203,0.1236,0.1285,0.1289,0.1377,0.1413,0.1415,0.1468,0.1570,0.1642,
0.1678,0.1688,0.1896,0.1940,0.1950,0.2085,0.2100,0.2122,0.2127,0.2134,
0.2165,0.2220,0.2241,0.2317,0.2334,0.2338,0.2348,0.2367,0.2387,0.2395,
0.2421,0.2466,0.2474,0.2488,0.2495,0.2522,0.2582,0.2598,0.2605,0.2607,
0.2627,0.2633,0.2642,0.2682,0.2724,0.2764,0.2851,0.2896,0.2969,0.3015,
0.3059,0.3065,0.3068,0.3109,0.3111,0.3181,0.3184,0.3216,0.3234,0.3241,
0.3244,0.3277,0.3366,0.3471,0.3493,0.3495,0.3680,0.3697,0.3715,0.3735,
0.3746,0.3825,0.3843,0.3852,0.3904,0.3967,0.4010,0.4031,0.4056,0.4097,
0.4124,0.4199,0.4294,0.4363,0.4376,0.4378,0.4491,0.4584,0.4599,0.4670,
0.4746,0.4789,0.4815,0.4826,0.4874,0.4907,0.4940,0.4944,0.4979,0.5000,
0.5016,0.5059,0.5071,0.5089,0.5131,0.5165,0.5198,0.5260,0.5360,0.5364,
0.5388,0.5419,0.5425,0.5445,0.5471,0.5602,0.5665,0.5680,0.5721,0.5793,
0.5803,0.5811,0.5814,0.5914,0.5923,0.5929,0.5940,0.5962,0.5975,0.5985,
0.5989,0.6014,0.6018,0.6020,0.6034,0.6038,0.6082,0.6096,0.6123,0.6130,
0.6137,0.6185,0.6249,0.6253,0.6257,0.6277,0.6414,0.6507,0.6526,0.6711,
0.6847,0.6882,0.6898,0.6923,0.6923,0.6937,0.6954,0.6959,0.6979,0.7047,
0.7289,0.7387,0.7388,0.7508,0.7536,0.7609,0.7650,0.7748,0.7785,0.7799,
0.7807,0.7902,0.7917,0.7945,0.7984,0.8013,0.8018,0.8058,0.8074,0.8103,
0.8152,0.8156,0.8164,0.8168,0.8343,0.8362,0.8406,0.8442,0.8460,0.8589,
0.8638,0.8655,0.8708,0.8719,0.8732,0.8732,0.8750,0.8814,0.8820,0.8880,
0.8880,0.8900,0.8927,0.8932,0.8934,0.8999,0.9033,0.9052,0.9057,0.9106,
0.9118,0.9181,0.9229,0.9251,0.9253,0.9321,0.9329,0.9359,0.9416,0.9468,
0.9583,0.9646,0.9667,0.9754,0.9861,0.9877,0.9889,0.9947,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.295066
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.