RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 12.8292 0.252457
2 to 25 15.76 20.7109 0.760512
3 to 26 15.74 30.9003 0.979463
4 to 27 16.07 5.8914 0.006114
5 to 28 15.90 15.3698 0.431139
6 to 29 15.53 26.1163 0.927633
7 to 30 15.95 20.4866 0.749898
8 to 31 15.78 20.2207 0.736905
9 to 32 15.71 14.8836 0.396136
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.453151
Tough bday spacings test for dh-ranFile-2018-06-24_00:31: 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 41 70 93 109 74 49 35 7 10 5
(O-E)^2/E 0.5 0.5 0.1 0.2 1.3 0.2 0.2 0.9 4.2 1.7 0.2
Birthday Spacings: Sum(O-E)^2/E= 10.156, p= 0.573
RESULTS OF GCD FOR dh-ranFile-2018-06-24_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.484656
p-value, dist. of gcd's: 0.251753
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.220 0.828 0.495 0.676 0.949 0.939 0.665 0.807
Bits 8 to 15---> 0.819 0.833 0.419 0.087 0.552 0.890 0.370 0.750
Bits 16 to 23---> 0.272 0.305 0.462 0.331 0.836 0.230 0.533 0.535
Bits 24 to 31---> 0.601 0.894 0.296 0.001 0.003 0.899 0.171 0.854
KS test for the above 32 p values: 0.625
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_00:31,
p-values for 5 runs: 0.5212, 0.8247, 0.4247, 0.4718, 0.2278
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5225 5134.0 1.613 1.644
r= 30 23143 23103.0 0.069 1.713
r= 31 11418 11551.5 1.543 3.257
chi-square = 3.257 with df = 3; p-value = 0.646
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5217 5134.0 1.341 1.480
r= 31 23014 23103.0 0.343 1.824
r= 32 11563 11551.5 0.011 1.835
chi-square = 1.835 with df = 3; p-value = 0.393
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_00:31
b-rank test for bits 1 to 8, p=0.09638
b-rank test for bits 2 to 9, p=0.72548
b-rank test for bits 3 to 10, p=0.40626
b-rank test for bits 4 to 11, p=0.65248
b-rank test for bits 5 to 12, p=0.73937
b-rank test for bits 6 to 13, p=0.15538
b-rank test for bits 7 to 14, p=0.20552
b-rank test for bits 8 to 15, p=0.59131
b-rank test for bits 9 to 16, p=0.81130
b-rank test for bits 10 to 17, p=0.41222
b-rank test for bits 11 to 18, p=0.37448
b-rank test for bits 12 to 19, p=0.87481
b-rank test for bits 13 to 20, p=0.81211
b-rank test for bits 14 to 21, p=0.96516
b-rank test for bits 15 to 22, p=0.91319
b-rank test for bits 16 to 23, p=0.15548
b-rank test for bits 17 to 24, p=0.37857
b-rank test for bits 18 to 25, p=0.16279
b-rank test for bits 19 to 26, p=0.14802
b-rank test for bits 20 to 27, p=0.00041
b-rank test for bits 21 to 28, p=0.15716
b-rank test for bits 22 to 29, p=0.58110
b-rank test for bits 23 to 30, p=0.63058
b-rank test for bits 24 to 31, p=0.67514
b-rank test for bits 25 to 32, p=0.69414
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 = 0.793314
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_00:31
(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 141655 -0.59 0.276180
2 141943 0.08 0.531352
3 142584 1.58 0.942525
4 141266 -1.50 0.066406
5 141634 -0.64 0.260017
6 142901 2.32 0.989748
7 142354 1.04 0.850586
8 141751 -0.37 0.355717
9 142100 0.45 0.672017
10 141764 -0.34 0.367095
11 142226 0.74 0.770315
12 142282 0.87 0.808048
13 141171 -1.73 0.042257
14 142007 0.23 0.590255
15 142658 1.75 0.959874
16 141820 -0.21 0.417335
17 141901 -0.02 0.492236
18 141399 -1.19 0.116560
19 141617 -0.68 0.247299
20 141627 -0.66 0.254739
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_00:31
Bits used No. missing words z-score p-value
23 to 32 141851 -0.2011 0.420295
22 to 31 141610 -1.0322 0.150996
21 to 30 141527 -1.3184 0.093688
20 to 29 141677 -0.8011 0.211526
19 to 28 141710 -0.6873 0.245933
18 to 27 141534 -1.2942 0.097791
17 to 26 141690 -0.7563 0.224732
16 to 25 141438 -1.6253 0.052052
15 to 24 141763 -0.5046 0.306925
14 to 23 141704 -0.7080 0.239462
13 to 22 141908 -0.0046 0.498170
12 to 21 141830 -0.2736 0.392215
11 to 20 141740 -0.5839 0.279645
10 to 19 141707 -0.6977 0.242686
9 to 18 141988 0.2713 0.606911
8 to 17 141884 -0.0873 0.465199
7 to 16 141631 -0.9598 0.168588
6 to 15 141690 -0.7563 0.224732
5 to 14 141792 -0.4046 0.342891
4 to 13 141595 -1.0839 0.139205
3 to 12 141997 0.3023 0.618792
2 to 11 142335 1.4678 0.928924
1 to 10 142374 1.6023 0.945457
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_00:31
Bits used No. missing words z-score p-value
28 to 32 141928 0.0633 0.525232
27 to 31 141393 -1.7503 0.040036
26 to 30 141809 -0.3401 0.366890
25 to 29 141685 -0.7604 0.223496
24 to 28 141632 -0.9401 0.173583
23 to 27 141458 -1.5299 0.063017
22 to 26 141606 -1.0282 0.151919
21 to 25 141907 -0.0079 0.496849
20 to 24 141631 -0.9435 0.172715
19 to 23 142006 0.3277 0.628429
18 to 22 142055 0.4938 0.689275
17 to 21 141861 -0.1638 0.434932
16 to 20 141933 0.0802 0.531976
15 to 19 141977 0.2294 0.590717
14 to 18 141738 -0.5808 0.280695
13 to 17 141735 -0.5909 0.277277
12 to 16 141466 -1.5028 0.066444
11 to 15 142125 0.7311 0.767636
10 to 14 141993 0.2836 0.611652
9 to 13 141391 -1.7571 0.039455
8 to 12 141750 -0.5401 0.294564
7 to 11 142280 1.2565 0.895534
6 to 10 141924 0.0497 0.519831
5 to 9 142079 0.5752 0.717406
4 to 8 141511 -1.3503 0.088465
3 to 7 142172 0.8904 0.813376
2 to 6 141654 -0.8655 0.193375
1 to 5 141802 -0.3638 0.357992
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_00:31
Bits used No. missing words z-score p-value
31 to 32 141761 -0.4376 0.330856
30 to 31 141842 -0.1986 0.421283
29 to 30 142036 0.3737 0.645671
28 to 29 141942 0.0964 0.538387
27 to 28 141916 0.0197 0.507849
26 to 27 141754 -0.4582 0.323404
25 to 26 141524 -1.1367 0.127839
24 to 25 141741 -0.4965 0.309754
23 to 24 142006 0.2852 0.612240
22 to 23 141729 -0.5319 0.297381
21 to 22 141807 -0.3019 0.381380
20 to 21 142504 1.7542 0.960301
19 to 20 141955 0.1347 0.553583
18 to 19 141741 -0.4965 0.309754
17 to 18 141825 -0.2488 0.401773
16 to 17 142082 0.5094 0.694747
15 to 16 142119 0.6185 0.731876
14 to 15 141438 -1.3904 0.082211
13 to 14 142269 1.0610 0.855649
12 to 13 142088 0.5271 0.700921
11 to 12 141700 -0.6175 0.268455
10 to 11 142125 0.6362 0.737675
9 to 10 141771 -0.4081 0.341617
8 to 9 141460 -1.3255 0.092510
7 to 8 141756 -0.4523 0.325526
6 to 7 141397 -1.5113 0.065356
5 to 6 141836 -0.2163 0.414372
4 to 5 142411 1.4799 0.930544
3 to 4 141973 0.1878 0.574490
2 to 3 142457 1.6155 0.946904
1 to 2 141566 -1.0128 0.155584
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2435.89 -0.907 0.182284
Test results for specific bytes for dh-ranFile-2018-06-24_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2588.95 1.258 0.895786
2 to 9 2520.94 0.296 0.616414
3 to 10 2368.58 -1.859 0.031548
4 to 11 2356.99 -2.022 0.021563
5 to 12 2340.76 -2.252 0.012160
6 to 13 2397.02 -1.456 0.072651
7 to 14 2665.66 2.343 0.990430
8 to 15 2408.95 -1.288 0.098933
9 to 16 2554.35 0.769 0.778932
10 to 17 2506.96 0.098 0.539184
11 to 18 2534.54 0.488 0.687378
12 to 19 2561.51 0.870 0.807799
13 to 20 2592.70 1.311 0.905072
14 to 21 2462.23 -0.534 0.296638
15 to 22 2465.72 -0.485 0.313897
16 to 23 2471.70 -0.400 0.344483
17 to 24 2538.60 0.546 0.707404
18 to 25 2337.94 -2.292 0.010956
19 to 26 2486.02 -0.198 0.421648
20 to 27 2509.20 0.130 0.551765
21 to 28 2441.03 -0.834 0.202136
22 to 29 2585.79 1.213 0.887487
23 to 30 2501.44 0.020 0.508134
24 to 31 2478.02 -0.311 0.377933
25 to 32 2540.88 0.578 0.718398
CDPARK for dh-ranFile-2018-06-24_00:31: 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
3528 0.2283 0.590298
3528 0.2283 0.590298
3530 0.3196 0.625377
3519 -0.1826 0.427537
3541 0.8219 0.794438
3512 -0.5023 0.307734
3521 -0.0913 0.463617
3533 0.4566 0.676028
3516 -0.3196 0.374623
3496 -1.2329 0.108811
Square side=100, avg. no. parked=3522.40 sample std.=11.99
p-value of the KSTEST for those 10 p-values: 0.482065
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_00:31
0.0481,0.9246,0.3394,0.4887,0.5228,0.8718,0.7858,0.7540,0.2401,0.8379,
The KS test for those 10 p-values: 0.627876
The 3DSPHERES test for dh-ranFile-2018-06-24_00:31
sample no r^3 equiv. uni.
1 68.349 0.897541
2 67.778 0.895572
3 30.036 0.632566
4 15.315 0.399803
5 100.034 0.964367
6 8.231 0.239954
7 12.862 0.348659
8 8.287 0.241357
9 9.113 0.261963
10 56.031 0.845522
11 43.198 0.763058
12 5.752 0.174478
13 53.018 0.829200
14 54.739 0.838724
15 16.692 0.426734
16 19.051 0.470080
17 27.775 0.603796
18 0.480 0.015881
19 21.545 0.512347
20 16.812 0.429020
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.779771
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 -0.4 -0.3 -1.6 1.0
-0.6 1.2 1.2 0.2 1.1 -0.2
-0.4 -0.3 0.2 -0.2 -0.3 0.2
-0.3 -0.9 0.1 -0.3 1.9 -0.1
0.5 -1.3 0.9 -0.7 -0.9 -1.5
0.8 -0.2 0.7 -0.3 0.2 0.4
-0.2 -0.1 -1.2 -0.7 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:24.541396
z-score=-1.904890, p-value=0.014465
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_00:31
Test no p-value
1 0.275795
2 0.001731
3 0.104981
4 0.283543
5 0.773227
6 0.236746
7 0.072946
8 0.177471
9 0.907543
10 0.563778
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.084807
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_00:31:
(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 66545 0.22 66430 0.84
3 25000.00 25120 0.58 25181 1.31
4 6666.67 6633 0.17 6693 0.10
5 1388.89 1433 1.40 1413 0.42
6 238.10 238 0.00 239 0.00
7 34.72 27 1.72 38 0.31
8 4.96 3 0.77 5 0.00
p=0.43812 p=0.18949
Number of rngs required: 688107, p-value: 0.367
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_00:31
No. of wins: Observed Expected
98502 98585.9
z-score=-0.375, pvalue=0.35381
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66542 66666.7 0.233 0.233
2 37539 37654.3 0.353 0.586
3 27032 26954.7 0.221 0.808
4 19181 19313.5 0.908 1.716
5 13867 13851.4 0.018 1.734
6 10093 9943.5 2.246 3.980
7 7259 7145.0 1.818 5.798
8 5113 5139.1 0.132 5.931
9 3743 3699.9 0.503 6.433
10 2712 2666.3 0.783 7.217
11 1963 1923.3 0.818 8.035
12 1369 1388.7 0.281 8.316
13 970 1003.7 1.132 9.448
14 698 726.1 1.091 10.539
15 489 525.8 2.580 13.119
16 391 381.2 0.255 13.374
17 269 276.5 0.206 13.579
18 182 200.8 1.765 15.345
19 152 146.0 0.248 15.593
20 124 106.2 2.978 18.571
21 312 287.1 2.157 20.728
Chisq= 20.73 for 20 degrees of freedom, p= 0.58668
SUMMARY of craptest
p-value for no. of wins: 0.353806
p-value for throws/game: 0.586680
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_00:31
No. of wins: Observed Expected
98482 98585.9
z-score=-0.465, pvalue=0.32114
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66368 66666.7 1.338 1.338
2 37571 37654.3 0.184 1.522
3 27274 26954.7 3.782 5.304
4 19500 19313.5 1.802 7.106
5 13927 13851.4 0.412 7.518
6 9648 9943.5 8.784 16.302
7 7356 7145.0 6.230 22.532
8 5084 5139.1 0.590 23.122
9 3688 3699.9 0.038 23.160
10 2592 2666.3 2.070 25.230
11 1902 1923.3 0.237 25.467
12 1373 1388.7 0.178 25.645
13 1064 1003.7 3.621 29.266
14 714 726.1 0.203 29.469
15 522 525.8 0.028 29.497
16 394 381.2 0.433 29.930
17 291 276.5 0.756 30.686
18 183 200.8 1.583 32.269
19 148 146.0 0.028 32.297
20 96 106.2 0.982 33.280
21 305 287.1 1.114 34.394
Chisq= 34.39 for 20 degrees of freedom, p= 0.97642
SUMMARY of craptest
p-value for no. of wins: 0.321139
p-value for throws/game: 0.976419
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0010,0.0017,0.0032,0.0061,0.0110,0.0122,0.0145,0.0159,0.0216,
0.0315,0.0395,0.0400,0.0423,0.0481,0.0521,0.0630,0.0654,0.0664,0.0664,
0.0727,0.0729,0.0822,0.0848,0.0873,0.0885,0.0925,0.0937,0.0964,0.0978,
0.0989,0.1050,0.1088,0.1166,0.1278,0.1392,0.1480,0.1510,0.1519,0.1554,
0.1555,0.1556,0.1572,0.1628,0.1686,0.1714,0.1727,0.1736,0.1745,0.1775,
0.1823,0.1895,0.1934,0.2021,0.2055,0.2115,0.2202,0.2235,0.2247,0.2247,
0.2278,0.2302,0.2367,0.2395,0.2400,0.2401,0.2414,0.2427,0.2459,0.2473,
0.2518,0.2525,0.2547,0.2600,0.2620,0.2685,0.2720,0.2758,0.2762,0.2773,
0.2796,0.2807,0.2835,0.2946,0.2957,0.2966,0.2974,0.3049,0.3069,0.3077,
0.3098,0.3098,0.3139,0.3211,0.3234,0.3255,0.3307,0.3309,0.3394,0.3416,
0.3429,0.3445,0.3487,0.3538,0.3557,0.3580,0.3666,0.3669,0.3671,0.3695,
0.3745,0.3746,0.3779,0.3786,0.3814,0.3922,0.3926,0.3961,0.3998,0.4018,
0.4063,0.4122,0.4144,0.4173,0.4193,0.4203,0.4213,0.4216,0.4247,0.4267,
0.4275,0.4290,0.4311,0.4349,0.4381,0.4532,0.4624,0.4636,0.4652,0.4701,
0.4718,0.4821,0.4847,0.4887,0.4922,0.4953,0.4968,0.4982,0.5078,0.5081,
0.5123,0.5198,0.5212,0.5228,0.5252,0.5314,0.5320,0.5326,0.5352,0.5384,
0.5392,0.5516,0.5518,0.5536,0.5638,0.5731,0.5745,0.5811,0.5867,0.5903,
0.5903,0.5903,0.5907,0.5913,0.6008,0.6038,0.6069,0.6117,0.6122,0.6164,
0.6188,0.6254,0.6254,0.6279,0.6284,0.6306,0.6326,0.6457,0.6463,0.6525,
0.6648,0.6720,0.6751,0.6757,0.6760,0.6874,0.6893,0.6941,0.6947,0.7009,
0.7074,0.7174,0.7184,0.7255,0.7319,0.7369,0.7377,0.7394,0.7499,0.7504,
0.7540,0.7605,0.7631,0.7676,0.7703,0.7732,0.7789,0.7798,0.7858,0.7933,
0.7944,0.8066,0.8078,0.8080,0.8113,0.8121,0.8134,0.8187,0.8247,0.8281,
0.8292,0.8325,0.8361,0.8379,0.8387,0.8455,0.8506,0.8541,0.8556,0.8718,
0.8748,0.8875,0.8900,0.8936,0.8955,0.8956,0.8958,0.8975,0.8991,0.9051,
0.9075,0.9132,0.9246,0.9276,0.9289,0.9305,0.9393,0.9425,0.9455,0.9469,
0.9493,0.9599,0.9603,0.9644,0.9652,0.9764,0.9795,0.9897,0.9904,
Overall p-value after applying KStest on 269 p-values = 0.182760
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.