RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.72 14.3917 0.360796
2 to 25 15.66 15.6865 0.453840
3 to 26 15.57 16.0593 0.480365
4 to 27 15.56 24.8695 0.902331
5 to 28 15.85 41.4705 0.999201
6 to 29 15.76 14.3517 0.357928
7 to 30 15.88 28.6146 0.961750
8 to 31 15.65 19.5030 0.699567
9 to 32 15.67 15.1939 0.418484
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.117695
Tough bday spacings test for dh-ranFile-2018-07-02_20:31: 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 3 48 63 89 101 86 40 37 22 5 6
(O-E)^2/E 4.1 3.5 1.4 0.8 0.1 0.8 2.8 1.8 3.4 0.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 20.060, p= 0.971
RESULTS OF GCD FOR dh-ranFile-2018-07-02_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.674708
p-value, dist. of gcd's: 0.154060
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.673 0.491 0.418 0.080 0.905 0.667 0.560 0.226
Bits 8 to 15---> 0.259 0.738 0.622 0.998 0.844 0.511 0.217 0.886
Bits 16 to 23---> 0.134 0.225 0.524 0.314 0.894 0.622 0.496 0.960
Bits 24 to 31---> 0.822 0.190 0.602 0.717 0.459 0.779 0.809 0.921
KS test for the above 32 p values: 0.807
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_20:31,
p-values for 5 runs: 0.5800, 0.8177, 0.8393, 0.8497, 0.1670
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 188 211.4 2.594 2.594
r= 29 5128 5134.0 0.007 2.601
r= 30 23095 23103.0 0.003 2.604
r= 31 11589 11551.5 0.122 2.725
chi-square = 2.725 with df = 3; p-value = 0.564
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5053 5134.0 1.278 1.306
r= 31 23263 23103.0 1.107 2.413
r= 32 11475 11551.5 0.507 2.920
chi-square = 2.920 with df = 3; p-value = 0.596
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_20:31
b-rank test for bits 1 to 8, p=0.44344
b-rank test for bits 2 to 9, p=0.19906
b-rank test for bits 3 to 10, p=0.26778
b-rank test for bits 4 to 11, p=0.52619
b-rank test for bits 5 to 12, p=0.54344
b-rank test for bits 6 to 13, p=0.79568
b-rank test for bits 7 to 14, p=0.69970
b-rank test for bits 8 to 15, p=0.36182
b-rank test for bits 9 to 16, p=0.56159
b-rank test for bits 10 to 17, p=0.11410
b-rank test for bits 11 to 18, p=0.62422
b-rank test for bits 12 to 19, p=0.24192
b-rank test for bits 13 to 20, p=0.76190
b-rank test for bits 14 to 21, p=0.65879
b-rank test for bits 15 to 22, p=0.28613
b-rank test for bits 16 to 23, p=0.04695
b-rank test for bits 17 to 24, p=0.42226
b-rank test for bits 18 to 25, p=0.33448
b-rank test for bits 19 to 26, p=0.61388
b-rank test for bits 20 to 27, p=0.19617
b-rank test for bits 21 to 28, p=0.76766
b-rank test for bits 22 to 29, p=0.00956
b-rank test for bits 23 to 30, p=0.23343
b-rank test for bits 24 to 31, p=0.82041
b-rank test for bits 25 to 32, p=0.95084
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 = 0.689961
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_20:31
(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 142107 0.46 0.677904
2 142358 1.05 0.852749
3 141831 -0.18 0.427394
4 142300 0.91 0.819321
5 142709 1.87 0.969146
6 141425 -1.13 0.128899
7 142081 0.40 0.655826
8 142476 1.32 0.907248
9 141339 -1.33 0.091340
10 142348 1.02 0.847302
11 141483 -1.00 0.159601
12 141686 -0.52 0.300905
13 141819 -0.21 0.416424
14 141935 0.06 0.523913
15 142114 0.48 0.683746
16 141894 -0.04 0.485714
17 142317 0.95 0.829578
18 141860 -0.12 0.454121
19 141363 -1.28 0.100894
20 141812 -0.23 0.410054
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_20:31
Bits used No. missing words z-score p-value
23 to 32 141898 -0.0391 0.484418
22 to 31 141209 -2.4149 0.007869
21 to 30 142174 0.9127 0.819288
20 to 29 141988 0.2713 0.606911
19 to 28 141739 -0.5873 0.278486
18 to 27 141726 -0.6322 0.263637
17 to 26 141737 -0.5942 0.276175
16 to 25 141626 -0.9770 0.164285
15 to 24 142018 0.3747 0.646067
14 to 23 142052 0.4920 0.688628
13 to 22 141702 -0.7149 0.237326
12 to 21 141467 -1.5253 0.063595
11 to 20 141972 0.2161 0.585547
10 to 19 141721 -0.6494 0.258036
9 to 18 141736 -0.5977 0.275024
8 to 17 142383 1.6333 0.948802
7 to 16 141925 0.0540 0.521546
6 to 15 141468 -1.5218 0.064026
5 to 14 141854 -0.1908 0.424344
4 to 13 141956 0.1609 0.563926
3 to 12 141747 -0.5598 0.287822
2 to 11 141365 -1.8770 0.030259
1 to 10 141855 -0.1873 0.425695
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_20:31
Bits used No. missing words z-score p-value
28 to 32 142207 1.0091 0.843525
27 to 31 141887 -0.0757 0.469831
26 to 30 141919 0.0328 0.513075
25 to 29 142196 0.9718 0.834416
24 to 28 141583 -1.1062 0.134319
23 to 27 141792 -0.3977 0.345415
22 to 26 142304 1.3379 0.909530
21 to 25 141764 -0.4926 0.311132
20 to 24 141911 0.0057 0.502258
19 to 23 141903 -0.0215 0.491440
18 to 22 142456 1.8531 0.968067
17 to 21 141965 0.1887 0.574841
16 to 20 141990 0.2735 0.607749
15 to 19 141555 -1.2011 0.114853
14 to 18 141639 -0.9164 0.179736
13 to 17 141295 -2.0825 0.018650
12 to 16 141830 -0.2689 0.393998
11 to 15 142286 1.2768 0.899172
10 to 14 142139 0.7785 0.781875
9 to 13 141462 -1.5164 0.064713
8 to 12 141707 -0.6859 0.246399
7 to 11 142344 1.4735 0.929686
6 to 10 141725 -0.6248 0.266036
5 to 9 141852 -0.1943 0.422955
4 to 8 141863 -0.1571 0.437602
3 to 7 142042 0.4497 0.673547
2 to 6 141796 -0.3842 0.350426
1 to 5 142205 1.0023 0.841894
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_20:31
Bits used No. missing words z-score p-value
31 to 32 141997 0.2586 0.602033
30 to 31 141755 -0.4553 0.324464
29 to 30 141844 -0.1927 0.423592
28 to 29 142103 0.5713 0.716101
27 to 28 141455 -1.3402 0.090089
26 to 27 141576 -0.9833 0.162736
25 to 26 141595 -0.9272 0.176904
24 to 25 141805 -0.3078 0.379133
23 to 24 142534 1.8427 0.967312
22 to 23 142252 1.0108 0.843950
21 to 22 142077 0.4946 0.689559
20 to 21 141956 0.1377 0.554749
19 to 20 141807 -0.3019 0.381380
18 to 19 141948 0.1141 0.545409
17 to 18 142359 1.3265 0.907656
16 to 17 141602 -0.9066 0.182315
15 to 16 141611 -0.8800 0.189422
14 to 15 141477 -1.2753 0.101100
13 to 14 142080 0.5035 0.692677
12 to 13 141853 -0.1662 0.434014
11 to 12 141573 -0.9921 0.160569
10 to 11 141537 -1.0983 0.136033
9 to 10 142218 0.9105 0.818729
8 to 9 142098 0.5565 0.711082
7 to 8 141758 -0.4464 0.327654
6 to 7 142110 0.5919 0.723057
5 to 6 141346 -1.6617 0.048282
4 to 5 141597 -0.9213 0.178440
3 to 4 142088 0.5271 0.700921
2 to 3 142156 0.7276 0.766583
1 to 2 141041 -2.5614 0.005212
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2497.69 -0.033 0.486950
Test results for specific bytes for dh-ranFile-2018-07-02_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2419.95 -1.132 0.128787
2 to 9 2556.07 0.793 0.786105
3 to 10 2592.63 1.310 0.904901
4 to 11 2535.22 0.498 0.690799
5 to 12 2582.06 1.161 0.877077
6 to 13 2518.88 0.267 0.605246
7 to 14 2530.10 0.426 0.664823
8 to 15 2566.87 0.946 0.827831
9 to 16 2561.70 0.873 0.808549
10 to 17 2295.87 -2.887 0.001945
11 to 18 2530.02 0.424 0.664391
12 to 19 2619.23 1.686 0.954119
13 to 20 2342.40 -2.229 0.012913
14 to 21 2447.29 -0.745 0.228004
15 to 22 2412.99 -1.231 0.109253
16 to 23 2612.45 1.590 0.944118
17 to 24 2493.76 -0.088 0.464848
18 to 25 2448.75 -0.725 0.234272
19 to 26 2484.70 -0.216 0.414367
20 to 27 2353.30 -2.075 0.019012
21 to 28 2511.95 0.169 0.567084
22 to 29 2535.95 0.508 0.694397
23 to 30 2493.21 -0.096 0.461766
24 to 31 2412.39 -1.239 0.107673
25 to 32 2512.13 0.172 0.568094
CDPARK for dh-ranFile-2018-07-02_20:31: 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
3515 -0.3653 0.357445
3505 -0.8219 0.205562
3505 -0.8219 0.205562
3511 -0.5479 0.291865
3531 0.3653 0.642555
3567 2.0091 0.977738
3530 0.3196 0.625377
3558 1.5982 0.944998
3536 0.5936 0.723613
3526 0.1370 0.554479
Square side=100, avg. no. parked=3528.40 sample std.=20.04
p-value of the KSTEST for those 10 p-values: 0.723614
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_20:31
0.1507,0.8761,0.0477,0.5162,0.3015,0.3094,0.0795,0.6678,0.4664,0.7484,
The KS test for those 10 p-values: 0.693256
The 3DSPHERES test for dh-ranFile-2018-07-02_20:31
sample no r^3 equiv. uni.
1 22.345 0.525182
2 12.987 0.351378
3 25.261 0.569161
4 46.100 0.784902
5 26.783 0.590476
6 26.143 0.581648
7 38.522 0.723093
8 22.527 0.528055
9 17.866 0.448722
10 14.596 0.385239
11 77.881 0.925432
12 7.254 0.214791
13 4.515 0.139722
14 90.328 0.950754
15 19.147 0.471779
16 72.158 0.909758
17 0.349 0.011557
18 19.947 0.485676
19 80.642 0.931987
20 47.745 0.796380
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.412173
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 -0.1 -1.0 1.5 0.2
1.1 -0.6 0.7 1.4 0.3 -0.2
-1.0 -1.6 0.3 0.9 -0.4 -0.5
1.8 0.0 0.6 -2.3 -0.1 -0.0
0.0 -0.4 0.2 0.3 -0.6 1.0
-0.6 1.8 1.5 0.0 0.6 -1.6
-0.2 -1.0 1.3 0.4 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:38.818648
z-score=-0.347114, p-value=0.388589
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_20:31
Test no p-value
1 0.319067
2 0.598579
3 0.009798
4 0.138774
5 0.468809
6 0.000002
7 0.211800
8 0.002502
9 0.432203
10 0.056366
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000262
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_20:31:
(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 66623 0.03 66549 0.21
3 25000.00 24931 0.19 25008 0.00
4 6666.67 6764 1.42 6684 0.05
5 1388.89 1403 0.14 1453 2.96
6 238.10 222 1.09 266 3.27
7 34.72 46 3.66 33 0.09
8 4.96 10 5.12 6 0.22
p=0.92994 p=0.65913
Number of rngs required: 689600, p-value: 0.919
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_20:31
No. of wins: Observed Expected
98370 98585.9
z-score=-0.965, pvalue=0.16716
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66640 66666.7 0.011 0.011
2 37621 37654.3 0.029 0.040
3 27212 26954.7 2.455 2.496
4 19197 19313.5 0.702 3.198
5 13773 13851.4 0.444 3.642
6 10000 9943.5 0.321 3.962
7 7281 7145.0 2.588 6.550
8 5111 5139.1 0.153 6.703
9 3709 3699.9 0.023 6.726
10 2614 2666.3 1.026 7.752
11 1871 1923.3 1.424 9.176
12 1352 1388.7 0.972 10.148
13 972 1003.7 1.002 11.150
14 670 726.1 4.340 15.490
15 535 525.8 0.160 15.650
16 428 381.2 5.759 21.408
17 277 276.5 0.001 21.409
18 199 200.8 0.017 21.426
19 160 146.0 1.346 22.771
20 106 106.2 0.000 22.772
21 272 287.1 0.796 23.567
Chisq= 23.57 for 20 degrees of freedom, p= 0.73820
SUMMARY of craptest
p-value for no. of wins: 0.167161
p-value for throws/game: 0.738201
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_20:31
No. of wins: Observed Expected
98787 98585.9
z-score= 0.900, pvalue=0.81584
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66596 66666.7 0.075 0.075
2 37594 37654.3 0.097 0.172
3 27048 26954.7 0.323 0.494
4 19448 19313.5 0.937 1.431
5 13759 13851.4 0.617 2.048
6 9941 9943.5 0.001 2.049
7 7160 7145.0 0.031 2.080
8 5101 5139.1 0.282 2.362
9 3705 3699.9 0.007 2.369
10 2587 2666.3 2.358 4.728
11 1949 1923.3 0.343 5.070
12 1454 1388.7 3.067 8.137
13 990 1003.7 0.187 8.324
14 769 726.1 2.530 10.854
15 511 525.8 0.419 11.273
16 371 381.2 0.270 11.543
17 261 276.5 0.873 12.416
18 190 200.8 0.584 13.000
19 165 146.0 2.477 15.477
20 124 106.2 2.978 18.455
21 277 287.1 0.356 18.811
Chisq= 18.81 for 20 degrees of freedom, p= 0.46588
SUMMARY of craptest
p-value for no. of wins: 0.815839
p-value for throws/game: 0.465882
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0003,0.0019,0.0025,0.0052,0.0079,0.0096,0.0098,0.0116,0.0129,
0.0186,0.0190,0.0303,0.0470,0.0477,0.0483,0.0564,0.0636,0.0640,0.0647,
0.0795,0.0799,0.0901,0.0913,0.1009,0.1011,0.1077,0.1093,0.1141,0.1149,
0.1177,0.1288,0.1289,0.1341,0.1343,0.1360,0.1388,0.1397,0.1507,0.1541,
0.1596,0.1606,0.1627,0.1643,0.1670,0.1672,0.1769,0.1784,0.1797,0.1823,
0.1894,0.1899,0.1962,0.1991,0.2056,0.2056,0.2118,0.2148,0.2174,0.2251,
0.2257,0.2280,0.2334,0.2343,0.2373,0.2419,0.2464,0.2580,0.2591,0.2636,
0.2660,0.2678,0.2750,0.2762,0.2785,0.2861,0.2878,0.2919,0.3009,0.3015,
0.3094,0.3111,0.3141,0.3191,0.3245,0.3277,0.3345,0.3454,0.3504,0.3514,
0.3574,0.3579,0.3608,0.3618,0.3791,0.3814,0.3852,0.3886,0.3940,0.4101,
0.4122,0.4144,0.4164,0.4181,0.4185,0.4223,0.4230,0.4236,0.4243,0.4257,
0.4274,0.4322,0.4340,0.4376,0.4434,0.4487,0.4538,0.4541,0.4591,0.4618,
0.4648,0.4659,0.4664,0.4688,0.4698,0.4718,0.4804,0.4844,0.4857,0.4857,
0.4870,0.4914,0.4914,0.4963,0.5023,0.5106,0.5131,0.5162,0.5215,0.5239,
0.5239,0.5252,0.5262,0.5281,0.5434,0.5454,0.5545,0.5547,0.5598,0.5616,
0.5639,0.5641,0.5671,0.5681,0.5692,0.5748,0.5800,0.5816,0.5855,0.5905,
0.5959,0.5986,0.6016,0.6020,0.6052,0.6069,0.6077,0.6139,0.6218,0.6225,
0.6242,0.6254,0.6426,0.6461,0.6558,0.6588,0.6591,0.6644,0.6648,0.6670,
0.6678,0.6733,0.6735,0.6747,0.6779,0.6837,0.6886,0.6896,0.6900,0.6908,
0.6927,0.6933,0.6944,0.6996,0.6997,0.7009,0.7111,0.7161,0.7166,0.7231,
0.7231,0.7236,0.7236,0.7381,0.7382,0.7484,0.7619,0.7666,0.7677,0.7787,
0.7819,0.7849,0.7861,0.7957,0.7964,0.8069,0.8085,0.8092,0.8158,0.8177,
0.8187,0.8193,0.8193,0.8204,0.8224,0.8278,0.8296,0.8344,0.8393,0.8419,
0.8435,0.8438,0.8440,0.8473,0.8497,0.8527,0.8761,0.8771,0.8856,0.8935,
0.8992,0.9023,0.9049,0.9053,0.9072,0.9077,0.9095,0.9098,0.9186,0.9209,
0.9254,0.9297,0.9299,0.9320,0.9441,0.9450,0.9488,0.9508,0.9508,0.9541,
0.9602,0.9618,0.9673,0.9681,0.9691,0.9713,0.9777,0.9975,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.754368
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.