RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_09:31
(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 6.5308 0.011150
2 to 25 15.78 17.6872 0.591172
3 to 26 15.64 23.2681 0.859275
4 to 27 15.49 23.9719 0.879798
5 to 28 15.54 14.7461 0.386237
6 to 29 15.87 12.5180 0.232195
7 to 30 15.85 22.2714 0.825495
8 to 31 15.91 16.6040 0.518511
9 to 32 15.92 10.3002 0.109446
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.907801
Tough bday spacings test for dh-ranFile-2018-07-10_09:31: 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 10 42 76 88 100 82 52 26 18 4 2
(O-E)^2/E 0.1 0.8 0.1 1.0 0.1 0.2 0.0 0.5 0.7 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 5.385, p= 0.136
RESULTS OF GCD FOR dh-ranFile-2018-07-10_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.594290
p-value, dist. of gcd's: 0.776500
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.503 0.007 0.283 0.979 0.998 0.430 0.358 0.716
Bits 8 to 15---> 0.686 0.274 0.428 0.388 0.164 0.417 0.794 0.513
Bits 16 to 23---> 0.039 0.630 0.409 0.640 0.678 0.380 0.208 0.062
Bits 24 to 31---> 0.617 0.166 0.211 0.320 0.548 0.312 0.150 0.520
KS test for the above 32 p values: 0.830
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_09:31,
p-values for 5 runs: 0.1220, 0.2217, 0.6030, 0.8724, 0.4878
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 223 211.4 0.634 0.634
r= 29 5149 5134.0 0.044 0.678
r= 30 23266 23103.0 1.149 1.828
r= 31 11362 11551.5 3.109 4.937
chi-square = 4.937 with df = 3; p-value = 0.824
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5126 5134.0 0.012 0.044
r= 31 22999 23103.0 0.469 0.513
r= 32 11661 11551.5 1.038 1.550
chi-square = 1.550 with df = 3; p-value = 0.329
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_09:31
b-rank test for bits 1 to 8, p=0.33599
b-rank test for bits 2 to 9, p=0.47702
b-rank test for bits 3 to 10, p=0.08227
b-rank test for bits 4 to 11, p=0.35555
b-rank test for bits 5 to 12, p=0.88466
b-rank test for bits 6 to 13, p=0.80317
b-rank test for bits 7 to 14, p=0.67589
b-rank test for bits 8 to 15, p=0.58266
b-rank test for bits 9 to 16, p=0.95480
b-rank test for bits 10 to 17, p=0.04395
b-rank test for bits 11 to 18, p=0.37968
b-rank test for bits 12 to 19, p=0.50807
b-rank test for bits 13 to 20, p=0.59190
b-rank test for bits 14 to 21, p=0.27637
b-rank test for bits 15 to 22, p=0.65957
b-rank test for bits 16 to 23, p=0.85316
b-rank test for bits 17 to 24, p=0.71864
b-rank test for bits 18 to 25, p=0.93621
b-rank test for bits 19 to 26, p=0.22692
b-rank test for bits 20 to 27, p=0.58076
b-rank test for bits 21 to 28, p=0.99417
b-rank test for bits 22 to 29, p=0.11577
b-rank test for bits 23 to 30, p=0.47449
b-rank test for bits 24 to 31, p=0.35529
b-rank test for bits 25 to 32, p=0.88453
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 = 0.706891
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_09:31
(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 141090 -1.91 0.027789
2 141834 -0.18 0.430145
3 142574 1.55 0.939785
4 141711 -0.46 0.321543
5 141706 -0.48 0.317369
6 141561 -0.81 0.207864
7 141588 -0.75 0.226395
8 142133 0.52 0.699371
9 142050 0.33 0.628797
10 141997 0.20 0.581150
11 143286 3.22 0.999351
12 142671 1.78 0.962430
13 141904 -0.01 0.495032
14 141687 -0.52 0.301719
15 141657 -0.59 0.277744
16 142502 1.38 0.916934
17 141706 -0.48 0.317369
18 142177 0.63 0.734145
19 142063 0.36 0.640218
20 141805 -0.24 0.403708
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_09:31
Bits used No. missing words z-score p-value
23 to 32 141980 0.2437 0.596264
22 to 31 141888 -0.0736 0.470684
21 to 30 142013 0.3575 0.639635
20 to 29 141827 -0.2839 0.388245
19 to 28 141791 -0.4080 0.341624
18 to 27 142112 0.6989 0.757681
17 to 26 141833 -0.2632 0.396196
16 to 25 142167 0.8885 0.812869
15 to 24 141777 -0.4563 0.324083
14 to 23 141800 -0.3770 0.353087
13 to 22 142037 0.4402 0.670119
12 to 21 141827 -0.2839 0.388245
11 to 20 141802 -0.3701 0.355653
10 to 19 141530 -1.3080 0.095431
9 to 18 141696 -0.7356 0.230981
8 to 17 142044 0.4644 0.678812
7 to 16 141790 -0.4115 0.340359
6 to 15 141190 -2.4804 0.006561
5 to 14 141009 -3.1046 0.000953
4 to 13 142027 0.4058 0.657540
3 to 12 141926 0.0575 0.522920
2 to 11 142217 1.0609 0.855639
1 to 10 141959 0.1713 0.567997
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_09:31
Bits used No. missing words z-score p-value
28 to 32 141882 -0.0926 0.463093
27 to 31 141903 -0.0215 0.491440
26 to 30 142332 1.4328 0.924040
25 to 29 141918 0.0294 0.511723
24 to 28 142150 0.8158 0.792702
23 to 27 141469 -1.4926 0.067765
22 to 26 141808 -0.3435 0.365614
21 to 25 142109 0.6768 0.750749
20 to 24 141942 0.1107 0.544091
19 to 23 141820 -0.3028 0.381016
18 to 22 142060 0.5107 0.695236
17 to 21 141738 -0.5808 0.280695
16 to 20 141835 -0.2520 0.400534
15 to 19 141920 0.0362 0.514426
14 to 18 141916 0.0226 0.509019
13 to 17 142214 1.0328 0.849147
12 to 16 141795 -0.3876 0.349171
11 to 15 141900 -0.0316 0.487385
10 to 14 141935 0.0870 0.534671
9 to 13 142101 0.6497 0.742066
8 to 12 142234 1.1006 0.864459
7 to 11 142587 2.2972 0.989196
6 to 10 141964 0.1853 0.573512
5 to 9 141576 -1.1299 0.129252
4 to 8 142334 1.4396 0.925004
3 to 7 142087 0.6023 0.726503
2 to 6 141897 -0.0418 0.483330
1 to 5 141944 0.1175 0.546778
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_09:31
Bits used No. missing words z-score p-value
31 to 32 141822 -0.2576 0.398354
30 to 31 142066 0.4622 0.678014
29 to 30 141575 -0.9862 0.162012
28 to 29 141791 -0.3491 0.363524
27 to 28 142326 1.2291 0.890486
26 to 27 141307 -1.7768 0.037802
25 to 26 141498 -1.2134 0.112496
24 to 25 142439 1.5624 0.940909
23 to 24 141769 -0.4140 0.339454
22 to 23 141963 0.1583 0.562897
21 to 22 141361 -1.6175 0.052886
20 to 21 142137 0.6716 0.749079
19 to 20 141439 -1.3874 0.082659
18 to 19 141856 -0.1573 0.437498
17 to 18 141171 -2.1780 0.014704
16 to 17 141776 -0.3933 0.347048
15 to 16 141758 -0.4464 0.327654
14 to 15 141941 0.0934 0.537216
13 to 14 141899 -0.0305 0.487845
12 to 13 141469 -1.2989 0.096988
11 to 12 141912 0.0079 0.503142
10 to 11 142104 0.5742 0.717100
9 to 10 142362 1.3353 0.909113
8 to 9 142177 0.7896 0.785116
7 to 8 142130 0.6509 0.742459
6 to 7 141876 -0.0983 0.460840
5 to 6 142349 1.2970 0.902678
4 to 5 141919 0.0285 0.511378
3 to 4 141457 -1.3343 0.091052
2 to 3 142141 0.6834 0.752821
1 to 2 141834 -0.2222 0.412074
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2511.12 0.157 0.562453
Test results for specific bytes for dh-ranFile-2018-07-10_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2592.13 1.303 0.903688
2 to 9 2482.91 -0.242 0.404492
3 to 10 2583.36 1.179 0.880771
4 to 11 2545.85 0.648 0.741655
5 to 12 2578.07 1.104 0.865214
6 to 13 2651.68 2.145 0.984027
7 to 14 2493.81 -0.088 0.465130
8 to 15 2473.19 -0.379 0.352263
9 to 16 2605.09 1.486 0.931385
10 to 17 2517.92 0.253 0.600009
11 to 18 2595.26 1.347 0.911035
12 to 19 2553.35 0.755 0.774732
13 to 20 2544.46 0.629 0.735230
14 to 21 2437.68 -0.881 0.189050
15 to 22 2538.91 0.550 0.708944
16 to 23 2566.41 0.939 0.826191
17 to 24 2558.01 0.820 0.794002
18 to 25 2495.83 -0.059 0.476469
19 to 26 2570.53 0.997 0.840717
20 to 27 2498.15 -0.026 0.489586
21 to 28 2508.79 0.124 0.549442
22 to 29 2542.54 0.602 0.726281
23 to 30 2673.64 2.456 0.992970
24 to 31 2488.22 -0.167 0.433869
25 to 32 2460.54 -0.558 0.288408
CDPARK for dh-ranFile-2018-07-10_09:31: 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
3480 -1.9635 0.024796
3521 -0.0913 0.463617
3510 -0.5936 0.276387
3534 0.5023 0.692266
3485 -1.7352 0.041356
3537 0.6393 0.738676
3525 0.0913 0.536383
3562 1.7808 0.962529
3503 -0.9132 0.180558
3532 0.4110 0.659449
Square side=100, avg. no. parked=3518.90 sample std.=23.71
p-value of the KSTEST for those 10 p-values: 0.819611
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_09:31
0.0528,0.0044,0.1712,0.7622,0.3395,0.0668,0.1033,0.7850,0.9531,0.3358,
The KS test for those 10 p-values: 0.074437
The 3DSPHERES test for dh-ranFile-2018-07-10_09:31
sample no r^3 equiv. uni.
1 8.097 0.236553
2 40.455 0.740368
3 1.031 0.033793
4 89.400 0.949208
5 79.782 0.930010
6 17.095 0.434386
7 56.973 0.850295
8 39.702 0.733774
9 9.463 0.270532
10 7.843 0.230062
11 65.647 0.887884
12 55.080 0.840544
13 16.942 0.431482
14 35.884 0.697635
15 44.976 0.776694
16 11.585 0.320345
17 0.986 0.032340
18 38.110 0.719263
19 62.610 0.875941
20 49.543 0.808223
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.164562
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 -1.3 0.3 1.0 -0.4
-0.2 2.0 0.2 0.8 -1.5 0.5
-0.7 0.0 0.9 -1.8 -0.5 0.1
-0.1 -0.6 0.4 1.4 -0.5 0.6
-0.4 0.6 -0.3 0.9 -0.5 -0.3
1.0 -0.5 1.5 2.1 -0.8 0.8
-1.9 1.5 1.7 0.4 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:41.209859
z-score=-0.086211, p-value=0.494486
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_09:31
Test no p-value
1 0.161372
2 0.009322
3 0.533809
4 0.136486
5 0.087259
6 0.406941
7 0.023707
8 0.762523
9 0.004037
10 0.422395
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.003260
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_09:31:
(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 66860 0.56 66589 0.09
3 25000.00 24840 1.02 25033 0.04
4 6666.67 6617 0.37 6744 0.90
5 1388.89 1369 0.28 1371 0.23
6 238.10 271 4.55 229 0.35
7 34.72 36 0.05 30 0.64
8 4.96 6 0.22 3 0.77
p=0.68396 p=0.19431
Number of rngs required: 688219, p-value: 0.416
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_09:31
No. of wins: Observed Expected
98578 98585.9
z-score=-0.035, pvalue=0.48598
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66365 66666.7 1.365 1.365
2 37510 37654.3 0.553 1.918
3 27218 26954.7 2.571 4.490
4 19429 19313.5 0.691 5.181
5 13880 13851.4 0.059 5.240
6 9995 9943.5 0.266 5.506
7 7108 7145.0 0.192 5.698
8 5141 5139.1 0.001 5.699
9 3717 3699.9 0.079 5.778
10 2652 2666.3 0.077 5.855
11 1892 1923.3 0.510 6.365
12 1392 1388.7 0.008 6.373
13 1028 1003.7 0.588 6.960
14 779 726.1 3.848 10.808
15 503 525.8 0.992 11.800
16 350 381.2 2.546 14.346
17 284 276.5 0.201 14.547
18 215 200.8 1.000 15.547
19 178 146.0 7.021 22.568
20 95 106.2 1.184 23.752
21 269 287.1 1.143 24.895
Chisq= 24.90 for 20 degrees of freedom, p= 0.79452
SUMMARY of craptest
p-value for no. of wins: 0.485981
p-value for throws/game: 0.794522
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_09:31
No. of wins: Observed Expected
98697 98585.9
z-score= 0.497, pvalue=0.69044
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66525 66666.7 0.301 0.301
2 37718 37654.3 0.108 0.409
3 27039 26954.7 0.263 0.672
4 19378 19313.5 0.216 0.888
5 13923 13851.4 0.370 1.258
6 9697 9943.5 6.113 7.371
7 7126 7145.0 0.051 7.421
8 5281 5139.1 3.920 11.341
9 3711 3699.9 0.034 11.374
10 2619 2666.3 0.839 12.213
11 1976 1923.3 1.442 13.656
12 1398 1388.7 0.062 13.718
13 996 1003.7 0.059 13.777
14 686 726.1 2.219 15.996
15 549 525.8 1.020 17.016
16 365 381.2 0.684 17.701
17 253 276.5 2.004 19.704
18 204 200.8 0.050 19.754
19 151 146.0 0.172 19.927
20 97 106.2 0.800 20.726
21 308 287.1 1.519 22.246
Chisq= 22.25 for 20 degrees of freedom, p= 0.67266
SUMMARY of craptest
p-value for no. of wins: 0.690437
p-value for throws/game: 0.672665
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0033,0.0040,0.0044,0.0066,0.0066,0.0093,0.0111,0.0147,0.0237,
0.0248,0.0278,0.0323,0.0338,0.0378,0.0389,0.0414,0.0440,0.0528,0.0529,
0.0619,0.0668,0.0678,0.0744,0.0823,0.0827,0.0873,0.0911,0.0954,0.0970,
0.1033,0.1094,0.1125,0.1158,0.1220,0.1293,0.1360,0.1365,0.1499,0.1614,
0.1620,0.1643,0.1646,0.1661,0.1712,0.1806,0.1891,0.1943,0.2079,0.2082,
0.2108,0.2217,0.2264,0.2269,0.2301,0.2310,0.2322,0.2366,0.2705,0.2743,
0.2764,0.2764,0.2777,0.2807,0.2832,0.2884,0.3017,0.3124,0.3174,0.3174,
0.3203,0.3204,0.3215,0.3241,0.3277,0.3293,0.3358,0.3360,0.3395,0.3395,
0.3404,0.3416,0.3470,0.3492,0.3523,0.3531,0.3553,0.3555,0.3557,0.3582,
0.3635,0.3656,0.3797,0.3803,0.3810,0.3862,0.3878,0.3882,0.3882,0.3962,
0.3984,0.4005,0.4037,0.4045,0.4069,0.4092,0.4121,0.4162,0.4166,0.4224,
0.4278,0.4301,0.4304,0.4315,0.4339,0.4344,0.4375,0.4608,0.4631,0.4636,
0.4651,0.4707,0.4745,0.4765,0.4770,0.4833,0.4860,0.4874,0.4878,0.4878,
0.4896,0.4914,0.4945,0.4950,0.5031,0.5034,0.5081,0.5090,0.5114,0.5117,
0.5132,0.5144,0.5185,0.5205,0.5229,0.5338,0.5347,0.5364,0.5372,0.5441,
0.5468,0.5482,0.5494,0.5625,0.5629,0.5680,0.5735,0.5808,0.5812,0.5827,
0.5912,0.5919,0.5943,0.5963,0.6000,0.6030,0.6168,0.6288,0.6298,0.6396,
0.6402,0.6405,0.6575,0.6594,0.6596,0.6701,0.6727,0.6759,0.6779,0.6780,
0.6788,0.6840,0.6858,0.6904,0.6923,0.6952,0.6976,0.6994,0.7069,0.7089,
0.7160,0.7171,0.7186,0.7193,0.7263,0.7265,0.7338,0.7341,0.7352,0.7387,
0.7404,0.7417,0.7421,0.7425,0.7491,0.7507,0.7528,0.7577,0.7622,0.7625,
0.7747,0.7765,0.7767,0.7850,0.7851,0.7927,0.7940,0.7941,0.7945,0.8032,
0.8082,0.8129,0.8196,0.8235,0.8255,0.8262,0.8301,0.8405,0.8407,0.8491,
0.8503,0.8532,0.8556,0.8593,0.8645,0.8652,0.8724,0.8759,0.8798,0.8808,
0.8845,0.8847,0.8879,0.8905,0.9027,0.9037,0.9078,0.9091,0.9110,0.9169,
0.9240,0.9250,0.9300,0.9314,0.9362,0.9398,0.9409,0.9492,0.9531,0.9548,
0.9624,0.9625,0.9793,0.9840,0.9892,0.9930,0.9942,0.9982,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.503459
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.