RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.82 12.2423 0.214751
2 to 25 15.78 18.9397 0.667995
3 to 26 15.45 21.6499 0.801439
4 to 27 15.83 26.9372 0.941005
5 to 28 15.67 21.4895 0.794844
6 to 29 15.69 16.0244 0.477892
7 to 30 15.78 15.2545 0.422845
8 to 31 15.72 32.2591 0.986030
9 to 32 16.04 12.4403 0.227229
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.370972
Tough bday spacings test for dh-ranFile-2018-07-03_06:31: 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 46 73 105 97 82 43 20 15 5 5
(O-E)^2/E 0.0 2.4 0.0 0.5 0.0 0.2 1.6 3.2 0.0 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 8.548, p= 0.425
RESULTS OF GCD FOR dh-ranFile-2018-07-03_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.516907
p-value, dist. of gcd's: 0.169019
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.568 0.382 0.421 0.326 0.722 0.527 0.819 0.071
Bits 8 to 15---> 0.912 0.606 0.320 0.317 0.317 0.613 0.825 0.444
Bits 16 to 23---> 0.465 0.198 0.853 0.391 0.434 0.858 0.200 0.716
Bits 24 to 31---> 0.821 0.494 0.705 0.154 0.333 0.877 0.864 0.791
KS test for the above 32 p values: 0.716
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_06:31,
p-values for 5 runs: 0.7930, 0.7752, 0.6965, 0.6253, 0.5828
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 227 211.4 1.148 1.148
r= 29 5176 5134.0 0.343 1.492
r= 30 23078 23103.0 0.027 1.519
r= 31 11519 11551.5 0.092 1.611
chi-square = 1.611 with df = 3; p-value = 0.343
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 212 211.4 0.002 0.002
r= 30 5110 5134.0 0.112 0.114
r= 31 23271 23103.0 1.221 1.335
r= 32 11407 11551.5 1.808 3.143
chi-square = 3.143 with df = 3; p-value = 0.630
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_06:31
b-rank test for bits 1 to 8, p=0.58542
b-rank test for bits 2 to 9, p=0.83856
b-rank test for bits 3 to 10, p=0.80063
b-rank test for bits 4 to 11, p=0.45925
b-rank test for bits 5 to 12, p=0.01929
b-rank test for bits 6 to 13, p=0.41515
b-rank test for bits 7 to 14, p=0.54991
b-rank test for bits 8 to 15, p=0.40760
b-rank test for bits 9 to 16, p=0.97014
b-rank test for bits 10 to 17, p=0.28954
b-rank test for bits 11 to 18, p=0.29469
b-rank test for bits 12 to 19, p=0.76773
b-rank test for bits 13 to 20, p=0.88440
b-rank test for bits 14 to 21, p=0.99565
b-rank test for bits 15 to 22, p=0.65955
b-rank test for bits 16 to 23, p=0.06964
b-rank test for bits 17 to 24, p=0.33422
b-rank test for bits 18 to 25, p=0.04946
b-rank test for bits 19 to 26, p=0.42958
b-rank test for bits 20 to 27, p=0.14987
b-rank test for bits 21 to 28, p=0.89057
b-rank test for bits 22 to 29, p=0.82303
b-rank test for bits 23 to 30, p=0.09061
b-rank test for bits 24 to 31, p=0.32834
b-rank test for bits 25 to 32, p=0.02634
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 = 0.764010
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_06:31
(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 141885 -0.06 0.477334
2 142281 0.87 0.807409
3 141942 0.08 0.530422
4 141811 -0.23 0.409146
5 142110 0.47 0.680413
6 142133 0.52 0.699371
7 142411 1.17 0.879427
8 141936 0.06 0.524843
9 142027 0.27 0.608315
10 141541 -0.86 0.194734
11 142075 0.39 0.650651
12 141830 -0.19 0.426477
13 141401 -1.19 0.117478
14 142250 0.80 0.786972
15 142424 1.20 0.885415
16 141555 -0.83 0.203871
17 142007 0.23 0.590255
18 141945 0.08 0.533210
19 142212 0.71 0.760271
20 142547 1.49 0.931873
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_06:31
Bits used No. missing words z-score p-value
23 to 32 141952 0.1471 0.558488
22 to 31 141713 -0.6770 0.249203
21 to 30 141909 -0.0011 0.499546
20 to 29 142011 0.3506 0.637051
19 to 28 142144 0.8092 0.790802
18 to 27 141724 -0.6391 0.261389
17 to 26 141701 -0.7184 0.236262
16 to 25 141886 -0.0804 0.467940
15 to 24 142085 0.6058 0.727663
14 to 23 142257 1.1989 0.884709
13 to 22 141947 0.1299 0.551676
12 to 21 141737 -0.5942 0.276175
11 to 20 141986 0.2644 0.604256
10 to 19 142384 1.6368 0.949163
9 to 18 142128 0.7540 0.774586
8 to 17 141903 -0.0218 0.491293
7 to 16 141835 -0.2563 0.398856
6 to 15 142141 0.7989 0.787815
5 to 14 142480 1.9678 0.975456
4 to 13 142032 0.4230 0.663852
3 to 12 142329 1.4471 0.926071
2 to 11 141802 -0.3701 0.355653
1 to 10 141871 -0.1322 0.447424
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_06:31
Bits used No. missing words z-score p-value
28 to 32 142159 0.8463 0.801318
27 to 31 142050 0.4768 0.683265
26 to 30 142241 1.1243 0.869558
25 to 29 141777 -0.4486 0.326869
24 to 28 142289 1.2870 0.900956
23 to 27 142003 0.3175 0.624578
22 to 26 141786 -0.4181 0.337949
21 to 25 141667 -0.8215 0.205693
20 to 24 142361 1.5311 0.937126
19 to 23 141563 -1.1740 0.120198
18 to 22 141841 -0.2316 0.408414
17 to 21 142232 1.0938 0.862978
16 to 20 141734 -0.5943 0.276143
15 to 19 141852 -0.1943 0.422955
14 to 18 142313 1.3684 0.914402
13 to 17 142168 0.8768 0.809715
12 to 16 141871 -0.1299 0.448310
11 to 15 142079 0.5752 0.717406
10 to 14 141940 0.1040 0.541402
9 to 13 141710 -0.6757 0.249617
8 to 12 141315 -2.0147 0.021969
7 to 11 142191 0.9548 0.830164
6 to 10 141733 -0.5977 0.275010
5 to 9 142067 0.5345 0.703493
4 to 8 141988 0.2667 0.605141
3 to 7 141892 -0.0587 0.476577
2 to 6 142002 0.3141 0.623291
1 to 5 141897 -0.0418 0.483330
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_06:31
Bits used No. missing words z-score p-value
31 to 32 141459 -1.3284 0.092022
30 to 31 141989 0.2350 0.592901
29 to 30 142320 1.2114 0.887132
28 to 29 141264 -1.9036 0.028479
27 to 28 141644 -0.7827 0.216906
26 to 27 141659 -0.7384 0.230125
25 to 26 141768 -0.4169 0.338375
24 to 25 141762 -0.4346 0.331926
23 to 24 142013 0.3058 0.620126
22 to 23 141524 -1.1367 0.127839
21 to 22 141540 -1.0895 0.137974
20 to 21 141949 0.1170 0.546578
19 to 20 141967 0.1701 0.567541
18 to 19 141426 -1.4258 0.076970
17 to 18 142458 1.6185 0.947222
16 to 17 142182 0.8043 0.789399
15 to 16 141949 0.1170 0.546578
14 to 15 141402 -1.4965 0.067255
13 to 14 142006 0.2852 0.612240
12 to 13 142635 2.1406 0.983848
11 to 12 142192 0.8338 0.797813
10 to 11 142039 0.3825 0.648958
9 to 10 141758 -0.4464 0.327654
8 to 9 141787 -0.3609 0.359104
7 to 8 142004 0.2793 0.609978
6 to 7 141886 -0.0688 0.472566
5 to 6 142040 0.3855 0.650051
4 to 5 141999 0.2645 0.604308
3 to 4 142144 0.6922 0.755607
2 to 3 142274 1.0757 0.858974
1 to 2 142215 0.9017 0.816387
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2547.48 0.672 0.749060
Test results for specific bytes for dh-ranFile-2018-07-03_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2371.82 -1.813 0.034932
2 to 9 2528.11 0.398 0.654501
3 to 10 2548.07 0.680 0.751669
4 to 11 2416.93 -1.175 0.120039
5 to 12 2466.72 -0.471 0.318939
6 to 13 2411.08 -1.257 0.104288
7 to 14 2528.36 0.401 0.655841
8 to 15 2492.56 -0.105 0.458117
9 to 16 2632.17 1.869 0.969195
10 to 17 2505.19 0.073 0.529245
11 to 18 2561.53 0.870 0.807890
12 to 19 2521.80 0.308 0.621099
13 to 20 2566.04 0.934 0.824851
14 to 21 2548.33 0.683 0.752851
15 to 22 2470.06 -0.423 0.335989
16 to 23 2519.18 0.271 0.606903
17 to 24 2422.03 -1.103 0.135101
18 to 25 2587.00 1.230 0.890717
19 to 26 2480.40 -0.277 0.390826
20 to 27 2621.61 1.720 0.957271
21 to 28 2550.34 0.712 0.761740
22 to 29 2334.10 -2.346 0.009483
23 to 30 2333.84 -2.350 0.009392
24 to 31 2653.30 2.168 0.984919
25 to 32 2510.80 0.153 0.560708
CDPARK for dh-ranFile-2018-07-03_06:31: 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
3565 1.9178 0.972432
3531 0.3653 0.642555
3516 -0.3196 0.374623
3503 -0.9132 0.180558
3524 0.0457 0.518210
3587 2.9224 0.998263
3505 -0.8219 0.205562
3549 1.1872 0.882429
3498 -1.1416 0.126820
3512 -0.5023 0.307734
Square side=100, avg. no. parked=3529.00 sample std.=27.86
p-value of the KSTEST for those 10 p-values: 0.444493
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_06:31
0.0309,0.5914,0.5515,0.1496,0.0441,0.9460,0.7209,0.0307,0.7452,0.1979,
The KS test for those 10 p-values: 0.177385
The 3DSPHERES test for dh-ranFile-2018-07-03_06:31
sample no r^3 equiv. uni.
1 2.924 0.092881
2 17.667 0.445057
3 71.015 0.906253
4 6.830 0.203618
5 3.750 0.117507
6 3.520 0.110696
7 74.404 0.916268
8 9.980 0.282986
9 2.470 0.079020
10 17.830 0.448074
11 0.002 0.000060
12 22.054 0.520565
13 3.527 0.110917
14 34.587 0.684284
15 76.675 0.922372
16 33.133 0.668607
17 12.916 0.349829
18 18.183 0.454531
19 2.066 0.066554
20 2.210 0.071028
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.031346
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.7 -0.7 -1.8 0.0 0.2 -0.8
1.5 -1.1 -1.3 0.5 -0.2 -0.5
-0.6 0.4 1.7 -0.4 1.0 -0.2
0.7 -0.2 -0.2 -0.1 -0.2 0.7
-0.6 -1.5 -0.2 -0.9 -0.7 1.0
-0.1 0.6 -1.1 0.7 0.1 -0.3
1.0 -0.4 0.1 1.0 -0.6 2.0
-1.1
Chi-square with 42 degrees of freedom:37.802443
z-score=-0.457991, p-value=0.344298
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_06:31
Test no p-value
1 0.079132
2 0.055352
3 0.724898
4 0.644754
5 0.061354
6 0.643514
7 0.101897
8 0.001502
9 0.855446
10 0.724758
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.054244
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_06:31:
(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 66525 0.30 66980 1.47
3 25000.00 25096 0.37 24805 1.52
4 6666.67 6608 0.52 6592 0.84
5 1388.89 1479 5.85 1367 0.35
6 238.10 247 0.33 214 2.44
7 34.72 40 0.80 36 0.05
8 4.96 4 0.19 5 0.00
p=0.78671 p=0.64665
Number of rngs required: 687364, p-value: 0.114
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_06:31
No. of wins: Observed Expected
98585 98585.9
z-score=-0.004, pvalue=0.49847
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66721 66666.7 0.044 0.044
2 37723 37654.3 0.125 0.170
3 26821 26954.7 0.663 0.833
4 19298 19313.5 0.012 0.845
5 13864 13851.4 0.011 0.857
6 9880 9943.5 0.406 1.263
7 7007 7145.0 2.666 3.929
8 5198 5139.1 0.676 4.605
9 3711 3699.9 0.034 4.638
10 2727 2666.3 1.382 6.020
11 2000 1923.3 3.056 9.077
12 1363 1388.7 0.477 9.554
13 1021 1003.7 0.298 9.852
14 694 726.1 1.423 11.274
15 510 525.8 0.477 11.751
16 380 381.2 0.003 11.755
17 291 276.5 0.756 12.511
18 228 200.8 3.676 16.187
19 154 146.0 0.440 16.627
20 97 106.2 0.800 17.426
21 312 287.1 2.157 19.583
Chisq= 19.58 for 20 degrees of freedom, p= 0.51574
SUMMARY of craptest
p-value for no. of wins: 0.498468
p-value for throws/game: 0.515743
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_06:31
No. of wins: Observed Expected
98663 98585.9
z-score= 0.345, pvalue=0.63496
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66576 66666.7 0.123 0.123
2 37546 37654.3 0.312 0.435
3 27195 26954.7 2.142 2.577
4 19231 19313.5 0.352 2.929
5 13917 13851.4 0.310 3.239
6 9958 9943.5 0.021 3.260
7 7069 7145.0 0.809 4.069
8 5172 5139.1 0.211 4.280
9 3715 3699.9 0.062 4.342
10 2622 2666.3 0.736 5.078
11 1917 1923.3 0.021 5.099
12 1379 1388.7 0.068 5.167
13 976 1003.7 0.765 5.932
14 758 726.1 1.398 7.330
15 530 525.8 0.033 7.363
16 393 381.2 0.368 7.732
17 262 276.5 0.764 8.496
18 190 200.8 0.584 9.080
19 163 146.0 1.983 11.063
20 129 106.2 4.888 15.951
21 302 287.1 0.772 16.723
Chisq= 16.72 for 20 degrees of freedom, p= 0.32911
SUMMARY of craptest
p-value for no. of wins: 0.634961
p-value for throws/game: 0.329107
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0015,0.0094,0.0095,0.0193,0.0220,0.0263,0.0285,0.0307,0.0309,
0.0313,0.0349,0.0441,0.0495,0.0542,0.0554,0.0614,0.0666,0.0673,0.0696,
0.0710,0.0713,0.0770,0.0790,0.0791,0.0906,0.0920,0.0929,0.1019,0.1043,
0.1107,0.1109,0.1136,0.1175,0.1175,0.1200,0.1202,0.1268,0.1278,0.1351,
0.1380,0.1496,0.1499,0.1544,0.1690,0.1774,0.1806,0.1947,0.1976,0.1979,
0.2003,0.2036,0.2039,0.2056,0.2057,0.2148,0.2169,0.2272,0.2301,0.2363,
0.2492,0.2496,0.2614,0.2750,0.2761,0.2762,0.2830,0.2895,0.2947,0.3077,
0.3175,0.3175,0.3189,0.3195,0.3260,0.3269,0.3277,0.3283,0.3291,0.3319,
0.3330,0.3342,0.3360,0.3379,0.3384,0.3430,0.3443,0.3498,0.3557,0.3591,
0.3710,0.3746,0.3820,0.3907,0.3908,0.3989,0.4076,0.4084,0.4091,0.4151,
0.4214,0.4228,0.4230,0.4245,0.4265,0.4296,0.4341,0.4437,0.4445,0.4451,
0.4474,0.4481,0.4483,0.4545,0.4581,0.4592,0.4645,0.4679,0.4726,0.4766,
0.4773,0.4779,0.4833,0.4913,0.4936,0.4985,0.4995,0.5157,0.5169,0.5182,
0.5206,0.5248,0.5274,0.5292,0.5304,0.5332,0.5414,0.5466,0.5466,0.5499,
0.5515,0.5517,0.5585,0.5607,0.5675,0.5680,0.5828,0.5854,0.5903,0.5914,
0.5929,0.6043,0.6043,0.6051,0.6060,0.6069,0.6083,0.6100,0.6122,0.6129,
0.6201,0.6211,0.6233,0.6246,0.6253,0.6299,0.6350,0.6371,0.6426,0.6435,
0.6448,0.6467,0.6490,0.6501,0.6507,0.6545,0.6558,0.6595,0.6639,0.6680,
0.6686,0.6804,0.6833,0.6843,0.6965,0.6994,0.7035,0.7055,0.7157,0.7162,
0.7174,0.7209,0.7219,0.7248,0.7249,0.7277,0.7452,0.7491,0.7517,0.7529,
0.7556,0.7603,0.7617,0.7640,0.7677,0.7746,0.7752,0.7867,0.7870,0.7878,
0.7894,0.7908,0.7912,0.7930,0.7948,0.7978,0.8006,0.8013,0.8014,0.8074,
0.8079,0.8097,0.8164,0.8193,0.8208,0.8230,0.8247,0.8249,0.8302,0.8386,
0.8528,0.8554,0.8578,0.8590,0.8630,0.8636,0.8696,0.8770,0.8794,0.8824,
0.8844,0.8847,0.8854,0.8871,0.8906,0.8907,0.9010,0.9063,0.9120,0.9144,
0.9163,0.9224,0.9261,0.9319,0.9371,0.9410,0.9460,0.9472,0.9492,0.9573,
0.9692,0.9701,0.9724,0.9755,0.9838,0.9849,0.9860,0.9957,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.545091
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.