RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.66 15.8392 0.464737
2 to 25 16.09 19.6799 0.709074
3 to 26 15.77 11.9732 0.198245
4 to 27 15.77 13.5113 0.298654
5 to 28 15.88 18.5636 0.645853
6 to 29 15.39 23.4630 0.865223
7 to 30 15.78 13.3623 0.288385
8 to 31 15.83 10.0955 0.100443
9 to 32 15.57 20.7026 0.760123
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.962892
Tough bday spacings test for dh-ranFile-2018-06-16_21:31: 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 14 34 72 85 115 86 51 22 11 4 6
(O-E)^2/E 2.6 0.2 0.0 1.6 3.1 0.8 0.0 2.0 1.0 1.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 13.296, p= 0.792
RESULTS OF GCD FOR dh-ranFile-2018-06-16_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.632143
p-value, dist. of gcd's: 0.596789
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.654 0.149 0.957 0.085 0.105 0.201 0.795 0.750
Bits 8 to 15---> 0.163 0.980 0.625 0.734 0.844 0.108 0.478 0.771
Bits 16 to 23---> 0.494 0.974 0.047 0.502 0.720 0.803 0.701 0.908
Bits 24 to 31---> 0.316 0.255 0.797 0.164 0.074 0.061 0.992 0.194
KS test for the above 32 p values: 0.668
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_21:31,
p-values for 5 runs: 0.7269, 0.2705, 0.7702, 0.7943, 0.0544
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5158 5134.0 0.112 0.114
r= 30 23078 23103.0 0.027 0.141
r= 31 11552 11551.5 0.000 0.141
chi-square = 0.141 with df = 3; p-value = 0.013
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 196 211.4 1.124 1.124
r= 30 5038 5134.0 1.795 2.920
r= 31 23173 23103.0 0.212 3.132
r= 32 11593 11551.5 0.149 3.281
chi-square = 3.281 with df = 3; p-value = 0.650
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_21:31
b-rank test for bits 1 to 8, p=0.77668
b-rank test for bits 2 to 9, p=0.72711
b-rank test for bits 3 to 10, p=0.99748
b-rank test for bits 4 to 11, p=0.98815
b-rank test for bits 5 to 12, p=0.09887
b-rank test for bits 6 to 13, p=0.27936
b-rank test for bits 7 to 14, p=0.38039
b-rank test for bits 8 to 15, p=0.22443
b-rank test for bits 9 to 16, p=0.79682
b-rank test for bits 10 to 17, p=0.63025
b-rank test for bits 11 to 18, p=0.24726
b-rank test for bits 12 to 19, p=0.63268
b-rank test for bits 13 to 20, p=0.46769
b-rank test for bits 14 to 21, p=0.34801
b-rank test for bits 15 to 22, p=0.40236
b-rank test for bits 16 to 23, p=0.37418
b-rank test for bits 17 to 24, p=0.37195
b-rank test for bits 18 to 25, p=0.78777
b-rank test for bits 19 to 26, p=0.63776
b-rank test for bits 20 to 27, p=0.92928
b-rank test for bits 21 to 28, p=0.19700
b-rank test for bits 22 to 29, p=0.06696
b-rank test for bits 23 to 30, p=0.34452
b-rank test for bits 24 to 31, p=0.43150
b-rank test for bits 25 to 32, p=0.99023
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 = 0.423618
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_21:31
(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 140600 -3.06 0.001110
2 141658 -0.59 0.278528
3 142210 0.70 0.758816
4 142224 0.74 0.768894
5 142422 1.20 0.884508
6 142161 0.59 0.721739
7 141513 -0.93 0.177222
8 140442 -3.43 0.000304
9 142143 0.55 0.707453
10 141588 -0.75 0.226395
11 142771 2.01 0.977956
12 141753 -0.37 0.357460
13 141311 -1.40 0.081061
14 142384 1.11 0.866294
15 141823 -0.20 0.420073
16 141684 -0.53 0.299280
17 141573 -0.79 0.215987
18 141700 -0.49 0.312389
19 142061 0.35 0.638469
20 142293 0.90 0.814987
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_21:31
Bits used No. missing words z-score p-value
23 to 32 141571 -1.1667 0.121675
22 to 31 141916 0.0230 0.509175
21 to 30 141816 -0.3218 0.373792
20 to 29 141799 -0.3804 0.351806
19 to 28 142038 0.4437 0.671367
18 to 27 141859 -0.1736 0.431109
17 to 26 141893 -0.0563 0.477547
16 to 25 142386 1.6437 0.949880
15 to 24 142030 0.4161 0.661333
14 to 23 142597 2.3713 0.991137
13 to 22 141816 -0.3218 0.373792
12 to 21 141996 0.2989 0.617477
11 to 20 142006 0.3333 0.630563
10 to 19 141981 0.2471 0.597599
9 to 18 142344 1.4989 0.933045
8 to 17 142185 0.9506 0.829093
7 to 16 141909 -0.0011 0.499546
6 to 15 141647 -0.9046 0.182842
5 to 14 141705 -0.7046 0.240534
4 to 13 141811 -0.3391 0.367279
3 to 12 141791 -0.4080 0.341624
2 to 11 141711 -0.6839 0.247020
1 to 10 141621 -0.9942 0.160053
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_21:31
Bits used No. missing words z-score p-value
28 to 32 141809 -0.3401 0.366890
27 to 31 142030 0.4091 0.658749
26 to 30 142686 2.6328 0.995766
25 to 29 142011 0.3446 0.634819
24 to 28 141509 -1.3571 0.087383
23 to 27 141979 0.2362 0.593349
22 to 26 141655 -0.8621 0.194306
21 to 25 141594 -1.0689 0.142554
20 to 24 141457 -1.5333 0.062598
19 to 23 142169 0.8802 0.810635
18 to 22 141348 -1.9028 0.028532
17 to 21 142037 0.4328 0.667413
16 to 20 142029 0.4057 0.657504
15 to 19 142417 1.7209 0.957367
14 to 18 141791 -0.4011 0.344166
13 to 17 142134 0.7616 0.776849
12 to 16 142194 0.9650 0.832723
11 to 15 141784 -0.4248 0.335474
10 to 14 142047 0.4667 0.679635
9 to 13 142215 1.0362 0.849938
8 to 12 142156 0.8362 0.798470
7 to 11 141764 -0.4926 0.311132
6 to 10 141330 -1.9638 0.024775
5 to 9 142009 0.3379 0.632267
4 to 8 141949 0.1345 0.553486
3 to 7 141679 -0.7808 0.217466
2 to 6 141342 -1.9232 0.027230
1 to 5 141775 -0.4554 0.324427
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_21:31
Bits used No. missing words z-score p-value
31 to 32 141884 -0.0747 0.470219
30 to 31 142185 0.8132 0.791944
29 to 30 141939 0.0875 0.534872
28 to 29 141739 -0.5024 0.307676
27 to 28 141974 0.1908 0.575646
26 to 27 141814 -0.2812 0.389275
25 to 26 141900 -0.0275 0.489022
24 to 25 141927 0.0521 0.520785
23 to 24 141842 -0.1986 0.421283
22 to 23 142067 0.4651 0.679071
21 to 22 142257 1.0256 0.847454
20 to 21 142076 0.4917 0.688517
19 to 20 141895 -0.0423 0.483141
18 to 19 141587 -0.9508 0.170846
17 to 18 142157 0.7306 0.767485
16 to 17 141731 -0.5260 0.299428
15 to 16 142287 1.1141 0.867376
14 to 15 141926 0.0492 0.519610
13 to 14 141932 0.0669 0.526659
12 to 13 142136 0.6686 0.748138
11 to 12 142713 2.3707 0.991123
10 to 11 142027 0.3471 0.635745
9 to 10 141648 -0.7709 0.220388
8 to 9 141579 -0.9744 0.164923
7 to 8 142097 0.5536 0.710073
6 to 7 142148 0.7040 0.759297
5 to 6 142553 1.8987 0.971200
4 to 5 142265 1.0492 0.852951
3 to 4 141576 -0.9833 0.162736
2 to 3 141823 -0.2547 0.399493
1 to 2 142279 1.0905 0.862247
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2478.81 -0.300 0.382200
Test results for specific bytes for dh-ranFile-2018-06-16_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2497.66 -0.033 0.486785
2 to 9 2574.09 1.048 0.852635
3 to 10 2462.32 -0.533 0.297081
4 to 11 2555.75 0.788 0.784791
5 to 12 2324.32 -2.485 0.006486
6 to 13 2585.57 1.210 0.886889
7 to 14 2464.37 -0.504 0.307149
8 to 15 2420.19 -1.129 0.129529
9 to 16 2409.67 -1.278 0.100709
10 to 17 2402.21 -1.383 0.083332
11 to 18 2647.70 2.089 0.981636
12 to 19 2361.37 -1.961 0.024968
13 to 20 2491.51 -0.120 0.452197
14 to 21 2495.42 -0.065 0.474153
15 to 22 2561.64 0.872 0.808303
16 to 23 2482.10 -0.253 0.400096
17 to 24 2416.28 -1.184 0.118217
18 to 25 2447.93 -0.736 0.230769
19 to 26 2370.49 -1.832 0.033513
20 to 27 2508.11 0.115 0.545643
21 to 28 2561.58 0.871 0.808098
22 to 29 2517.68 0.250 0.598701
23 to 30 2561.10 0.864 0.806236
24 to 31 2351.07 -2.106 0.017594
25 to 32 2517.83 0.252 0.599525
CDPARK for dh-ranFile-2018-06-16_21:31: 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
3508 -0.6849 0.246694
3505 -0.8219 0.205562
3552 1.3242 0.907282
3516 -0.3196 0.374623
3491 -1.4612 0.071982
3508 -0.6849 0.246694
3515 -0.3653 0.357445
3576 2.4201 0.992242
3496 -1.2329 0.108811
3510 -0.5936 0.276387
Square side=100, avg. no. parked=3517.70 sample std.=24.86
p-value of the KSTEST for those 10 p-values: 0.124536
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_21:31
0.8292,0.2539,0.0330,0.3454,0.7777,0.8183,0.7196,0.8700,0.7940,0.0126,
The KS test for those 10 p-values: 0.282087
The 3DSPHERES test for dh-ranFile-2018-06-16_21:31
sample no r^3 equiv. uni.
1 8.487 0.246395
2 26.364 0.584719
3 13.649 0.365530
4 4.865 0.149703
5 139.782 0.990528
6 33.343 0.670908
7 55.050 0.840387
8 60.507 0.866932
9 9.476 0.270854
10 0.784 0.025779
11 14.349 0.380157
12 7.280 0.215470
13 43.535 0.765704
14 9.994 0.283335
15 21.371 0.509514
16 70.336 0.904108
17 13.928 0.371402
18 10.435 0.293791
19 82.944 0.937011
20 64.561 0.883752
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.740737
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 0.3 -1.0 1.0 -0.2
-0.5 0.3 -0.9 1.7 -0.2 1.3
0.2 0.3 0.8 0.9 -0.8 -1.4
-0.4 0.4 -0.4 0.6 -0.4 -1.2
-1.2 0.8 0.0 1.0 0.7 0.0
-0.7 -0.3 0.1 0.1 -0.9 0.1
-2.8 0.5 -0.4 -1.3 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:31.976438
z-score=-1.093660, p-value=0.131174
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_21:31
Test no p-value
1 0.047655
2 0.045183
3 0.133782
4 0.808081
5 0.590347
6 0.451420
7 0.644598
8 0.348621
9 0.029536
10 0.005542
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.019751
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_21:31:
(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 66619 0.03 66759 0.13
3 25000.00 25092 0.34 24963 0.05
4 6666.67 6691 0.09 6612 0.45
5 1388.89 1345 1.39 1385 0.01
6 238.10 223 0.96 242 0.06
7 34.72 24 3.31 34 0.01
8 4.96 5 0.00 4 0.19
p=0.58964 p=0.01109
Number of rngs required: 688815, p-value: 0.683
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_21:31
No. of wins: Observed Expected
98315 98585.9
z-score=-1.211, pvalue=0.11286
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66601 66666.7 0.065 0.065
2 37727 37654.3 0.140 0.205
3 26909 26954.7 0.078 0.283
4 19511 19313.5 2.020 2.303
5 13811 13851.4 0.118 2.421
6 9809 9943.5 1.820 4.241
7 7147 7145.0 0.001 4.242
8 5057 5139.1 1.311 5.553
9 3777 3699.9 1.608 7.161
10 2653 2666.3 0.066 7.227
11 1978 1923.3 1.554 8.781
12 1361 1388.7 0.554 9.335
13 1024 1003.7 0.410 9.745
14 715 726.1 0.171 9.916
15 556 525.8 1.730 11.646
16 365 381.2 0.684 12.331
17 264 276.5 0.569 12.899
18 220 200.8 1.830 14.729
19 143 146.0 0.061 14.790
20 82 106.2 5.521 20.311
21 290 287.1 0.029 20.340
Chisq= 20.34 for 20 degrees of freedom, p= 0.56315
SUMMARY of craptest
p-value for no. of wins: 0.112864
p-value for throws/game: 0.563146
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_21:31
No. of wins: Observed Expected
98839 98585.9
z-score= 1.132, pvalue=0.87122
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66701 66666.7 0.018 0.018
2 37774 37654.3 0.380 0.398
3 26772 26954.7 1.239 1.637
4 19179 19313.5 0.936 2.573
5 14051 13851.4 2.876 5.449
6 9945 9943.5 0.000 5.449
7 7049 7145.0 1.291 6.739
8 5200 5139.1 0.722 7.462
9 3655 3699.9 0.544 8.006
10 2645 2666.3 0.170 8.176
11 1952 1923.3 0.427 8.603
12 1384 1388.7 0.016 8.619
13 1028 1003.7 0.588 9.207
14 752 726.1 0.921 10.128
15 544 525.8 0.627 10.755
16 354 381.2 1.934 12.689
17 249 276.5 2.743 15.432
18 213 200.8 0.737 16.169
19 178 146.0 7.021 23.191
20 82 106.2 5.521 28.711
21 293 287.1 0.121 28.832
Chisq= 28.83 for 20 degrees of freedom, p= 0.90888
SUMMARY of craptest
p-value for no. of wins: 0.871224
p-value for throws/game: 0.908882
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0011,0.0055,0.0065,0.0111,0.0126,0.0135,0.0176,0.0198,0.0248,
0.0250,0.0258,0.0272,0.0285,0.0295,0.0330,0.0335,0.0452,0.0466,0.0477,
0.0544,0.0613,0.0626,0.0670,0.0720,0.0736,0.0811,0.0833,0.0847,0.0874,
0.0989,0.1004,0.1007,0.1045,0.1080,0.1088,0.1129,0.1182,0.1217,0.1245,
0.1295,0.1312,0.1338,0.1426,0.1490,0.1497,0.1601,0.1627,0.1632,0.1643,
0.1649,0.1708,0.1772,0.1828,0.1936,0.1943,0.1970,0.1982,0.2015,0.2056,
0.2155,0.2160,0.2175,0.2204,0.2244,0.2264,0.2308,0.2405,0.2464,0.2467,
0.2467,0.2470,0.2473,0.2539,0.2555,0.2705,0.2709,0.2764,0.2785,0.2794,
0.2821,0.2833,0.2884,0.2938,0.2971,0.2987,0.2993,0.2994,0.3071,0.3077,
0.3111,0.3124,0.3158,0.3244,0.3355,0.3416,0.3442,0.3445,0.3454,0.3480,
0.3486,0.3518,0.3574,0.3575,0.3655,0.3669,0.3673,0.3714,0.3720,0.3738,
0.3738,0.3742,0.3746,0.3802,0.3804,0.3822,0.3893,0.3995,0.4001,0.4024,
0.4201,0.4213,0.4236,0.4311,0.4315,0.4514,0.4522,0.4647,0.4677,0.4702,
0.4742,0.4775,0.4783,0.4831,0.4868,0.4890,0.4938,0.4995,0.5017,0.5092,
0.5095,0.5196,0.5208,0.5267,0.5349,0.5456,0.5535,0.5631,0.5756,0.5847,
0.5896,0.5903,0.5933,0.5968,0.5976,0.5987,0.5995,0.6175,0.6246,0.6303,
0.6306,0.6321,0.6323,0.6327,0.6348,0.6357,0.6378,0.6385,0.6446,0.6459,
0.6496,0.6538,0.6575,0.6587,0.6613,0.6674,0.6681,0.6709,0.6714,0.6791,
0.6796,0.6825,0.6885,0.7005,0.7075,0.7091,0.7101,0.7196,0.7198,0.7217,
0.7269,0.7271,0.7339,0.7407,0.7481,0.7501,0.7588,0.7593,0.7601,0.7657,
0.7675,0.7689,0.7702,0.7712,0.7767,0.7768,0.7777,0.7848,0.7878,0.7919,
0.7924,0.7940,0.7943,0.7946,0.7968,0.7975,0.7985,0.8034,0.8062,0.8081,
0.8081,0.8083,0.8106,0.8150,0.8183,0.8291,0.8292,0.8327,0.8404,0.8436,
0.8475,0.8499,0.8526,0.8530,0.8622,0.8652,0.8663,0.8669,0.8674,0.8700,
0.8712,0.8838,0.8845,0.8869,0.9041,0.9073,0.9082,0.9089,0.9293,0.9330,
0.9370,0.9499,0.9573,0.9574,0.9629,0.9712,0.9737,0.9780,0.9803,0.9816,
0.9881,0.9902,0.9905,0.9911,0.9911,0.9917,0.9922,0.9958,0.9975,
Overall p-value after applying KStest on 269 p-values = 0.431980
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.