RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 13.6784 0.310276
2 to 25 15.98 27.3016 0.946210
3 to 26 15.59 25.1249 0.908052
4 to 27 15.79 35.9065 0.995280
5 to 28 15.84 12.1343 0.208061
6 to 29 15.79 21.6841 0.802826
7 to 30 15.95 16.4774 0.509720
8 to 31 15.87 24.1055 0.883403
9 to 32 15.72 20.4306 0.747201
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.037281
Tough bday spacings test for dh-ranFile-2018-07-06_08:31: 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 38 82 90 98 69 56 37 16 5 4
(O-E)^2/E 1.9 0.1 1.0 0.6 0.0 1.1 0.3 1.8 0.1 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.184, p= 0.292
RESULTS OF GCD FOR dh-ranFile-2018-07-06_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.192075
p-value, dist. of gcd's: 0.322996
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.426 0.290 0.443 0.969 0.429 0.550 0.376 0.294
Bits 8 to 15---> 0.804 0.313 0.804 0.299 0.733 0.948 0.579 0.702
Bits 16 to 23---> 0.265 0.658 0.569 0.629 0.827 0.595 0.603 0.990
Bits 24 to 31---> 0.795 0.155 0.484 0.838 0.125 0.372 0.151 0.859
KS test for the above 32 p values: 0.707
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_08:31,
p-values for 5 runs: 0.3093, 0.1581, 0.1108, 0.2053, 0.3954
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5143 5134.0 0.016 0.765
r= 30 23124 23103.0 0.019 0.784
r= 31 11509 11551.5 0.157 0.940
chi-square = 0.940 with df = 3; p-value = 0.184
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 216 211.4 0.099 0.099
r= 30 5092 5134.0 0.344 0.443
r= 31 23131 23103.0 0.034 0.477
r= 32 11561 11551.5 0.008 0.485
chi-square = 0.485 with df = 3; p-value = 0.078
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_08:31
b-rank test for bits 1 to 8, p=0.32416
b-rank test for bits 2 to 9, p=0.33866
b-rank test for bits 3 to 10, p=0.43430
b-rank test for bits 4 to 11, p=0.07898
b-rank test for bits 5 to 12, p=0.04072
b-rank test for bits 6 to 13, p=0.67273
b-rank test for bits 7 to 14, p=0.86015
b-rank test for bits 8 to 15, p=0.10365
b-rank test for bits 9 to 16, p=0.97119
b-rank test for bits 10 to 17, p=0.98714
b-rank test for bits 11 to 18, p=0.07652
b-rank test for bits 12 to 19, p=0.80426
b-rank test for bits 13 to 20, p=0.45876
b-rank test for bits 14 to 21, p=0.75783
b-rank test for bits 15 to 22, p=0.47293
b-rank test for bits 16 to 23, p=0.49179
b-rank test for bits 17 to 24, p=0.76450
b-rank test for bits 18 to 25, p=0.29401
b-rank test for bits 19 to 26, p=0.35537
b-rank test for bits 20 to 27, p=0.04934
b-rank test for bits 21 to 28, p=0.02458
b-rank test for bits 22 to 29, p=0.81981
b-rank test for bits 23 to 30, p=0.36818
b-rank test for bits 24 to 31, p=0.18517
b-rank test for bits 25 to 32, p=0.65889
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 = 0.582690
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_08:31
(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 141238 -1.57 0.058379
2 141636 -0.64 0.261535
3 141118 -1.85 0.032236
4 140882 -2.40 0.008191
5 141630 -0.65 0.256994
6 141803 -0.25 0.401899
7 142234 0.76 0.775947
8 141667 -0.57 0.285632
9 141402 -1.19 0.117939
10 142744 1.95 0.974422
11 142768 2.01 0.977585
12 142065 0.36 0.641965
13 141679 -0.54 0.295235
14 142193 0.66 0.746264
15 142195 0.67 0.747759
16 141856 -0.12 0.450419
17 141809 -0.23 0.407331
18 142350 1.03 0.848402
19 141408 -1.17 0.120733
20 142518 1.42 0.922505
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_08:31
Bits used No. missing words z-score p-value
23 to 32 142423 1.7713 0.961743
22 to 31 141859 -0.1736 0.431109
21 to 30 141898 -0.0391 0.484418
20 to 29 141973 0.2196 0.586890
19 to 28 142713 2.7713 0.997208
18 to 27 142189 0.9644 0.832572
17 to 26 141713 -0.6770 0.249203
16 to 25 141961 0.1782 0.570706
15 to 24 141997 0.3023 0.618792
14 to 23 142507 2.0609 0.980345
13 to 22 142233 1.1161 0.867811
12 to 21 142218 1.0644 0.856422
11 to 20 141509 -1.3804 0.083724
10 to 19 142233 1.1161 0.867811
9 to 18 141895 -0.0494 0.480295
8 to 17 142249 1.1713 0.879256
7 to 16 142209 1.0333 0.849279
6 to 15 142291 1.3161 0.905930
5 to 14 142125 0.7437 0.771468
4 to 13 141753 -0.5391 0.294920
3 to 12 141895 -0.0494 0.480295
2 to 11 142367 1.5782 0.942737
1 to 10 141961 0.1782 0.570706
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_08:31
Bits used No. missing words z-score p-value
28 to 32 141590 -1.0825 0.139521
27 to 31 141698 -0.7164 0.236881
26 to 30 142133 0.7582 0.775835
25 to 29 141583 -1.1062 0.134319
24 to 28 141339 -1.9333 0.026598
23 to 27 142069 0.5413 0.705834
22 to 26 142210 1.0192 0.845951
21 to 25 142042 0.4497 0.673547
20 to 24 141899 -0.0350 0.486033
19 to 23 141555 -1.2011 0.114853
18 to 22 142186 0.9379 0.825843
17 to 21 141934 0.0836 0.533324
16 to 20 141710 -0.6757 0.249617
15 to 19 142443 1.8091 0.964778
14 to 18 141453 -1.5469 0.060946
13 to 17 142814 3.0667 0.998918
12 to 16 141776 -0.4520 0.325647
11 to 15 141883 -0.0893 0.464440
10 to 14 141828 -0.2757 0.391391
9 to 13 141659 -0.8486 0.198059
8 to 12 141995 0.2904 0.614248
7 to 11 141412 -1.6859 0.045911
6 to 10 141235 -2.2859 0.011131
5 to 9 142029 0.4057 0.657504
4 to 8 141704 -0.6960 0.243204
3 to 7 141567 -1.1604 0.122935
2 to 6 141637 -0.9232 0.177964
1 to 5 141605 -1.0316 0.151123
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_08:31
Bits used No. missing words z-score p-value
31 to 32 142712 2.3678 0.991052
30 to 31 142048 0.4091 0.658751
29 to 30 141597 -0.9213 0.178440
28 to 29 141194 -2.1101 0.017424
27 to 28 142278 1.0875 0.861597
26 to 27 142252 1.0108 0.843950
25 to 26 141562 -1.0246 0.152783
24 to 25 141880 -0.0865 0.465527
23 to 24 141768 -0.4169 0.338375
22 to 23 141928 0.0551 0.521960
21 to 22 141584 -0.9597 0.168609
20 to 21 142152 0.7158 0.762955
19 to 20 141861 -0.1426 0.443316
18 to 19 141866 -0.1278 0.449147
17 to 18 141573 -0.9921 0.160569
16 to 17 141976 0.1967 0.577956
15 to 16 142042 0.3914 0.652233
14 to 15 142323 1.2203 0.888818
13 to 14 142080 0.5035 0.692677
12 to 13 141916 0.0197 0.507849
11 to 12 142169 0.7660 0.778158
10 to 11 141685 -0.6617 0.254069
9 to 10 142107 0.5831 0.720086
8 to 9 141993 0.2468 0.597474
7 to 8 141505 -1.1927 0.116491
6 to 7 142466 1.6421 0.949715
5 to 6 141708 -0.5939 0.276292
4 to 5 141292 -1.8210 0.034301
3 to 4 141207 -2.0718 0.019143
2 to 3 142294 1.1347 0.871754
1 to 2 142029 0.3530 0.637959
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2468.15 -0.450 0.326214
Test results for specific bytes for dh-ranFile-2018-07-06_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2495.20 -0.068 0.472921
2 to 9 2396.92 -1.458 0.072460
3 to 10 2601.21 1.431 0.923834
4 to 11 2523.24 0.329 0.628772
5 to 12 2386.89 -1.600 0.054834
6 to 13 2512.82 0.181 0.571949
7 to 14 2538.10 0.539 0.704976
8 to 15 2528.27 0.400 0.655336
9 to 16 2438.04 -0.876 0.190437
10 to 17 2427.72 -1.022 0.153360
11 to 18 2579.10 1.119 0.868361
12 to 19 2586.06 1.217 0.888225
13 to 20 2547.09 0.666 0.747262
14 to 21 2500.34 0.005 0.501940
15 to 22 2378.16 -1.723 0.042439
16 to 23 2559.34 0.839 0.799333
17 to 24 2635.03 1.910 0.971912
18 to 25 2446.31 -0.759 0.223849
19 to 26 2413.35 -1.225 0.110198
20 to 27 2427.20 -1.030 0.151614
21 to 28 2385.06 -1.625 0.052035
22 to 29 2353.66 -2.070 0.019249
23 to 30 2422.90 -1.090 0.137789
24 to 31 2509.38 0.133 0.552778
25 to 32 2502.88 0.041 0.516233
CDPARK for dh-ranFile-2018-07-06_08:31: 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
3527 0.1826 0.572463
3496 -1.2329 0.108811
3534 0.5023 0.692266
3520 -0.1370 0.445521
3546 1.0502 0.853193
3561 1.7352 0.958644
3551 1.2785 0.899470
3524 0.0457 0.518210
3503 -0.9132 0.180558
3487 -1.6438 0.050105
Square side=100, avg. no. parked=3524.90 sample std.=23.01
p-value of the KSTEST for those 10 p-values: 0.947327
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_08:31
0.5371,0.5582,0.8489,0.9191,0.2933,0.6163,0.3380,0.4949,0.1121,0.7716,
The KS test for those 10 p-values: 0.837062
The 3DSPHERES test for dh-ranFile-2018-07-06_08:31
sample no r^3 equiv. uni.
1 48.629 0.802295
2 7.198 0.213318
3 8.957 0.258131
4 24.208 0.553781
5 115.826 0.978950
6 175.488 0.997119
7 12.188 0.333863
8 15.386 0.401222
9 17.037 0.433295
10 24.142 0.552792
11 40.347 0.739431
12 6.825 0.203470
13 68.465 0.897936
14 43.363 0.764354
15 10.419 0.293418
16 0.778 0.025595
17 37.477 0.713276
18 68.284 0.897320
19 21.964 0.519110
20 47.728 0.796266
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.458187
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.3 -1.6 -0.4 0.8 0.5
0.7 0.2 -1.1 0.4 0.0 0.6
0.5 0.5 -0.2 0.2 -1.8 -1.5
0.1 1.4 0.3 0.4 0.5 0.2
-0.1 0.4 0.8 -0.3 -1.6 -0.3
-1.5 -0.7 0.1 1.6 -1.5 -1.2
-0.5 -0.4 0.5 0.4 1.6 -1.0
0.8
Chi-square with 42 degrees of freedom:34.335730
z-score=-0.836240, p-value=0.206299
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_08:31
Test no p-value
1 0.055649
2 0.168893
3 0.000935
4 0.003139
5 0.000331
6 0.000476
7 0.160216
8 0.013825
9 0.363724
10 0.486042
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000000
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_08:31:
(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 66839 0.45 66632 0.02
3 25000.00 24907 0.35 24951 0.10
4 6666.67 6625 0.26 6745 0.92
5 1388.89 1370 0.26 1404 0.16
6 238.10 229 0.35 234 0.07
7 34.72 25 2.72 33 0.09
8 4.96 4 0.19 0 4.96
p=0.39908 p=0.61110
Number of rngs required: 690299, p-value: 0.988
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_08:31
No. of wins: Observed Expected
98966 98585.9
z-score= 1.700, pvalue=0.95545
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66896 66666.7 0.789 0.789
2 37792 37654.3 0.503 1.292
3 26935 26954.7 0.014 1.307
4 19213 19313.5 0.523 1.829
5 13873 13851.4 0.034 1.863
6 9787 9943.5 2.464 4.327
7 7176 7145.0 0.134 4.462
8 5197 5139.1 0.653 5.115
9 3693 3699.9 0.013 5.127
10 2643 2666.3 0.204 5.331
11 1812 1923.3 6.444 11.775
12 1350 1388.7 1.081 12.856
13 988 1003.7 0.246 13.102
14 718 726.1 0.091 13.193
15 494 525.8 1.927 15.121
16 369 381.2 0.387 15.508
17 300 276.5 1.990 17.498
18 174 200.8 3.584 21.083
19 163 146.0 1.983 23.066
20 111 106.2 0.216 23.281
21 316 287.1 2.906 26.188
Chisq= 26.19 for 20 degrees of freedom, p= 0.84029
SUMMARY of craptest
p-value for no. of wins: 0.955455
p-value for throws/game: 0.840294
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_08:31
No. of wins: Observed Expected
98439 98585.9
z-score=-0.657, pvalue=0.25564
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66768 66666.7 0.154 0.154
2 37656 37654.3 0.000 0.154
3 26701 26954.7 2.388 2.543
4 19304 19313.5 0.005 2.547
5 13699 13851.4 1.677 4.224
6 9939 9943.5 0.002 4.226
7 7211 7145.0 0.609 4.836
8 5211 5139.1 1.007 5.842
9 3706 3699.9 0.010 5.853
10 2672 2666.3 0.012 5.865
11 1924 1923.3 0.000 5.865
12 1443 1388.7 2.120 7.985
13 1030 1003.7 0.688 8.673
14 738 726.1 0.194 8.867
15 559 525.8 2.092 10.959
16 392 381.2 0.309 11.267
17 284 276.5 0.201 11.469
18 209 200.8 0.332 11.801
19 144 146.0 0.027 11.828
20 105 106.2 0.014 11.842
21 305 287.1 1.114 12.956
Chisq= 12.96 for 20 degrees of freedom, p= 0.12075
SUMMARY of craptest
p-value for no. of wins: 0.255643
p-value for throws/game: 0.120745
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0003,0.0005,0.0009,0.0031,0.0082,0.0111,0.0138,0.0174,0.0191,
0.0192,0.0246,0.0256,0.0266,0.0322,0.0343,0.0373,0.0407,0.0424,0.0459,
0.0493,0.0501,0.0520,0.0548,0.0556,0.0584,0.0609,0.0725,0.0765,0.0778,
0.0790,0.0837,0.1036,0.1088,0.1102,0.1108,0.1121,0.1149,0.1165,0.1179,
0.1207,0.1207,0.1229,0.1251,0.1343,0.1378,0.1395,0.1511,0.1511,0.1516,
0.1528,0.1534,0.1554,0.1581,0.1602,0.1606,0.1686,0.1689,0.1780,0.1784,
0.1806,0.1843,0.1852,0.1904,0.1921,0.1981,0.2035,0.2053,0.2063,0.2081,
0.2133,0.2238,0.2369,0.2432,0.2492,0.2496,0.2541,0.2556,0.2570,0.2581,
0.2615,0.2652,0.2763,0.2856,0.2897,0.2920,0.2933,0.2934,0.2937,0.2940,
0.2949,0.2952,0.2993,0.3093,0.3103,0.3126,0.3230,0.3242,0.3256,0.3262,
0.3339,0.3380,0.3384,0.3387,0.3554,0.3637,0.3682,0.3716,0.3759,0.3914,
0.3954,0.3991,0.4012,0.4019,0.4073,0.4257,0.4289,0.4311,0.4333,0.4343,
0.4433,0.4433,0.4455,0.4491,0.4504,0.4582,0.4588,0.4644,0.4655,0.4729,
0.4729,0.4803,0.4803,0.4837,0.4844,0.4860,0.4860,0.4918,0.4949,0.5019,
0.5078,0.5097,0.5162,0.5182,0.5191,0.5220,0.5333,0.5371,0.5495,0.5528,
0.5528,0.5538,0.5582,0.5695,0.5707,0.5707,0.5719,0.5725,0.5780,0.5794,
0.5827,0.5869,0.5949,0.5975,0.6028,0.6111,0.6142,0.6163,0.6188,0.6288,
0.6290,0.6380,0.6420,0.6522,0.6553,0.6575,0.6584,0.6588,0.6589,0.6727,
0.6735,0.6923,0.6927,0.7023,0.7050,0.7058,0.7071,0.7133,0.7201,0.7332,
0.7394,0.7463,0.7472,0.7473,0.7478,0.7578,0.7630,0.7644,0.7645,0.7715,
0.7716,0.7758,0.7759,0.7782,0.7950,0.7963,0.7993,0.8023,0.8028,0.8038,
0.8043,0.8043,0.8198,0.8258,0.8266,0.8326,0.8371,0.8381,0.8403,0.8440,
0.8460,0.8484,0.8489,0.8493,0.8532,0.8564,0.8587,0.8602,0.8616,0.8678,
0.8678,0.8684,0.8718,0.8793,0.8834,0.8882,0.8888,0.8973,0.8979,0.8995,
0.9059,0.9081,0.9191,0.9225,0.9238,0.9427,0.9462,0.9473,0.9476,0.9497,
0.9555,0.9586,0.9617,0.9648,0.9687,0.9712,0.9719,0.9744,0.9776,0.9790,
0.9803,0.9871,0.9877,0.9902,0.9911,0.9953,0.9971,0.9972,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.141179
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.