RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.84 18.8741 0.664193
2 to 25 15.93 10.7379 0.130142
3 to 26 15.65 21.3190 0.787653
4 to 27 15.55 27.0789 0.943080
5 to 28 15.68 17.0509 0.549076
6 to 29 15.90 9.6318 0.081662
7 to 30 15.77 25.3079 0.911973
8 to 31 15.88 24.0639 0.882290
9 to 32 15.80 22.6716 0.839750
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.139553
Tough bday spacings test for dh-ranFile-2018-06-16_07:31: 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 11 39 86 96 90 72 55 27 16 6 2
(O-E)^2/E 0.4 0.2 2.2 0.0 0.6 0.5 0.2 0.3 0.1 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 5.465, p= 0.142
RESULTS OF GCD FOR dh-ranFile-2018-06-16_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.337108
p-value, dist. of gcd's: 0.296616
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.567 0.634 0.697 0.386 0.365 0.839 0.078 0.985
Bits 8 to 15---> 0.940 0.940 0.480 0.156 0.152 0.441 0.783 0.422
Bits 16 to 23---> 0.291 0.693 0.072 0.989 0.837 0.594 0.536 0.204
Bits 24 to 31---> 0.169 0.576 0.750 0.247 0.274 0.176 0.732 0.738
KS test for the above 32 p values: 0.103
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_07:31,
p-values for 5 runs: 0.6477, 0.3995, 0.4911, 0.8338, 0.7426
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 175 211.4 6.273 6.273
r= 29 5129 5134.0 0.005 6.278
r= 30 23195 23103.0 0.366 6.644
r= 31 11501 11551.5 0.221 6.865
chi-square = 6.865 with df = 3; p-value = 0.924
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 224 211.4 0.749 0.749
r= 30 5203 5134.0 0.927 1.676
r= 31 22915 23103.0 1.531 3.206
r= 32 11658 11551.5 0.981 4.188
chi-square = 4.188 with df = 3; p-value = 0.758
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_07:31
b-rank test for bits 1 to 8, p=0.14560
b-rank test for bits 2 to 9, p=0.59395
b-rank test for bits 3 to 10, p=0.61325
b-rank test for bits 4 to 11, p=0.84480
b-rank test for bits 5 to 12, p=0.75686
b-rank test for bits 6 to 13, p=0.62452
b-rank test for bits 7 to 14, p=0.44173
b-rank test for bits 8 to 15, p=0.97273
b-rank test for bits 9 to 16, p=0.47269
b-rank test for bits 10 to 17, p=0.04858
b-rank test for bits 11 to 18, p=0.07626
b-rank test for bits 12 to 19, p=0.02431
b-rank test for bits 13 to 20, p=0.36136
b-rank test for bits 14 to 21, p=0.69451
b-rank test for bits 15 to 22, p=0.80823
b-rank test for bits 16 to 23, p=0.90439
b-rank test for bits 17 to 24, p=0.65523
b-rank test for bits 18 to 25, p=0.13456
b-rank test for bits 19 to 26, p=0.83651
b-rank test for bits 20 to 27, p=0.14469
b-rank test for bits 21 to 28, p=0.91231
b-rank test for bits 22 to 29, p=0.81309
b-rank test for bits 23 to 30, p=0.38980
b-rank test for bits 24 to 31, p=0.30371
b-rank test for bits 25 to 32, p=0.07134
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 = 0.853913
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_07:31
(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 141460 -1.05 0.146897
2 141021 -2.08 0.018968
3 141859 -0.12 0.453195
4 142302 0.92 0.820547
5 141934 0.06 0.522982
6 141784 -0.29 0.384827
7 142065 0.36 0.641965
8 142178 0.63 0.734911
9 141753 -0.37 0.357460
10 142009 0.23 0.592070
11 141266 -1.50 0.066406
12 141265 -1.51 0.066105
13 142312 0.94 0.826601
14 142114 0.48 0.683746
15 142094 0.43 0.666937
16 142324 0.97 0.833691
17 142201 0.68 0.752214
18 142438 1.24 0.891624
19 141296 -1.43 0.075927
20 142358 1.05 0.852749
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_07:31
Bits used No. missing words z-score p-value
23 to 32 142012 0.3540 0.638344
22 to 31 142063 0.5299 0.701908
21 to 30 142020 0.3816 0.648629
20 to 29 142114 0.7058 0.759831
19 to 28 141690 -0.7563 0.224732
18 to 27 142121 0.7299 0.767273
17 to 26 142186 0.9540 0.829967
16 to 25 142031 0.4196 0.662594
15 to 24 141988 0.2713 0.606911
14 to 23 142097 0.6471 0.741229
13 to 22 141916 0.0230 0.509175
12 to 21 142820 3.1402 0.999156
11 to 20 141866 -0.1494 0.440614
10 to 19 142176 0.9196 0.821097
9 to 18 141604 -1.0529 0.146202
8 to 17 142150 0.8299 0.796701
7 to 16 142141 0.7989 0.787815
6 to 15 142885 3.3644 0.999616
5 to 14 141520 -1.3425 0.089714
4 to 13 142051 0.4885 0.687408
3 to 12 141903 -0.0218 0.491293
2 to 11 142229 1.1023 0.864837
1 to 10 141757 -0.5253 0.299696
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_07:31
Bits used No. missing words z-score p-value
28 to 32 141621 -0.9774 0.164188
27 to 31 142006 0.3277 0.628429
26 to 30 142191 0.9548 0.830164
25 to 29 142353 1.5040 0.933705
24 to 28 141749 -0.5435 0.293396
23 to 27 141600 -1.0486 0.147187
22 to 26 142240 1.1209 0.868838
21 to 25 141583 -1.1062 0.134319
20 to 24 142013 0.3514 0.637365
19 to 23 142030 0.4091 0.658749
18 to 22 141697 -0.7198 0.235836
17 to 21 141395 -1.7435 0.040624
16 to 20 141398 -1.7333 0.041519
15 to 19 142023 0.3853 0.650001
14 to 18 142489 1.9650 0.975292
13 to 17 142121 0.7175 0.763475
12 to 16 141844 -0.2215 0.412368
11 to 15 142108 0.6735 0.749672
10 to 14 141761 -0.5028 0.307548
9 to 13 141870 -0.1333 0.446969
8 to 12 142166 0.8701 0.807868
7 to 11 141727 -0.6181 0.268265
6 to 10 141852 -0.1943 0.422955
5 to 9 142144 0.7955 0.786836
4 to 8 141745 -0.5571 0.288746
3 to 7 142237 1.1107 0.866661
2 to 6 142155 0.8328 0.797516
1 to 5 142007 0.3311 0.629710
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_07:31
Bits used No. missing words z-score p-value
31 to 32 141428 -1.4199 0.077825
30 to 31 141543 -1.0806 0.139933
29 to 30 141248 -1.9508 0.025539
28 to 29 141560 -1.0305 0.151394
27 to 28 142150 0.7099 0.761130
26 to 27 142538 1.8545 0.968165
25 to 26 141370 -1.5909 0.055811
24 to 25 141506 -1.1898 0.117070
23 to 24 141719 -0.5614 0.287247
22 to 23 141812 -0.2871 0.387014
21 to 22 141543 -1.0806 0.139933
20 to 21 141335 -1.6942 0.045115
19 to 20 141788 -0.3579 0.360207
18 to 19 142026 0.3442 0.634637
17 to 18 141532 -1.1131 0.132840
16 to 17 141731 -0.5260 0.299428
15 to 16 142053 0.4238 0.664146
14 to 15 141621 -0.8505 0.197515
13 to 14 141677 -0.6853 0.246565
12 to 13 141748 -0.4759 0.317073
11 to 12 141634 -0.8122 0.208343
10 to 11 142497 1.7335 0.958500
9 to 10 142452 1.6008 0.945289
8 to 9 141797 -0.3314 0.370187
7 to 8 142195 0.8427 0.800298
6 to 7 142901 2.9253 0.998279
5 to 6 141897 -0.0364 0.485493
4 to 5 141788 -0.3579 0.360207
3 to 4 142005 0.2822 0.611110
2 to 3 141978 0.2026 0.580263
1 to 2 142237 0.9666 0.833123
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2447.55 -0.742 0.229102
Test results for specific bytes for dh-ranFile-2018-06-16_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2395.81 -1.473 0.070312
2 to 9 2437.87 -0.879 0.189814
3 to 10 2391.22 -1.538 0.061975
4 to 11 2575.17 1.063 0.856126
5 to 12 2458.92 -0.581 0.280655
6 to 13 2465.58 -0.487 0.313195
7 to 14 2535.87 0.507 0.694013
8 to 15 2470.56 -0.416 0.338572
9 to 16 2471.66 -0.401 0.344262
10 to 17 2565.63 0.928 0.823335
11 to 18 2576.19 1.078 0.859379
12 to 19 2550.90 0.720 0.764183
13 to 20 2418.09 -1.158 0.123345
14 to 21 2448.54 -0.728 0.233389
15 to 22 2544.61 0.631 0.735946
16 to 23 2439.01 -0.862 0.194212
17 to 24 2510.82 0.153 0.560815
18 to 25 2410.48 -1.266 0.102762
19 to 26 2416.01 -1.188 0.117454
20 to 27 2576.54 1.082 0.860484
21 to 28 2505.47 0.077 0.530829
22 to 29 2512.91 0.183 0.572459
23 to 30 2516.68 0.236 0.593258
24 to 31 2498.80 -0.017 0.493236
25 to 32 2556.56 0.800 0.788098
CDPARK for dh-ranFile-2018-06-16_07:31: 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
3487 -1.6438 0.050105
3488 -1.5982 0.055002
3486 -1.6895 0.045562
3567 2.0091 0.977738
3521 -0.0913 0.463617
3519 -0.1826 0.427537
3528 0.2283 0.590298
3566 1.9635 0.975204
3513 -0.4566 0.323972
3524 0.0457 0.518210
Square side=100, avg. no. parked=3519.90 sample std.=27.79
p-value of the KSTEST for those 10 p-values: 0.275918
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_07:31
0.5373,0.5715,0.0553,0.3501,0.8856,0.3097,0.5734,0.7097,0.0739,0.7291,
The KS test for those 10 p-values: 0.887156
The 3DSPHERES test for dh-ranFile-2018-06-16_07:31
sample no r^3 equiv. uni.
1 8.327 0.242372
2 27.633 0.601918
3 14.925 0.391957
4 12.740 0.346016
5 16.679 0.426490
6 15.956 0.412491
7 24.847 0.563180
8 42.513 0.757581
9 30.493 0.638118
10 10.433 0.293737
11 34.903 0.687591
12 46.774 0.789680
13 6.979 0.207548
14 6.199 0.186695
15 4.756 0.146617
16 99.020 0.963141
17 32.012 0.655986
18 7.767 0.228109
19 57.721 0.853982
20 53.529 0.832087
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.755877
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.7 -2.0 0.1 -1.0 1.7 -0.8
-0.0 -0.1 -0.2 -2.7 0.8 0.0
-0.6 0.4 -0.8 0.3 0.2 -1.5
-0.1 0.1 1.2 1.1 -0.0 -0.2
1.5 0.7 -0.2 -0.3 0.8 -0.7
0.4 0.7 -0.9 0.0 -0.2 -0.3
-0.5 0.2 -0.4 -1.3 0.1 -1.0
0.8
Chi-square with 42 degrees of freedom:39.350223
z-score=-0.289114, p-value=0.412071
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_07:31
Test no p-value
1 0.064665
2 0.489794
3 0.857041
4 0.076923
5 0.533389
6 0.135636
7 0.137452
8 0.068148
9 0.244845
10 0.005035
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.006134
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_07:31:
(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 66633 0.02 66669 0.00
3 25000.00 24989 0.00 24989 0.00
4 6666.67 6731 0.62 6636 0.14
5 1388.89 1352 0.98 1418 0.61
6 238.10 260 2.02 247 0.33
7 34.72 29 0.94 36 0.05
8 4.96 5 0.00 4 0.19
p=0.40135 p=0.02958
Number of rngs required: 688383, p-value: 0.491
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_07:31
No. of wins: Observed Expected
98692 98585.9
z-score= 0.475, pvalue=0.68251
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66741 66666.7 0.083 0.083
2 37616 37654.3 0.039 0.122
3 27067 26954.7 0.468 0.589
4 19130 19313.5 1.743 2.332
5 13893 13851.4 0.125 2.457
6 10042 9943.5 0.975 3.432
7 7219 7145.0 0.766 4.198
8 5103 5139.1 0.253 4.451
9 3668 3699.9 0.274 4.725
10 2666 2666.3 0.000 4.725
11 1928 1923.3 0.011 4.737
12 1370 1388.7 0.253 4.990
13 952 1003.7 2.665 7.654
14 691 726.1 1.701 9.355
15 532 525.8 0.072 9.427
16 402 381.2 1.140 10.568
17 265 276.5 0.482 11.049
18 194 200.8 0.232 11.281
19 151 146.0 0.172 11.454
20 102 106.2 0.167 11.621
21 268 287.1 1.272 12.893
Chisq= 12.89 for 20 degrees of freedom, p= 0.11809
SUMMARY of craptest
p-value for no. of wins: 0.682509
p-value for throws/game: 0.118091
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_07:31
No. of wins: Observed Expected
98510 98585.9
z-score=-0.339, pvalue=0.36720
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66467 66666.7 0.598 0.598
2 37685 37654.3 0.025 0.623
3 26743 26954.7 1.663 2.286
4 19496 19313.5 1.725 4.011
5 13737 13851.4 0.945 4.957
6 10030 9943.5 0.752 5.708
7 7255 7145.0 1.693 7.401
8 5196 5139.1 0.631 8.032
9 3645 3699.9 0.814 8.845
10 2768 2666.3 3.879 12.725
11 1933 1923.3 0.049 12.773
12 1417 1388.7 0.575 13.348
13 1011 1003.7 0.053 13.401
14 678 726.1 3.192 16.593
15 506 525.8 0.748 17.341
16 398 381.2 0.745 18.086
17 273 276.5 0.045 18.131
18 194 200.8 0.232 18.363
19 154 146.0 0.440 18.803
20 113 106.2 0.433 19.237
21 301 287.1 0.672 19.908
Chisq= 19.91 for 20 degrees of freedom, p= 0.53633
SUMMARY of craptest
p-value for no. of wins: 0.367198
p-value for throws/game: 0.536329
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0050,0.0061,0.0190,0.0243,0.0255,0.0296,0.0406,0.0415,0.0451,0.0456,
0.0486,0.0501,0.0550,0.0553,0.0558,0.0620,0.0647,0.0661,0.0664,0.0681,
0.0703,0.0713,0.0718,0.0739,0.0759,0.0763,0.0769,0.0778,0.0780,0.0817,
0.0897,0.1028,0.1032,0.1171,0.1175,0.1181,0.1233,0.1301,0.1328,0.1343,
0.1346,0.1356,0.1375,0.1396,0.1399,0.1399,0.1420,0.1447,0.1456,0.1462,
0.1466,0.1469,0.1472,0.1514,0.1524,0.1563,0.1642,0.1688,0.1764,0.1867,
0.1898,0.1942,0.1975,0.2043,0.2075,0.2083,0.2247,0.2281,0.2291,0.2334,
0.2358,0.2424,0.2448,0.2466,0.2474,0.2683,0.2739,0.2759,0.2807,0.2872,
0.2887,0.2911,0.2934,0.2937,0.2966,0.2994,0.2997,0.3037,0.3075,0.3097,
0.3132,0.3171,0.3240,0.3371,0.3386,0.3443,0.3460,0.3501,0.3575,0.3602,
0.3602,0.3614,0.3649,0.3672,0.3702,0.3848,0.3857,0.3870,0.3898,0.3920,
0.3995,0.4014,0.4121,0.4124,0.4125,0.4217,0.4230,0.4265,0.4275,0.4406,
0.4414,0.4417,0.4470,0.4532,0.4636,0.4727,0.4803,0.4855,0.4898,0.4908,
0.4911,0.4913,0.4932,0.5092,0.5182,0.5230,0.5308,0.5334,0.5361,0.5363,
0.5373,0.5491,0.5608,0.5632,0.5673,0.5715,0.5725,0.5734,0.5764,0.5803,
0.5903,0.5921,0.5933,0.5939,0.5939,0.6019,0.6069,0.6111,0.6133,0.6245,
0.6284,0.6297,0.6344,0.6346,0.6374,0.6381,0.6383,0.6420,0.6477,0.6486,
0.6500,0.6552,0.6560,0.6587,0.6626,0.6641,0.6642,0.6669,0.6825,0.6837,
0.6874,0.6876,0.6931,0.6940,0.6945,0.6973,0.7019,0.7097,0.7291,0.7316,
0.7349,0.7359,0.7376,0.7412,0.7426,0.7496,0.7497,0.7522,0.7559,0.7569,
0.7576,0.7581,0.7598,0.7611,0.7635,0.7642,0.7673,0.7828,0.7868,0.7877,
0.7878,0.7881,0.7897,0.7967,0.7975,0.8003,0.8079,0.8082,0.8131,0.8205,
0.8211,0.8233,0.8266,0.8300,0.8302,0.8321,0.8331,0.8337,0.8338,0.8365,
0.8367,0.8391,0.8398,0.8448,0.8527,0.8539,0.8540,0.8561,0.8570,0.8594,
0.8605,0.8648,0.8667,0.8688,0.8823,0.8856,0.8872,0.8916,0.9044,0.9120,
0.9123,0.9237,0.9337,0.9397,0.9397,0.9431,0.9453,0.9585,0.9631,0.9682,
0.9727,0.9752,0.9753,0.9777,0.9853,0.9887,0.9983,0.9992,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.504564
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.