RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 21.0826 0.777384
2 to 25 15.70 18.4349 0.638085
3 to 26 15.29 41.2338 0.999136
4 to 27 15.78 17.1041 0.552662
5 to 28 16.02 17.8396 0.600972
6 to 29 15.58 23.0116 0.851126
7 to 30 15.35 24.4001 0.891035
8 to 31 15.75 15.9239 0.470763
9 to 32 15.66 16.3903 0.503643
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.041801
Tough bday spacings test for dh-ranFile-2018-07-05_13:31: 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 39 66 98 98 79 53 29 13 11 5
(O-E)^2/E 0.0 0.2 0.7 0.0 0.0 0.0 0.0 0.0 0.2 2.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 4.282, p= 0.066
RESULTS OF GCD FOR dh-ranFile-2018-07-05_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.483621
p-value, dist. of gcd's: 0.212341
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.914 0.635 0.328 0.344 0.686 0.756 0.188 0.438
Bits 8 to 15---> 0.601 0.317 0.606 0.681 0.765 0.141 0.996 0.275
Bits 16 to 23---> 0.836 0.934 0.375 0.734 0.499 0.146 0.337 0.404
Bits 24 to 31---> 0.532 0.613 0.845 0.908 0.761 0.808 0.859 0.291
KS test for the above 32 p values: 0.847
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_13:31,
p-values for 5 runs: 0.3707, 0.3923, 0.1941, 0.6919, 0.4955
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5074 5134.0 0.701 0.702
r= 30 23138 23103.0 0.053 0.755
r= 31 11577 11551.5 0.056 0.811
chi-square = 0.811 with df = 3; p-value = 0.153
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 188 211.4 2.594 2.594
r= 30 5030 5134.0 2.107 4.701
r= 31 23293 23103.0 1.562 6.263
r= 32 11489 11551.5 0.338 6.601
chi-square = 6.601 with df = 3; p-value = 0.914
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_13:31
b-rank test for bits 1 to 8, p=0.84372
b-rank test for bits 2 to 9, p=0.65940
b-rank test for bits 3 to 10, p=0.74569
b-rank test for bits 4 to 11, p=0.03694
b-rank test for bits 5 to 12, p=0.02242
b-rank test for bits 6 to 13, p=0.29849
b-rank test for bits 7 to 14, p=0.74836
b-rank test for bits 8 to 15, p=0.64050
b-rank test for bits 9 to 16, p=0.22313
b-rank test for bits 10 to 17, p=0.26406
b-rank test for bits 11 to 18, p=0.71730
b-rank test for bits 12 to 19, p=0.99254
b-rank test for bits 13 to 20, p=0.90783
b-rank test for bits 14 to 21, p=0.90538
b-rank test for bits 15 to 22, p=0.55982
b-rank test for bits 16 to 23, p=0.70252
b-rank test for bits 17 to 24, p=0.04276
b-rank test for bits 18 to 25, p=0.84097
b-rank test for bits 19 to 26, p=0.54166
b-rank test for bits 20 to 27, p=0.39248
b-rank test for bits 21 to 28, p=0.81643
b-rank test for bits 22 to 29, p=0.59848
b-rank test for bits 23 to 30, p=0.69914
b-rank test for bits 24 to 31, p=0.77066
b-rank test for bits 25 to 32, p=0.11533
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 = 0.280951
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_13:31
(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 141597 -0.73 0.232774
2 142280 0.87 0.806769
3 141626 -0.66 0.253990
4 142093 0.43 0.666088
5 142154 0.57 0.716223
6 141957 0.11 0.544342
7 142434 1.23 0.889875
8 142194 0.67 0.747012
9 142619 1.66 0.951352
10 142291 0.89 0.813737
11 141233 -1.58 0.057029
12 141853 -0.13 0.447646
13 140766 -2.67 0.003778
14 141944 0.08 0.532281
15 141730 -0.42 0.337610
16 141962 0.12 0.548971
17 141779 -0.30 0.380370
18 141880 -0.07 0.472683
19 141262 -1.51 0.065209
20 141483 -1.00 0.159601
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_13:31
Bits used No. missing words z-score p-value
23 to 32 141657 -0.8701 0.192122
22 to 31 141896 -0.0460 0.481669
21 to 30 141838 -0.2460 0.402855
20 to 29 141946 0.1264 0.550312
19 to 28 142037 0.4402 0.670119
18 to 27 141747 -0.5598 0.287822
17 to 26 142389 1.6540 0.950940
16 to 25 141760 -0.5149 0.303301
15 to 24 141568 -1.1770 0.119598
14 to 23 141620 -0.9977 0.159215
13 to 22 142161 0.8678 0.807256
12 to 21 141941 0.1092 0.543481
11 to 20 142614 2.4299 0.992448
10 to 19 141829 -0.2770 0.390890
9 to 18 141876 -0.1149 0.454250
8 to 17 141916 0.0230 0.509175
7 to 16 141856 -0.1839 0.427047
6 to 15 142078 0.5816 0.719589
5 to 14 141868 -0.1425 0.443336
4 to 13 141831 -0.2701 0.393540
3 to 12 142115 0.7092 0.760902
2 to 11 142165 0.8816 0.811009
1 to 10 141853 -0.1942 0.422994
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_13:31
Bits used No. missing words z-score p-value
28 to 32 141774 -0.4587 0.323208
27 to 31 141357 -1.8723 0.030582
26 to 30 141857 -0.1774 0.429601
25 to 29 141759 -0.5096 0.305168
24 to 28 142072 0.5514 0.709328
23 to 27 142239 1.1175 0.868115
22 to 26 142269 1.2192 0.888620
21 to 25 141846 -0.2147 0.415009
20 to 24 141735 -0.5909 0.277277
19 to 23 142299 1.3209 0.906735
18 to 22 141932 0.0768 0.530628
17 to 21 142110 0.6802 0.751823
16 to 20 141623 -0.9706 0.165871
15 to 19 142094 0.6260 0.734343
14 to 18 141617 -0.9909 0.160855
13 to 17 141775 -0.4554 0.324427
12 to 16 141614 -1.0011 0.158385
11 to 15 142136 0.7684 0.778867
10 to 14 142381 1.5989 0.945077
9 to 13 142071 0.5480 0.708166
8 to 12 141919 0.0328 0.513075
7 to 11 142308 1.3514 0.911720
6 to 10 141876 -0.1130 0.455022
5 to 9 142020 0.3752 0.646227
4 to 8 141936 0.0904 0.536018
3 to 7 141323 -1.9876 0.023430
2 to 6 141400 -1.7265 0.042125
1 to 5 141636 -0.9265 0.177082
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_13:31
Bits used No. missing words z-score p-value
31 to 32 142708 2.3560 0.990763
30 to 31 142046 0.4032 0.656583
29 to 30 142108 0.5860 0.721078
28 to 29 142712 2.3678 0.991052
27 to 28 142216 0.9046 0.817170
26 to 27 141741 -0.4965 0.309754
25 to 26 142212 0.8928 0.814026
24 to 25 142190 0.8279 0.796146
23 to 24 142430 1.5359 0.937719
22 to 23 142201 0.8604 0.805211
21 to 22 141970 0.1790 0.571018
20 to 21 141745 -0.4847 0.313927
19 to 20 142118 0.6155 0.730903
18 to 19 142605 2.0521 0.979921
17 to 18 142154 0.7217 0.764773
16 to 17 142268 1.0580 0.854978
15 to 16 141839 -0.2075 0.417824
14 to 15 142080 0.5035 0.692677
13 to 14 142015 0.3117 0.622370
12 to 13 141682 -0.6706 0.251241
11 to 12 141868 -0.1219 0.451482
10 to 11 141772 -0.4051 0.342701
9 to 10 142268 1.0580 0.854978
8 to 9 141194 -2.1101 0.017424
7 to 8 142274 1.0757 0.858974
6 to 7 141964 0.1613 0.564059
5 to 6 142128 0.6450 0.740551
4 to 5 141764 -0.4287 0.334070
3 to 4 141462 -1.3196 0.093491
2 to 3 141748 -0.4759 0.317073
1 to 2 142511 1.7748 0.962038
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2434.41 -0.928 0.176809
Test results for specific bytes for dh-ranFile-2018-07-05_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2528.19 0.399 0.654935
2 to 9 2594.72 1.340 0.909804
3 to 10 2538.25 0.541 0.705731
4 to 11 2540.82 0.577 0.718125
5 to 12 2493.06 -0.098 0.460935
6 to 13 2388.20 -1.581 0.056930
7 to 14 2555.04 0.778 0.781837
8 to 15 2480.93 -0.270 0.393677
9 to 16 2544.67 0.632 0.736214
10 to 17 2445.83 -0.766 0.221810
11 to 18 2477.49 -0.318 0.375131
12 to 19 2477.43 -0.319 0.374787
13 to 20 2511.72 0.166 0.565824
14 to 21 2423.03 -1.088 0.138194
15 to 22 2541.94 0.593 0.723454
16 to 23 2535.88 0.507 0.694067
17 to 24 2555.09 0.779 0.782032
18 to 25 2459.61 -0.571 0.283929
19 to 26 2500.78 0.011 0.504376
20 to 27 2551.36 0.726 0.766201
21 to 28 2457.78 -0.597 0.275205
22 to 29 2527.35 0.387 0.650541
23 to 30 2379.96 -1.698 0.044788
24 to 31 2482.25 -0.251 0.400902
25 to 32 2539.03 0.552 0.709530
CDPARK for dh-ranFile-2018-07-05_13:31: 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
3520 -0.1370 0.445521
3530 0.3196 0.625377
3492 -1.4155 0.078457
3548 1.1416 0.873180
3506 -0.7763 0.218799
3527 0.1826 0.572463
3503 -0.9132 0.180558
3532 0.4110 0.659449
3508 -0.6849 0.246694
3487 -1.6438 0.050105
Square side=100, avg. no. parked=3515.30 sample std.=18.33
p-value of the KSTEST for those 10 p-values: 0.452820
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_13:31
0.1976,0.2571,0.7823,0.0258,0.4589,0.8312,0.5478,0.6867,0.1682,0.0966,
The KS test for those 10 p-values: 0.539671
The 3DSPHERES test for dh-ranFile-2018-07-05_13:31
sample no r^3 equiv. uni.
1 11.185 0.311214
2 69.510 0.901430
3 13.433 0.360949
4 2.168 0.069712
5 3.544 0.111415
6 4.178 0.130014
7 4.931 0.151578
8 3.536 0.111183
9 35.795 0.696741
10 7.583 0.223353
11 16.094 0.415190
12 43.849 0.768142
13 5.786 0.175398
14 38.411 0.722067
15 14.226 0.377626
16 25.613 0.574186
17 12.406 0.338692
18 28.693 0.615744
19 15.096 0.395415
20 13.617 0.364852
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.114881
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.1 -0.1 0.2 1.4 -1.1
1.1 -0.7 -0.9 1.2 -0.4 -1.5
0.3 -0.5 0.9 -0.4 0.3 -1.4
2.4 0.1 -0.6 -0.0 0.0 -1.5
1.9 -1.4 -0.0 -0.5 1.4 1.0
1.2 -0.7 -0.6 -0.2 -0.1 0.6
0.0 0.8 -2.0 -0.1 0.1 -1.0
1.8
Chi-square with 42 degrees of freedom:44.153691
z-score=0.234987, p-value=0.619285
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_13:31
Test no p-value
1 0.266230
2 0.252470
3 0.534602
4 0.005049
5 0.349661
6 0.082275
7 0.116950
8 0.557259
9 0.484293
10 0.779675
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.134959
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_13:31:
(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 66742 0.09 66738 0.08
3 25000.00 25003 0.00 25003 0.00
4 6666.67 6656 0.02 6593 0.81
5 1388.89 1361 0.56 1374 0.16
6 238.10 210 3.32 245 0.20
7 34.72 25 2.72 38 0.31
8 4.96 2 1.77 8 1.86
p=0.79405 p=0.24591
Number of rngs required: 687188, p-value: 0.078
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_13:31
No. of wins: Observed Expected
98359 98585.9
z-score=-1.015, pvalue=0.15514
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66583 66666.7 0.105 0.105
2 37783 37654.3 0.440 0.545
3 26989 26954.7 0.044 0.588
4 19360 19313.5 0.112 0.700
5 13780 13851.4 0.368 1.069
6 9944 9943.5 0.000 1.069
7 7174 7145.0 0.117 1.186
8 5022 5139.1 2.667 3.853
9 3719 3699.9 0.099 3.952
10 2694 2666.3 0.288 4.240
11 1894 1923.3 0.447 4.687
12 1412 1388.7 0.390 5.077
13 985 1003.7 0.349 5.426
14 748 726.1 0.658 6.084
15 531 525.8 0.051 6.135
16 373 381.2 0.174 6.309
17 260 276.5 0.989 7.298
18 219 200.8 1.644 8.942
19 143 146.0 0.061 9.003
20 112 106.2 0.315 9.318
21 275 287.1 0.511 9.829
Chisq= 9.83 for 20 degrees of freedom, p= 0.02884
SUMMARY of craptest
p-value for no. of wins: 0.155138
p-value for throws/game: 0.028835
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_13:31
No. of wins: Observed Expected
98869 98585.9
z-score= 1.266, pvalue=0.89731
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66998 66666.7 1.647 1.647
2 37803 37654.3 0.587 2.234
3 26975 26954.7 0.015 2.249
4 19232 19313.5 0.344 2.593
5 13665 13851.4 2.509 5.102
6 9809 9943.5 1.820 6.922
7 7080 7145.0 0.592 7.514
8 5221 5139.1 1.306 8.820
9 3703 3699.9 0.003 8.823
10 2740 2666.3 2.037 10.860
11 1872 1923.3 1.370 12.230
12 1362 1388.7 0.515 12.745
13 977 1003.7 0.711 13.456
14 702 726.1 0.803 14.258
15 503 525.8 0.992 15.250
16 362 381.2 0.962 16.212
17 264 276.5 0.569 16.781
18 182 200.8 1.765 18.546
19 154 146.0 0.440 18.986
20 108 106.2 0.030 19.016
21 288 287.1 0.003 19.019
Chisq= 19.02 for 20 degrees of freedom, p= 0.47941
SUMMARY of craptest
p-value for no. of wins: 0.897310
p-value for throws/game: 0.479415
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0038,0.0050,0.0174,0.0224,0.0234,0.0258,0.0288,0.0306,0.0369,0.0418,
0.0421,0.0428,0.0448,0.0501,0.0569,0.0570,0.0652,0.0663,0.0697,0.0782,
0.0785,0.0823,0.0935,0.0966,0.1112,0.1114,0.1149,0.1153,0.1170,0.1196,
0.1300,0.1350,0.1382,0.1412,0.1459,0.1516,0.1532,0.1551,0.1584,0.1592,
0.1596,0.1609,0.1659,0.1682,0.1754,0.1768,0.1771,0.1806,0.1882,0.1921,
0.1941,0.1976,0.2123,0.2188,0.2218,0.2231,0.2234,0.2328,0.2459,0.2467,
0.2512,0.2525,0.2540,0.2571,0.2641,0.2662,0.2752,0.2754,0.2773,0.2810,
0.2839,0.2878,0.2908,0.2985,0.3033,0.3052,0.3098,0.3112,0.3139,0.3170,
0.3171,0.3232,0.3244,0.3277,0.3341,0.3374,0.3376,0.3387,0.3427,0.3435,
0.3497,0.3609,0.3649,0.3707,0.3748,0.3749,0.3751,0.3776,0.3804,0.3909,
0.3923,0.3925,0.3935,0.3937,0.3954,0.4009,0.4029,0.4041,0.4150,0.4152,
0.4178,0.4230,0.4270,0.4296,0.4380,0.4433,0.4455,0.4476,0.4515,0.4528,
0.4542,0.4550,0.4589,0.4609,0.4708,0.4727,0.4794,0.4817,0.4836,0.4843,
0.4955,0.4989,0.5036,0.5044,0.5092,0.5131,0.5306,0.5316,0.5323,0.5346,
0.5360,0.5397,0.5417,0.5435,0.5443,0.5478,0.5490,0.5503,0.5527,0.5573,
0.5598,0.5641,0.5658,0.5710,0.5725,0.5742,0.5985,0.6006,0.6010,0.6063,
0.6129,0.6157,0.6193,0.6224,0.6254,0.6354,0.6381,0.6405,0.6462,0.6505,
0.6549,0.6566,0.6594,0.6594,0.6661,0.6701,0.6812,0.6859,0.6867,0.6919,
0.6927,0.6941,0.6967,0.6991,0.7025,0.7057,0.7082,0.7093,0.7095,0.7162,
0.7173,0.7181,0.7196,0.7211,0.7221,0.7235,0.7309,0.7339,0.7343,0.7362,
0.7406,0.7457,0.7470,0.7484,0.7518,0.7562,0.7608,0.7609,0.7648,0.7653,
0.7662,0.7681,0.7707,0.7774,0.7789,0.7797,0.7818,0.7820,0.7823,0.7941,
0.7961,0.8052,0.8068,0.8073,0.8077,0.8110,0.8137,0.8140,0.8164,0.8172,
0.8312,0.8361,0.8410,0.8437,0.8447,0.8466,0.8511,0.8550,0.8550,0.8588,
0.8590,0.8681,0.8732,0.8886,0.8899,0.8910,0.8973,0.9014,0.9054,0.9067,
0.9078,0.9083,0.9098,0.9117,0.9135,0.9142,0.9338,0.9377,0.9451,0.9509,
0.9514,0.9620,0.9799,0.9908,0.9911,0.9924,0.9925,0.9959,0.9991,
Overall p-value after applying KStest on 269 p-values = 0.671125
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.