RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 9.5455 0.078419
2 to 25 15.69 16.6244 0.519917
3 to 26 15.70 17.0140 0.546579
4 to 27 15.75 22.3026 0.826640
5 to 28 16.16 22.9877 0.850348
6 to 29 15.64 13.6593 0.308944
7 to 30 15.91 15.2075 0.419464
8 to 31 15.67 20.2014 0.735941
9 to 32 15.85 11.9942 0.199514
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.985864
Tough bday spacings test for dh-ranFile-2018-06-25_05:31: 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 42 70 103 90 67 48 40 14 10 6
(O-E)^2/E 0.1 0.8 0.1 0.3 0.6 1.6 0.3 3.5 0.1 1.7 0.9
Birthday Spacings: Sum(O-E)^2/E= 10.035, p= 0.563
RESULTS OF GCD FOR dh-ranFile-2018-06-25_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.401730
p-value, dist. of gcd's: 0.763881
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.341 0.717 0.234 0.233 0.181 0.328 0.972 0.822
Bits 8 to 15---> 0.436 0.193 0.603 0.083 0.135 0.552 0.135 0.567
Bits 16 to 23---> 0.672 0.487 0.698 0.609 0.298 0.051 0.796 0.334
Bits 24 to 31---> 0.855 0.196 0.051 0.552 0.156 0.484 0.087 0.396
KS test for the above 32 p values: 0.856
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_05:31,
p-values for 5 runs: 0.6780, 0.6241, 0.3811, 0.7196, 0.5042
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 176 211.4 5.933 5.933
r= 29 5172 5134.0 0.281 6.215
r= 30 23206 23103.0 0.459 6.673
r= 31 11446 11551.5 0.964 7.637
chi-square = 7.637 with df = 3; p-value = 0.946
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5190 5134.0 0.611 0.946
r= 31 23149 23103.0 0.091 1.037
r= 32 11458 11551.5 0.757 1.794
chi-square = 1.794 with df = 3; p-value = 0.384
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_05:31
b-rank test for bits 1 to 8, p=0.68231
b-rank test for bits 2 to 9, p=0.00591
b-rank test for bits 3 to 10, p=0.61282
b-rank test for bits 4 to 11, p=0.97096
b-rank test for bits 5 to 12, p=0.74245
b-rank test for bits 6 to 13, p=0.85285
b-rank test for bits 7 to 14, p=0.79230
b-rank test for bits 8 to 15, p=0.41302
b-rank test for bits 9 to 16, p=0.08913
b-rank test for bits 10 to 17, p=0.50871
b-rank test for bits 11 to 18, p=0.48586
b-rank test for bits 12 to 19, p=0.68828
b-rank test for bits 13 to 20, p=0.23928
b-rank test for bits 14 to 21, p=0.21881
b-rank test for bits 15 to 22, p=0.48602
b-rank test for bits 16 to 23, p=0.87404
b-rank test for bits 17 to 24, p=0.61244
b-rank test for bits 18 to 25, p=0.36148
b-rank test for bits 19 to 26, p=0.51096
b-rank test for bits 20 to 27, p=0.55695
b-rank test for bits 21 to 28, p=0.21279
b-rank test for bits 22 to 29, p=0.79011
b-rank test for bits 23 to 30, p=0.42760
b-rank test for bits 24 to 31, p=0.86887
b-rank test for bits 25 to 32, p=0.13121
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 = 0.842741
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_05:31
(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 142240 0.77 0.780119
2 141791 -0.28 0.391093
3 142841 2.18 0.985252
4 141900 -0.02 0.491304
5 142586 1.58 0.943062
6 141510 -0.93 0.175406
7 141645 -0.62 0.268422
8 141430 -1.12 0.131372
9 141807 -0.24 0.405518
10 142229 0.75 0.772436
11 141965 0.13 0.551745
12 142011 0.24 0.593884
13 142113 0.48 0.682915
14 141940 0.07 0.528563
15 141947 0.09 0.535067
16 142902 2.32 0.989811
17 141274 -1.48 0.068849
18 142438 1.24 0.891624
19 141542 -0.86 0.195378
20 141663 -0.58 0.282464
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_05:31
Bits used No. missing words z-score p-value
23 to 32 141616 -1.0115 0.155893
22 to 31 141363 -1.8839 0.029789
21 to 30 142043 0.4609 0.677576
20 to 29 141486 -1.4598 0.072178
19 to 28 141689 -0.7598 0.223699
18 to 27 141828 -0.2804 0.389567
17 to 26 142018 0.3747 0.646067
16 to 25 142020 0.3816 0.648629
15 to 24 141967 0.1989 0.578815
14 to 23 141932 0.0782 0.531155
13 to 22 142683 2.6678 0.996183
12 to 21 142075 0.5713 0.716094
11 to 20 141685 -0.7736 0.219598
10 to 19 141730 -0.6184 0.268163
9 to 18 141817 -0.3184 0.375099
8 to 17 142366 1.5747 0.942340
7 to 16 142177 0.9230 0.821996
6 to 15 141627 -0.9736 0.165140
5 to 14 141885 -0.0839 0.466569
4 to 13 142113 0.7023 0.758757
3 to 12 142411 1.7299 0.958176
2 to 11 142296 1.3333 0.908791
1 to 10 142703 2.7368 0.996898
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_05:31
Bits used No. missing words z-score p-value
28 to 32 142451 1.8362 0.966834
27 to 31 141953 0.1480 0.558842
26 to 30 141704 -0.6960 0.243204
25 to 29 141797 -0.3808 0.351683
24 to 28 141574 -1.1367 0.127829
23 to 27 141555 -1.2011 0.114853
22 to 26 141837 -0.2452 0.403156
21 to 25 141980 0.2396 0.594664
20 to 24 142275 1.2396 0.892431
19 to 23 142273 1.2328 0.891171
18 to 22 142240 1.1209 0.868838
17 to 21 141548 -1.2248 0.110316
16 to 20 141455 -1.5401 0.061768
15 to 19 142505 2.0192 0.978268
14 to 18 142187 0.9413 0.826713
13 to 17 141928 0.0633 0.525232
12 to 16 141822 -0.2960 0.383602
11 to 15 141825 -0.2859 0.387491
10 to 14 141405 -1.7096 0.043671
9 to 13 141486 -1.4350 0.075641
8 to 12 141777 -0.4486 0.326869
7 to 11 141735 -0.5909 0.277277
6 to 10 142275 1.2396 0.892431
5 to 9 141877 -0.1096 0.456366
4 to 8 142255 1.1718 0.879354
3 to 7 142268 1.2158 0.887975
2 to 6 142137 0.7718 0.779873
1 to 5 142243 1.1311 0.870990
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_05:31
Bits used No. missing words z-score p-value
31 to 32 142178 0.7925 0.785976
30 to 31 141545 -1.0747 0.141250
29 to 30 141617 -0.8623 0.194253
28 to 29 142074 0.4858 0.686429
27 to 28 141814 -0.2812 0.389275
26 to 27 142176 0.7866 0.784253
25 to 26 141843 -0.1957 0.422437
24 to 25 141665 -0.7207 0.235536
23 to 24 142493 1.7217 0.957442
22 to 23 141887 -0.0659 0.473741
21 to 22 141736 -0.5113 0.304571
20 to 21 142407 1.4681 0.928955
19 to 20 142016 0.3147 0.623490
18 to 19 142402 1.4533 0.926930
17 to 18 142348 1.2940 0.902169
16 to 17 141768 -0.4169 0.338375
15 to 16 141401 -1.4995 0.066872
14 to 15 142001 0.2704 0.606579
13 to 14 141741 -0.4965 0.309754
12 to 13 142269 1.0610 0.855649
11 to 12 141483 -1.2576 0.104266
10 to 11 142255 1.0197 0.846059
9 to 10 142020 0.3265 0.627962
8 to 9 141638 -0.8004 0.211744
7 to 8 141706 -0.5998 0.274322
6 to 7 141721 -0.5555 0.289261
5 to 6 141631 -0.8210 0.205814
4 to 5 141910 0.0020 0.500789
3 to 4 141590 -0.9420 0.173102
2 to 3 141731 -0.5260 0.299428
1 to 2 142190 0.8279 0.796146
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2545.61 0.645 0.740550
Test results for specific bytes for dh-ranFile-2018-06-25_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2462.43 -0.531 0.297609
2 to 9 2488.52 -0.162 0.435541
3 to 10 2564.82 0.917 0.820332
4 to 11 2570.80 1.001 0.841648
5 to 12 2500.92 0.013 0.505208
6 to 13 2489.83 -0.144 0.442843
7 to 14 2584.09 1.189 0.882812
8 to 15 2493.54 -0.091 0.463621
9 to 16 2545.37 0.642 0.739424
10 to 17 2488.51 -0.162 0.435484
11 to 18 2421.87 -1.105 0.134602
12 to 19 2475.02 -0.353 0.361959
13 to 20 2505.10 0.072 0.528743
14 to 21 2377.77 -1.729 0.041936
15 to 22 2522.03 0.312 0.622290
16 to 23 2504.32 0.061 0.524373
17 to 24 2471.23 -0.407 0.342047
18 to 25 2528.62 0.405 0.657154
19 to 26 2435.21 -0.916 0.179780
20 to 27 2432.48 -0.955 0.169831
21 to 28 2503.24 0.046 0.518296
22 to 29 2426.39 -1.041 0.148948
23 to 30 2475.18 -0.351 0.362777
24 to 31 2484.43 -0.220 0.412848
25 to 32 2433.42 -0.942 0.173206
CDPARK for dh-ranFile-2018-06-25_05:31: 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
3535 0.5479 0.708135
3507 -0.7306 0.232514
3552 1.3242 0.907282
3505 -0.8219 0.205562
3555 1.4612 0.928018
3507 -0.7306 0.232514
3544 0.9589 0.831196
3515 -0.3653 0.357445
3546 1.0502 0.853193
3520 -0.1370 0.445521
Square side=100, avg. no. parked=3528.60 sample std.=18.91
p-value of the KSTEST for those 10 p-values: 0.529559
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_05:31
0.9321,0.7906,0.8511,0.7735,0.7672,0.5250,0.9773,0.4563,0.7073,0.3609,
The KS test for those 10 p-values: 0.030547
The 3DSPHERES test for dh-ranFile-2018-06-25_05:31
sample no r^3 equiv. uni.
1 4.047 0.126201
2 23.366 0.541073
3 0.339 0.011235
4 24.489 0.557928
5 9.394 0.268839
6 95.475 0.958519
7 13.320 0.358540
8 68.212 0.897072
9 93.428 0.955589
10 51.671 0.821356
11 4.254 0.132193
12 33.991 0.677945
13 48.531 0.801647
14 6.112 0.184312
15 12.776 0.346806
16 39.536 0.732290
17 17.633 0.444432
18 4.193 0.130442
19 70.096 0.903338
20 18.961 0.468490
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.955288
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.1 -0.4 0.6 0.1
0.1 -0.1 -0.9 -0.6 0.8 0.3
0.8 -0.8 0.6 0.6 -1.0 -0.8
1.1 1.2 0.8 -0.8 0.6 -0.7
-1.6 0.5 -0.8 0.1 -0.2 -0.7
1.8 -1.5 -1.9 0.2 -1.0 -0.3
-0.7 -0.7 0.1 0.4 -0.6 1.0
-1.1
Chi-square with 42 degrees of freedom:29.929692
z-score=-1.316979, p-value=0.081510
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_05:31
Test no p-value
1 0.040824
2 0.013600
3 0.698053
4 0.174925
5 0.704966
6 0.084029
7 0.050713
8 0.036486
9 0.205120
10 0.284651
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001236
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_05:31:
(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 66750 0.10 66572 0.13
3 25000.00 24903 0.38 25247 2.44
4 6666.67 6688 0.07 6537 2.52
5 1388.89 1359 0.64 1386 0.01
6 238.10 261 2.20 213 2.65
7 34.72 35 0.00 41 1.14
8 4.96 3 0.77 3 0.77
p=0.34662 p=0.86021
Number of rngs required: 689229, p-value: 0.831
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_05:31
No. of wins: Observed Expected
98432 98585.9
z-score=-0.688, pvalue=0.24568
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66846 66666.7 0.482 0.482
2 37918 37654.3 1.846 2.329
3 26814 26954.7 0.735 3.064
4 19276 19313.5 0.073 3.136
5 13758 13851.4 0.630 3.766
6 9837 9943.5 1.142 4.908
7 7155 7145.0 0.014 4.922
8 5027 5139.1 2.444 7.366
9 3697 3699.9 0.002 7.368
10 2716 2666.3 0.927 8.295
11 1950 1923.3 0.370 8.664
12 1343 1388.7 1.507 10.171
13 1013 1003.7 0.086 10.257
14 718 726.1 0.091 10.348
15 501 525.8 1.173 11.521
16 389 381.2 0.162 11.683
17 277 276.5 0.001 11.684
18 213 200.8 0.737 12.421
19 140 146.0 0.245 12.666
20 101 106.2 0.256 12.923
21 311 287.1 1.987 14.910
Chisq= 14.91 for 20 degrees of freedom, p= 0.21845
SUMMARY of craptest
p-value for no. of wins: 0.245681
p-value for throws/game: 0.218447
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_05:31
No. of wins: Observed Expected
98715 98585.9
z-score= 0.578, pvalue=0.71823
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66768 66666.7 0.154 0.154
2 37645 37654.3 0.002 0.156
3 26967 26954.7 0.006 0.162
4 19413 19313.5 0.513 0.675
5 13877 13851.4 0.047 0.722
6 9804 9943.5 1.958 2.680
7 7083 7145.0 0.538 3.219
8 5085 5139.1 0.569 3.788
9 3794 3699.9 2.395 6.183
10 2665 2666.3 0.001 6.184
11 1886 1923.3 0.725 6.908
12 1369 1388.7 0.281 7.189
13 1016 1003.7 0.150 7.339
14 722 726.1 0.024 7.363
15 485 525.8 3.171 10.534
16 374 381.2 0.134 10.668
17 286 276.5 0.324 10.992
18 199 200.8 0.017 11.008
19 183 146.0 9.386 20.394
20 107 106.2 0.006 20.400
21 272 287.1 0.796 21.195
Chisq= 21.20 for 20 degrees of freedom, p= 0.61429
SUMMARY of craptest
p-value for no. of wins: 0.718231
p-value for throws/game: 0.614286
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0059,0.0112,0.0136,0.0298,0.0305,0.0365,0.0408,0.0419,0.0437,
0.0507,0.0513,0.0513,0.0618,0.0669,0.0688,0.0722,0.0756,0.0784,0.0815,
0.0829,0.0840,0.0870,0.0891,0.1043,0.1103,0.1149,0.1262,0.1278,0.1304,
0.1312,0.1314,0.1322,0.1346,0.1349,0.1350,0.1413,0.1489,0.1559,0.1563,
0.1651,0.1698,0.1731,0.1732,0.1749,0.1754,0.1798,0.1808,0.1843,0.1935,
0.1943,0.1954,0.1959,0.1995,0.2051,0.2056,0.2058,0.2117,0.2128,0.2184,
0.2188,0.2196,0.2237,0.2325,0.2325,0.2333,0.2343,0.2355,0.2393,0.2432,
0.2457,0.2682,0.2684,0.2688,0.2743,0.2773,0.2825,0.2847,0.2893,0.2976,
0.2977,0.2994,0.3046,0.3089,0.3098,0.3269,0.3276,0.3335,0.3384,0.3407,
0.3420,0.3466,0.3468,0.3517,0.3574,0.3585,0.3609,0.3615,0.3620,0.3628,
0.3751,0.3811,0.3836,0.3838,0.3875,0.3893,0.3896,0.3911,0.3955,0.4017,
0.4032,0.4055,0.4128,0.4130,0.4195,0.4224,0.4276,0.4355,0.4355,0.4365,
0.4428,0.4444,0.4455,0.4563,0.4564,0.4636,0.4666,0.4685,0.4737,0.4837,
0.4859,0.4860,0.4869,0.4913,0.5008,0.5042,0.5052,0.5087,0.5110,0.5183,
0.5199,0.5244,0.5250,0.5252,0.5286,0.5287,0.5296,0.5312,0.5351,0.5411,
0.5466,0.5517,0.5518,0.5522,0.5570,0.5579,0.5588,0.5625,0.5674,0.5788,
0.5939,0.5947,0.6028,0.6066,0.6091,0.6124,0.6128,0.6143,0.6223,0.6235,
0.6241,0.6280,0.6461,0.6486,0.6572,0.6721,0.6776,0.6779,0.6780,0.6823,
0.6829,0.6864,0.6883,0.6977,0.6981,0.7050,0.7073,0.7081,0.7161,0.7170,
0.7182,0.7196,0.7323,0.7359,0.7394,0.7405,0.7424,0.7588,0.7639,0.7672,
0.7724,0.7735,0.7799,0.7801,0.7843,0.7860,0.7901,0.7906,0.7923,0.7959,
0.7961,0.8016,0.8203,0.8214,0.8220,0.8223,0.8266,0.8267,0.8306,0.8312,
0.8416,0.8427,0.8461,0.8503,0.8511,0.8529,0.8532,0.8553,0.8556,0.8561,
0.8602,0.8688,0.8689,0.8710,0.8740,0.8794,0.8828,0.8880,0.8912,0.8916,
0.8924,0.8924,0.8971,0.9022,0.9033,0.9073,0.9088,0.9269,0.9280,0.9290,
0.9321,0.9423,0.9431,0.9459,0.9553,0.9556,0.9574,0.9582,0.9585,0.9668,
0.9710,0.9718,0.9773,0.9783,0.9853,0.9859,0.9898,0.9962,0.9969,
Overall p-value after applying KStest on 269 p-values = 0.971046
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.