RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_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 15.67 26.6945 0.937297
2 to 25 15.62 14.5420 0.371568
3 to 26 15.44 24.9205 0.903497
4 to 27 15.75 12.2838 0.217341
5 to 28 15.73 14.6349 0.378241
6 to 29 15.68 23.9255 0.878528
7 to 30 15.80 15.2016 0.419034
8 to 31 15.73 16.3610 0.501597
9 to 32 15.67 15.0289 0.406600
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.456000
Tough bday spacings test for dh-ranFile-2018-06-29_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 10 25 67 104 92 78 58 30 21 9 6
(O-E)^2/E 0.1 3.7 0.5 0.4 0.3 0.0 0.7 0.0 2.5 0.9 0.9
Birthday Spacings: Sum(O-E)^2/E= 10.007, p= 0.560
RESULTS OF GCD FOR dh-ranFile-2018-06-29_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.376928
p-value, dist. of gcd's: 0.229997
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.485 0.721 0.092 0.658 0.638 0.503 0.946 0.057
Bits 8 to 15---> 0.669 0.176 0.032 0.923 0.621 0.651 0.701 0.241
Bits 16 to 23---> 0.289 0.103 0.998 0.592 0.755 0.171 0.845 0.503
Bits 24 to 31---> 0.184 0.889 0.373 0.749 0.960 0.607 0.512 0.018
KS test for the above 32 p values: 0.214
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_01:31,
p-values for 5 runs: 0.4140, 0.4406, 0.2047, 0.6599, 0.3247
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5013 5134.0 2.852 3.124
r= 30 23153 23103.0 0.108 3.232
r= 31 11615 11551.5 0.349 3.581
chi-square = 3.581 with df = 3; p-value = 0.690
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 196 211.4 1.124 1.124
r= 30 5136 5134.0 0.001 1.125
r= 31 23314 23103.0 1.926 3.051
r= 32 11354 11551.5 3.378 6.429
chi-square = 6.429 with df = 3; p-value = 0.907
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_01:31
b-rank test for bits 1 to 8, p=0.94218
b-rank test for bits 2 to 9, p=0.78079
b-rank test for bits 3 to 10, p=0.13931
b-rank test for bits 4 to 11, p=0.30872
b-rank test for bits 5 to 12, p=0.30433
b-rank test for bits 6 to 13, p=0.49325
b-rank test for bits 7 to 14, p=0.67803
b-rank test for bits 8 to 15, p=0.90902
b-rank test for bits 9 to 16, p=0.01166
b-rank test for bits 10 to 17, p=0.49066
b-rank test for bits 11 to 18, p=0.00993
b-rank test for bits 12 to 19, p=0.22461
b-rank test for bits 13 to 20, p=0.93054
b-rank test for bits 14 to 21, p=0.81249
b-rank test for bits 15 to 22, p=0.93090
b-rank test for bits 16 to 23, p=0.64589
b-rank test for bits 17 to 24, p=0.18043
b-rank test for bits 18 to 25, p=0.64477
b-rank test for bits 19 to 26, p=0.50648
b-rank test for bits 20 to 27, p=0.72464
b-rank test for bits 21 to 28, p=0.11789
b-rank test for bits 22 to 29, p=0.83663
b-rank test for bits 23 to 30, p=0.14260
b-rank test for bits 24 to 31, p=0.72337
b-rank test for bits 25 to 32, p=0.96916
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 = 0.516132
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_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 141718 -0.45 0.327426
2 141389 -1.22 0.112045
3 141552 -0.83 0.201892
4 142265 0.83 0.797015
5 141719 -0.44 0.328270
6 141823 -0.20 0.420073
7 141302 -1.42 0.077950
8 141870 -0.09 0.463392
9 141630 -0.65 0.256994
10 142144 0.55 0.708255
11 142075 0.39 0.650651
12 142155 0.57 0.717015
13 141919 0.02 0.509013
14 141401 -1.19 0.117478
15 141805 -0.24 0.403708
16 142775 2.02 0.978442
17 141857 -0.12 0.451344
18 142184 0.64 0.739483
19 142258 0.81 0.792364
20 141909 -0.00 0.499692
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_01:31
Bits used No. missing words z-score p-value
23 to 32 142126 0.7471 0.772510
22 to 31 141803 -0.3667 0.356938
21 to 30 141945 0.1230 0.548947
20 to 29 141963 0.1851 0.573413
19 to 28 141604 -1.0529 0.146202
18 to 27 141653 -0.8839 0.188376
17 to 26 141866 -0.1494 0.440614
16 to 25 141833 -0.2632 0.396196
15 to 24 142090 0.6230 0.733358
14 to 23 141080 -2.8598 0.002120
13 to 22 142157 0.8540 0.803457
12 to 21 141648 -0.9011 0.183758
11 to 20 141503 -1.4011 0.080586
10 to 19 141294 -2.1218 0.016926
9 to 18 141815 -0.3253 0.372486
8 to 17 141841 -0.2356 0.406864
7 to 16 141847 -0.2149 0.414911
6 to 15 141597 -1.0770 0.140740
5 to 14 141427 -1.6632 0.048136
4 to 13 142053 0.4954 0.689846
3 to 12 142412 1.7333 0.958483
2 to 11 142102 0.6644 0.746776
1 to 10 142302 1.3540 0.912137
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_01:31
Bits used No. missing words z-score p-value
28 to 32 141652 -0.8723 0.191521
27 to 31 141757 -0.5164 0.302797
26 to 30 141495 -1.4045 0.080084
25 to 29 142308 1.3514 0.911720
24 to 28 142468 1.8938 0.970874
23 to 27 141959 0.1684 0.566855
22 to 26 142169 0.8802 0.810635
21 to 25 142215 1.0362 0.849938
20 to 24 142042 0.4497 0.673547
19 to 23 141638 -0.9198 0.178848
18 to 22 141788 -0.4113 0.340431
17 to 21 141780 -0.4384 0.330546
16 to 20 141524 -1.3062 0.095742
15 to 19 142439 1.7955 0.963712
14 to 18 141551 -1.2147 0.112244
13 to 17 141889 -0.0689 0.472529
12 to 16 141784 -0.4248 0.335474
11 to 15 142074 0.5582 0.711647
10 to 14 141730 -0.6079 0.271628
9 to 13 142165 0.8667 0.806941
8 to 12 141849 -0.2045 0.418978
7 to 11 142059 0.5074 0.694048
6 to 10 141530 -1.2859 0.099245
5 to 9 141514 -1.3401 0.090106
4 to 8 141964 0.1853 0.573512
3 to 7 142203 0.9955 0.840251
2 to 6 141550 -1.2181 0.111599
1 to 5 141982 0.2463 0.597290
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_01:31
Bits used No. missing words z-score p-value
31 to 32 141333 -1.7001 0.044557
30 to 31 142378 1.3825 0.916592
29 to 30 141772 -0.4051 0.342701
28 to 29 141856 -0.1573 0.437498
27 to 28 141689 -0.6499 0.257865
26 to 27 142119 0.6185 0.731876
25 to 26 141747 -0.4788 0.316023
24 to 25 141584 -0.9597 0.168609
23 to 24 142102 0.5683 0.715101
22 to 23 142044 0.3973 0.654411
21 to 22 141889 -0.0600 0.476090
20 to 21 142130 0.6509 0.742459
19 to 20 141963 0.1583 0.562897
18 to 19 142014 0.3088 0.621248
17 to 18 142176 0.7866 0.784253
16 to 17 141611 -0.8800 0.189422
15 to 16 142318 1.2055 0.885998
14 to 15 141783 -0.3727 0.354703
13 to 14 141734 -0.5172 0.302509
12 to 13 141521 -1.1455 0.125998
11 to 12 141782 -0.3756 0.353605
10 to 11 142508 1.7660 0.961301
9 to 10 141979 0.2055 0.581416
8 to 9 141816 -0.2753 0.391539
7 to 8 142667 2.2350 0.987292
6 to 7 142007 0.2881 0.613370
5 to 6 142194 0.8397 0.799471
4 to 5 142466 1.6421 0.949715
3 to 4 141512 -1.1721 0.120586
2 to 3 141779 -0.3845 0.350321
1 to 2 142173 0.7778 0.781653
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2463.56 -0.515 0.303160
Test results for specific bytes for dh-ranFile-2018-06-29_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2497.20 -0.040 0.484207
2 to 9 2579.01 1.117 0.868096
3 to 10 2573.30 1.037 0.850035
4 to 11 2559.75 0.845 0.800929
5 to 12 2455.28 -0.632 0.263561
6 to 13 2554.77 0.775 0.780713
7 to 14 2496.83 -0.045 0.482136
8 to 15 2536.50 0.516 0.697143
9 to 16 2605.76 1.496 0.932624
10 to 17 2420.07 -1.130 0.129164
11 to 18 2420.39 -1.126 0.130127
12 to 19 2571.30 1.008 0.843369
13 to 20 2557.84 0.818 0.793306
14 to 21 2410.14 -1.271 0.101906
15 to 22 2490.79 -0.130 0.448169
16 to 23 2528.69 0.406 0.657547
17 to 24 2435.14 -0.917 0.179512
18 to 25 2617.21 1.658 0.951300
19 to 26 2385.09 -1.625 0.052071
20 to 27 2520.86 0.295 0.615988
21 to 28 2533.88 0.479 0.684068
22 to 29 2504.59 0.065 0.525871
23 to 30 2581.00 1.146 0.874014
24 to 31 2538.46 0.544 0.706735
25 to 32 2365.71 -1.899 0.028777
CDPARK for dh-ranFile-2018-06-29_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
3539 0.7306 0.767486
3492 -1.4155 0.078457
3503 -0.9132 0.180558
3528 0.2283 0.590298
3557 1.5525 0.939730
3522 -0.0457 0.481790
3498 -1.1416 0.126820
3509 -0.6393 0.261324
3534 0.5023 0.692266
3547 1.0959 0.863437
Square side=100, avg. no. parked=3522.90 sample std.=20.78
p-value of the KSTEST for those 10 p-values: 0.993734
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_01:31
0.9273,0.8600,0.3781,0.3998,0.6375,0.4693,0.9121,0.9937,0.4728,0.8818,
The KS test for those 10 p-values: 0.037634
The 3DSPHERES test for dh-ranFile-2018-06-29_01:31
sample no r^3 equiv. uni.
1 16.623 0.425414
2 10.855 0.303592
3 6.072 0.183231
4 12.565 0.342181
5 11.165 0.310761
6 55.868 0.844678
7 7.480 0.220672
8 10.815 0.302663
9 45.283 0.778961
10 46.044 0.784504
11 36.624 0.705004
12 28.842 0.617647
13 15.951 0.412385
14 46.452 0.787410
15 0.720 0.023707
16 83.631 0.938437
17 1.499 0.048729
18 15.931 0.411997
19 70.572 0.904860
20 41.175 0.746531
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.921378
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 1.3 0.5 0.0 -0.2
-1.6 1.1 -0.2 -0.6 -2.0 -0.5
1.3 2.3 1.5 0.1 0.7 -2.1
1.1 -2.3 0.4 -3.3 -1.0 1.2
1.0 0.6 -0.6 1.1 1.0 1.3
1.3 0.5 0.0 0.4 0.2 -0.1
0.3 -0.1 -0.8 -0.7 -1.3 1.0
1.8
Chi-square with 42 degrees of freedom:60.034547
z-score=1.967730, p-value=0.964946
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_01:31
Test no p-value
1 0.587331
2 0.711948
3 0.041383
4 0.093693
5 0.056018
6 0.051999
7 0.432948
8 0.176575
9 0.176493
10 0.808023
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.034888
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_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 66644 0.01 66786 0.21
3 25000.00 24987 0.01 25131 0.69
4 6666.67 6708 0.26 6452 6.91
5 1388.89 1396 0.04 1329 2.58
6 238.10 225 0.72 261 2.20
7 34.72 37 0.15 33 0.09
8 4.96 2 1.77 7 0.84
p=0.18410 p=0.96455
Number of rngs required: 687265, p-value: 0.093
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_01:31
No. of wins: Observed Expected
98147 98585.9
z-score=-1.963, pvalue=0.02483
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66892 66666.7 0.762 0.762
2 37665 37654.3 0.003 0.765
3 27031 26954.7 0.216 0.980
4 19094 19313.5 2.494 3.474
5 13887 13851.4 0.091 3.566
6 10028 9943.5 0.717 4.283
7 7114 7145.0 0.135 4.418
8 5119 5139.1 0.078 4.496
9 3671 3699.9 0.225 4.721
10 2601 2666.3 1.599 6.320
11 1904 1923.3 0.194 6.515
12 1346 1388.7 1.315 7.830
13 1005 1003.7 0.002 7.832
14 732 726.1 0.047 7.879
15 564 525.8 2.770 10.649
16 348 381.2 2.883 13.532
17 295 276.5 1.232 14.764
18 191 200.8 0.481 15.246
19 172 146.0 4.636 19.882
20 76 106.2 8.595 28.477
21 265 287.1 1.703 30.180
Chisq= 30.18 for 20 degrees of freedom, p= 0.93302
SUMMARY of craptest
p-value for no. of wins: 0.024833
p-value for throws/game: 0.933018
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_01:31
No. of wins: Observed Expected
98511 98585.9
z-score=-0.335, pvalue=0.36888
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66798 66666.7 0.259 0.259
2 37308 37654.3 3.185 3.444
3 26926 26954.7 0.031 3.475
4 19399 19313.5 0.379 3.853
5 13813 13851.4 0.107 3.960
6 9975 9943.5 0.100 4.060
7 7273 7145.0 2.292 6.352
8 5117 5139.1 0.095 6.446
9 3816 3699.9 3.645 10.092
10 2687 2666.3 0.161 10.253
11 1919 1923.3 0.010 10.262
12 1364 1388.7 0.441 10.703
13 1001 1003.7 0.007 10.710
14 726 726.1 0.000 10.710
15 520 525.8 0.065 10.775
16 375 381.2 0.099 10.874
17 256 276.5 1.526 12.400
18 174 200.8 3.584 15.984
19 143 146.0 0.061 16.045
20 102 106.2 0.167 16.213
21 308 287.1 1.519 17.732
Chisq= 17.73 for 20 degrees of freedom, p= 0.39494
SUMMARY of craptest
p-value for no. of wins: 0.368884
p-value for throws/game: 0.394941
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0021,0.0099,0.0117,0.0169,0.0182,0.0237,0.0248,0.0288,0.0316,0.0349,
0.0376,0.0414,0.0446,0.0481,0.0487,0.0520,0.0521,0.0560,0.0570,0.0780,
0.0785,0.0801,0.0806,0.0901,0.0918,0.0925,0.0937,0.0957,0.0992,0.1019,
0.1029,0.1116,0.1120,0.1122,0.1175,0.1179,0.1206,0.1260,0.1268,0.1292,
0.1301,0.1393,0.1407,0.1426,0.1462,0.1686,0.1714,0.1764,0.1765,0.1766,
0.1788,0.1795,0.1804,0.1806,0.1832,0.1838,0.1840,0.1841,0.1884,0.1894,
0.1915,0.2019,0.2047,0.2139,0.2173,0.2207,0.2246,0.2300,0.2409,0.2570,
0.2579,0.2613,0.2636,0.2716,0.2887,0.3025,0.3027,0.3028,0.3032,0.3036,
0.3043,0.3087,0.3108,0.3160,0.3247,0.3274,0.3283,0.3305,0.3355,0.3404,
0.3422,0.3427,0.3503,0.3536,0.3547,0.3569,0.3689,0.3716,0.3725,0.3734,
0.3769,0.3781,0.3782,0.3915,0.3949,0.3962,0.3998,0.4037,0.4066,0.4069,
0.4120,0.4124,0.4140,0.4149,0.4190,0.4190,0.4201,0.4254,0.4329,0.4375,
0.4406,0.4406,0.4482,0.4513,0.4560,0.4634,0.4693,0.4725,0.4728,0.4761,
0.4818,0.4821,0.4842,0.4848,0.4907,0.4933,0.4997,0.5016,0.5028,0.5034,
0.5065,0.5090,0.5117,0.5161,0.5259,0.5489,0.5601,0.5629,0.5669,0.5734,
0.5735,0.5814,0.5873,0.5903,0.5924,0.5973,0.6072,0.6134,0.6160,0.6176,
0.6212,0.6213,0.6375,0.6382,0.6448,0.6459,0.6507,0.6512,0.6544,0.6575,
0.6579,0.6599,0.6693,0.6735,0.6780,0.6841,0.6896,0.6898,0.6923,0.6940,
0.6971,0.7012,0.7050,0.7067,0.7083,0.7116,0.7119,0.7151,0.7170,0.7205,
0.7234,0.7246,0.7319,0.7334,0.7395,0.7425,0.7465,0.7468,0.7490,0.7555,
0.7675,0.7725,0.7790,0.7807,0.7808,0.7817,0.7843,0.7845,0.7874,0.7924,
0.7933,0.7970,0.7995,0.8009,0.8035,0.8069,0.8080,0.8106,0.8125,0.8366,
0.8403,0.8434,0.8447,0.8452,0.8499,0.8500,0.8600,0.8634,0.8681,0.8740,
0.8785,0.8818,0.8860,0.8890,0.9035,0.9049,0.9075,0.9090,0.9117,0.9121,
0.9121,0.9166,0.9214,0.9226,0.9273,0.9305,0.9309,0.9326,0.9330,0.9373,
0.9384,0.9397,0.9422,0.9455,0.9497,0.9513,0.9585,0.9595,0.9613,0.9637,
0.9646,0.9649,0.9692,0.9709,0.9784,0.9873,0.9937,0.9937,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.815872
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.