RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.99 9.7275 0.085351
2 to 25 15.86 20.2828 0.739977
3 to 26 15.58 23.6016 0.869329
4 to 27 15.62 15.2784 0.424562
5 to 28 15.48 43.9188 0.999648
6 to 29 15.71 15.0652 0.409216
7 to 30 15.93 23.5402 0.867525
8 to 31 15.92 13.8489 0.322234
9 to 32 15.64 13.5389 0.300570
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.403890
Tough bday spacings test for dh-ranFile-2018-06-19_07:31: 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 12 33 77 97 95 78 54 25 17 7 5
(O-E)^2/E 0.9 0.4 0.2 0.0 0.1 0.0 0.1 0.8 0.3 0.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 2.883, p= 0.016
RESULTS OF GCD FOR dh-ranFile-2018-06-19_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.637465
p-value, dist. of gcd's: 0.173133
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.919 0.872 0.157 0.137 0.551 0.171 0.030 0.606
Bits 8 to 15---> 0.057 0.436 0.481 0.060 0.073 0.157 0.555 0.399
Bits 16 to 23---> 0.337 0.851 0.228 0.904 0.272 0.767 0.586 0.917
Bits 24 to 31---> 0.568 0.968 0.227 0.081 0.432 0.603 0.157 0.414
KS test for the above 32 p values: 0.697
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_07:31,
p-values for 5 runs: 0.3853, 0.9017, 0.5400, 0.5926, 0.3141
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 221 211.4 0.434 0.434
r= 29 5005 5134.0 3.242 3.676
r= 30 23128 23103.0 0.027 3.703
r= 31 11646 11551.5 0.773 4.476
chi-square = 4.476 with df = 3; p-value = 0.786
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5092 5134.0 0.344 0.371
r= 31 23083 23103.0 0.017 0.389
r= 32 11616 11551.5 0.360 0.749
chi-square = 0.749 with df = 3; p-value = 0.138
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_07:31
b-rank test for bits 1 to 8, p=0.43031
b-rank test for bits 2 to 9, p=0.45953
b-rank test for bits 3 to 10, p=0.83600
b-rank test for bits 4 to 11, p=0.89728
b-rank test for bits 5 to 12, p=0.35756
b-rank test for bits 6 to 13, p=0.25526
b-rank test for bits 7 to 14, p=0.80030
b-rank test for bits 8 to 15, p=0.11024
b-rank test for bits 9 to 16, p=0.10055
b-rank test for bits 10 to 17, p=0.50630
b-rank test for bits 11 to 18, p=0.45047
b-rank test for bits 12 to 19, p=0.47648
b-rank test for bits 13 to 20, p=0.99093
b-rank test for bits 14 to 21, p=0.65534
b-rank test for bits 15 to 22, p=0.90980
b-rank test for bits 16 to 23, p=0.70891
b-rank test for bits 17 to 24, p=0.64869
b-rank test for bits 18 to 25, p=0.77822
b-rank test for bits 19 to 26, p=0.77489
b-rank test for bits 20 to 27, p=0.12625
b-rank test for bits 21 to 28, p=0.38570
b-rank test for bits 22 to 29, p=0.27857
b-rank test for bits 23 to 30, p=0.65765
b-rank test for bits 24 to 31, p=0.89166
b-rank test for bits 25 to 32, p=0.89115
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 = 0.322253
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_07:31
(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 142946 2.42 0.992285
2 142191 0.66 0.744765
3 142484 1.34 0.910313
4 141405 -1.18 0.119330
5 142031 0.28 0.611900
6 141863 -0.11 0.456900
7 141724 -0.43 0.332502
8 141606 -0.71 0.239251
9 141672 -0.55 0.289615
10 142392 1.13 0.870284
11 142399 1.14 0.873707
12 141868 -0.10 0.461536
13 141900 -0.02 0.491304
14 141628 -0.66 0.255490
15 142449 1.26 0.896330
16 142174 0.62 0.731840
17 142193 0.66 0.746264
18 141216 -1.62 0.052624
19 140871 -2.43 0.007633
20 141351 -1.30 0.096030
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_07:31
Bits used No. missing words z-score p-value
23 to 32 141549 -1.2425 0.107023
22 to 31 142076 0.5747 0.717261
21 to 30 141907 -0.0080 0.496795
20 to 29 142107 0.6816 0.752261
19 to 28 141897 -0.0425 0.483043
18 to 27 141758 -0.5218 0.300895
17 to 26 142164 0.8782 0.810075
16 to 25 142284 1.2920 0.901815
15 to 24 141362 -1.8873 0.029557
14 to 23 141777 -0.4563 0.324083
13 to 22 142634 2.4989 0.993770
12 to 21 141979 0.2402 0.594928
11 to 20 142057 0.5092 0.694696
10 to 19 142570 2.2782 0.988642
9 to 18 142186 0.9540 0.829967
8 to 17 142116 0.7127 0.761970
7 to 16 141871 -0.1322 0.447424
6 to 15 141850 -0.2046 0.418948
5 to 14 141789 -0.4149 0.339096
4 to 13 142333 1.4609 0.927983
3 to 12 141833 -0.2632 0.396196
2 to 11 142041 0.4540 0.675098
1 to 10 141569 -1.1736 0.120287
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_07:31
Bits used No. missing words z-score p-value
28 to 32 142119 0.7107 0.761379
27 to 31 141757 -0.5164 0.302797
26 to 30 141873 -0.1232 0.450993
25 to 29 141614 -1.0011 0.158385
24 to 28 141655 -0.8621 0.194306
23 to 27 141579 -1.1198 0.131407
22 to 26 141816 -0.3164 0.375860
21 to 25 142574 2.2531 0.987874
20 to 24 141851 -0.1977 0.421629
19 to 23 141877 -0.1096 0.456366
18 to 22 142029 0.4057 0.657504
17 to 21 141758 -0.5130 0.303982
16 to 20 141777 -0.4486 0.326869
15 to 19 141822 -0.2960 0.383602
14 to 18 141592 -1.0757 0.141032
13 to 17 142022 0.3819 0.648744
12 to 16 141555 -1.2011 0.114853
11 to 15 142132 0.7548 0.774820
10 to 14 141734 -0.5943 0.276143
9 to 13 142173 0.8938 0.814285
8 to 12 141493 -1.4113 0.079080
7 to 11 142199 0.9819 0.836933
6 to 10 142384 1.6091 0.946197
5 to 9 142234 1.1006 0.864459
4 to 8 141632 -0.9401 0.173583
3 to 7 141733 -0.5977 0.275010
2 to 6 142077 0.5684 0.715109
1 to 5 142286 1.2768 0.899172
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_07:31
Bits used No. missing words z-score p-value
31 to 32 141814 -0.2812 0.389275
30 to 31 142177 0.7896 0.785116
29 to 30 141837 -0.2134 0.415522
28 to 29 141841 -0.2016 0.420129
27 to 28 142311 1.1849 0.881965
26 to 27 142044 0.3973 0.654411
25 to 26 142188 0.8220 0.794472
24 to 25 142102 0.5683 0.715101
23 to 24 141129 -2.3019 0.010672
22 to 23 142432 1.5418 0.938439
21 to 22 141822 -0.2576 0.398354
20 to 21 141852 -0.1691 0.432853
19 to 20 142269 1.0610 0.855649
18 to 19 142230 0.9459 0.827908
17 to 18 142197 0.8486 0.801944
16 to 17 141597 -0.9213 0.178440
15 to 16 141965 0.1642 0.565220
14 to 15 141514 -1.1662 0.121774
13 to 14 142013 0.3058 0.620126
12 to 13 142394 1.4297 0.923599
11 to 12 141317 -1.7473 0.040294
10 to 11 141847 -0.1839 0.427060
9 to 10 142220 0.9164 0.820280
8 to 9 141406 -1.4847 0.068805
7 to 8 142159 0.7365 0.769284
6 to 7 142050 0.4150 0.660913
5 to 6 142249 1.0020 0.841823
4 to 5 141564 -1.0187 0.154179
3 to 4 142354 1.3117 0.905191
2 to 3 142276 1.0816 0.860290
1 to 2 142295 1.1377 0.872371
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2531.78 0.449 0.673454
Test results for specific bytes for dh-ranFile-2018-06-19_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2625.07 1.769 0.961538
2 to 9 2461.15 -0.549 0.291371
3 to 10 2547.25 0.668 0.748004
4 to 11 2476.45 -0.333 0.369566
5 to 12 2446.58 -0.756 0.224963
6 to 13 2531.83 0.450 0.673707
7 to 14 2529.54 0.418 0.661916
8 to 15 2567.01 0.948 0.828354
9 to 16 2446.61 -0.755 0.225130
10 to 17 2517.74 0.251 0.599025
11 to 18 2526.75 0.378 0.647407
12 to 19 2490.03 -0.141 0.443911
13 to 20 2570.09 0.991 0.839203
14 to 21 2580.79 1.142 0.873376
15 to 22 2500.05 0.001 0.500278
16 to 23 2526.43 0.374 0.645704
17 to 24 2396.49 -1.464 0.071626
18 to 25 2494.98 -0.071 0.471720
19 to 26 2491.43 -0.121 0.451753
20 to 27 2479.78 -0.286 0.387430
21 to 28 2507.44 0.105 0.541902
22 to 29 2412.47 -1.238 0.107874
23 to 30 2555.09 0.779 0.782040
24 to 31 2568.57 0.970 0.833902
25 to 32 2363.48 -1.931 0.026759
CDPARK for dh-ranFile-2018-06-19_07:31: 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
3527 0.1826 0.572463
3541 0.8219 0.794438
3528 0.2283 0.590298
3528 0.2283 0.590298
3512 -0.5023 0.307734
3528 0.2283 0.590298
3532 0.4110 0.659449
3521 -0.0913 0.463617
3568 2.0548 0.980051
3530 0.3196 0.625377
Square side=100, avg. no. parked=3531.50 sample std.=14.04
p-value of the KSTEST for those 10 p-values: 0.120972
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_07:31
0.2881,0.4680,0.2553,0.8026,0.6606,0.3446,0.4419,0.7530,0.2893,0.8052,
The KS test for those 10 p-values: 0.550011
The 3DSPHERES test for dh-ranFile-2018-06-19_07:31
sample no r^3 equiv. uni.
1 19.542 0.478691
2 8.357 0.243140
3 32.784 0.664722
4 5.163 0.158092
5 3.432 0.108110
6 19.573 0.479228
7 0.592 0.019538
8 7.354 0.217404
9 31.621 0.651470
10 16.116 0.415613
11 161.580 0.995420
12 53.463 0.831717
13 5.024 0.154184
14 50.192 0.812331
15 3.251 0.102700
16 17.315 0.438517
17 1.786 0.057787
18 14.313 0.379424
19 5.829 0.176587
20 48.610 0.802168
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.241993
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.9 -0.4 -0.4 1.3 1.3
-1.4 0.7 -2.5 -0.4 0.4 0.4
-0.1 0.1 0.9 -0.5 0.2 0.7
0.5 -1.3 0.3 -1.3 0.3 -1.1
0.5 1.1 1.4 -0.2 -0.8 0.8
-0.5 0.4 -1.2 -1.9 -0.2 1.3
0.5 -0.1 0.9 -1.3 0.9 -1.0
0.8
Chi-square with 42 degrees of freedom:41.944042
z-score=-0.006106, p-value=0.526598
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_07:31
Test no p-value
1 0.547518
2 0.215267
3 0.025793
4 0.829796
5 0.187265
6 0.391461
7 0.004412
8 0.080893
9 0.016582
10 0.058784
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001282
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_07:31:
(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 66746 0.09 66817 0.34
3 25000.00 24952 0.09 24851 0.89
4 6666.67 6688 0.07 6687 0.06
5 1388.89 1354 0.88 1375 0.14
6 238.10 226 0.61 237 0.01
7 34.72 28 1.30 29 0.94
8 4.96 5 0.00 3 0.77
p=0.19703 p=0.21018
Number of rngs required: 687204, p-value: 0.081
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_07:31
No. of wins: Observed Expected
98955 98585.9
z-score= 1.651, pvalue=0.95063
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66507 66666.7 0.382 0.382
2 37777 37654.3 0.400 0.782
3 27019 26954.7 0.153 0.935
4 19166 19313.5 1.126 2.061
5 13987 13851.4 1.327 3.388
6 10085 9943.5 2.012 5.401
7 7085 7145.0 0.504 5.905
8 5130 5139.1 0.016 5.921
9 3769 3699.9 1.292 7.213
10 2631 2666.3 0.467 7.680
11 1868 1923.3 1.592 9.272
12 1331 1388.7 2.401 11.672
13 1061 1003.7 3.269 14.942
14 728 726.1 0.005 14.947
15 524 525.8 0.006 14.953
16 343 381.2 3.819 18.772
17 252 276.5 2.178 20.949
18 195 200.8 0.169 21.118
19 152 146.0 0.248 21.366
20 115 106.2 0.727 22.093
21 275 287.1 0.511 22.604
Chisq= 22.60 for 20 degrees of freedom, p= 0.69135
SUMMARY of craptest
p-value for no. of wins: 0.950632
p-value for throws/game: 0.691348
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_07:31
No. of wins: Observed Expected
98717 98585.9
z-score= 0.587, pvalue=0.72124
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67117 66666.7 3.042 3.042
2 37436 37654.3 1.266 4.308
3 27114 26954.7 0.941 5.249
4 19152 19313.5 1.350 6.599
5 13665 13851.4 2.509 9.108
6 9991 9943.5 0.226 9.334
7 7152 7145.0 0.007 9.341
8 5081 5139.1 0.656 9.997
9 3623 3699.9 1.597 11.594
10 2710 2666.3 0.716 12.310
11 1856 1923.3 2.357 14.667
12 1427 1388.7 1.054 15.721
13 982 1003.7 0.470 16.191
14 727 726.1 0.001 16.192
15 518 525.8 0.117 16.309
16 390 381.2 0.205 16.514
17 313 276.5 4.807 21.322
18 201 200.8 0.000 21.322
19 177 146.0 6.590 27.911
20 93 106.2 1.644 29.556
21 275 287.1 0.511 30.067
Chisq= 30.07 for 20 degrees of freedom, p= 0.93122
SUMMARY of craptest
p-value for no. of wins: 0.721244
p-value for throws/game: 0.931219
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0013,0.0044,0.0076,0.0107,0.0159,0.0166,0.0195,0.0258,0.0268,0.0296,
0.0301,0.0403,0.0526,0.0568,0.0578,0.0588,0.0603,0.0688,0.0716,0.0730,
0.0791,0.0807,0.0809,0.0810,0.0854,0.0960,0.1005,0.1027,0.1070,0.1079,
0.1081,0.1102,0.1149,0.1193,0.1203,0.1210,0.1218,0.1262,0.1314,0.1369,
0.1383,0.1410,0.1542,0.1542,0.1568,0.1573,0.1574,0.1581,0.1584,0.1714,
0.1731,0.1736,0.1766,0.1784,0.1873,0.1943,0.1970,0.2102,0.2153,0.2174,
0.2250,0.2251,0.2270,0.2284,0.2393,0.2420,0.2431,0.2553,0.2553,0.2555,
0.2720,0.2750,0.2761,0.2786,0.2881,0.2893,0.2896,0.2914,0.3006,0.3009,
0.3028,0.3040,0.3077,0.3141,0.3222,0.3223,0.3241,0.3269,0.3325,0.3375,
0.3391,0.3446,0.3576,0.3696,0.3759,0.3794,0.3836,0.3853,0.3857,0.3874,
0.3893,0.3915,0.3962,0.3984,0.3987,0.4039,0.4092,0.4144,0.4155,0.4156,
0.4189,0.4201,0.4216,0.4246,0.4271,0.4303,0.4315,0.4329,0.4365,0.4385,
0.4419,0.4439,0.4474,0.4505,0.4510,0.4518,0.4564,0.4569,0.4595,0.4615,
0.4636,0.4680,0.4717,0.4765,0.4787,0.4792,0.4813,0.4830,0.4913,0.4968,
0.5003,0.5063,0.5266,0.5400,0.5419,0.5475,0.5500,0.5512,0.5552,0.5652,
0.5684,0.5725,0.5855,0.5903,0.5903,0.5903,0.5926,0.5949,0.5990,0.6032,
0.6060,0.6119,0.6201,0.6254,0.6375,0.6457,0.6474,0.6487,0.6487,0.6515,
0.6544,0.6553,0.6575,0.6577,0.6594,0.6606,0.6609,0.6619,0.6647,0.6735,
0.6737,0.6751,0.6913,0.6947,0.6971,0.7089,0.7151,0.7151,0.7173,0.7212,
0.7318,0.7400,0.7448,0.7463,0.7480,0.7523,0.7530,0.7614,0.7620,0.7669,
0.7693,0.7748,0.7749,0.7782,0.7820,0.7851,0.7855,0.7944,0.7945,0.8003,
0.8019,0.8022,0.8026,0.8052,0.8101,0.8123,0.8143,0.8203,0.8279,0.8284,
0.8298,0.8300,0.8317,0.8339,0.8360,0.8369,0.8392,0.8418,0.8512,0.8556,
0.8603,0.8645,0.8675,0.8693,0.8703,0.8724,0.8724,0.8734,0.8737,0.8820,
0.8912,0.8917,0.8963,0.8973,0.8992,0.9017,0.9018,0.9043,0.9052,0.9098,
0.9103,0.9175,0.9194,0.9236,0.9280,0.9312,0.9384,0.9462,0.9506,0.9615,
0.9679,0.9801,0.9879,0.9886,0.9909,0.9923,0.9938,0.9954,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.916403
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.