RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.48 33.5621 0.990442
2 to 25 15.51 20.7515 0.762396
3 to 26 15.89 13.8411 0.321687
4 to 27 15.82 13.2687 0.281978
5 to 28 16.01 16.4601 0.508518
6 to 29 16.16 23.5502 0.867819
7 to 30 15.92 16.7371 0.527687
8 to 31 15.88 17.5554 0.582606
9 to 32 15.73 18.1943 0.623314
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.360302
Tough bday spacings test for dh-ranFile-2018-06-20_18:31: 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 10 41 85 109 90 75 45 19 13 9 4
(O-E)^2/E 0.1 0.5 1.9 1.3 0.6 0.1 1.0 3.9 0.2 0.9 0.0
Birthday Spacings: Sum(O-E)^2/E= 10.484, p= 0.601
RESULTS OF GCD FOR dh-ranFile-2018-06-20_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.465371
p-value, dist. of gcd's: 0.206082
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.486 0.574 0.841 0.179 0.702 0.215 0.778 0.047
Bits 8 to 15---> 0.210 0.932 0.297 0.154 0.035 0.652 0.203 0.347
Bits 16 to 23---> 0.159 0.581 0.366 0.048 0.801 0.948 0.941 0.445
Bits 24 to 31---> 0.148 0.249 0.350 0.883 0.690 0.622 0.540 0.161
KS test for the above 32 p values: 0.383
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_18:31,
p-values for 5 runs: 0.5172, 0.4262, 0.3534, 0.6653, 0.4417
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 210 211.4 0.010 0.010
r= 29 5115 5134.0 0.070 0.080
r= 30 23014 23103.0 0.343 0.423
r= 31 11661 11551.5 1.038 1.461
chi-square = 1.461 with df = 3; p-value = 0.309
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5114 5134.0 0.078 0.413
r= 31 23001 23103.0 0.451 0.864
r= 32 11682 11551.5 1.474 2.338
chi-square = 2.338 with df = 3; p-value = 0.495
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_18:31
b-rank test for bits 1 to 8, p=0.11860
b-rank test for bits 2 to 9, p=0.21032
b-rank test for bits 3 to 10, p=0.10566
b-rank test for bits 4 to 11, p=0.40654
b-rank test for bits 5 to 12, p=0.34164
b-rank test for bits 6 to 13, p=0.57518
b-rank test for bits 7 to 14, p=0.69840
b-rank test for bits 8 to 15, p=0.87070
b-rank test for bits 9 to 16, p=0.63892
b-rank test for bits 10 to 17, p=0.02271
b-rank test for bits 11 to 18, p=0.28065
b-rank test for bits 12 to 19, p=0.76860
b-rank test for bits 13 to 20, p=0.86923
b-rank test for bits 14 to 21, p=0.03637
b-rank test for bits 15 to 22, p=0.61980
b-rank test for bits 16 to 23, p=0.60315
b-rank test for bits 17 to 24, p=0.91847
b-rank test for bits 18 to 25, p=0.68675
b-rank test for bits 19 to 26, p=0.78364
b-rank test for bits 20 to 27, p=0.64914
b-rank test for bits 21 to 28, p=0.61650
b-rank test for bits 22 to 29, p=0.46098
b-rank test for bits 23 to 30, p=0.05805
b-rank test for bits 24 to 31, p=0.94350
b-rank test for bits 25 to 32, p=0.74647
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 = 0.727874
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_18:31
(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 142443 1.25 0.893782
2 141931 0.05 0.520190
3 142330 0.98 0.837165
4 142877 2.26 0.988118
5 142625 1.67 0.952750
6 142081 0.40 0.655826
7 141792 -0.27 0.391990
8 141798 -0.26 0.397387
9 142169 0.61 0.727977
10 142382 1.10 0.865284
11 141754 -0.36 0.358332
12 142225 0.74 0.769605
13 141473 -1.02 0.153992
14 142694 1.83 0.966624
15 140744 -2.72 0.003237
16 141764 -0.34 0.367095
17 141801 -0.25 0.400093
18 142177 0.63 0.734145
19 141947 0.09 0.535067
20 141791 -0.28 0.391093
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_18:31
Bits used No. missing words z-score p-value
23 to 32 142227 1.0954 0.863332
22 to 31 142305 1.3644 0.913776
21 to 30 141452 -1.5770 0.057398
20 to 29 142024 0.3954 0.653731
19 to 28 142634 2.4989 0.993770
18 to 27 141782 -0.4391 0.330306
17 to 26 142012 0.3540 0.638344
16 to 25 142060 0.5196 0.698312
15 to 24 141746 -0.5632 0.286647
14 to 23 141707 -0.6977 0.242686
13 to 22 141708 -0.6942 0.243765
12 to 21 141821 -0.3046 0.380341
11 to 20 141871 -0.1322 0.447424
10 to 19 142172 0.9058 0.817468
9 to 18 142489 1.9989 0.977188
8 to 17 142239 1.1368 0.872188
7 to 16 142462 1.9058 0.971659
6 to 15 141911 0.0058 0.502297
5 to 14 142306 1.3678 0.914317
4 to 13 141729 -0.6218 0.267028
3 to 12 141917 0.0264 0.510550
2 to 11 142706 2.7471 0.996994
1 to 10 141381 -1.8218 0.034241
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_18:31
Bits used No. missing words z-score p-value
28 to 32 142035 0.4260 0.664946
27 to 31 141954 0.1514 0.560179
26 to 30 141752 -0.5333 0.296905
25 to 29 141766 -0.4859 0.313532
24 to 28 141674 -0.7977 0.212514
23 to 27 142674 2.5921 0.995230
22 to 26 142438 1.7921 0.963442
21 to 25 142136 0.7684 0.778867
20 to 24 142066 0.5311 0.702320
19 to 23 142469 1.8972 0.971098
18 to 22 141742 -0.5672 0.285282
17 to 21 141982 0.2463 0.597290
16 to 20 141487 -1.4316 0.076125
15 to 19 141730 -0.6079 0.271628
14 to 18 142030 0.4091 0.658749
13 to 17 142570 2.2396 0.987440
12 to 16 142092 0.6192 0.732114
11 to 15 142609 2.3718 0.991148
10 to 14 141548 -1.2248 0.110316
9 to 13 141523 -1.3096 0.095167
8 to 12 141544 -1.2384 0.107783
7 to 11 141970 0.2057 0.581472
6 to 10 141684 -0.7638 0.222484
5 to 9 141639 -0.9164 0.179736
4 to 8 142036 0.4294 0.666180
3 to 7 141711 -0.6723 0.250695
2 to 6 141643 -0.9028 0.183312
1 to 5 141707 -0.6859 0.246399
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_18:31
Bits used No. missing words z-score p-value
31 to 32 141392 -1.5260 0.063499
30 to 31 141421 -1.4405 0.074863
29 to 30 141639 -0.7974 0.212600
28 to 29 141457 -1.3343 0.091052
27 to 28 141686 -0.6588 0.255015
26 to 27 141461 -1.3225 0.093000
25 to 26 141716 -0.5703 0.284239
24 to 25 142102 0.5683 0.715101
23 to 24 141773 -0.4022 0.343786
22 to 23 142391 1.4209 0.922321
21 to 22 141794 -0.3402 0.366851
20 to 21 141947 0.1111 0.544240
19 to 20 142179 0.7955 0.786835
18 to 19 141670 -0.7060 0.240098
17 to 18 141340 -1.6794 0.046533
16 to 17 142326 1.2291 0.890486
15 to 16 142070 0.4740 0.682233
14 to 15 141577 -0.9803 0.163463
13 to 14 141683 -0.6676 0.252182
12 to 13 141813 -0.2842 0.388144
11 to 12 141347 -1.6588 0.048579
10 to 11 141802 -0.3166 0.375771
9 to 10 142218 0.9105 0.818729
8 to 9 140943 -2.8505 0.002182
7 to 8 141919 0.0285 0.511378
6 to 7 142008 0.2911 0.614498
5 to 6 141473 -1.2871 0.099028
4 to 5 142158 0.7335 0.768385
3 to 4 141710 -0.5880 0.278268
2 to 3 142004 0.2793 0.609978
1 to 2 142311 1.1849 0.881965
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2661.21 2.280 0.988690
Test results for specific bytes for dh-ranFile-2018-06-20_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2472.62 -0.387 0.349323
2 to 9 2650.78 2.132 0.983513
3 to 10 2546.72 0.661 0.745616
4 to 11 2492.45 -0.107 0.457470
5 to 12 2606.98 1.513 0.934850
6 to 13 2459.53 -0.572 0.283534
7 to 14 2572.63 1.027 0.847821
8 to 15 2505.95 0.084 0.533525
9 to 16 2592.77 1.312 0.905228
10 to 17 2555.34 0.783 0.783058
11 to 18 2420.10 -1.130 0.129245
12 to 19 2570.84 1.002 0.841801
13 to 20 2484.72 -0.216 0.414465
14 to 21 2527.32 0.386 0.650391
15 to 22 2556.25 0.795 0.786823
16 to 23 2542.25 0.597 0.724907
17 to 24 2667.21 2.365 0.990979
18 to 25 2436.75 -0.895 0.185518
19 to 26 2461.30 -0.547 0.292097
20 to 27 2382.41 -1.663 0.048154
21 to 28 2462.71 -0.527 0.298965
22 to 29 2593.36 1.320 0.906638
23 to 30 2489.30 -0.151 0.439883
24 to 31 2473.94 -0.369 0.356235
25 to 32 2531.09 0.440 0.669898
CDPARK for dh-ranFile-2018-06-20_18:31: 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
3505 -0.8219 0.205562
3566 1.9635 0.975204
3530 0.3196 0.625377
3496 -1.2329 0.108811
3549 1.1872 0.882429
3555 1.4612 0.928018
3515 -0.3653 0.357445
3521 -0.0913 0.463617
3517 -0.2740 0.392053
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3526.70 sample std.=21.72
p-value of the KSTEST for those 10 p-values: 0.810257
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_18:31
0.9807,0.6851,0.1928,0.1263,0.2091,0.0625,0.5995,0.9850,0.0562,0.0400,
The KS test for those 10 p-values: 0.068519
The 3DSPHERES test for dh-ranFile-2018-06-20_18:31
sample no r^3 equiv. uni.
1 32.393 0.660321
2 32.693 0.663707
3 0.090 0.002981
4 20.101 0.488304
5 2.585 0.082573
6 0.295 0.009800
7 53.747 0.833303
8 13.666 0.365896
9 20.716 0.498693
10 39.751 0.734208
11 10.236 0.289072
12 43.007 0.761546
13 6.167 0.185814
14 48.345 0.800412
15 51.007 0.817358
16 4.515 0.139721
17 117.281 0.979947
18 16.713 0.427124
19 6.251 0.188099
20 126.087 0.985048
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.688595
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.4 -1.1 -0.7 -1.7
-0.7 0.7 0.8 2.0 0.2 1.2
-1.0 0.6 -0.0 -0.3 -0.5 -1.0
-0.4 0.7 -0.1 0.6 1.2 0.1
-1.0 -0.1 -0.1 -0.9 -0.2 0.2
-0.3 0.0 -1.3 0.0 0.2 1.1
-1.2 -1.0 -2.0 -0.7 -1.3 -1.0
0.8
Chi-square with 42 degrees of freedom:33.564863
z-score=-0.920349, p-value=0.179766
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_18:31
Test no p-value
1 0.727329
2 0.907305
3 0.925349
4 0.836774
5 0.328170
6 0.000830
7 0.619821
8 0.715354
9 0.415634
10 0.055109
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.401933
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_18:31:
(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 66444 0.74 66807 0.30
3 25000.00 25269 2.89 24893 0.46
4 6666.67 6630 0.20 6646 0.06
5 1388.89 1357 0.73 1362 0.52
6 238.10 256 1.35 245 0.20
7 34.72 35 0.00 38 0.31
8 4.96 8 1.86 8 1.86
p=0.74564 p=0.28433
Number of rngs required: 688740, p-value: 0.651
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_18:31
No. of wins: Observed Expected
98364 98585.9
z-score=-0.992, pvalue=0.16053
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66620 66666.7 0.033 0.033
2 37490 37654.3 0.717 0.750
3 27234 26954.7 2.893 3.643
4 19365 19313.5 0.138 3.781
5 13934 13851.4 0.492 4.273
6 10009 9943.5 0.431 4.704
7 7063 7145.0 0.942 5.646
8 5009 5139.1 3.292 8.938
9 3576 3699.9 4.147 13.085
10 2636 2666.3 0.344 13.429
11 1933 1923.3 0.049 13.477
12 1404 1388.7 0.168 13.645
13 1029 1003.7 0.637 14.282
14 729 726.1 0.011 14.293
15 572 525.8 4.053 18.346
16 422 381.2 4.378 22.724
17 278 276.5 0.008 22.732
18 192 200.8 0.388 23.120
19 159 146.0 1.160 24.281
20 91 106.2 2.180 26.460
21 255 287.1 3.592 30.052
Chisq= 30.05 for 20 degrees of freedom, p= 0.93099
SUMMARY of craptest
p-value for no. of wins: 0.160530
p-value for throws/game: 0.930986
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_18:31
No. of wins: Observed Expected
98859 98585.9
z-score= 1.222, pvalue=0.88908
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66928 66666.7 1.024 1.024
2 37665 37654.3 0.003 1.027
3 27028 26954.7 0.199 1.227
4 19456 19313.5 1.052 2.279
5 13746 13851.4 0.802 3.081
6 9735 9943.5 4.374 7.455
7 7071 7145.0 0.767 8.222
8 5109 5139.1 0.176 8.398
9 3713 3699.9 0.047 8.444
10 2688 2666.3 0.177 8.621
11 1888 1923.3 0.649 9.270
12 1353 1388.7 0.920 10.190
13 982 1003.7 0.470 10.659
14 752 726.1 0.921 11.580
15 477 525.8 4.536 16.116
16 383 381.2 0.009 16.125
17 289 276.5 0.561 16.686
18 194 200.8 0.232 16.918
19 150 146.0 0.110 17.029
20 105 106.2 0.014 17.043
21 288 287.1 0.003 17.046
Chisq= 17.05 for 20 degrees of freedom, p= 0.34999
SUMMARY of craptest
p-value for no. of wins: 0.889080
p-value for throws/game: 0.349989
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0022,0.0030,0.0032,0.0098,0.0227,0.0342,0.0351,0.0364,0.0400,
0.0465,0.0473,0.0476,0.0482,0.0486,0.0551,0.0562,0.0574,0.0580,0.0625,
0.0635,0.0685,0.0749,0.0761,0.0826,0.0911,0.0930,0.0952,0.0990,0.1057,
0.1078,0.1088,0.1103,0.1186,0.1263,0.1292,0.1397,0.1477,0.1540,0.1541,
0.1590,0.1605,0.1613,0.1635,0.1786,0.1797,0.1798,0.1833,0.1855,0.1858,
0.1881,0.1928,0.2029,0.2056,0.2061,0.2091,0.2098,0.2103,0.2125,0.2126,
0.2155,0.2225,0.2401,0.2427,0.2438,0.2464,0.2491,0.2507,0.2522,0.2550,
0.2670,0.2716,0.2783,0.2806,0.2820,0.2835,0.2842,0.2843,0.2853,0.2866,
0.2891,0.2921,0.2969,0.2972,0.2990,0.3086,0.3135,0.3217,0.3240,0.3282,
0.3303,0.3416,0.3438,0.3473,0.3493,0.3500,0.3501,0.3534,0.3562,0.3574,
0.3583,0.3603,0.3659,0.3665,0.3669,0.3671,0.3758,0.3803,0.3828,0.3881,
0.3911,0.3920,0.3921,0.3974,0.4001,0.4019,0.4065,0.4145,0.4156,0.4262,
0.4271,0.4399,0.4417,0.4447,0.4474,0.4575,0.4610,0.4636,0.4654,0.4856,
0.4883,0.4947,0.4987,0.5023,0.5085,0.5106,0.5114,0.5172,0.5202,0.5277,
0.5335,0.5351,0.5399,0.5442,0.5602,0.5735,0.5752,0.5813,0.5815,0.5826,
0.5973,0.5995,0.6009,0.6032,0.6100,0.6145,0.6165,0.6198,0.6198,0.6217,
0.6233,0.6254,0.6383,0.6389,0.6491,0.6504,0.6510,0.6525,0.6537,0.6558,
0.6587,0.6603,0.6637,0.6649,0.6653,0.6662,0.6699,0.6822,0.6851,0.6867,
0.6886,0.6897,0.6983,0.6984,0.7015,0.7023,0.7151,0.7154,0.7249,0.7273,
0.7279,0.7280,0.7321,0.7341,0.7342,0.7456,0.7456,0.7465,0.7615,0.7624,
0.7684,0.7686,0.7696,0.7784,0.7789,0.7831,0.7836,0.7868,0.7868,0.8004,
0.8014,0.8103,0.8174,0.8175,0.8187,0.8333,0.8368,0.8372,0.8414,0.8418,
0.8478,0.8633,0.8653,0.8678,0.8692,0.8707,0.8722,0.8820,0.8824,0.8833,
0.8891,0.8905,0.8938,0.9052,0.9066,0.9073,0.9138,0.9143,0.9185,0.9223,
0.9253,0.9280,0.9310,0.9324,0.9348,0.9414,0.9435,0.9479,0.9528,0.9634,
0.9666,0.9711,0.9717,0.9752,0.9772,0.9799,0.9807,0.9835,0.9850,0.9850,
0.9874,0.9881,0.9887,0.9904,0.9910,0.9911,0.9938,0.9952,0.9970,
Overall p-value after applying KStest on 269 p-values = 0.318975
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.