RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.71 21.7869 0.806946
2 to 25 15.82 16.6168 0.519396
3 to 26 15.93 15.1924 0.418373
4 to 27 15.89 11.3560 0.162532
5 to 28 15.66 14.6234 0.377416
6 to 29 16.03 12.8961 0.256889
7 to 30 15.76 20.4205 0.746710
8 to 31 15.69 25.7634 0.921120
9 to 32 15.80 13.3012 0.284199
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.926021
Tough bday spacings test for dh-ranFile-2018-07-06_13:31: 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 12 33 81 96 100 79 41 34 12 10 2
(O-E)^2/E 0.9 0.4 0.8 0.0 0.1 0.0 2.4 0.6 0.6 1.7 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.458, p= 0.416
RESULTS OF GCD FOR dh-ranFile-2018-07-06_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.797371
p-value, dist. of gcd's: 0.916914
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.686 0.251 0.823 0.176 0.905 0.736 0.459 0.962
Bits 8 to 15---> 0.631 0.160 0.094 0.092 0.941 0.232 0.663 0.916
Bits 16 to 23---> 0.136 0.432 0.184 0.343 0.480 0.328 0.346 0.492
Bits 24 to 31---> 0.363 0.652 0.920 0.787 0.284 0.993 0.076 0.227
KS test for the above 32 p values: 0.203
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_13:31,
p-values for 5 runs: 0.8167, 0.7552, 0.7415, 0.1659, 0.3416
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5095 5134.0 0.296 1.302
r= 30 23163 23103.0 0.156 1.458
r= 31 11516 11551.5 0.109 1.567
chi-square = 1.567 with df = 3; p-value = 0.333
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5279 5134.0 4.095 4.300
r= 31 22996 23103.0 0.496 4.796
r= 32 11507 11551.5 0.172 4.967
chi-square = 4.967 with df = 3; p-value = 0.826
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_13:31
b-rank test for bits 1 to 8, p=0.23763
b-rank test for bits 2 to 9, p=0.11398
b-rank test for bits 3 to 10, p=0.39591
b-rank test for bits 4 to 11, p=0.58911
b-rank test for bits 5 to 12, p=0.40026
b-rank test for bits 6 to 13, p=0.33195
b-rank test for bits 7 to 14, p=0.01515
b-rank test for bits 8 to 15, p=0.19908
b-rank test for bits 9 to 16, p=0.39240
b-rank test for bits 10 to 17, p=0.33916
b-rank test for bits 11 to 18, p=0.09094
b-rank test for bits 12 to 19, p=0.05507
b-rank test for bits 13 to 20, p=0.75658
b-rank test for bits 14 to 21, p=0.75987
b-rank test for bits 15 to 22, p=0.70262
b-rank test for bits 16 to 23, p=0.41621
b-rank test for bits 17 to 24, p=0.71910
b-rank test for bits 18 to 25, p=0.25547
b-rank test for bits 19 to 26, p=0.71312
b-rank test for bits 20 to 27, p=0.44009
b-rank test for bits 21 to 28, p=0.44936
b-rank test for bits 22 to 29, p=0.58397
b-rank test for bits 23 to 30, p=0.95329
b-rank test for bits 24 to 31, p=0.04601
b-rank test for bits 25 to 32, p=0.47779
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 = 0.212813
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_13:31
(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 142523 1.43 0.924187
2 142113 0.48 0.682915
3 141883 -0.06 0.475473
4 142436 1.23 0.890752
5 142239 0.77 0.779426
6 141368 -1.26 0.102973
7 141481 -1.00 0.158469
8 141365 -1.27 0.101722
9 142050 0.33 0.628797
10 142075 0.39 0.650651
11 142090 0.42 0.663534
12 141734 -0.41 0.341032
13 141746 -0.38 0.351375
14 141390 -1.21 0.112491
15 141621 -0.67 0.250261
16 141934 0.06 0.522982
17 141334 -1.34 0.089437
18 141197 -1.66 0.048024
19 141647 -0.61 0.269964
20 142096 0.44 0.668634
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_13:31
Bits used No. missing words z-score p-value
23 to 32 141809 -0.3460 0.364684
22 to 31 142087 0.6127 0.729948
21 to 30 141826 -0.2873 0.386924
20 to 29 142531 2.1437 0.983971
19 to 28 141724 -0.6391 0.261389
18 to 27 141784 -0.4322 0.332808
17 to 26 141916 0.0230 0.509175
16 to 25 142125 0.7437 0.771468
15 to 24 141841 -0.2356 0.406864
14 to 23 141787 -0.4218 0.336575
13 to 22 141497 -1.4218 0.077538
12 to 21 141847 -0.2149 0.414911
11 to 20 141774 -0.4667 0.320373
10 to 19 141770 -0.4804 0.315454
9 to 18 141627 -0.9736 0.165140
8 to 17 141371 -1.8563 0.031705
7 to 16 141934 0.0851 0.533897
6 to 15 141912 0.0092 0.503673
5 to 14 141721 -0.6494 0.258036
4 to 13 141917 0.0264 0.510550
3 to 12 141970 0.2092 0.582857
2 to 11 142131 0.7644 0.777679
1 to 10 142382 1.6299 0.948438
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_13:31
Bits used No. missing words z-score p-value
28 to 32 141414 -1.6791 0.046568
27 to 31 142059 0.5074 0.694048
26 to 30 141634 -0.9333 0.175327
25 to 29 141841 -0.2316 0.408414
24 to 28 141527 -1.2960 0.097482
23 to 27 141655 -0.8621 0.194306
22 to 26 141744 -0.5604 0.287589
21 to 25 141579 -1.1198 0.131407
20 to 24 142264 1.2023 0.885371
19 to 23 141922 0.0429 0.517129
18 to 22 141618 -0.9876 0.161684
17 to 21 141513 -1.3435 0.089556
16 to 20 141959 0.1684 0.566855
15 to 19 141597 -1.0587 0.144858
14 to 18 141628 -0.9537 0.170128
13 to 17 141749 -0.5435 0.293396
12 to 16 141519 -1.3232 0.092892
11 to 15 141936 0.0904 0.536018
10 to 14 142124 0.7277 0.766600
9 to 13 141763 -0.4960 0.309935
8 to 12 141610 -1.0147 0.155130
7 to 11 141595 -1.0655 0.143319
6 to 10 141582 -1.1096 0.133587
5 to 9 141629 -0.9503 0.170987
4 to 8 142248 1.1480 0.874523
3 to 7 142095 0.6294 0.735453
2 to 6 141974 0.2192 0.586761
1 to 5 141973 0.2158 0.585440
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_13:31
Bits used No. missing words z-score p-value
31 to 32 141636 -0.8063 0.210040
30 to 31 141719 -0.5614 0.287247
29 to 30 142037 0.3766 0.646767
28 to 29 142211 0.8899 0.813235
27 to 28 141562 -1.0246 0.152783
26 to 27 141705 -0.6027 0.273340
25 to 26 142035 0.3707 0.644573
24 to 25 141496 -1.2193 0.111372
23 to 24 141706 -0.5998 0.274322
22 to 23 141948 0.1141 0.545409
21 to 22 142134 0.6627 0.746253
20 to 21 141805 -0.3078 0.379133
19 to 20 141984 0.2203 0.587168
18 to 19 142053 0.4238 0.664146
17 to 18 142203 0.8663 0.806833
16 to 17 142215 0.9017 0.816387
15 to 16 141696 -0.6293 0.264579
14 to 15 141603 -0.9036 0.183096
13 to 14 141943 0.0993 0.539559
12 to 13 142024 0.3383 0.632416
11 to 12 141681 -0.6735 0.250302
10 to 11 142367 1.3501 0.911501
9 to 10 141806 -0.3048 0.380256
8 to 9 142853 2.7837 0.997313
7 to 8 141925 0.0462 0.518434
6 to 7 142302 1.1583 0.876633
5 to 6 142061 0.4474 0.672708
4 to 5 142157 0.7306 0.767485
3 to 4 141978 0.2026 0.580263
2 to 3 142457 1.6155 0.946904
1 to 2 142102 0.5683 0.715101
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2568.22 0.965 0.832654
Test results for specific bytes for dh-ranFile-2018-07-06_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2463.81 -0.512 0.304387
2 to 9 2395.62 -1.476 0.069953
3 to 10 2482.00 -0.255 0.399530
4 to 11 2628.63 1.819 0.965552
5 to 12 2535.17 0.497 0.690528
6 to 13 2439.67 -0.853 0.196769
7 to 14 2488.01 -0.170 0.432692
8 to 15 2646.03 2.065 0.980546
9 to 16 2453.57 -0.657 0.255701
10 to 17 2435.94 -0.906 0.182468
11 to 18 2623.40 1.745 0.959521
12 to 19 2430.32 -0.985 0.162211
13 to 20 2602.19 1.445 0.925798
14 to 21 2527.52 0.389 0.651427
15 to 22 2437.74 -0.880 0.189302
16 to 23 2454.14 -0.649 0.258289
17 to 24 2535.37 0.500 0.691515
18 to 25 2577.04 1.090 0.862037
19 to 26 2458.03 -0.594 0.276401
20 to 27 2486.82 -0.186 0.426084
21 to 28 2572.56 1.026 0.847599
22 to 29 2584.85 1.200 0.884929
23 to 30 2484.07 -0.225 0.410876
24 to 31 2604.02 1.471 0.929367
25 to 32 2517.65 0.250 0.598571
CDPARK for dh-ranFile-2018-07-06_13:31: 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
3548 1.1416 0.873180
3523 0.0000 0.500000
3515 -0.3653 0.357445
3525 0.0913 0.536383
3568 2.0548 0.980051
3517 -0.2740 0.392053
3499 -1.0959 0.136563
3556 1.5068 0.934075
3515 -0.3653 0.357445
3525 0.0913 0.536383
Square side=100, avg. no. parked=3529.10 sample std.=20.29
p-value of the KSTEST for those 10 p-values: 0.536266
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_13:31
0.9068,0.1291,0.4546,0.5000,0.8004,0.4067,0.3868,0.0124,0.6744,0.4026,
The KS test for those 10 p-values: 0.801110
The 3DSPHERES test for dh-ranFile-2018-07-06_13:31
sample no r^3 equiv. uni.
1 40.790 0.743250
2 4.818 0.148371
3 0.845 0.027768
4 14.191 0.376893
5 14.079 0.374566
6 14.549 0.384284
7 6.102 0.184051
8 65.102 0.885830
9 50.325 0.813160
10 150.229 0.993313
11 34.086 0.678963
12 38.703 0.724759
13 27.057 0.594198
14 44.699 0.774617
15 15.350 0.400497
16 11.776 0.324663
17 13.964 0.372149
18 91.865 0.953213
19 6.662 0.199129
20 77.773 0.925162
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.724083
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 3.0 1.5 -0.3 -0.2 -0.6
0.8 0.4 -0.6 -0.8 -0.6 0.4
0.1 -0.6 -0.7 1.5 -0.1 0.1
-0.4 -0.3 -0.5 -0.7 1.2 -0.1
0.7 -1.1 1.5 0.9 1.0 0.5
0.5 1.2 -2.2 -1.3 -0.5 -1.0
-2.1 -0.4 -0.4 -0.1 0.9 1.0
-1.1
Chi-square with 42 degrees of freedom:42.849819
z-score=0.092723, p-value=0.565451
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_13:31
Test no p-value
1 0.784877
2 0.000020
3 0.269295
4 0.435345
5 0.656642
6 0.258298
7 0.215727
8 0.420618
9 0.617207
10 0.056175
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.116085
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_13:31:
(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 66674 0.00 66721 0.04
3 25000.00 25100 0.40 25026 0.03
4 6666.67 6600 0.67 6595 0.77
5 1388.89 1387 0.00 1351 1.03
6 238.10 208 3.80 254 1.06
7 34.72 25 2.72 48 5.08
8 4.96 5 0.00 4 0.19
p=0.73075 p=0.77641
Number of rngs required: 688275, p-value: 0.441
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_13:31
No. of wins: Observed Expected
98707 98585.9
z-score= 0.542, pvalue=0.70603
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66805 66666.7 0.287 0.287
2 37610 37654.3 0.052 0.339
3 26903 26954.7 0.099 0.438
4 19157 19313.5 1.268 1.706
5 13724 13851.4 1.172 2.878
6 10025 9943.5 0.667 3.545
7 7120 7145.0 0.088 3.633
8 5247 5139.1 2.267 5.900
9 3762 3699.9 1.043 6.943
10 2632 2666.3 0.441 7.384
11 1969 1923.3 1.084 8.469
12 1408 1388.7 0.267 8.736
13 1018 1003.7 0.203 8.939
14 675 726.1 3.602 12.541
15 501 525.8 1.173 13.714
16 400 381.2 0.932 14.646
17 281 276.5 0.072 14.718
18 190 200.8 0.584 15.302
19 146 146.0 0.000 15.302
20 133 106.2 6.754 22.057
21 294 287.1 0.165 22.222
Chisq= 22.22 for 20 degrees of freedom, p= 0.67140
SUMMARY of craptest
p-value for no. of wins: 0.706027
p-value for throws/game: 0.671402
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_13:31
No. of wins: Observed Expected
98980 98585.9
z-score= 1.763, pvalue=0.96104
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66874 66666.7 0.645 0.645
2 37628 37654.3 0.018 0.663
3 26889 26954.7 0.160 0.824
4 19371 19313.5 0.171 0.995
5 13654 13851.4 2.814 3.809
6 9999 9943.5 0.309 4.118
7 7111 7145.0 0.162 4.280
8 5158 5139.1 0.070 4.350
9 3668 3699.9 0.274 4.624
10 2754 2666.3 2.885 7.509
11 1879 1923.3 1.022 8.531
12 1419 1388.7 0.659 9.190
13 951 1003.7 2.769 11.959
14 759 726.1 1.487 13.446
15 493 525.8 2.050 15.496
16 378 381.2 0.026 15.522
17 272 276.5 0.075 15.597
18 191 200.8 0.481 16.078
19 146 146.0 0.000 16.078
20 107 106.2 0.006 16.083
21 299 287.1 0.492 16.576
Chisq= 16.58 for 20 degrees of freedom, p= 0.31966
SUMMARY of craptest
p-value for no. of wins: 0.961035
p-value for throws/game: 0.319662
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0124,0.0152,0.0278,0.0317,0.0460,0.0466,0.0480,0.0551,0.0562,
0.0700,0.0764,0.0775,0.0894,0.0896,0.0909,0.0923,0.0929,0.0942,0.0975,
0.1017,0.1030,0.1114,0.1125,0.1140,0.1161,0.1291,0.1314,0.1336,0.1356,
0.1366,0.1433,0.1449,0.1484,0.1528,0.1551,0.1585,0.1597,0.1617,0.1622,
0.1625,0.1651,0.1659,0.1701,0.1710,0.1753,0.1764,0.1825,0.1831,0.1839,
0.1841,0.1893,0.1943,0.1968,0.1991,0.1991,0.2034,0.2100,0.2128,0.2157,
0.2270,0.2318,0.2376,0.2503,0.2503,0.2508,0.2555,0.2557,0.2569,0.2580,
0.2583,0.2583,0.2614,0.2646,0.2693,0.2700,0.2733,0.2743,0.2764,0.2839,
0.2842,0.2872,0.2876,0.2934,0.3044,0.3099,0.3155,0.3197,0.3204,0.3247,
0.3275,0.3320,0.3328,0.3331,0.3366,0.3392,0.3410,0.3416,0.3430,0.3461,
0.3514,0.3574,0.3574,0.3633,0.3647,0.3721,0.3746,0.3769,0.3774,0.3791,
0.3803,0.3843,0.3868,0.3869,0.3921,0.3924,0.3959,0.3995,0.4003,0.4005,
0.4026,0.4067,0.4069,0.4084,0.4109,0.4149,0.4158,0.4162,0.4184,0.4206,
0.4261,0.4322,0.4327,0.4353,0.4401,0.4415,0.4494,0.4546,0.4592,0.4755,
0.4778,0.4805,0.4917,0.5000,0.5000,0.5037,0.5092,0.5106,0.5171,0.5184,
0.5194,0.5230,0.5339,0.5360,0.5363,0.5364,0.5364,0.5396,0.5454,0.5655,
0.5669,0.5803,0.5829,0.5840,0.5854,0.5868,0.5872,0.5891,0.5942,0.5986,
0.6172,0.6288,0.6306,0.6324,0.6446,0.6468,0.6507,0.6514,0.6521,0.6566,
0.6627,0.6635,0.6641,0.6686,0.6714,0.6727,0.6744,0.6790,0.6829,0.6859,
0.6905,0.6915,0.6940,0.7026,0.7060,0.7131,0.7151,0.7191,0.7241,0.7248,
0.7299,0.7307,0.7355,0.7359,0.7415,0.7433,0.7463,0.7467,0.7552,0.7566,
0.7599,0.7666,0.7675,0.7715,0.7746,0.7764,0.7777,0.7794,0.7849,0.7871,
0.7974,0.8004,0.8011,0.8068,0.8069,0.8132,0.8132,0.8164,0.8167,0.8233,
0.8258,0.8327,0.8476,0.8620,0.8732,0.8745,0.8766,0.8849,0.8854,0.8858,
0.8908,0.9050,0.9068,0.9115,0.9155,0.9169,0.9203,0.9211,0.9242,0.9252,
0.9258,0.9260,0.9294,0.9341,0.9409,0.9469,0.9484,0.9532,0.9533,0.9595,
0.9610,0.9624,0.9656,0.9801,0.9805,0.9840,0.9927,0.9933,0.9973,
Overall p-value after applying KStest on 269 p-values = 0.332169
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.