RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-10-28_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 15.57 16.6963 0.524879
2 to 25 15.49 26.8925 0.940337
3 to 26 15.67 23.0081 0.851012
4 to 27 15.60 19.6292 0.706366
5 to 28 15.51 23.8249 0.875730
6 to 29 15.56 17.9501 0.608006
7 to 30 15.64 19.8437 0.717699
8 to 31 15.63 22.8289 0.845094
9 to 32 15.92 9.5765 0.079574
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.073362
Tough bday spacings test for dh-ranFile-2018-10-28_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 8 34 73 98 100 71 62 30 13 8 3
(O-E)^2/E 0.1 0.2 0.0 0.0 0.1 0.7 1.9 0.0 0.2 0.3 0.3
Birthday Spacings: Sum(O-E)^2/E= 3.738, p= 0.042
RESULTS OF GCD FOR dh-ranFile-2018-10-28_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.824065
p-value, dist. of gcd's: 0.834105
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-10-28_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.481 0.221 0.209 0.086 0.283 0.536 0.459 0.458
Bits 8 to 15---> 0.617 0.216 0.096 0.842 0.886 0.553 0.625 0.088
Bits 16 to 23---> 0.981 0.538 0.669 0.306 0.749 0.495 0.932 0.506
Bits 24 to 31---> 0.888 0.714 0.494 0.309 0.022 0.215 0.101 0.223
KS test for the above 32 p values: 0.323
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-10-28_20:31,
p-values for 5 runs: 0.9246, 0.1774, 0.7632, 0.8640, 0.4980
Rank test for binary matrices (31x31) for dh-ranFile-2018-10-28_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 235 211.4 2.630 2.630
r= 29 5298 5134.0 5.238 7.868
r= 30 22970 23103.0 0.766 8.635
r= 31 11497 11551.5 0.257 8.892
chi-square = 8.892 with df = 3; p-value = 0.969
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-10-28_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 180 211.4 4.669 4.669
r= 30 5187 5134.0 0.547 5.216
r= 31 23021 23103.0 0.291 5.507
r= 32 11612 11551.5 0.317 5.824
chi-square = 5.824 with df = 3; p-value = 0.879
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-10-28_20:31
b-rank test for bits 1 to 8, p=0.81563
b-rank test for bits 2 to 9, p=0.83742
b-rank test for bits 3 to 10, p=0.53530
b-rank test for bits 4 to 11, p=0.97760
b-rank test for bits 5 to 12, p=0.14516
b-rank test for bits 6 to 13, p=0.05508
b-rank test for bits 7 to 14, p=0.05513
b-rank test for bits 8 to 15, p=0.16047
b-rank test for bits 9 to 16, p=0.85774
b-rank test for bits 10 to 17, p=0.58281
b-rank test for bits 11 to 18, p=0.39285
b-rank test for bits 12 to 19, p=0.91343
b-rank test for bits 13 to 20, p=0.36732
b-rank test for bits 14 to 21, p=0.82132
b-rank test for bits 15 to 22, p=0.82498
b-rank test for bits 16 to 23, p=0.06845
b-rank test for bits 17 to 24, p=0.76847
b-rank test for bits 18 to 25, p=0.88284
b-rank test for bits 19 to 26, p=0.96196
b-rank test for bits 20 to 27, p=0.60038
b-rank test for bits 21 to 28, p=0.00203
b-rank test for bits 22 to 29, p=0.74178
b-rank test for bits 23 to 30, p=0.90234
b-rank test for bits 24 to 31, p=0.89694
b-rank test for bits 25 to 32, p=0.14618
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 = 0.072224
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-10-28_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 141762 -0.34 0.365337
2 141900 -0.02 0.491304
3 142324 0.97 0.833691
4 141145 -1.79 0.037064
5 141108 -1.87 0.030585
6 141811 -0.23 0.409146
7 141832 -0.18 0.428310
8 141976 0.16 0.561893
9 142002 0.22 0.585708
10 142473 1.32 0.906078
11 141375 -1.25 0.105936
12 142364 1.06 0.855953
13 141883 -0.06 0.475473
14 142252 0.80 0.788327
15 142455 1.27 0.898833
16 141684 -0.53 0.299280
17 142509 1.40 0.919408
18 141951 0.10 0.538780
19 141822 -0.20 0.419160
20 141111 -1.87 0.031073
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-10-28_20:31
Bits used No. missing words z-score p-value
23 to 32 141623 -0.9873 0.161737
22 to 31 142042 0.4575 0.676338
21 to 30 141572 -1.1632 0.122373
20 to 29 141720 -0.6529 0.256923
19 to 28 141268 -2.2115 0.013501
18 to 27 142199 0.9989 0.841069
17 to 26 141890 -0.0667 0.473428
16 to 25 141959 0.1713 0.567997
15 to 24 142387 1.6471 0.950235
14 to 23 141847 -0.2149 0.414911
13 to 22 141937 0.0954 0.538007
12 to 21 142059 0.5161 0.697109
11 to 20 141771 -0.4770 0.316681
10 to 19 141609 -1.0356 0.150190
9 to 18 142086 0.6092 0.728806
8 to 17 141917 0.0264 0.510550
7 to 16 142078 0.5816 0.719589
6 to 15 141604 -1.0529 0.146202
5 to 14 141707 -0.6977 0.242686
4 to 13 141843 -0.2287 0.409542
3 to 12 142222 1.0782 0.859522
2 to 11 142002 0.3196 0.625346
1 to 10 141604 -1.0529 0.146202
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-10-28_20:31
Bits used No. missing words z-score p-value
28 to 32 142433 1.7752 0.962064
27 to 31 141954 0.1514 0.560179
26 to 30 142209 1.0158 0.845145
25 to 29 141707 -0.6859 0.246399
24 to 28 142071 0.5480 0.708166
23 to 27 141810 -0.3367 0.368167
22 to 26 142246 1.1413 0.873118
21 to 25 141490 -1.4215 0.077592
20 to 24 141918 0.0294 0.511723
19 to 23 141691 -0.7401 0.229619
18 to 22 141779 -0.4418 0.329318
17 to 21 142064 0.5243 0.699967
16 to 20 141767 -0.4825 0.314734
15 to 19 142493 1.9785 0.976066
14 to 18 141836 -0.2486 0.401844
13 to 17 141793 -0.3943 0.346665
12 to 16 141885 -0.0825 0.467135
11 to 15 141203 -2.3943 0.008325
10 to 14 141497 -1.3977 0.081097
9 to 13 142323 1.4023 0.919583
8 to 12 142210 1.0192 0.845951
7 to 11 141847 -0.2113 0.416331
6 to 10 142192 0.9582 0.831020
5 to 9 141867 -0.1435 0.442951
4 to 8 141408 -1.6994 0.044620
3 to 7 142217 1.0429 0.851514
2 to 6 141935 0.0870 0.534671
1 to 5 142010 0.3413 0.633544
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-10-28_20:31
Bits used No. missing words z-score p-value
31 to 32 141841 -0.2016 0.420129
30 to 31 142208 0.8810 0.810850
29 to 30 141220 -2.0334 0.021005
28 to 29 141593 -0.9331 0.175377
27 to 28 141561 -1.0275 0.152087
26 to 27 141864 -0.1337 0.446813
25 to 26 142638 2.1495 0.984201
24 to 25 142370 1.3589 0.912912
23 to 24 142030 0.3560 0.639064
22 to 23 141631 -0.8210 0.205814
21 to 22 142035 0.3707 0.644573
20 to 21 141450 -1.3550 0.087716
19 to 20 141839 -0.2075 0.417824
18 to 19 140910 -2.9479 0.001600
17 to 18 142224 0.9282 0.823356
16 to 17 141621 -0.8505 0.197515
15 to 16 141947 0.1111 0.544240
14 to 15 142105 0.5772 0.718097
13 to 14 141951 0.1229 0.548915
12 to 13 141436 -1.3963 0.081319
11 to 12 141684 -0.6647 0.253124
10 to 11 142360 1.3294 0.908144
9 to 10 142047 0.4061 0.657668
8 to 9 141818 -0.2694 0.393807
7 to 8 141925 0.0462 0.518434
6 to 7 142001 0.2704 0.606579
5 to 6 141596 -0.9243 0.177671
4 to 5 141623 -0.8446 0.199158
3 to 4 142111 0.5949 0.724044
2 to 3 141237 -1.9833 0.023668
1 to 2 142076 0.4917 0.688517
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-10-28_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2616.95 1.654 0.950927
Test results for specific bytes for dh-ranFile-2018-10-28_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2447.44 -0.743 0.228666
2 to 9 2449.81 -0.710 0.238922
3 to 10 2472.69 -0.386 0.349650
4 to 11 2448.34 -0.731 0.232520
5 to 12 2483.32 -0.236 0.406749
6 to 13 2575.86 1.073 0.858318
7 to 14 2419.12 -1.144 0.126357
8 to 15 2501.68 0.024 0.509462
9 to 16 2480.27 -0.279 0.390126
10 to 17 2457.32 -0.604 0.273070
11 to 18 2457.88 -0.596 0.275685
12 to 19 2437.59 -0.883 0.188713
13 to 20 2448.40 -0.730 0.232794
14 to 21 2531.13 0.440 0.670096
15 to 22 2508.33 0.118 0.546862
16 to 23 2535.26 0.499 0.690968
17 to 24 2652.48 2.156 0.984476
18 to 25 2478.77 -0.300 0.381994
19 to 26 2497.92 -0.029 0.488276
20 to 27 2469.38 -0.433 0.332495
21 to 28 2696.08 2.773 0.997223
22 to 29 2492.41 -0.107 0.457245
23 to 30 2464.29 -0.505 0.306759
24 to 31 2548.26 0.682 0.752529
25 to 32 2545.00 0.636 0.737750
CDPARK for dh-ranFile-2018-10-28_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
3554 1.4155 0.921543
3507 -0.7306 0.232514
3514 -0.4110 0.340551
3541 0.8219 0.794438
3508 -0.6849 0.246694
3541 0.8219 0.794438
3525 0.0913 0.536383
3535 0.5479 0.708135
3570 2.1461 0.984068
3511 -0.5479 0.291865
Square side=100, avg. no. parked=3530.60 sample std.=20.23
p-value of the KSTEST for those 10 p-values: 0.508679
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-10-28_20:31
0.1548,0.1611,0.1693,0.3766,0.2416,0.0220,0.9253,0.2557,0.8386,0.7253,
The KS test for those 10 p-values: 0.245517
The 3DSPHERES test for dh-ranFile-2018-10-28_20:31
sample no r^3 equiv. uni.
1 20.340 0.492371
2 14.013 0.373187
3 34.187 0.680040
4 72.018 0.909336
5 0.553 0.018261
6 0.259 0.008589
7 1.860 0.060121
8 4.638 0.143245
9 23.198 0.538499
10 73.872 0.914770
11 7.780 0.228438
12 122.658 0.983238
13 1.649 0.053494
14 12.853 0.348474
15 8.332 0.242509
16 68.005 0.896360
17 0.412 0.013629
18 74.212 0.915731
19 9.164 0.263219
20 27.593 0.601388
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.117354
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-10-28_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.6 0.3 0.0 -1.5 -0.8
-1.1 -0.5 -0.9 1.2 -1.0 1.8
-0.5 0.9 -1.4 -0.4 0.4 0.8
1.4 -0.2 -1.1 0.0 0.2 -1.0
0.2 0.3 -0.4 -0.2 -0.8 0.8
0.2 0.4 0.9 -0.4 -1.6 2.2
-0.5 0.5 -0.4 -0.1 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:33.057620
z-score=-0.975694, p-value=0.163330
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-10-28_20:31
Test no p-value
1 0.008433
2 0.228473
3 0.029779
4 0.818105
5 0.824989
6 0.511910
7 0.238294
8 0.387356
9 0.029409
10 0.948891
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.149582
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-10-28_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 66625 0.03 66762 0.14
3 25000.00 24978 0.02 25002 0.00
4 6666.67 6758 1.25 6552 1.97
5 1388.89 1379 0.07 1398 0.06
6 238.10 224 0.83 247 0.33
7 34.72 33 0.09 33 0.09
8 4.96 2 1.77 5 0.00
p=0.33051 p=0.14141
Number of rngs required: 687634, p-value: 0.187
RESULTS OF CRAPS TEST for dh-ranFile-2018-10-28_20:31
No. of wins: Observed Expected
98695 98585.9
z-score= 0.488, pvalue=0.68728
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66715 66666.7 0.035 0.035
2 37649 37654.3 0.001 0.036
3 27134 26954.7 1.192 1.228
4 19324 19313.5 0.006 1.234
5 13867 13851.4 0.018 1.251
6 9932 9943.5 0.013 1.265
7 7154 7145.0 0.011 1.276
8 5014 5139.1 3.044 4.320
9 3674 3699.9 0.181 4.501
10 2600 2666.3 1.648 6.149
11 1957 1923.3 0.589 6.739
12 1357 1388.7 0.725 7.464
13 967 1003.7 1.343 8.807
14 763 726.1 1.871 10.678
15 537 525.8 0.237 10.915
16 368 381.2 0.454 11.369
17 274 276.5 0.023 11.392
18 199 200.8 0.017 11.409
19 148 146.0 0.028 11.437
20 103 106.2 0.097 11.534
21 264 287.1 1.861 13.395
Chisq= 13.39 for 20 degrees of freedom, p= 0.14019
SUMMARY of craptest
p-value for no. of wins: 0.687276
p-value for throws/game: 0.140192
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-10-28_20:31
No. of wins: Observed Expected
98655 98585.9
z-score= 0.309, pvalue=0.62143
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66777 66666.7 0.183 0.183
2 37396 37654.3 1.772 1.955
3 27128 26954.7 1.114 3.069
4 19375 19313.5 0.196 3.265
5 13858 13851.4 0.003 3.268
6 9897 9943.5 0.218 3.486
7 7179 7145.0 0.162 3.647
8 4991 5139.1 4.266 7.914
9 3759 3699.9 0.945 8.859
10 2725 2666.3 1.292 10.151
11 1938 1923.3 0.112 10.263
12 1315 1388.7 3.916 14.179
13 1001 1003.7 0.007 14.186
14 688 726.1 2.003 16.189
15 563 525.8 2.627 18.816
16 379 381.2 0.012 18.828
17 264 276.5 0.569 19.397
18 213 200.8 0.737 20.134
19 140 146.0 0.245 20.379
20 114 106.2 0.571 20.950
21 300 287.1 0.578 21.528
Chisq= 21.53 for 20 degrees of freedom, p= 0.63336
SUMMARY of craptest
p-value for no. of wins: 0.621431
p-value for throws/game: 0.633357
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0020,0.0083,0.0084,0.0086,0.0135,0.0136,0.0183,0.0210,0.0218,
0.0220,0.0237,0.0294,0.0298,0.0306,0.0311,0.0371,0.0416,0.0446,0.0535,
0.0551,0.0551,0.0601,0.0685,0.0722,0.0734,0.0776,0.0796,0.0811,0.0813,
0.0862,0.0877,0.0882,0.0960,0.1011,0.1059,0.1174,0.1224,0.1264,0.1402,
0.1414,0.1432,0.1452,0.1462,0.1462,0.1462,0.1496,0.1502,0.1521,0.1548,
0.1605,0.1611,0.1617,0.1633,0.1693,0.1754,0.1774,0.1777,0.1868,0.1887,
0.1975,0.1992,0.2058,0.2085,0.2149,0.2159,0.2209,0.2227,0.2284,0.2285,
0.2287,0.2296,0.2325,0.2325,0.2328,0.2383,0.2389,0.2416,0.2425,0.2427,
0.2455,0.2464,0.2467,0.2531,0.2557,0.2569,0.2632,0.2731,0.2757,0.2827,
0.2919,0.2993,0.3062,0.3068,0.3086,0.3147,0.3167,0.3225,0.3293,0.3305,
0.3325,0.3406,0.3467,0.3485,0.3497,0.3653,0.3673,0.3682,0.3732,0.3766,
0.3820,0.3874,0.3901,0.3929,0.3938,0.4018,0.4067,0.4091,0.4095,0.4149,
0.4163,0.4178,0.4192,0.4201,0.4283,0.4430,0.4468,0.4572,0.4577,0.4590,
0.4671,0.4734,0.4755,0.4814,0.4883,0.4913,0.4924,0.4944,0.4954,0.4980,
0.5064,0.5087,0.5095,0.5106,0.5117,0.5119,0.5184,0.5249,0.5347,0.5353,
0.5363,0.5364,0.5380,0.5382,0.5385,0.5388,0.5442,0.5469,0.5489,0.5526,
0.5602,0.5619,0.5680,0.5828,0.5857,0.6004,0.6014,0.6066,0.6080,0.6165,
0.6214,0.6253,0.6254,0.6334,0.6335,0.6391,0.6446,0.6577,0.6693,0.6701,
0.6763,0.6800,0.6873,0.6885,0.6910,0.6971,0.7000,0.7064,0.7081,0.7082,
0.7140,0.7177,0.7181,0.7196,0.7240,0.7253,0.7288,0.7378,0.7418,0.7494,
0.7525,0.7632,0.7685,0.7883,0.7944,0.7944,0.8108,0.8156,0.8181,0.8213,
0.8234,0.8241,0.8250,0.8250,0.8310,0.8337,0.8341,0.8374,0.8386,0.8411,
0.8415,0.8451,0.8451,0.8460,0.8510,0.8515,0.8560,0.8577,0.8583,0.8595,
0.8640,0.8731,0.8757,0.8795,0.8828,0.8855,0.8882,0.8964,0.8969,0.8988,
0.9023,0.9061,0.9081,0.9093,0.9129,0.9134,0.9148,0.9157,0.9194,0.9196,
0.9215,0.9246,0.9253,0.9316,0.9403,0.9489,0.9502,0.9509,0.9620,0.9621,
0.9692,0.9761,0.9776,0.9810,0.9832,0.9841,0.9842,0.9845,0.9972,
Overall p-value after applying KStest on 269 p-values = 0.264144
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.