RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.86 26.4506 0.933367
2 to 25 16.16 12.8387 0.253087
3 to 26 15.61 24.6636 0.897504
4 to 27 15.56 19.8845 0.719819
5 to 28 15.50 27.5409 0.949403
6 to 29 15.75 15.9561 0.473050
7 to 30 15.68 16.7576 0.529095
8 to 31 15.39 26.1823 0.928797
9 to 32 15.84 7.1812 0.018922
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.134116
Tough bday spacings test for dh-ranFile-2018-06-28_23:31: 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 9 26 91 110 85 73 51 29 18 5 3
(O-E)^2/E 0.0 3.1 4.3 1.6 1.6 0.3 0.0 0.0 0.7 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 12.290, p= 0.734
RESULTS OF GCD FOR dh-ranFile-2018-06-28_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.688891
p-value, dist. of gcd's: 0.915237
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.402 0.238 0.532 0.714 0.406 0.784 0.025 0.371
Bits 8 to 15---> 0.201 0.289 0.388 0.807 0.990 0.682 0.786 0.154
Bits 16 to 23---> 0.908 0.781 0.750 0.133 0.734 0.231 0.770 0.278
Bits 24 to 31---> 0.627 0.372 0.046 0.209 0.708 0.393 0.427 0.543
KS test for the above 32 p values: 0.243
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_23:31,
p-values for 5 runs: 0.0521, 0.7373, 0.1416, 0.5689, 0.1780
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5230 5134.0 1.795 1.822
r= 30 23026 23103.0 0.257 2.079
r= 31 11535 11551.5 0.024 2.103
chi-square = 2.103 with df = 3; p-value = 0.449
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 222 211.4 0.530 0.530
r= 30 4995 5134.0 3.764 4.294
r= 31 23328 23103.0 2.190 6.484
r= 32 11455 11551.5 0.807 7.290
chi-square = 7.290 with df = 3; p-value = 0.937
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_23:31
b-rank test for bits 1 to 8, p=0.98170
b-rank test for bits 2 to 9, p=0.84754
b-rank test for bits 3 to 10, p=0.97790
b-rank test for bits 4 to 11, p=0.98320
b-rank test for bits 5 to 12, p=0.91614
b-rank test for bits 6 to 13, p=0.20362
b-rank test for bits 7 to 14, p=0.70182
b-rank test for bits 8 to 15, p=0.26805
b-rank test for bits 9 to 16, p=0.93601
b-rank test for bits 10 to 17, p=0.68737
b-rank test for bits 11 to 18, p=0.87957
b-rank test for bits 12 to 19, p=0.67784
b-rank test for bits 13 to 20, p=0.72061
b-rank test for bits 14 to 21, p=0.10194
b-rank test for bits 15 to 22, p=0.43070
b-rank test for bits 16 to 23, p=0.64053
b-rank test for bits 17 to 24, p=0.93008
b-rank test for bits 18 to 25, p=0.32134
b-rank test for bits 19 to 26, p=0.55110
b-rank test for bits 20 to 27, p=0.23769
b-rank test for bits 21 to 28, p=0.38819
b-rank test for bits 22 to 29, p=0.51814
b-rank test for bits 23 to 30, p=0.91152
b-rank test for bits 24 to 31, p=0.28913
b-rank test for bits 25 to 32, p=0.86265
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 = 0.016480
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_23:31
(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 142013 0.24 0.595695
2 142265 0.83 0.797015
3 142685 1.81 0.965031
4 141756 -0.36 0.360079
5 141707 -0.47 0.318202
6 142416 1.18 0.881756
7 141655 -0.59 0.276180
8 141878 -0.07 0.470823
9 142054 0.34 0.632324
10 141433 -1.11 0.132871
11 141797 -0.26 0.396486
12 141351 -1.30 0.096030
13 142073 0.38 0.648920
14 141625 -0.66 0.253242
15 142290 0.89 0.813110
16 142112 0.47 0.682082
17 141523 -0.90 0.183358
18 141342 -1.33 0.092497
19 141660 -0.58 0.280099
20 142727 1.91 0.971962
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_23:31
Bits used No. missing words z-score p-value
23 to 32 141675 -0.8080 0.209535
22 to 31 141723 -0.6425 0.260269
21 to 30 141350 -1.9287 0.026883
20 to 29 141596 -1.0804 0.139971
19 to 28 142070 0.5540 0.710222
18 to 27 142154 0.8437 0.800579
17 to 26 142019 0.3782 0.647349
16 to 25 142197 0.9920 0.839393
15 to 24 141486 -1.4598 0.072178
14 to 23 141883 -0.0908 0.463829
13 to 22 142188 0.9609 0.831707
12 to 21 141689 -0.7598 0.223699
11 to 20 142170 0.8989 0.815637
10 to 19 142227 1.0954 0.863332
9 to 18 141809 -0.3460 0.364684
8 to 17 141800 -0.3770 0.353087
7 to 16 141773 -0.4701 0.319141
6 to 15 141567 -1.1804 0.118911
5 to 14 141678 -0.7977 0.212525
4 to 13 141813 -0.3322 0.369880
3 to 12 141934 0.0851 0.533897
2 to 11 141415 -1.7046 0.044136
1 to 10 142399 1.6885 0.954344
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_23:31
Bits used No. missing words z-score p-value
28 to 32 142059 0.5074 0.694048
27 to 31 141925 0.0531 0.521181
26 to 30 142101 0.6497 0.742066
25 to 29 141571 -1.1469 0.125715
24 to 28 142004 0.3209 0.625863
23 to 27 141538 -1.2587 0.104061
22 to 26 141787 -0.4147 0.339189
21 to 25 141987 0.2633 0.603836
20 to 24 142055 0.4938 0.689275
19 to 23 142473 1.9107 0.971981
18 to 22 141562 -1.1774 0.119520
17 to 21 141267 -2.1774 0.014726
16 to 20 141860 -0.1672 0.433598
15 to 19 142040 0.4429 0.671099
14 to 18 141754 -0.5265 0.299256
13 to 17 141939 0.1006 0.540057
12 to 16 141669 -0.8147 0.207628
11 to 15 141726 -0.6215 0.267149
10 to 14 141670 -0.8113 0.208600
9 to 13 141478 -1.4621 0.071852
8 to 12 142370 1.5616 0.940808
7 to 11 142131 0.7514 0.773801
6 to 10 142096 0.6328 0.736561
5 to 9 141796 -0.3842 0.350426
4 to 8 141517 -1.3299 0.091770
3 to 7 141556 -1.1977 0.115511
2 to 6 142482 1.9413 0.973886
1 to 5 141885 -0.0825 0.467135
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_23:31
Bits used No. missing words z-score p-value
31 to 32 141753 -0.4612 0.322345
30 to 31 142484 1.6952 0.954980
29 to 30 141676 -0.6883 0.245635
28 to 29 141489 -1.2399 0.107504
27 to 28 141598 -0.9184 0.179211
26 to 27 141710 -0.5880 0.278268
25 to 26 141554 -1.0482 0.147280
24 to 25 141933 0.0698 0.527833
23 to 24 141504 -1.1957 0.115914
22 to 23 142154 0.7217 0.764773
21 to 22 142066 0.4622 0.678014
20 to 21 141384 -1.5496 0.060613
19 to 20 142368 1.3530 0.911974
18 to 19 141689 -0.6499 0.257865
17 to 18 142383 1.3973 0.918832
16 to 17 142001 0.2704 0.606579
15 to 16 141715 -0.5732 0.283240
14 to 15 141727 -0.5378 0.295342
13 to 14 142593 2.0167 0.978138
12 to 13 142138 0.6745 0.750017
11 to 12 141849 -0.1780 0.429375
10 to 11 141788 -0.3579 0.360207
9 to 10 142347 1.2911 0.901659
8 to 9 142472 1.6598 0.951522
7 to 8 142454 1.6067 0.945939
6 to 7 141115 -2.3432 0.009561
5 to 6 141244 -1.9626 0.024845
4 to 5 142104 0.5742 0.717100
3 to 4 141869 -0.1190 0.452651
2 to 3 141872 -0.1101 0.456158
1 to 2 141641 -0.7915 0.214316
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2671.83 2.430 0.992451
Test results for specific bytes for dh-ranFile-2018-06-28_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2584.95 1.201 0.885188
2 to 9 2579.05 1.118 0.868195
3 to 10 2469.60 -0.430 0.333620
4 to 11 2525.51 0.361 0.640878
5 to 12 2629.70 1.834 0.966694
6 to 13 2446.31 -0.759 0.223827
7 to 14 2427.97 -1.019 0.154195
8 to 15 2566.77 0.944 0.827475
9 to 16 2598.87 1.398 0.918968
10 to 17 2632.67 1.876 0.969685
11 to 18 2442.65 -0.811 0.208662
12 to 19 2436.47 -0.898 0.184474
13 to 20 2532.35 0.458 0.676350
14 to 21 2419.94 -1.132 0.128771
15 to 22 2531.24 0.442 0.670678
16 to 23 2445.67 -0.768 0.221122
17 to 24 2397.07 -1.456 0.072749
18 to 25 2379.89 -1.699 0.044694
19 to 26 2478.36 -0.306 0.379779
20 to 27 2672.24 2.436 0.992571
21 to 28 2459.94 -0.567 0.285512
22 to 29 2491.46 -0.121 0.451940
23 to 30 2560.03 0.849 0.802046
24 to 31 2545.43 0.642 0.739702
25 to 32 2503.23 0.046 0.518194
CDPARK for dh-ranFile-2018-06-28_23:31: 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
3495 -1.2785 0.100530
3494 -1.3242 0.092718
3512 -0.5023 0.307734
3559 1.6438 0.949895
3560 1.6895 0.954438
3537 0.6393 0.738676
3536 0.5936 0.723613
3495 -1.2785 0.100530
3529 0.2740 0.607947
3541 0.8219 0.794438
Square side=100, avg. no. parked=3525.80 sample std.=24.17
p-value of the KSTEST for those 10 p-values: 0.521509
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_23:31
0.8938,0.0370,0.8743,0.5659,0.2552,0.5095,0.2834,0.1248,0.5431,0.8375,
The KS test for those 10 p-values: 0.972143
The 3DSPHERES test for dh-ranFile-2018-06-28_23:31
sample no r^3 equiv. uni.
1 8.997 0.259116
2 3.448 0.108579
3 87.424 0.945749
4 23.739 0.546748
5 29.752 0.629066
6 42.744 0.759442
7 85.225 0.941624
8 13.958 0.372036
9 1.311 0.042770
10 87.019 0.945012
11 12.031 0.330381
12 126.419 0.985212
13 3.408 0.107386
14 54.193 0.835762
15 17.766 0.446892
16 4.006 0.124988
17 45.398 0.779809
18 43.048 0.761866
19 47.428 0.794215
20 2.936 0.093236
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.438093
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.8 -0.3 -0.9 -0.4
-0.7 1.0 -0.4 1.0 0.3 -0.6
-0.5 1.2 -0.3 -0.4 0.4 -1.0
0.4 -0.5 0.5 -1.6 -0.5 1.6
0.2 -2.4 2.0 0.8 2.2 0.4
1.3 -1.1 -0.3 1.1 -0.2 -0.1
0.5 -0.1 -0.8 -0.7 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:35.258198
z-score=-0.735591, p-value=0.240323
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_23:31
Test no p-value
1 0.136190
2 0.758312
3 0.442138
4 0.024883
5 0.111019
6 0.237604
7 0.068322
8 0.278446
9 0.002634
10 0.032306
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000709
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_23:31:
(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 66502 0.41 66692 0.01
3 25000.00 25116 0.54 24993 0.00
4 6666.67 6763 1.39 6690 0.08
5 1388.89 1372 0.21 1378 0.09
6 238.10 210 3.32 205 4.60
7 34.72 33 0.09 37 0.15
8 4.96 3 0.77 4 0.19
p=0.65221 p=0.47077
Number of rngs required: 687748, p-value: 0.225
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_23:31
No. of wins: Observed Expected
98701 98585.9
z-score= 0.515, pvalue=0.69672
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66743 66666.7 0.087 0.087
2 37800 37654.3 0.564 0.651
3 27062 26954.7 0.427 1.078
4 19210 19313.5 0.554 1.632
5 13699 13851.4 1.677 3.309
6 9876 9943.5 0.459 3.768
7 7205 7145.0 0.503 4.272
8 5190 5139.1 0.505 4.776
9 3703 3699.9 0.003 4.779
10 2682 2666.3 0.092 4.871
11 1890 1923.3 0.578 5.449
12 1344 1388.7 1.441 6.890
13 1025 1003.7 0.451 7.342
14 717 726.1 0.115 7.457
15 514 525.8 0.266 7.723
16 394 381.2 0.433 8.156
17 251 276.5 2.359 10.515
18 194 200.8 0.232 10.747
19 131 146.0 1.538 12.285
20 101 106.2 0.256 12.541
21 269 287.1 1.143 13.684
Chisq= 13.68 for 20 degrees of freedom, p= 0.15386
SUMMARY of craptest
p-value for no. of wins: 0.696716
p-value for throws/game: 0.153861
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_23:31
No. of wins: Observed Expected
98865 98585.9
z-score= 1.248, pvalue=0.89407
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66718 66666.7 0.040 0.040
2 37877 37654.3 1.317 1.356
3 26926 26954.7 0.031 1.387
4 19124 19313.5 1.859 3.246
5 13828 13851.4 0.040 3.285
6 9919 9943.5 0.061 3.346
7 7063 7145.0 0.942 4.287
8 5173 5139.1 0.224 4.511
9 3656 3699.9 0.520 5.032
10 2596 2666.3 1.853 6.885
11 1922 1923.3 0.001 6.886
12 1453 1388.7 2.973 9.859
13 1064 1003.7 3.621 13.480
14 759 726.1 1.487 14.967
15 486 525.8 3.018 17.985
16 402 381.2 1.140 19.125
17 298 276.5 1.665 20.791
18 205 200.8 0.087 20.877
19 128 146.0 2.216 23.093
20 109 106.2 0.073 23.166
21 294 287.1 0.165 23.331
Chisq= 23.33 for 20 degrees of freedom, p= 0.72717
SUMMARY of craptest
p-value for no. of wins: 0.894073
p-value for throws/game: 0.727169
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0026,0.0096,0.0147,0.0165,0.0189,0.0246,0.0248,0.0249,0.0269,
0.0323,0.0370,0.0428,0.0441,0.0447,0.0465,0.0521,0.0606,0.0683,0.0719,
0.0722,0.0727,0.0918,0.0925,0.0927,0.0932,0.0960,0.1005,0.1005,0.1019,
0.1041,0.1074,0.1075,0.1086,0.1110,0.1155,0.1159,0.1189,0.1195,0.1248,
0.1250,0.1257,0.1288,0.1329,0.1329,0.1341,0.1362,0.1400,0.1416,0.1473,
0.1539,0.1542,0.1543,0.1780,0.1792,0.1834,0.1845,0.2006,0.2036,0.2076,
0.2086,0.2087,0.2092,0.2095,0.2125,0.2143,0.2211,0.2237,0.2238,0.2246,
0.2310,0.2376,0.2376,0.2377,0.2403,0.2435,0.2456,0.2531,0.2532,0.2552,
0.2579,0.2591,0.2603,0.2671,0.2680,0.2762,0.2779,0.2783,0.2784,0.2801,
0.2832,0.2834,0.2855,0.2891,0.2894,0.2953,0.2993,0.3077,0.3182,0.3191,
0.3213,0.3223,0.3304,0.3336,0.3392,0.3504,0.3531,0.3601,0.3602,0.3647,
0.3699,0.3714,0.3717,0.3720,0.3798,0.3882,0.3883,0.3934,0.3965,0.4015,
0.4064,0.4267,0.4294,0.4307,0.4336,0.4381,0.4421,0.4469,0.4487,0.4519,
0.4527,0.4562,0.4638,0.4671,0.4708,0.4708,0.4731,0.5095,0.5181,0.5182,
0.5212,0.5215,0.5278,0.5291,0.5320,0.5339,0.5401,0.5431,0.5433,0.5467,
0.5511,0.5659,0.5689,0.5957,0.6038,0.6066,0.6079,0.6259,0.6267,0.6291,
0.6323,0.6405,0.6409,0.6473,0.6489,0.6522,0.6707,0.6711,0.6763,0.6778,
0.6780,0.6821,0.6821,0.6874,0.6889,0.6893,0.6940,0.6967,0.7018,0.7085,
0.7102,0.7144,0.7171,0.7198,0.7206,0.7236,0.7272,0.7338,0.7339,0.7366,
0.7373,0.7387,0.7397,0.7421,0.7500,0.7500,0.7583,0.7594,0.7619,0.7648,
0.7696,0.7738,0.7798,0.7806,0.7844,0.7863,0.7942,0.7944,0.7970,0.8006,
0.8020,0.8069,0.8131,0.8156,0.8275,0.8317,0.8358,0.8375,0.8394,0.8475,
0.8627,0.8633,0.8682,0.8743,0.8796,0.8818,0.8852,0.8938,0.8941,0.8975,
0.9017,0.9084,0.9115,0.9120,0.9152,0.9161,0.9188,0.9190,0.9288,0.9301,
0.9334,0.9360,0.9368,0.9408,0.9416,0.9450,0.9457,0.9459,0.9494,0.9499,
0.9515,0.9543,0.9544,0.9550,0.9650,0.9667,0.9697,0.9720,0.9720,0.9721,
0.9739,0.9779,0.9781,0.9817,0.9832,0.9852,0.9905,0.9925,0.9926,
Overall p-value after applying KStest on 269 p-values = 0.124343
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.