RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.62 14.0782 0.338439
2 to 25 15.86 13.0662 0.268259
3 to 26 15.90 12.6324 0.239575
4 to 27 15.80 23.0102 0.851082
5 to 28 15.90 13.6466 0.308057
6 to 29 15.87 19.5919 0.704367
7 to 30 15.92 7.1766 0.018855
8 to 31 15.75 15.0080 0.405097
9 to 32 15.76 14.1118 0.340829
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.269552
Tough bday spacings test for dh-ranFile-2018-06-20_03:31: 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 4 36 76 102 88 78 56 34 17 7 2
(O-E)^2/E 2.9 0.0 0.1 0.2 1.0 0.0 0.3 0.6 0.3 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 6.435, p= 0.223
RESULTS OF GCD FOR dh-ranFile-2018-06-20_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.507026
p-value, dist. of gcd's: 0.753855
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.133 0.975 0.380 0.744 0.489 0.150 0.435 0.762
Bits 8 to 15---> 0.421 0.535 0.804 0.267 0.232 0.136 0.583 0.915
Bits 16 to 23---> 0.867 0.664 0.730 0.368 0.359 0.496 0.980 0.107
Bits 24 to 31---> 0.736 0.995 0.551 0.162 0.673 0.658 0.079 0.510
KS test for the above 32 p values: 0.240
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_03:31,
p-values for 5 runs: 0.2276, 0.5007, 0.0035, 0.8214, 0.3512
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5216 5134.0 1.309 2.039
r= 30 23074 23103.0 0.037 2.075
r= 31 11511 11551.5 0.142 2.217
chi-square = 2.217 with df = 3; p-value = 0.471
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 190 211.4 2.170 2.170
r= 30 5185 5134.0 0.506 2.676
r= 31 22996 23103.0 0.496 3.172
r= 32 11629 11551.5 0.520 3.692
chi-square = 3.692 with df = 3; p-value = 0.703
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_03:31
b-rank test for bits 1 to 8, p=0.63175
b-rank test for bits 2 to 9, p=0.59041
b-rank test for bits 3 to 10, p=0.91694
b-rank test for bits 4 to 11, p=0.83599
b-rank test for bits 5 to 12, p=0.91549
b-rank test for bits 6 to 13, p=0.67754
b-rank test for bits 7 to 14, p=0.85700
b-rank test for bits 8 to 15, p=0.81867
b-rank test for bits 9 to 16, p=0.90532
b-rank test for bits 10 to 17, p=0.54832
b-rank test for bits 11 to 18, p=0.36658
b-rank test for bits 12 to 19, p=0.72453
b-rank test for bits 13 to 20, p=0.09786
b-rank test for bits 14 to 21, p=0.08207
b-rank test for bits 15 to 22, p=0.55391
b-rank test for bits 16 to 23, p=0.14883
b-rank test for bits 17 to 24, p=0.81318
b-rank test for bits 18 to 25, p=0.72767
b-rank test for bits 19 to 26, p=0.16749
b-rank test for bits 20 to 27, p=0.02809
b-rank test for bits 21 to 28, p=0.62892
b-rank test for bits 22 to 29, p=0.19771
b-rank test for bits 23 to 30, p=0.92006
b-rank test for bits 24 to 31, p=0.99942
b-rank test for bits 25 to 32, p=0.99649
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 = 0.045647
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_03:31
(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 142224 0.74 0.768894
2 142174 0.62 0.731840
3 142232 0.75 0.774546
4 142680 1.80 0.964119
5 141791 -0.28 0.391093
6 142080 0.40 0.654966
7 141585 -0.76 0.224291
8 142042 0.31 0.621711
9 141955 0.11 0.542489
10 142156 0.58 0.717805
11 142381 1.10 0.864776
12 141923 0.03 0.512740
13 141932 0.05 0.521121
14 141496 -0.97 0.167091
15 142956 2.45 0.992767
16 142276 0.86 0.804196
17 142273 0.85 0.802253
18 142395 1.13 0.871759
19 141579 -0.77 0.220117
20 142292 0.89 0.814363
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_03:31
Bits used No. missing words z-score p-value
23 to 32 141946 0.1264 0.550312
22 to 31 141646 -0.9080 0.181930
21 to 30 142001 0.3161 0.624038
20 to 29 141923 0.0471 0.518798
19 to 28 141968 0.2023 0.580163
18 to 27 141742 -0.5770 0.281970
17 to 26 141769 -0.4839 0.314230
16 to 25 142025 0.3989 0.655003
15 to 24 141426 -1.6667 0.047792
14 to 23 141934 0.0851 0.533897
13 to 22 142044 0.4644 0.678812
12 to 21 142196 0.9885 0.838550
11 to 20 142085 0.6058 0.727663
10 to 19 141777 -0.4563 0.324083
9 to 18 141797 -0.3873 0.349251
8 to 17 141867 -0.1460 0.441974
7 to 16 141932 0.0782 0.531155
6 to 15 142010 0.3471 0.635756
5 to 14 141898 -0.0391 0.484418
4 to 13 142028 0.4092 0.658806
3 to 12 141869 -0.1391 0.444698
2 to 11 142061 0.5230 0.699513
1 to 10 141679 -0.7942 0.213528
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_03:31
Bits used No. missing words z-score p-value
28 to 32 142115 0.6972 0.757157
27 to 31 141538 -1.2587 0.104061
26 to 30 142170 0.8836 0.811551
25 to 29 141764 -0.4926 0.311132
24 to 28 141680 -0.7774 0.218464
23 to 27 141953 0.1480 0.558842
22 to 26 142172 0.8904 0.813376
21 to 25 141781 -0.4350 0.331775
20 to 24 141511 -1.3503 0.088465
19 to 23 141891 -0.0621 0.475227
18 to 22 141328 -1.9706 0.024384
17 to 21 141803 -0.3604 0.359259
16 to 20 142162 0.8565 0.804142
15 to 19 142251 1.1582 0.876610
14 to 18 142374 1.5752 0.942389
13 to 17 141908 -0.0045 0.498201
12 to 16 142326 1.4124 0.921090
11 to 15 141999 0.3040 0.619423
10 to 14 141852 -0.1943 0.422955
9 to 13 142125 0.7311 0.767636
8 to 12 141858 -0.1740 0.430933
7 to 11 142066 0.5311 0.702320
6 to 10 142012 0.3480 0.636093
5 to 9 141895 -0.0486 0.480629
4 to 8 142593 2.3175 0.989762
3 to 7 141672 -0.8045 0.210552
2 to 6 141887 -0.0757 0.469831
1 to 5 141698 -0.7164 0.236881
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_03:31
Bits used No. missing words z-score p-value
31 to 32 142743 2.4592 0.993038
30 to 31 142504 1.7542 0.960301
29 to 30 141832 -0.2281 0.409780
28 to 29 141715 -0.5732 0.283240
27 to 28 142111 0.5949 0.724044
26 to 27 141580 -0.9715 0.165656
25 to 26 142274 1.0757 0.858974
24 to 25 141996 0.2557 0.600895
23 to 24 141359 -1.6234 0.052253
22 to 23 141957 0.1406 0.555915
21 to 22 142451 1.5978 0.944961
20 to 21 142352 1.3058 0.904192
19 to 20 141873 -0.1072 0.457328
18 to 19 141930 0.0610 0.524310
17 to 18 141948 0.1141 0.545409
16 to 17 141750 -0.4700 0.319178
15 to 16 142306 1.1701 0.879023
14 to 15 141611 -0.8800 0.189422
13 to 14 141826 -0.2458 0.402914
12 to 13 141890 -0.0570 0.477264
11 to 12 141572 -0.9951 0.159850
10 to 11 142362 1.3353 0.909113
9 to 10 141961 0.1524 0.560572
8 to 9 141962 0.1554 0.561735
7 to 8 142221 0.9194 0.821052
6 to 7 140962 -2.7945 0.002599
5 to 6 141472 -1.2901 0.098515
4 to 5 141472 -1.2901 0.098515
3 to 4 142074 0.4858 0.686429
2 to 3 141246 -1.9567 0.025190
1 to 2 141759 -0.4435 0.328720
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2527.47 0.389 0.651182
Test results for specific bytes for dh-ranFile-2018-06-20_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2536.79 0.520 0.698568
2 to 9 2407.88 -1.303 0.096317
3 to 10 2524.16 0.342 0.633678
4 to 11 2603.90 1.469 0.929142
5 to 12 2423.13 -1.087 0.138487
6 to 13 2534.56 0.489 0.687507
7 to 14 2537.93 0.536 0.704175
8 to 15 2617.07 1.656 0.951095
9 to 16 2482.29 -0.251 0.401092
10 to 17 2468.66 -0.443 0.328810
11 to 18 2434.40 -0.928 0.176784
12 to 19 2469.17 -0.436 0.331433
13 to 20 2576.46 1.081 0.860224
14 to 21 2442.34 -0.815 0.207431
15 to 22 2473.85 -0.370 0.355780
16 to 23 2562.51 0.884 0.811658
17 to 24 2451.97 -0.679 0.248472
18 to 25 2501.03 0.015 0.505814
19 to 26 2448.28 -0.731 0.232268
20 to 27 2534.76 0.492 0.688495
21 to 28 2618.75 1.679 0.953462
22 to 29 2493.85 -0.087 0.465337
23 to 30 2468.81 -0.441 0.329591
24 to 31 2575.13 1.062 0.855985
25 to 32 2407.18 -1.313 0.094657
CDPARK for dh-ranFile-2018-06-20_03:31: 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
3535 0.5479 0.708135
3515 -0.3653 0.357445
3538 0.6849 0.753306
3525 0.0913 0.536383
3517 -0.2740 0.392053
3529 0.2740 0.607947
3538 0.6849 0.753306
3476 -2.1461 0.015932
3518 -0.2283 0.409702
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3521.00 sample std.=17.16
p-value of the KSTEST for those 10 p-values: 0.480645
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_03:31
0.9079,0.8434,0.1284,0.7523,0.9220,0.1528,0.1100,0.1549,0.9505,0.9166,
The KS test for those 10 p-values: 0.079077
The 3DSPHERES test for dh-ranFile-2018-06-20_03:31
sample no r^3 equiv. uni.
1 66.878 0.892393
2 14.789 0.389184
3 0.823 0.027047
4 129.963 0.986860
5 31.983 0.655653
6 8.825 0.254855
7 13.883 0.370464
8 14.732 0.388032
9 3.582 0.112559
10 4.094 0.127575
11 26.834 0.591169
12 45.484 0.780441
13 93.443 0.955611
14 56.221 0.846496
15 7.997 0.233999
16 4.545 0.140588
17 41.185 0.746610
18 13.298 0.358072
19 7.828 0.229665
20 21.800 0.516485
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.952614
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 0.3 1.5 -0.5 -0.7
0.0 1.0 1.6 -1.2 -0.2 0.7
0.1 1.2 -0.1 -1.0 -1.9 -2.0
0.8 0.9 1.3 0.3 0.7 0.1
0.2 0.9 -0.9 -0.3 -0.7 0.2
1.3 -2.0 -1.7 1.5 -0.2 0.6
-1.6 -1.7 -1.6 2.1 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:52.937157
z-score=1.193342, p-value=0.879897
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_03:31
Test no p-value
1 0.030233
2 0.005142
3 0.795034
4 0.779696
5 0.192832
6 0.012881
7 0.046312
8 0.972319
9 0.022665
10 0.421081
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002824
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_03:31:
(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 66374 1.28 66685 0.01
3 25000.00 25205 1.68 24968 0.04
4 6666.67 6734 0.68 6666 0.00
5 1388.89 1410 0.32 1413 0.42
6 238.10 236 0.02 230 0.28
7 34.72 35 0.00 33 0.09
8 4.96 5 0.00 4 0.19
p=0.32166 p=0.01480
Number of rngs required: 690018, p-value: 0.971
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_03:31
No. of wins: Observed Expected
98478 98585.9
z-score=-0.482, pvalue=0.31476
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66410 66666.7 0.988 0.988
2 37798 37654.3 0.548 1.536
3 27028 26954.7 0.199 1.736
4 19179 19313.5 0.936 2.672
5 13966 13851.4 0.948 3.620
6 9954 9943.5 0.011 3.631
7 7049 7145.0 1.291 4.921
8 5173 5139.1 0.224 5.145
9 3752 3699.9 0.735 5.880
10 2659 2666.3 0.020 5.900
11 1877 1923.3 1.116 7.016
12 1444 1388.7 2.199 9.214
13 1064 1003.7 3.621 12.835
14 740 726.1 0.265 13.100
15 499 525.8 1.370 14.469
16 369 381.2 0.387 14.857
17 275 276.5 0.009 14.865
18 225 200.8 2.909 17.774
19 142 146.0 0.109 17.883
20 95 106.2 1.184 19.067
21 302 287.1 0.772 19.839
Chisq= 19.84 for 20 degrees of freedom, p= 0.53196
SUMMARY of craptest
p-value for no. of wins: 0.314759
p-value for throws/game: 0.531956
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_03:31
No. of wins: Observed Expected
99113 98585.9
z-score= 2.358, pvalue=0.99081
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66905 66666.7 0.852 0.852
2 37517 37654.3 0.501 1.353
3 26811 26954.7 0.766 2.119
4 19308 19313.5 0.002 2.121
5 13792 13851.4 0.255 2.376
6 9936 9943.5 0.006 2.381
7 7211 7145.0 0.609 2.991
8 5199 5139.1 0.699 3.689
9 3732 3699.9 0.279 3.969
10 2594 2666.3 1.960 5.929
11 1925 1923.3 0.001 5.930
12 1315 1388.7 3.916 9.846
13 1032 1003.7 0.797 10.643
14 757 726.1 1.311 11.954
15 509 525.8 0.539 12.493
16 372 381.2 0.220 12.713
17 297 276.5 1.514 14.227
18 202 200.8 0.007 14.234
19 184 146.0 9.900 24.133
20 106 106.2 0.000 24.134
21 296 287.1 0.275 24.409
Chisq= 24.41 for 20 degrees of freedom, p= 0.77501
SUMMARY of craptest
p-value for no. of wins: 0.990805
p-value for throws/game: 0.775011
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0026,0.0028,0.0035,0.0051,0.0129,0.0148,0.0159,0.0189,0.0227,0.0244,
0.0252,0.0270,0.0281,0.0302,0.0456,0.0463,0.0478,0.0523,0.0787,0.0791,
0.0821,0.0885,0.0947,0.0963,0.0979,0.0985,0.0985,0.1041,0.1068,0.1100,
0.1126,0.1276,0.1284,0.1327,0.1355,0.1385,0.1406,0.1488,0.1501,0.1528,
0.1549,0.1599,0.1617,0.1657,0.1671,0.1675,0.1768,0.1819,0.1894,0.1928,
0.1977,0.2074,0.2106,0.2135,0.2185,0.2201,0.2225,0.2243,0.2276,0.2297,
0.2322,0.2323,0.2340,0.2369,0.2396,0.2399,0.2485,0.2549,0.2670,0.2683,
0.2696,0.2820,0.2832,0.3081,0.3111,0.3142,0.3148,0.3192,0.3217,0.3241,
0.3287,0.3288,0.3296,0.3314,0.3318,0.3384,0.3408,0.3493,0.3512,0.3558,
0.3574,0.3581,0.3593,0.3594,0.3666,0.3684,0.3705,0.3799,0.3880,0.3892,
0.3911,0.3921,0.4011,0.4029,0.4051,0.4097,0.4098,0.4211,0.4213,0.4230,
0.4275,0.4309,0.4354,0.4420,0.4447,0.4573,0.4653,0.4698,0.4715,0.4752,
0.4773,0.4806,0.4806,0.4844,0.4893,0.4961,0.4982,0.5007,0.5058,0.5070,
0.5100,0.5127,0.5165,0.5188,0.5211,0.5243,0.5312,0.5320,0.5339,0.5355,
0.5364,0.5425,0.5454,0.5483,0.5503,0.5508,0.5539,0.5559,0.5588,0.5606,
0.5617,0.5802,0.5825,0.5904,0.5912,0.6009,0.6079,0.6194,0.6217,0.6240,
0.6289,0.6318,0.6337,0.6358,0.6361,0.6512,0.6550,0.6550,0.6557,0.6584,
0.6588,0.6642,0.6732,0.6775,0.6788,0.6864,0.6875,0.6885,0.6986,0.6995,
0.7023,0.7033,0.7042,0.7044,0.7081,0.7178,0.7240,0.7245,0.7277,0.7277,
0.7302,0.7318,0.7365,0.7437,0.7466,0.7523,0.7533,0.7533,0.7539,0.7572,
0.7619,0.7676,0.7689,0.7745,0.7750,0.7797,0.7804,0.7950,0.8023,0.8040,
0.8041,0.8042,0.8116,0.8117,0.8132,0.8134,0.8144,0.8187,0.8211,0.8214,
0.8360,0.8386,0.8434,0.8465,0.8511,0.8560,0.8570,0.8590,0.8602,0.8648,
0.8666,0.8718,0.8766,0.8790,0.8799,0.8924,0.9042,0.9053,0.9079,0.9091,
0.9153,0.9155,0.9166,0.9169,0.9201,0.9211,0.9220,0.9291,0.9424,0.9450,
0.9505,0.9511,0.9526,0.9535,0.9556,0.9603,0.9641,0.9714,0.9723,0.9751,
0.9801,0.9869,0.9898,0.9908,0.9928,0.9930,0.9947,0.9965,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.593899
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.