RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.05 13.8511 0.322387
2 to 25 15.85 12.6002 0.237488
3 to 26 15.82 7.4979 0.023861
4 to 27 15.86 19.7088 0.710605
5 to 28 15.76 16.0857 0.482233
6 to 29 15.76 21.7717 0.806342
7 to 30 15.87 18.1945 0.623329
8 to 31 15.93 11.4266 0.166453
9 to 32 15.92 19.2808 0.687347
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.856518
Tough bday spacings test for dh-ranFile-2018-07-04_06:31: 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 44 75 97 90 72 49 37 19 9 1
(O-E)^2/E 0.5 1.5 0.0 0.0 0.6 0.5 0.2 1.8 1.1 0.9 2.3
Birthday Spacings: Sum(O-E)^2/E= 9.374, p= 0.503
RESULTS OF GCD FOR dh-ranFile-2018-07-04_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.014787
p-value, dist. of gcd's: 0.091182
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.866 0.979 0.190 0.199 0.062 0.094 0.653 0.078
Bits 8 to 15---> 0.366 0.330 0.527 0.415 0.214 0.642 0.098 0.299
Bits 16 to 23---> 0.200 0.588 0.027 0.549 0.823 0.086 0.543 0.122
Bits 24 to 31---> 0.090 0.307 0.353 0.176 0.754 0.124 0.203 0.345
KS test for the above 32 p values: 0.995
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_06:31,
p-values for 5 runs: 0.4809, 0.9476, 0.0526, 0.8192, 0.2082
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5168 5134.0 0.225 0.573
r= 30 23110 23103.0 0.002 0.575
r= 31 11502 11551.5 0.212 0.788
chi-square = 0.788 with df = 3; p-value = 0.148
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5043 5134.0 1.613 1.752
r= 31 23158 23103.0 0.131 1.883
r= 32 11593 11551.5 0.149 2.032
chi-square = 2.032 with df = 3; p-value = 0.434
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_06:31
b-rank test for bits 1 to 8, p=0.15238
b-rank test for bits 2 to 9, p=0.36054
b-rank test for bits 3 to 10, p=0.29945
b-rank test for bits 4 to 11, p=0.21097
b-rank test for bits 5 to 12, p=0.94839
b-rank test for bits 6 to 13, p=0.96731
b-rank test for bits 7 to 14, p=0.16897
b-rank test for bits 8 to 15, p=0.16615
b-rank test for bits 9 to 16, p=0.34525
b-rank test for bits 10 to 17, p=0.26768
b-rank test for bits 11 to 18, p=0.32319
b-rank test for bits 12 to 19, p=0.37790
b-rank test for bits 13 to 20, p=0.72489
b-rank test for bits 14 to 21, p=0.47230
b-rank test for bits 15 to 22, p=0.95802
b-rank test for bits 16 to 23, p=0.10950
b-rank test for bits 17 to 24, p=0.42500
b-rank test for bits 18 to 25, p=0.15057
b-rank test for bits 19 to 26, p=0.25304
b-rank test for bits 20 to 27, p=0.85929
b-rank test for bits 21 to 28, p=0.35182
b-rank test for bits 22 to 29, p=0.18572
b-rank test for bits 23 to 30, p=0.85655
b-rank test for bits 24 to 31, p=0.52091
b-rank test for bits 25 to 32, p=0.54554
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 = 0.174044
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_06:31
(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 141924 0.03 0.513671
2 141996 0.20 0.580237
3 141148 -1.78 0.037636
4 142113 0.48 0.682915
5 141510 -0.93 0.175406
6 142385 1.11 0.866797
7 141810 -0.23 0.408238
8 140876 -2.41 0.007882
9 141928 0.04 0.517397
10 141784 -0.29 0.384827
11 142342 1.01 0.843971
12 141469 -1.03 0.151785
13 141822 -0.20 0.419160
14 142384 1.11 0.866294
15 141743 -0.39 0.348778
16 141418 -1.15 0.125491
17 141571 -0.79 0.214621
18 142268 0.84 0.798989
19 142027 0.27 0.608315
20 141919 0.02 0.509013
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_06:31
Bits used No. missing words z-score p-value
23 to 32 141650 -0.8942 0.185596
22 to 31 141977 0.2333 0.592253
21 to 30 141766 -0.4942 0.310568
20 to 29 142044 0.4644 0.678812
19 to 28 142291 1.3161 0.905930
18 to 27 141763 -0.5046 0.306925
17 to 26 142203 1.0127 0.844388
16 to 25 141884 -0.0873 0.465199
15 to 24 141414 -1.7080 0.043815
14 to 23 141592 -1.0942 0.136925
13 to 22 141320 -2.0322 0.021068
12 to 21 141834 -0.2598 0.397525
11 to 20 141324 -2.0184 0.021776
10 to 19 141948 0.1333 0.553040
9 to 18 141696 -0.7356 0.230981
8 to 17 142044 0.4644 0.678812
7 to 16 141816 -0.3218 0.373792
6 to 15 142097 0.6471 0.741229
5 to 14 141718 -0.6598 0.254704
4 to 13 142097 0.6471 0.741229
3 to 12 142157 0.8540 0.803457
2 to 11 142517 2.0954 0.981933
1 to 10 141631 -0.9598 0.168588
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_06:31
Bits used No. missing words z-score p-value
28 to 32 141329 -1.9672 0.024579
27 to 31 141571 -1.1469 0.125715
26 to 30 141510 -1.3537 0.087922
25 to 29 142226 1.0735 0.858467
24 to 28 142029 0.4057 0.657504
23 to 27 141778 -0.4452 0.328093
22 to 26 142049 0.4735 0.682057
21 to 25 141758 -0.5130 0.303982
20 to 24 141794 -0.3909 0.347917
19 to 23 141816 -0.3164 0.375860
18 to 22 141385 -1.7774 0.037752
17 to 21 142225 1.0701 0.857706
16 to 20 141919 0.0328 0.513075
15 to 19 142044 0.4565 0.675988
14 to 18 141712 -0.6689 0.251775
13 to 17 141802 -0.3638 0.357992
12 to 16 141715 -0.6587 0.255030
11 to 15 141924 0.0497 0.519831
10 to 14 142240 1.1209 0.868838
9 to 13 142016 0.3616 0.641172
8 to 12 141948 0.1311 0.552146
7 to 11 142099 0.6429 0.739872
6 to 10 141991 0.2768 0.609051
5 to 9 142234 1.1006 0.864459
4 to 8 141924 0.0497 0.519831
3 to 7 141523 -1.3096 0.095167
2 to 6 141477 -1.4655 0.071389
1 to 5 142290 1.2904 0.901545
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_06:31
Bits used No. missing words z-score p-value
31 to 32 142295 1.1377 0.872371
30 to 31 141838 -0.2104 0.416673
29 to 30 142067 0.4651 0.679071
28 to 29 141929 0.0580 0.523135
27 to 28 141695 -0.6322 0.263614
26 to 27 141272 -1.8800 0.030052
25 to 26 141578 -0.9774 0.164192
24 to 25 141782 -0.3756 0.353605
23 to 24 142036 0.3737 0.645671
22 to 23 141316 -1.7502 0.040039
21 to 22 141745 -0.4847 0.313927
20 to 21 141790 -0.3520 0.362417
19 to 20 141822 -0.2576 0.398354
18 to 19 142240 0.9754 0.835326
17 to 18 142111 0.5949 0.724044
16 to 17 141674 -0.6942 0.243782
15 to 16 141676 -0.6883 0.245635
14 to 15 141629 -0.8269 0.204138
13 to 14 141604 -0.9007 0.183880
12 to 13 142011 0.2999 0.617878
11 to 12 142114 0.6037 0.726994
10 to 11 142071 0.4769 0.683284
9 to 10 142348 1.2940 0.902169
8 to 9 142260 1.0344 0.849531
7 to 8 141476 -1.2783 0.100579
6 to 7 142183 0.8073 0.790249
5 to 6 142810 2.6568 0.996056
4 to 5 142357 1.3206 0.906676
3 to 4 141943 0.0993 0.539559
2 to 3 141174 -2.1691 0.015037
1 to 2 141990 0.2380 0.594046
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2466.24 -0.477 0.316510
Test results for specific bytes for dh-ranFile-2018-07-04_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2561.28 0.867 0.806938
2 to 9 2435.90 -0.906 0.182350
3 to 10 2503.60 0.051 0.520282
4 to 11 2376.60 -1.745 0.040483
5 to 12 2496.30 -0.052 0.479134
6 to 13 2512.97 0.183 0.572743
7 to 14 2472.18 -0.393 0.347022
8 to 15 2404.95 -1.344 0.089435
9 to 16 2422.27 -1.099 0.135819
10 to 17 2561.86 0.875 0.809185
11 to 18 2517.36 0.246 0.596976
12 to 19 2385.27 -1.623 0.052343
13 to 20 2488.87 -0.157 0.437486
14 to 21 2547.18 0.667 0.747690
15 to 22 2457.47 -0.602 0.273746
16 to 23 2493.02 -0.099 0.460709
17 to 24 2465.86 -0.483 0.314608
18 to 25 2461.88 -0.539 0.294899
19 to 26 2488.56 -0.162 0.435760
20 to 27 2481.58 -0.260 0.397246
21 to 28 2593.59 1.324 0.907183
22 to 29 2553.57 0.758 0.775645
23 to 30 2444.50 -0.785 0.216249
24 to 31 2549.24 0.696 0.756888
25 to 32 2547.85 0.677 0.750703
CDPARK for dh-ranFile-2018-07-04_06:31: 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
3540 0.7763 0.781201
3515 -0.3653 0.357445
3474 -2.2374 0.012629
3503 -0.9132 0.180558
3515 -0.3653 0.357445
3529 0.2740 0.607947
3515 -0.3653 0.357445
3493 -1.3699 0.085365
3549 1.1872 0.882429
3501 -1.0046 0.157553
Square side=100, avg. no. parked=3513.40 sample std.=21.11
p-value of the KSTEST for those 10 p-values: 0.299621
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_06:31
0.6688,0.8266,0.0245,0.3575,0.2253,0.5727,0.5792,0.9793,0.6869,0.9379,
The KS test for those 10 p-values: 0.570355
The 3DSPHERES test for dh-ranFile-2018-07-04_06:31
sample no r^3 equiv. uni.
1 31.397 0.648854
2 34.845 0.686979
3 5.146 0.157626
4 56.307 0.846938
5 79.894 0.930270
6 1.657 0.053721
7 9.088 0.261354
8 26.717 0.589583
9 4.812 0.148204
10 11.661 0.322059
11 18.116 0.453308
12 29.596 0.627128
13 86.361 0.943792
14 8.684 0.251331
15 20.244 0.490743
16 16.389 0.420909
17 23.459 0.542502
18 15.619 0.405864
19 30.602 0.639427
20 25.862 0.577710
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.779763
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 0.1 0.0 0.2 -1.5
0.3 2.4 0.8 1.5 -0.0 -0.7
-1.4 0.9 -0.2 -0.5 0.8 -0.1
-0.1 -1.2 -0.2 -0.8 0.7 1.5
-1.8 0.2 -0.7 1.6 -0.6 -0.2
1.5 -0.9 3.4 -0.3 -0.1 0.8
-0.2 -0.4 -0.4 -1.3 0.9 0.0
0.8
Chi-square with 42 degrees of freedom:46.063838
z-score=0.443401, p-value=0.692205
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_06:31
Test no p-value
1 0.003934
2 0.295030
3 0.123178
4 0.454870
5 0.042307
6 0.301639
7 0.000138
8 0.813172
9 0.039960
10 0.281572
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000858
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_06:31:
(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 66699 0.02 66859 0.55
3 25000.00 24978 0.02 24908 0.34
4 6666.67 6614 0.42 6569 1.43
5 1388.89 1426 0.99 1383 0.02
6 238.10 241 0.04 247 0.33
7 34.72 38 0.31 29 0.94
8 4.96 3 0.77 4 0.19
p=0.13859 p=0.29770
Number of rngs required: 688959, p-value: 0.739
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_06:31
No. of wins: Observed Expected
98448 98585.9
z-score=-0.617, pvalue=0.26875
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66377 66666.7 1.259 1.259
2 37667 37654.3 0.004 1.263
3 27114 26954.7 0.941 2.204
4 19392 19313.5 0.319 2.523
5 13661 13851.4 2.618 5.141
6 10031 9943.5 0.769 5.910
7 7132 7145.0 0.024 5.934
8 5184 5139.1 0.393 6.327
9 3714 3699.9 0.054 6.381
10 2682 2666.3 0.092 6.473
11 1988 1923.3 2.175 8.648
12 1361 1388.7 0.554 9.202
13 1026 1003.7 0.495 9.697
14 723 726.1 0.014 9.710
15 506 525.8 0.748 10.459
16 382 381.2 0.002 10.460
17 298 276.5 1.665 12.126
18 202 200.8 0.007 12.133
19 149 146.0 0.062 12.195
20 122 106.2 2.346 14.541
21 289 287.1 0.012 14.553
Chisq= 14.55 for 20 degrees of freedom, p= 0.19862
SUMMARY of craptest
p-value for no. of wins: 0.268755
p-value for throws/game: 0.198620
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_06:31
No. of wins: Observed Expected
98633 98585.9
z-score= 0.211, pvalue=0.58350
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66611 66666.7 0.046 0.046
2 37742 37654.3 0.204 0.251
3 26554 26954.7 5.958 6.208
4 19482 19313.5 1.471 7.679
5 13964 13851.4 0.915 8.594
6 9931 9943.5 0.016 8.610
7 7125 7145.0 0.056 8.666
8 5219 5139.1 1.243 9.909
9 3660 3699.9 0.430 10.339
10 2630 2666.3 0.494 10.833
11 1887 1923.3 0.686 11.519
12 1404 1388.7 0.168 11.687
13 1033 1003.7 0.854 12.541
14 722 726.1 0.024 12.565
15 528 525.8 0.009 12.574
16 394 381.2 0.433 13.007
17 297 276.5 1.514 14.521
18 232 200.8 4.838 19.358
19 167 146.0 3.025 22.384
20 121 106.2 2.058 24.442
21 297 287.1 0.340 24.782
Chisq= 24.78 for 20 degrees of freedom, p= 0.79011
SUMMARY of craptest
p-value for no. of wins: 0.583495
p-value for throws/game: 0.790107
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0009,0.0039,0.0079,0.0126,0.0148,0.0150,0.0211,0.0218,0.0239,
0.0245,0.0246,0.0267,0.0301,0.0376,0.0378,0.0400,0.0400,0.0405,0.0423,
0.0438,0.0523,0.0526,0.0537,0.0622,0.0714,0.0784,0.0854,0.0863,0.0879,
0.0894,0.0903,0.0912,0.0943,0.0952,0.0976,0.1006,0.1095,0.1220,0.1232,
0.1241,0.1255,0.1257,0.1358,0.1369,0.1386,0.1476,0.1482,0.1506,0.1518,
0.1524,0.1576,0.1576,0.1642,0.1662,0.1665,0.1686,0.1690,0.1740,0.1754,
0.1762,0.1806,0.1824,0.1839,0.1856,0.1857,0.1899,0.1986,0.1994,0.2003,
0.2031,0.2041,0.2082,0.2110,0.2139,0.2146,0.2162,0.2253,0.2310,0.2375,
0.2438,0.2456,0.2513,0.2518,0.2530,0.2547,0.2550,0.2614,0.2636,0.2677,
0.2688,0.2737,0.2816,0.2949,0.2950,0.2977,0.2994,0.2995,0.2996,0.3016,
0.3040,0.3069,0.3071,0.3106,0.3139,0.3146,0.3165,0.3221,0.3224,0.3232,
0.3281,0.3300,0.3447,0.3453,0.3470,0.3479,0.3488,0.3518,0.3527,0.3536,
0.3574,0.3574,0.3574,0.3575,0.3580,0.3605,0.3624,0.3657,0.3738,0.3759,
0.3779,0.3848,0.3972,0.3975,0.3984,0.4059,0.4082,0.4146,0.4167,0.4192,
0.4209,0.4250,0.4342,0.4358,0.4375,0.4533,0.4549,0.4607,0.4652,0.4723,
0.4791,0.4809,0.4822,0.4907,0.5029,0.5090,0.5131,0.5137,0.5174,0.5198,
0.5198,0.5203,0.5209,0.5231,0.5269,0.5396,0.5425,0.5429,0.5455,0.5492,
0.5521,0.5530,0.5704,0.5727,0.5727,0.5777,0.5792,0.5802,0.5835,0.5880,
0.5896,0.5923,0.5940,0.5970,0.6079,0.6083,0.6091,0.6179,0.6233,0.6271,
0.6394,0.6412,0.6421,0.6457,0.6489,0.6527,0.6575,0.6688,0.6760,0.6788,
0.6788,0.6791,0.6821,0.6829,0.6833,0.6869,0.6870,0.6873,0.6922,0.7106,
0.7240,0.7249,0.7270,0.7394,0.7399,0.7412,0.7412,0.7477,0.7507,0.7535,
0.7569,0.7756,0.7798,0.7812,0.7901,0.7902,0.7990,0.8035,0.8063,0.8069,
0.8092,0.8132,0.8192,0.8228,0.8266,0.8353,0.8440,0.8444,0.8469,0.8495,
0.8565,0.8566,0.8577,0.8585,0.8593,0.8645,0.8655,0.8663,0.8668,0.8688,
0.8724,0.8824,0.9015,0.9022,0.9059,0.9067,0.9072,0.9303,0.9379,0.9438,
0.9476,0.9484,0.9580,0.9673,0.9792,0.9793,0.9819,0.9949,0.9961,
Overall p-value after applying KStest on 269 p-values = 0.001560
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.