RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.16 37.3017 0.996938
2 to 25 15.54 19.9172 0.721512
3 to 26 15.69 20.7265 0.761236
4 to 27 16.10 28.0373 0.955496
5 to 28 15.54 18.7272 0.655585
6 to 29 15.74 16.4201 0.505729
7 to 30 15.76 14.6057 0.376140
8 to 31 15.92 21.5120 0.795778
9 to 32 15.73 15.2694 0.423913
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.066417
Tough bday spacings test for dh-ranFile-2018-06-28_10:31: 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 50 71 96 83 92 40 29 13 13 4
(O-E)^2/E 0.0 4.9 0.1 0.0 2.2 2.5 2.8 0.0 0.2 6.2 0.0
Birthday Spacings: Sum(O-E)^2/E= 18.874, p= 0.958
RESULTS OF GCD FOR dh-ranFile-2018-06-28_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.674791
p-value, dist. of gcd's: 0.149729
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.980 0.366 0.369 0.912 0.147 0.033 0.563 0.783
Bits 8 to 15---> 0.997 0.859 0.580 0.718 0.996 0.601 0.797 0.918
Bits 16 to 23---> 0.718 0.351 0.799 0.967 0.813 0.817 0.292 0.814
Bits 24 to 31---> 0.281 0.206 0.647 0.006 0.363 0.345 0.313 0.862
KS test for the above 32 p values: 0.956
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_10:31,
p-values for 5 runs: 0.6618, 0.6670, 0.5937, 0.1867, 0.4771
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 213 211.4 0.012 0.012
r= 29 5144 5134.0 0.019 0.031
r= 30 23036 23103.0 0.195 0.226
r= 31 11607 11551.5 0.266 0.492
chi-square = 0.492 with df = 3; p-value = 0.079
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5096 5134.0 0.281 0.617
r= 31 23190 23103.0 0.327 0.944
r= 32 11511 11551.5 0.142 1.086
chi-square = 1.086 with df = 3; p-value = 0.220
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_10:31
b-rank test for bits 1 to 8, p=0.86440
b-rank test for bits 2 to 9, p=0.47616
b-rank test for bits 3 to 10, p=0.84724
b-rank test for bits 4 to 11, p=0.94246
b-rank test for bits 5 to 12, p=0.96295
b-rank test for bits 6 to 13, p=0.96896
b-rank test for bits 7 to 14, p=0.97831
b-rank test for bits 8 to 15, p=0.72526
b-rank test for bits 9 to 16, p=0.80006
b-rank test for bits 10 to 17, p=0.99252
b-rank test for bits 11 to 18, p=0.96565
b-rank test for bits 12 to 19, p=0.83607
b-rank test for bits 13 to 20, p=0.37775
b-rank test for bits 14 to 21, p=0.09967
b-rank test for bits 15 to 22, p=0.53602
b-rank test for bits 16 to 23, p=0.09424
b-rank test for bits 17 to 24, p=0.51774
b-rank test for bits 18 to 25, p=0.07110
b-rank test for bits 19 to 26, p=0.12040
b-rank test for bits 20 to 27, p=0.28559
b-rank test for bits 21 to 28, p=0.79041
b-rank test for bits 22 to 29, p=0.63386
b-rank test for bits 23 to 30, p=0.57476
b-rank test for bits 24 to 31, p=0.90170
b-rank test for bits 25 to 32, p=0.32861
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 = 0.015560
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_10:31
(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 141670 -0.56 0.288019
2 141456 -1.06 0.144758
3 142318 0.95 0.830170
4 141978 0.16 0.563734
5 141974 0.15 0.560051
6 142555 1.51 0.934296
7 141679 -0.54 0.295235
8 142211 0.70 0.759544
9 141713 -0.46 0.323219
10 141552 -0.83 0.201892
11 142361 1.06 0.854357
12 141894 -0.04 0.485714
13 141669 -0.56 0.287222
14 142046 0.32 0.625259
15 141613 -0.69 0.244356
16 142065 0.36 0.641965
17 141777 -0.31 0.378591
18 142280 0.87 0.806769
19 141824 -0.20 0.420987
20 142292 0.89 0.814363
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_10:31
Bits used No. missing words z-score p-value
23 to 32 141805 -0.3598 0.359514
22 to 31 141830 -0.2736 0.392215
21 to 30 141726 -0.6322 0.263637
20 to 29 141825 -0.2908 0.385605
19 to 28 141985 0.2609 0.602927
18 to 27 142251 1.1782 0.880636
17 to 26 142405 1.7092 0.956294
16 to 25 142017 0.3713 0.644784
15 to 24 142108 0.6851 0.753350
14 to 23 141968 0.2023 0.580163
13 to 22 141916 0.0230 0.509175
12 to 21 141907 -0.0080 0.496795
11 to 20 141857 -0.1804 0.428400
10 to 19 141787 -0.4218 0.336575
9 to 18 141755 -0.5322 0.297303
8 to 17 141855 -0.1873 0.425695
7 to 16 142208 1.0299 0.848471
6 to 15 141908 -0.0046 0.498170
5 to 14 141644 -0.9149 0.180114
4 to 13 141617 -1.0080 0.156719
3 to 12 141391 -1.7873 0.036941
2 to 11 141823 -0.2977 0.382970
1 to 10 142146 0.8161 0.792780
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_10:31
Bits used No. missing words z-score p-value
28 to 32 141819 -0.3062 0.379725
27 to 31 142156 0.8362 0.798470
26 to 30 141830 -0.2689 0.393998
25 to 29 142159 0.8463 0.801318
24 to 28 141931 0.0735 0.529279
23 to 27 142405 1.6802 0.953544
22 to 26 141580 -1.1164 0.132131
21 to 25 141856 -0.1808 0.428270
20 to 24 142125 0.7311 0.767636
19 to 23 141782 -0.4316 0.333006
18 to 22 142090 0.6124 0.729877
17 to 21 142348 1.4870 0.931495
16 to 20 141944 0.1175 0.546778
15 to 19 142026 0.3955 0.653760
14 to 18 142074 0.5582 0.711647
13 to 17 142539 2.1345 0.983598
12 to 16 141882 -0.0926 0.463093
11 to 15 142393 1.6396 0.949452
10 to 14 142187 0.9413 0.826713
9 to 13 141948 0.1311 0.552146
8 to 12 141537 -1.2621 0.103450
7 to 11 141824 -0.2893 0.386193
6 to 10 141168 -2.5130 0.005986
5 to 9 141821 -0.2994 0.382308
4 to 8 141573 -1.1401 0.127122
3 to 7 142013 0.3514 0.637365
2 to 6 142509 2.0328 0.978963
1 to 5 141808 -0.3435 0.365614
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_10:31
Bits used No. missing words z-score p-value
31 to 32 142104 0.5742 0.717100
30 to 31 141533 -1.1101 0.133474
29 to 30 141571 -0.9980 0.159134
28 to 29 141512 -1.1721 0.120586
27 to 28 142291 1.1259 0.869890
26 to 27 142037 0.3766 0.646767
25 to 26 141733 -0.5201 0.301480
24 to 25 141550 -1.0600 0.144579
23 to 24 142478 1.6775 0.953277
22 to 23 142400 1.4474 0.926108
21 to 22 142122 0.6273 0.734784
20 to 21 141977 0.1996 0.579110
19 to 20 142839 2.7424 0.996950
18 to 19 142445 1.5801 0.942963
17 to 18 141725 -0.5437 0.293308
16 to 17 141921 0.0344 0.513731
15 to 16 141814 -0.2812 0.389275
14 to 15 141577 -0.9803 0.163463
13 to 14 142094 0.5447 0.707037
12 to 13 141563 -1.0216 0.153480
11 to 12 141732 -0.5231 0.300453
10 to 11 141486 -1.2488 0.105876
9 to 10 141930 0.0610 0.524310
8 to 9 141944 0.1023 0.540729
7 to 8 142217 0.9076 0.817950
6 to 7 141482 -1.2606 0.103734
5 to 6 141520 -1.1485 0.125388
4 to 5 141671 -0.7030 0.241016
3 to 4 142358 1.3235 0.907167
2 to 3 141665 -0.7207 0.235536
1 to 2 142120 0.6214 0.732847
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2539.35 0.556 0.711043
Test results for specific bytes for dh-ranFile-2018-06-28_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2468.13 -0.451 0.326114
2 to 9 2506.94 0.098 0.539092
3 to 10 2548.23 0.682 0.752419
4 to 11 2635.37 1.914 0.972215
5 to 12 2467.35 -0.462 0.322155
6 to 13 2423.13 -1.087 0.138496
7 to 14 2419.44 -1.139 0.127293
8 to 15 2435.43 -0.913 0.180583
9 to 16 2559.52 0.842 0.800049
10 to 17 2588.55 1.252 0.894770
11 to 18 2557.25 0.810 0.790912
12 to 19 2486.05 -0.197 0.421802
13 to 20 2516.87 0.239 0.594283
14 to 21 2483.35 -0.236 0.406904
15 to 22 2512.56 0.178 0.570476
16 to 23 2505.69 0.080 0.532064
17 to 24 2424.27 -1.071 0.142090
18 to 25 2411.46 -1.252 0.105250
19 to 26 2545.11 0.638 0.738264
20 to 27 2440.41 -0.843 0.199694
21 to 28 2473.97 -0.368 0.356398
22 to 29 2376.18 -1.751 0.039967
23 to 30 2449.92 -0.708 0.239409
24 to 31 2494.64 -0.076 0.469816
25 to 32 2439.60 -0.854 0.196483
CDPARK for dh-ranFile-2018-06-28_10:31: 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
3547 1.0959 0.863437
3502 -0.9589 0.168804
3523 0.0000 0.500000
3504 -0.8676 0.192812
3532 0.4110 0.659449
3472 -2.3288 0.009936
3570 2.1461 0.984068
3526 0.1370 0.554479
3526 0.1370 0.554479
3565 1.9178 0.972432
Square side=100, avg. no. parked=3526.70 sample std.=28.13
p-value of the KSTEST for those 10 p-values: 0.529764
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_10:31
0.0464,0.7717,0.4069,0.1056,0.1946,0.5635,0.4790,0.3451,0.2357,0.9779,
The KS test for those 10 p-values: 0.607603
The 3DSPHERES test for dh-ranFile-2018-06-28_10:31
sample no r^3 equiv. uni.
1 27.942 0.606004
2 24.451 0.557381
3 20.432 0.493927
4 2.753 0.087676
5 13.519 0.362768
6 31.542 0.650555
7 17.267 0.437623
8 5.555 0.169032
9 36.151 0.700314
10 34.495 0.683307
11 11.184 0.311196
12 0.083 0.002762
13 7.370 0.217823
14 7.667 0.225510
15 24.325 0.555510
16 5.520 0.168056
17 7.532 0.222033
18 8.573 0.248554
19 0.781 0.025697
20 23.099 0.536975
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.040062
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.1 3.7 -0.5 -0.7 1.8
1.1 -0.8 0.4 1.0 0.5 -0.4
1.1 0.1 -1.0 1.0 1.2 -0.8
-1.8 0.3 0.2 -1.3 1.1 -0.1
-0.5 -1.8 0.2 -0.2 -1.3 0.1
1.8 0.4 0.7 0.7 -0.9 -1.7
0.7 2.1 0.1 1.5 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:56.226384
z-score=1.552226, p-value=0.930036
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_10:31
Test no p-value
1 0.019429
2 0.010143
3 0.344758
4 0.618546
5 0.667461
6 0.039578
7 0.048410
8 0.805927
9 0.001642
10 0.464702
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.003169
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_10:31:
(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 66871 0.63 66568 0.15
3 25000.00 24901 0.39 25129 0.67
4 6666.67 6606 0.55 6631 0.19
5 1388.89 1346 1.32 1369 0.28
6 238.10 235 0.04 259 1.84
7 34.72 38 0.31 38 0.31
8 4.96 2 1.77 5 0.00
p=0.45766 p=0.24714
Number of rngs required: 689381, p-value: 0.872
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_10:31
No. of wins: Observed Expected
98606 98585.9
z-score= 0.090, pvalue=0.53589
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66644 66666.7 0.008 0.008
2 37729 37654.3 0.148 0.156
3 26717 26954.7 2.097 2.253
4 19381 19313.5 0.236 2.489
5 13780 13851.4 0.368 2.857
6 9990 9943.5 0.217 3.074
7 7082 7145.0 0.556 3.630
8 5084 5139.1 0.590 4.220
9 3718 3699.9 0.089 4.309
10 2742 2666.3 2.149 6.458
11 1964 1923.3 0.860 7.318
12 1432 1388.7 1.348 8.666
13 1015 1003.7 0.127 8.793
14 797 726.1 6.915 15.708
15 503 525.8 0.992 16.699
16 400 381.2 0.932 17.631
17 261 276.5 0.873 18.505
18 218 200.8 1.468 19.973
19 148 146.0 0.028 20.000
20 108 106.2 0.030 20.030
21 287 287.1 0.000 20.031
Chisq= 20.03 for 20 degrees of freedom, p= 0.54398
SUMMARY of craptest
p-value for no. of wins: 0.535890
p-value for throws/game: 0.543977
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_10:31
No. of wins: Observed Expected
98822 98585.9
z-score= 1.056, pvalue=0.85455
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66662 66666.7 0.000 0.000
2 37530 37654.3 0.410 0.411
3 27222 26954.7 2.650 3.061
4 19320 19313.5 0.002 3.063
5 13778 13851.4 0.389 3.452
6 9892 9943.5 0.267 3.719
7 7169 7145.0 0.080 3.800
8 5155 5139.1 0.049 3.849
9 3675 3699.9 0.167 4.016
10 2677 2666.3 0.043 4.059
11 1942 1923.3 0.181 4.241
12 1379 1388.7 0.068 4.309
13 998 1003.7 0.033 4.341
14 682 726.1 2.683 7.025
15 518 525.8 0.117 7.141
16 361 381.2 1.065 8.207
17 284 276.5 0.201 8.408
18 181 200.8 1.958 10.366
19 147 146.0 0.007 10.373
20 127 106.2 4.067 14.440
21 301 287.1 0.672 15.112
Chisq= 15.11 for 20 degrees of freedom, p= 0.23003
SUMMARY of craptest
p-value for no. of wins: 0.854553
p-value for throws/game: 0.230031
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0028,0.0032,0.0060,0.0060,0.0099,0.0101,0.0156,0.0194,0.0257,
0.0325,0.0369,0.0396,0.0400,0.0401,0.0464,0.0484,0.0664,0.0711,0.0794,
0.0877,0.0942,0.0997,0.1035,0.1037,0.1053,0.1056,0.1059,0.1204,0.1206,
0.1254,0.1271,0.1273,0.1321,0.1335,0.1385,0.1421,0.1446,0.1448,0.1467,
0.1497,0.1535,0.1567,0.1591,0.1635,0.1681,0.1688,0.1690,0.1801,0.1806,
0.1867,0.1928,0.1946,0.1965,0.1997,0.2019,0.2059,0.2178,0.2195,0.2220,
0.2255,0.2300,0.2355,0.2357,0.2394,0.2410,0.2444,0.2471,0.2486,0.2636,
0.2814,0.2856,0.2872,0.2880,0.2919,0.2933,0.2952,0.2973,0.3005,0.3015,
0.3112,0.3128,0.3222,0.3232,0.3261,0.3286,0.3330,0.3366,0.3448,0.3450,
0.3451,0.3512,0.3564,0.3595,0.3626,0.3628,0.3656,0.3657,0.3692,0.3761,
0.3777,0.3786,0.3797,0.3823,0.3830,0.3856,0.3862,0.3893,0.3922,0.3940,
0.4069,0.4069,0.4210,0.4218,0.4239,0.4257,0.4283,0.4284,0.4376,0.4577,
0.4631,0.4647,0.4698,0.4762,0.4771,0.4790,0.4857,0.4939,0.4968,0.4982,
0.5000,0.5057,0.5092,0.5137,0.5177,0.5243,0.5293,0.5298,0.5321,0.5359,
0.5360,0.5370,0.5391,0.5407,0.5440,0.5468,0.5521,0.5545,0.5545,0.5555,
0.5574,0.5601,0.5635,0.5635,0.5637,0.5705,0.5748,0.5791,0.5802,0.5802,
0.5937,0.5943,0.6007,0.6029,0.6060,0.6076,0.6185,0.6253,0.6339,0.6374,
0.6420,0.6448,0.6468,0.6470,0.6506,0.6538,0.6556,0.6594,0.6618,0.6670,
0.6675,0.6748,0.6833,0.7003,0.7070,0.7110,0.7116,0.7171,0.7180,0.7182,
0.7215,0.7253,0.7299,0.7328,0.7348,0.7383,0.7524,0.7533,0.7595,0.7612,
0.7676,0.7717,0.7830,0.7904,0.7909,0.7928,0.7958,0.7974,0.7985,0.7992,
0.8000,0.8001,0.8013,0.8059,0.8068,0.8129,0.8140,0.8144,0.8173,0.8180,
0.8267,0.8302,0.8361,0.8472,0.8485,0.8544,0.8546,0.8588,0.8623,0.8634,
0.8644,0.8699,0.8719,0.8806,0.8948,0.9017,0.9072,0.9117,0.9182,0.9261,
0.9300,0.9315,0.9343,0.9425,0.9430,0.9495,0.9533,0.9535,0.9555,0.9560,
0.9563,0.9581,0.9630,0.9656,0.9669,0.9690,0.9722,0.9724,0.9779,0.9783,
0.9790,0.9798,0.9836,0.9841,0.9925,0.9958,0.9969,0.9970,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.588557
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.