RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.76 19.3575 0.691597
2 to 25 15.73 14.9860 0.403510
3 to 26 15.44 26.6146 0.936032
4 to 27 15.85 17.1825 0.557928
5 to 28 15.65 22.6107 0.837641
6 to 29 15.90 10.0669 0.099219
7 to 30 15.94 12.5748 0.235847
8 to 31 15.73 16.8934 0.538388
9 to 32 15.52 28.2820 0.958251
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.694167
Tough bday spacings test for dh-ranFile-2018-07-09_11:31: 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 7 32 83 97 94 82 52 19 23 8 3
(O-E)^2/E 0.5 0.6 1.3 0.0 0.1 0.2 0.0 3.9 4.4 0.3 0.3
Birthday Spacings: Sum(O-E)^2/E= 11.612, p= 0.688
RESULTS OF GCD FOR dh-ranFile-2018-07-09_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.398834
p-value, dist. of gcd's: 0.505771
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.009 0.192 0.573 0.502 0.816 0.232 0.670 0.005
Bits 8 to 15---> 0.737 0.777 0.002 0.372 0.842 0.727 0.964 0.836
Bits 16 to 23---> 0.774 0.373 0.976 0.646 0.257 0.637 0.719 0.089
Bits 24 to 31---> 0.839 0.907 0.005 0.185 0.445 0.656 0.197 0.177
KS test for the above 32 p values: 0.755
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_11:31,
p-values for 5 runs: 0.3388, 0.2465, 0.9307, 0.7153, 0.7929
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 196 211.4 1.124 1.124
r= 29 5062 5134.0 1.010 2.134
r= 30 23156 23103.0 0.121 2.256
r= 31 11586 11551.5 0.103 2.359
chi-square = 2.359 with df = 3; p-value = 0.499
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 234 211.4 2.412 2.412
r= 30 5215 5134.0 1.278 3.690
r= 31 23163 23103.0 0.156 3.845
r= 32 11388 11551.5 2.315 6.160
chi-square = 6.160 with df = 3; p-value = 0.896
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_11:31
b-rank test for bits 1 to 8, p=0.13850
b-rank test for bits 2 to 9, p=0.61600
b-rank test for bits 3 to 10, p=0.85785
b-rank test for bits 4 to 11, p=0.97806
b-rank test for bits 5 to 12, p=0.50646
b-rank test for bits 6 to 13, p=0.66531
b-rank test for bits 7 to 14, p=0.57252
b-rank test for bits 8 to 15, p=0.00032
b-rank test for bits 9 to 16, p=0.45192
b-rank test for bits 10 to 17, p=0.01901
b-rank test for bits 11 to 18, p=0.93102
b-rank test for bits 12 to 19, p=0.71312
b-rank test for bits 13 to 20, p=0.21035
b-rank test for bits 14 to 21, p=0.80156
b-rank test for bits 15 to 22, p=0.49589
b-rank test for bits 16 to 23, p=0.95475
b-rank test for bits 17 to 24, p=0.59400
b-rank test for bits 18 to 25, p=0.07323
b-rank test for bits 19 to 26, p=0.61141
b-rank test for bits 20 to 27, p=0.99672
b-rank test for bits 21 to 28, p=0.80124
b-rank test for bits 22 to 29, p=0.71817
b-rank test for bits 23 to 30, p=0.16882
b-rank test for bits 24 to 31, p=0.17168
b-rank test for bits 25 to 32, p=0.66072
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 = 0.332095
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_11:31
(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 141900 -0.02 0.491304
2 142532 1.45 0.927143
3 142133 0.52 0.699371
4 141388 -1.22 0.111600
5 142047 0.32 0.626144
6 142268 0.84 0.798989
7 141280 -1.47 0.070727
8 141791 -0.28 0.391093
9 141351 -1.30 0.096030
10 141228 -1.59 0.055704
11 141955 0.11 0.542489
12 141934 0.06 0.522982
13 142886 2.28 0.988754
14 142161 0.59 0.721739
15 142235 0.76 0.776645
16 142284 0.88 0.809321
17 141669 -0.56 0.287222
18 141706 -0.48 0.317369
19 142985 2.51 0.994019
20 141447 -1.08 0.140024
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_11:31
Bits used No. missing words z-score p-value
23 to 32 141926 0.0575 0.522920
22 to 31 141944 0.1196 0.547581
21 to 30 141825 -0.2908 0.385605
20 to 29 141504 -1.3977 0.081103
19 to 28 142233 1.1161 0.867811
18 to 27 142114 0.7058 0.759831
17 to 26 141655 -0.8770 0.190243
16 to 25 142095 0.6402 0.738992
15 to 24 141835 -0.2563 0.398856
14 to 23 142356 1.5402 0.938249
13 to 22 142348 1.5127 0.934816
12 to 21 141712 -0.6804 0.248110
11 to 20 142300 1.3471 0.911032
10 to 19 141898 -0.0391 0.484418
9 to 18 142145 0.8127 0.791792
8 to 17 142789 3.0333 0.998791
7 to 16 141979 0.2402 0.594928
6 to 15 142440 1.8299 0.966367
5 to 14 141615 -1.0149 0.155069
4 to 13 141762 -0.5080 0.305715
3 to 12 142005 0.3299 0.629261
2 to 11 141711 -0.6839 0.247020
1 to 10 141531 -1.3046 0.096017
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_11:31
Bits used No. missing words z-score p-value
28 to 32 142186 0.9379 0.825843
27 to 31 142312 1.3650 0.913871
26 to 30 141662 -0.8384 0.200901
25 to 29 141289 -2.1028 0.017741
24 to 28 141773 -0.4621 0.321992
23 to 27 142126 0.7345 0.768670
22 to 26 142420 1.7311 0.958282
21 to 25 142170 0.8836 0.811551
20 to 24 141341 -1.9265 0.027018
19 to 23 141848 -0.2079 0.417654
18 to 22 141279 -2.1367 0.016311
17 to 21 141829 -0.2723 0.392694
16 to 20 142000 0.3074 0.620714
15 to 19 141778 -0.4452 0.328093
14 to 18 141977 0.2294 0.590717
13 to 17 141515 -1.3367 0.090658
12 to 16 142290 1.2904 0.901545
11 to 15 142265 1.2057 0.886026
10 to 14 141834 -0.2554 0.399224
9 to 13 141802 -0.3638 0.357992
8 to 12 141853 -0.1909 0.424283
7 to 11 141646 -0.8926 0.186024
6 to 10 141945 0.1209 0.548121
5 to 9 142106 0.6667 0.747511
4 to 8 141800 -0.3706 0.355464
3 to 7 141935 0.0870 0.534671
2 to 6 141687 -0.7537 0.225526
1 to 5 142154 0.8294 0.796558
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_11:31
Bits used No. missing words z-score p-value
31 to 32 142027 0.3471 0.635745
30 to 31 141881 -0.0836 0.466699
29 to 30 142121 0.6244 0.733816
28 to 29 142454 1.6067 0.945939
27 to 28 141825 -0.2488 0.401773
26 to 27 141718 -0.5644 0.286243
25 to 26 142338 1.2645 0.896977
24 to 25 142481 1.6863 0.954135
23 to 24 141382 -1.5555 0.059908
22 to 23 142317 1.2026 0.885428
21 to 22 141591 -0.9390 0.173859
20 to 21 142339 1.2675 0.897505
19 to 20 142593 2.0167 0.978138
18 to 19 142163 0.7483 0.772857
17 to 18 141913 0.0108 0.504319
16 to 17 141828 -0.2399 0.405199
15 to 16 141796 -0.3343 0.369074
14 to 15 141575 -0.9862 0.162012
13 to 14 142285 1.1082 0.866106
12 to 13 141785 -0.3668 0.356901
11 to 12 142036 0.3737 0.645671
10 to 11 141710 -0.5880 0.278268
9 to 10 141893 -0.0482 0.480790
8 to 9 141805 -0.3078 0.379133
7 to 8 141641 -0.7915 0.214316
6 to 7 142064 0.4563 0.675896
5 to 6 141805 -0.3078 0.379133
4 to 5 141916 0.0197 0.507849
3 to 4 141897 -0.0364 0.485493
2 to 3 141779 -0.3845 0.350321
1 to 2 142468 1.6480 0.950323
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2509.83 0.139 0.555267
Test results for specific bytes for dh-ranFile-2018-07-09_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2472.52 -0.389 0.348800
2 to 9 2571.43 1.010 0.843805
3 to 10 2490.29 -0.137 0.445417
4 to 11 2452.27 -0.675 0.249829
5 to 12 2608.10 1.529 0.936835
6 to 13 2549.14 0.695 0.756442
7 to 14 2424.45 -1.068 0.142672
8 to 15 2425.26 -1.057 0.145247
9 to 16 2535.70 0.505 0.693192
10 to 17 2544.57 0.630 0.735751
11 to 18 2477.71 -0.315 0.376309
12 to 19 2502.94 0.042 0.516564
13 to 20 2570.85 1.002 0.841830
14 to 21 2560.90 0.861 0.805433
15 to 22 2528.17 0.398 0.654802
16 to 23 2523.12 0.327 0.628176
17 to 24 2431.89 -0.963 0.167713
18 to 25 2514.76 0.209 0.582668
19 to 26 2468.82 -0.441 0.329623
20 to 27 2376.17 -1.751 0.039953
21 to 28 2534.76 0.492 0.688503
22 to 29 2398.52 -1.435 0.075623
23 to 30 2495.88 -0.058 0.476775
24 to 31 2448.34 -0.731 0.232514
25 to 32 2552.38 0.741 0.770576
CDPARK for dh-ranFile-2018-07-09_11:31: 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
3525 0.0913 0.536383
3513 -0.4566 0.323972
3557 1.5525 0.939730
3504 -0.8676 0.192812
3519 -0.1826 0.427537
3505 -0.8219 0.205562
3479 -2.0091 0.022262
3527 0.1826 0.572463
3521 -0.0913 0.463617
3494 -1.3242 0.092718
Square side=100, avg. no. parked=3514.40 sample std.=20.05
p-value of the KSTEST for those 10 p-values: 0.312757
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_11:31
0.7178,0.4414,0.9371,0.5955,0.1563,0.1145,0.4608,0.1849,0.4461,0.1154,
The KS test for those 10 p-values: 0.523592
The 3DSPHERES test for dh-ranFile-2018-07-09_11:31
sample no r^3 equiv. uni.
1 25.423 0.571491
2 31.201 0.646559
3 14.161 0.376273
4 29.319 0.623673
5 3.127 0.098972
6 41.775 0.751544
7 8.076 0.235999
8 34.271 0.680939
9 36.849 0.707207
10 1.966 0.063446
11 56.802 0.849442
12 75.480 0.919217
13 21.119 0.505374
14 34.763 0.686126
15 4.626 0.142890
16 33.005 0.667186
17 3.733 0.117015
18 13.408 0.360411
19 29.074 0.620588
20 57.294 0.851891
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.626883
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.5 -1.6 -1.4 -0.5 -1.2
0.0 0.7 -0.6 -0.3 0.7 0.8
1.4 -1.2 0.2 2.2 0.7 -1.5
-0.5 -0.7 0.6 -0.3 -0.6 0.9
-0.9 -1.5 0.2 -0.5 -0.2 -0.7
-1.5 1.8 1.8 0.2 -1.6 0.2
0.3 0.8 0.1 1.0 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:40.846195
z-score=-0.125890, p-value=0.478438
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_11:31
Test no p-value
1 0.923739
2 0.168232
3 0.164370
4 0.815988
5 0.773395
6 0.065442
7 0.998321
8 0.156271
9 0.900977
10 0.155013
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.141627
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_11:31:
(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 66337 1.63 66864 0.58
3 25000.00 25290 3.36 25022 0.02
4 6666.67 6737 0.74 6508 3.78
5 1388.89 1349 1.15 1328 2.67
6 238.10 249 0.50 236 0.02
7 34.72 29 0.94 35 0.00
8 4.96 8 1.86 6 0.22
p=0.88300 p=0.70498
Number of rngs required: 689245, p-value: 0.835
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_11:31
No. of wins: Observed Expected
98395 98585.9
z-score=-0.854, pvalue=0.19665
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66653 66666.7 0.003 0.003
2 37773 37654.3 0.374 0.377
3 26893 26954.7 0.141 0.518
4 19299 19313.5 0.011 0.529
5 13895 13851.4 0.137 0.666
6 9969 9943.5 0.065 0.731
7 7271 7145.0 2.221 2.952
8 5001 5139.1 3.710 6.662
9 3652 3699.9 0.619 7.281
10 2642 2666.3 0.221 7.503
11 1873 1923.3 1.317 8.820
12 1372 1388.7 0.202 9.021
13 1025 1003.7 0.451 9.473
14 720 726.1 0.052 9.525
15 544 525.8 0.627 10.152
16 341 381.2 4.229 14.382
17 305 276.5 2.929 17.311
18 203 200.8 0.023 17.334
19 162 146.0 1.757 19.091
20 115 106.2 0.727 19.818
21 292 287.1 0.083 19.901
Chisq= 19.90 for 20 degrees of freedom, p= 0.53586
SUMMARY of craptest
p-value for no. of wins: 0.196655
p-value for throws/game: 0.535859
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_11:31
No. of wins: Observed Expected
98799 98585.9
z-score= 0.953, pvalue=0.82978
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66821 66666.7 0.357 0.357
2 37585 37654.3 0.128 0.485
3 26757 26954.7 1.451 1.935
4 19162 19313.5 1.188 3.123
5 13993 13851.4 1.447 4.570
6 10217 9943.5 7.520 12.091
7 7201 7145.0 0.439 12.529
8 5063 5139.1 1.126 13.655
9 3698 3699.9 0.001 13.656
10 2632 2666.3 0.441 14.097
11 1930 1923.3 0.023 14.121
12 1367 1388.7 0.340 14.461
13 966 1003.7 1.417 15.878
14 742 726.1 0.346 16.224
15 472 525.8 5.512 21.736
16 382 381.2 0.002 21.738
17 297 276.5 1.514 23.252
18 193 200.8 0.305 23.557
19 130 146.0 1.750 25.307
20 106 106.2 0.000 25.308
21 286 287.1 0.004 25.312
Chisq= 25.31 for 20 degrees of freedom, p= 0.81025
SUMMARY of craptest
p-value for no. of wins: 0.829779
p-value for throws/game: 0.810251
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0024,0.0046,0.0047,0.0088,0.0163,0.0177,0.0190,0.0223,0.0270,
0.0400,0.0557,0.0599,0.0634,0.0654,0.0707,0.0732,0.0756,0.0811,0.0886,
0.0907,0.0927,0.0960,0.0960,0.0990,0.0992,0.1116,0.1145,0.1154,0.1170,
0.1385,0.1400,0.1416,0.1427,0.1429,0.1452,0.1550,0.1551,0.1563,0.1563,
0.1620,0.1644,0.1677,0.1682,0.1688,0.1717,0.1739,0.1774,0.1849,0.1853,
0.1860,0.1902,0.1918,0.1928,0.1967,0.1972,0.2009,0.2056,0.2103,0.2143,
0.2255,0.2318,0.2325,0.2358,0.2360,0.2465,0.2470,0.2481,0.2498,0.2566,
0.2783,0.2862,0.2872,0.3057,0.3128,0.3174,0.3220,0.3240,0.3281,0.3296,
0.3321,0.3388,0.3488,0.3503,0.3555,0.3569,0.3580,0.3604,0.3691,0.3723,
0.3728,0.3763,0.3763,0.3791,0.3791,0.3856,0.3911,0.3927,0.3988,0.3989,
0.3992,0.4018,0.4035,0.4052,0.4177,0.4243,0.4275,0.4414,0.4446,0.4454,
0.4461,0.4519,0.4608,0.4636,0.4667,0.4768,0.4784,0.4808,0.4844,0.4855,
0.4913,0.4959,0.4986,0.5017,0.5043,0.5054,0.5058,0.5065,0.5078,0.5166,
0.5229,0.5230,0.5236,0.5347,0.5359,0.5364,0.5384,0.5425,0.5476,0.5481,
0.5553,0.5579,0.5715,0.5725,0.5725,0.5732,0.5827,0.5907,0.5940,0.5949,
0.5955,0.6114,0.6160,0.6206,0.6207,0.6237,0.6261,0.6269,0.6282,0.6293,
0.6357,0.6369,0.6457,0.6463,0.6466,0.6548,0.6559,0.6607,0.6653,0.6672,
0.6700,0.6759,0.6809,0.6861,0.6881,0.6885,0.6916,0.6932,0.6942,0.6994,
0.7050,0.7072,0.7131,0.7153,0.7178,0.7182,0.7189,0.7217,0.7271,0.7338,
0.7358,0.7372,0.7390,0.7475,0.7515,0.7552,0.7564,0.7598,0.7687,0.7706,
0.7729,0.7734,0.7740,0.7766,0.7766,0.7918,0.7929,0.7966,0.7990,0.8012,
0.8016,0.8054,0.8093,0.8103,0.8116,0.8159,0.8160,0.8258,0.8298,0.8353,
0.8355,0.8376,0.8387,0.8418,0.8421,0.8438,0.8494,0.8519,0.8578,0.8661,
0.8678,0.8830,0.8854,0.8860,0.8959,0.8970,0.8975,0.9010,0.9015,0.9073,
0.9110,0.9139,0.9192,0.9237,0.9271,0.9307,0.9310,0.9348,0.9360,0.9368,
0.9371,0.9382,0.9397,0.9459,0.9503,0.9541,0.9548,0.9583,0.9583,0.9644,
0.9664,0.9757,0.9781,0.9781,0.9888,0.9940,0.9967,0.9983,0.9988,
Overall p-value after applying KStest on 269 p-values = 0.362706
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.