RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_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 15.88 23.4570 0.865044
2 to 25 15.49 18.0571 0.614751
3 to 26 15.73 14.7787 0.388579
4 to 27 15.62 24.4563 0.892443
5 to 28 15.54 25.0886 0.907256
6 to 29 15.74 16.5560 0.515181
7 to 30 15.57 25.2536 0.910825
8 to 31 15.61 19.1940 0.682487
9 to 32 15.45 27.0753 0.943027
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.012475
Tough bday spacings test for dh-ranFile-2018-06-26_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 5 46 79 85 98 70 62 35 8 8 4
(O-E)^2/E 1.9 2.4 0.4 1.6 0.0 0.8 1.9 0.9 3.2 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 13.507, p= 0.803
RESULTS OF GCD FOR dh-ranFile-2018-06-26_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.072172
p-value, dist. of gcd's: 0.519441
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.131 0.111 0.501 0.576 0.253 0.676 0.886 0.632
Bits 8 to 15---> 0.336 0.280 0.645 0.608 0.278 0.901 0.046 0.700
Bits 16 to 23---> 0.469 0.897 0.354 0.416 0.589 0.290 0.655 0.724
Bits 24 to 31---> 0.888 0.193 0.737 0.746 0.973 0.285 0.072 0.585
KS test for the above 32 p values: 0.159
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_10:31,
p-values for 5 runs: 0.2497, 0.3882, 0.6325, 0.2883, 0.7123
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 229 211.4 1.462 1.462
r= 29 5136 5134.0 0.001 1.463
r= 30 22957 23103.0 0.923 2.386
r= 31 11678 11551.5 1.385 3.771
chi-square = 3.771 with df = 3; p-value = 0.713
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 241 211.4 4.139 4.139
r= 30 5030 5134.0 2.107 6.246
r= 31 23277 23103.0 1.310 7.556
r= 32 11452 11551.5 0.857 8.414
chi-square = 8.414 with df = 3; p-value = 0.962
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_10:31
b-rank test for bits 1 to 8, p=0.80629
b-rank test for bits 2 to 9, p=0.26780
b-rank test for bits 3 to 10, p=0.10930
b-rank test for bits 4 to 11, p=0.74289
b-rank test for bits 5 to 12, p=0.36518
b-rank test for bits 6 to 13, p=0.67848
b-rank test for bits 7 to 14, p=0.72410
b-rank test for bits 8 to 15, p=0.14017
b-rank test for bits 9 to 16, p=0.25051
b-rank test for bits 10 to 17, p=0.89321
b-rank test for bits 11 to 18, p=0.33135
b-rank test for bits 12 to 19, p=0.79126
b-rank test for bits 13 to 20, p=0.49333
b-rank test for bits 14 to 21, p=0.18202
b-rank test for bits 15 to 22, p=0.14676
b-rank test for bits 16 to 23, p=0.48336
b-rank test for bits 17 to 24, p=0.87152
b-rank test for bits 18 to 25, p=0.65567
b-rank test for bits 19 to 26, p=0.68154
b-rank test for bits 20 to 27, p=0.17826
b-rank test for bits 21 to 28, p=0.90103
b-rank test for bits 22 to 29, p=0.30954
b-rank test for bits 23 to 30, p=0.36792
b-rank test for bits 24 to 31, p=0.50233
b-rank test for bits 25 to 32, p=0.50821
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 = 0.770283
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_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 142367 1.07 0.857538
2 141682 -0.53 0.297659
3 142274 0.85 0.802902
4 142224 0.74 0.768894
5 142123 0.50 0.691191
6 142373 1.08 0.860672
7 141683 -0.53 0.298469
8 141809 -0.23 0.407331
9 142088 0.42 0.661827
10 141971 0.14 0.557285
11 142206 0.69 0.755894
12 142379 1.10 0.863758
13 142688 1.82 0.965569
14 142255 0.81 0.790351
15 141066 -1.97 0.024396
16 141389 -1.22 0.112045
17 142107 0.46 0.677904
18 142121 0.49 0.689543
19 142149 0.56 0.712252
20 142357 1.05 0.852210
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_10:31
Bits used No. missing words z-score p-value
23 to 32 142058 0.5127 0.695904
22 to 31 141998 0.3058 0.620106
21 to 30 142045 0.4678 0.680046
20 to 29 141485 -1.4632 0.071705
19 to 28 141756 -0.5287 0.298498
18 to 27 142012 0.3540 0.638344
17 to 26 141600 -1.0667 0.143064
16 to 25 142292 1.3196 0.906508
15 to 24 141992 0.2851 0.612204
14 to 23 141796 -0.3908 0.347975
13 to 22 142301 1.3506 0.911586
12 to 21 141568 -1.1770 0.119598
11 to 20 141373 -1.8494 0.032199
10 to 19 141304 -2.0873 0.018428
9 to 18 141278 -2.1770 0.014740
8 to 17 142411 1.7299 0.958176
7 to 16 141888 -0.0736 0.470684
6 to 15 141892 -0.0598 0.476174
5 to 14 142513 2.0816 0.981311
4 to 13 141479 -1.4839 0.068918
3 to 12 141725 -0.6356 0.262512
2 to 11 141866 -0.1494 0.440614
1 to 10 141626 -0.9770 0.164285
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_10:31
Bits used No. missing words z-score p-value
28 to 32 141778 -0.4452 0.328093
27 to 31 141778 -0.4452 0.328093
26 to 30 141556 -1.1977 0.115511
25 to 29 141928 0.0633 0.525232
24 to 28 142225 1.0701 0.857706
23 to 27 141774 -0.4587 0.323208
22 to 26 141987 0.2633 0.603836
21 to 25 141457 -1.5333 0.062598
20 to 24 141473 -1.4791 0.069559
19 to 23 142177 0.9074 0.817891
18 to 22 141847 -0.2113 0.416331
17 to 21 142369 1.5582 0.940407
16 to 20 141742 -0.5672 0.285282
15 to 19 141745 -0.5571 0.288746
14 to 18 142560 2.2057 0.986296
13 to 17 142405 1.6802 0.953544
12 to 16 141216 -2.3503 0.009380
11 to 15 142293 1.3006 0.903298
10 to 14 141744 -0.5604 0.287589
9 to 13 141571 -1.1469 0.125715
8 to 12 142143 0.7921 0.785849
7 to 11 141949 0.1345 0.553486
6 to 10 141524 -1.3062 0.095742
5 to 9 141810 -0.3367 0.368167
4 to 8 142099 0.6429 0.739872
3 to 7 141910 0.0023 0.500906
2 to 6 141645 -0.8960 0.185117
1 to 5 142017 0.3650 0.642438
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_10:31
Bits used No. missing words z-score p-value
31 to 32 141753 -0.4612 0.322345
30 to 31 141833 -0.2252 0.410927
29 to 30 141325 -1.7237 0.042382
28 to 29 141927 0.0521 0.520785
27 to 28 142191 0.8309 0.796981
26 to 27 141398 -1.5083 0.065733
25 to 26 142128 0.6450 0.740551
24 to 25 141866 -0.1278 0.449147
23 to 24 142014 0.3088 0.621248
22 to 23 141559 -1.0334 0.150703
21 to 22 141833 -0.2252 0.410927
20 to 21 141758 -0.4464 0.327654
19 to 20 142288 1.1170 0.868007
18 to 19 142075 0.4887 0.687474
17 to 18 142146 0.6981 0.757456
16 to 17 141512 -1.1721 0.120586
15 to 16 141789 -0.3550 0.361311
14 to 15 141896 -0.0393 0.484317
13 to 14 141670 -0.7060 0.240098
12 to 13 142229 0.9430 0.827154
11 to 12 141731 -0.5260 0.299428
10 to 11 141640 -0.7945 0.213457
9 to 10 141434 -1.4022 0.080435
8 to 9 141514 -1.1662 0.121774
7 to 8 141823 -0.2547 0.399493
6 to 7 142221 0.9194 0.821052
5 to 6 142162 0.7453 0.771967
4 to 5 142534 1.8427 0.967312
3 to 4 142186 0.8161 0.792789
2 to 3 142346 1.2881 0.901147
1 to 2 142049 0.4120 0.659832
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2560.13 0.850 0.802437
Test results for specific bytes for dh-ranFile-2018-06-26_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2531.15 0.441 0.670230
2 to 9 2423.08 -1.088 0.138339
3 to 10 2390.05 -1.555 0.059990
4 to 11 2520.18 0.285 0.612336
5 to 12 2492.65 -0.104 0.458590
6 to 13 2563.65 0.900 0.815993
7 to 14 2497.11 -0.041 0.483720
8 to 15 2493.27 -0.095 0.462109
9 to 16 2560.37 0.854 0.803395
10 to 17 2551.00 0.721 0.764609
11 to 18 2450.47 -0.701 0.241801
12 to 19 2501.61 0.023 0.509076
13 to 20 2546.59 0.659 0.745034
14 to 21 2545.19 0.639 0.738619
15 to 22 2497.24 -0.039 0.484430
16 to 23 2316.21 -2.599 0.004672
17 to 24 2539.86 0.564 0.713516
18 to 25 2487.60 -0.175 0.430388
19 to 26 2518.23 0.258 0.601749
20 to 27 2476.74 -0.329 0.371090
21 to 28 2436.09 -0.904 0.183049
22 to 29 2548.66 0.688 0.754342
23 to 30 2540.28 0.570 0.715524
24 to 31 2617.06 1.656 0.951093
25 to 32 2651.73 2.146 0.984055
CDPARK for dh-ranFile-2018-06-26_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
3508 -0.6849 0.246694
3513 -0.4566 0.323972
3504 -0.8676 0.192812
3498 -1.1416 0.126820
3539 0.7306 0.767486
3526 0.1370 0.554479
3531 0.3653 0.642555
3547 1.0959 0.863437
3517 -0.2740 0.392053
3560 1.6895 0.954438
Square side=100, avg. no. parked=3524.30 sample std.=18.98
p-value of the KSTEST for those 10 p-values: 0.995410
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_10:31
0.3764,0.4544,0.2676,0.0325,0.7411,0.1087,0.7987,0.0638,0.7835,0.0030,
The KS test for those 10 p-values: 0.102436
The 3DSPHERES test for dh-ranFile-2018-06-26_10:31
sample no r^3 equiv. uni.
1 9.153 0.262961
2 18.379 0.458076
3 20.599 0.496735
4 4.120 0.128332
5 26.844 0.591305
6 0.414 0.013719
7 35.423 0.692954
8 6.423 0.192729
9 45.512 0.780645
10 21.061 0.504422
11 9.699 0.276238
12 20.333 0.492250
13 2.975 0.094419
14 12.775 0.346766
15 36.701 0.705764
16 73.174 0.912763
17 15.531 0.404114
18 67.506 0.894622
19 29.277 0.623148
20 32.439 0.660848
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.866964
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 1.8 -0.8 -0.1 0.4
0.5 0.1 1.7 0.7 -0.0 -2.9
-1.0 -0.8 1.3 0.5 0.3 -0.5
-0.4 -0.5 0.1 2.4 0.5 1.0
-1.6 0.1 0.7 -1.8 -0.2 -0.7
0.8 -0.4 -0.4 -1.1 0.5 0.4
-1.4 -0.7 0.9 0.4 1.6 -1.0
2.7
Chi-square with 42 degrees of freedom:51.853764
z-score=1.075134, p-value=0.858244
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_10:31
Test no p-value
1 0.003904
2 0.421541
3 0.122923
4 0.759668
5 0.428175
6 0.846732
7 0.457124
8 0.027603
9 0.608735
10 0.926478
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.545790
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_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 66557 0.18 66355 1.46
3 25000.00 25207 1.71 25030 0.04
4 6666.67 6571 1.37 6866 5.96
5 1388.89 1392 0.01 1444 2.19
6 238.10 230 0.28 262 2.40
7 34.72 38 0.31 32 0.21
8 4.96 4 0.19 10 5.12
p=0.32943 p=0.99200
Number of rngs required: 688536, p-value: 0.561
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_10:31
No. of wins: Observed Expected
98604 98585.9
z-score= 0.081, pvalue=0.53233
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66592 66666.7 0.084 0.084
2 37804 37654.3 0.595 0.679
3 26936 26954.7 0.013 0.692
4 19377 19313.5 0.209 0.901
5 13761 13851.4 0.590 1.491
6 10080 9943.5 1.873 3.364
7 7060 7145.0 1.012 4.375
8 5078 5139.1 0.726 5.101
9 3663 3699.9 0.367 5.468
10 2617 2666.3 0.911 6.380
11 1899 1923.3 0.308 6.688
12 1433 1388.7 1.411 8.098
13 983 1003.7 0.428 8.526
14 748 726.1 0.658 9.184
15 563 525.8 2.627 11.810
16 374 381.2 0.134 11.945
17 292 276.5 0.864 12.809
18 194 200.8 0.232 13.041
19 151 146.0 0.172 13.214
20 106 106.2 0.000 13.214
21 289 287.1 0.012 13.226
Chisq= 13.23 for 20 degrees of freedom, p= 0.13254
SUMMARY of craptest
p-value for no. of wins: 0.532334
p-value for throws/game: 0.132537
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_10:31
No. of wins: Observed Expected
98481 98585.9
z-score=-0.469, pvalue=0.31954
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66055 66666.7 5.612 5.612
2 37857 37654.3 1.091 6.703
3 27021 26954.7 0.163 6.866
4 19428 19313.5 0.679 7.545
5 13950 13851.4 0.702 8.247
6 9964 9943.5 0.042 8.289
7 7078 7145.0 0.629 8.918
8 5174 5139.1 0.237 9.155
9 3619 3699.9 1.767 10.922
10 2740 2666.3 2.037 12.960
11 1982 1923.3 1.790 14.749
12 1342 1388.7 1.573 16.323
13 1027 1003.7 0.540 16.863
14 771 726.1 2.771 19.634
15 557 525.8 1.847 21.481
16 350 381.2 2.546 24.027
17 299 276.5 1.824 25.851
18 207 200.8 0.190 26.041
19 167 146.0 3.025 29.066
20 121 106.2 2.058 31.124
21 291 287.1 0.053 31.177
Chisq= 31.18 for 20 degrees of freedom, p= 0.94710
SUMMARY of craptest
p-value for no. of wins: 0.319539
p-value for throws/game: 0.947099
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0030,0.0039,0.0047,0.0094,0.0125,0.0137,0.0147,0.0184,0.0244,0.0276,
0.0322,0.0325,0.0424,0.0459,0.0600,0.0626,0.0638,0.0657,0.0689,0.0696,
0.0717,0.0719,0.0722,0.0804,0.0944,0.0957,0.1024,0.1087,0.1093,0.1111,
0.1120,0.1155,0.1196,0.1206,0.1218,0.1229,0.1257,0.1268,0.1283,0.1308,
0.1325,0.1383,0.1402,0.1431,0.1468,0.1507,0.1586,0.1643,0.1783,0.1820,
0.1830,0.1851,0.1927,0.1928,0.1929,0.2135,0.2401,0.2418,0.2467,0.2497,
0.2505,0.2533,0.2625,0.2630,0.2676,0.2678,0.2762,0.2777,0.2799,0.2852,
0.2853,0.2876,0.2883,0.2887,0.2897,0.2977,0.2985,0.2985,0.2994,0.3095,
0.3195,0.3223,0.3232,0.3240,0.3277,0.3281,0.3281,0.3294,0.3314,0.3364,
0.3468,0.3480,0.3542,0.3613,0.3652,0.3679,0.3682,0.3711,0.3764,0.3882,
0.3886,0.3921,0.3995,0.4041,0.4073,0.4109,0.4109,0.4157,0.4163,0.4215,
0.4282,0.4304,0.4406,0.4491,0.4544,0.4571,0.4581,0.4586,0.4621,0.4693,
0.4707,0.4762,0.4834,0.4837,0.4843,0.4844,0.4922,0.4933,0.4967,0.5009,
0.5012,0.5023,0.5044,0.5082,0.5091,0.5152,0.5194,0.5208,0.5252,0.5323,
0.5458,0.5535,0.5545,0.5573,0.5608,0.5761,0.5848,0.5886,0.5913,0.6017,
0.6038,0.6076,0.6087,0.6122,0.6123,0.6148,0.6201,0.6212,0.6231,0.6322,
0.6325,0.6383,0.6424,0.6426,0.6453,0.6554,0.6557,0.6598,0.6608,0.6618,
0.6702,0.6764,0.6779,0.6785,0.6800,0.6815,0.6825,0.6875,0.6895,0.6912,
0.6930,0.6959,0.6997,0.7058,0.7123,0.7123,0.7127,0.7135,0.7155,0.7236,
0.7241,0.7367,0.7386,0.7399,0.7406,0.7411,0.7429,0.7450,0.7456,0.7543,
0.7559,0.7575,0.7597,0.7646,0.7675,0.7689,0.7703,0.7720,0.7806,0.7835,
0.7858,0.7904,0.7913,0.7928,0.7970,0.7987,0.8024,0.8029,0.8033,0.8034,
0.8063,0.8160,0.8179,0.8211,0.8272,0.8467,0.8522,0.8575,0.8577,0.8582,
0.8607,0.8634,0.8638,0.8650,0.8670,0.8680,0.8715,0.8856,0.8877,0.8924,
0.8932,0.8946,0.8969,0.9010,0.9011,0.9014,0.9033,0.9065,0.9073,0.9108,
0.9116,0.9128,0.9265,0.9404,0.9430,0.9471,0.9511,0.9535,0.9544,0.9582,
0.9618,0.9656,0.9673,0.9734,0.9813,0.9841,0.9863,0.9920,0.9954,
Overall p-value after applying KStest on 269 p-values = 0.734396
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.