RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_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 16.00 17.7299 0.593931
2 to 25 15.70 15.7521 0.458527
3 to 26 15.75 13.1179 0.271739
4 to 27 16.11 35.6864 0.994951
5 to 28 16.01 7.8324 0.030000
6 to 29 15.86 18.5209 0.643283
7 to 30 15.91 10.6459 0.125633
8 to 31 15.92 23.4036 0.863434
9 to 32 15.50 20.2185 0.736793
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.894623
Tough bday spacings test for dh-ranFile-2018-06-16_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 14 31 71 102 89 79 55 33 16 5 5
(O-E)^2/E 2.6 0.9 0.1 0.2 0.8 0.0 0.2 0.4 0.1 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 5.672, p= 0.158
RESULTS OF GCD FOR dh-ranFile-2018-06-16_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.431234
p-value, dist. of gcd's: 0.080610
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.898 0.378 0.022 0.174 0.140 0.230 0.731 0.379
Bits 8 to 15---> 0.416 0.496 0.036 0.387 0.484 0.903 0.897 0.918
Bits 16 to 23---> 0.014 0.333 0.056 0.323 0.809 0.035 0.539 0.420
Bits 24 to 31---> 0.279 0.860 0.792 0.736 0.124 0.760 0.167 0.232
KS test for the above 32 p values: 0.749
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_13:31,
p-values for 5 runs: 0.2616, 0.6935, 0.6630, 0.2554, 0.5972
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 244 211.4 5.021 5.021
r= 29 5112 5134.0 0.094 5.116
r= 30 23042 23103.0 0.161 5.277
r= 31 11602 11551.5 0.221 5.498
chi-square = 5.498 with df = 3; p-value = 0.861
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 237 211.4 3.095 3.095
r= 30 5218 5134.0 1.374 4.469
r= 31 23083 23103.0 0.017 4.487
r= 32 11462 11551.5 0.694 5.181
chi-square = 5.181 with df = 3; p-value = 0.841
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_13:31
b-rank test for bits 1 to 8, p=0.57020
b-rank test for bits 2 to 9, p=0.22908
b-rank test for bits 3 to 10, p=0.33658
b-rank test for bits 4 to 11, p=0.77341
b-rank test for bits 5 to 12, p=0.59999
b-rank test for bits 6 to 13, p=0.58103
b-rank test for bits 7 to 14, p=0.32160
b-rank test for bits 8 to 15, p=0.67750
b-rank test for bits 9 to 16, p=0.44128
b-rank test for bits 10 to 17, p=0.71816
b-rank test for bits 11 to 18, p=0.61746
b-rank test for bits 12 to 19, p=0.65199
b-rank test for bits 13 to 20, p=0.89091
b-rank test for bits 14 to 21, p=0.92972
b-rank test for bits 15 to 22, p=0.80974
b-rank test for bits 16 to 23, p=0.62169
b-rank test for bits 17 to 24, p=0.80048
b-rank test for bits 18 to 25, p=0.97596
b-rank test for bits 19 to 26, p=0.09816
b-rank test for bits 20 to 27, p=0.44488
b-rank test for bits 21 to 28, p=0.14261
b-rank test for bits 22 to 29, p=0.56510
b-rank test for bits 23 to 30, p=0.01673
b-rank test for bits 24 to 31, p=0.54403
b-rank test for bits 25 to 32, p=0.04725
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 = 0.666147
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_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 141555 -0.83 0.203871
2 141618 -0.68 0.248038
3 141805 -0.24 0.403708
4 142168 0.60 0.727201
5 141978 0.16 0.563734
6 141417 -1.15 0.125009
7 141738 -0.40 0.344466
8 142384 1.11 0.866294
9 142918 2.36 0.990781
10 142791 2.06 0.980300
11 141592 -0.74 0.229218
12 142086 0.41 0.660116
13 142298 0.91 0.818089
14 141805 -0.24 0.403708
15 141514 -0.92 0.177830
16 141916 0.02 0.506217
17 141552 -0.83 0.201892
18 141461 -1.05 0.147435
19 141558 -0.82 0.205862
20 141729 -0.42 0.336756
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_13:31
Bits used No. missing words z-score p-value
23 to 32 142002 0.3196 0.625346
22 to 31 142169 0.8954 0.814717
21 to 30 141587 -1.1115 0.133180
20 to 29 142083 0.5989 0.725368
19 to 28 142329 1.4471 0.926071
18 to 27 141348 -1.9356 0.026457
17 to 26 141959 0.1713 0.567997
16 to 25 142262 1.2161 0.888027
15 to 24 141702 -0.7149 0.237326
14 to 23 141884 -0.0873 0.465199
13 to 22 141970 0.2092 0.582857
12 to 21 141345 -1.9460 0.025829
11 to 20 142116 0.7127 0.761970
10 to 19 141769 -0.4839 0.314230
9 to 18 141740 -0.5839 0.279645
8 to 17 141882 -0.0942 0.462459
7 to 16 141904 -0.0184 0.492668
6 to 15 141862 -0.1632 0.435178
5 to 14 142068 0.5471 0.707858
4 to 13 142121 0.7299 0.767273
3 to 12 141890 -0.0667 0.473428
2 to 11 142364 1.5678 0.941539
1 to 10 142754 2.9127 0.998208
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_13:31
Bits used No. missing words z-score p-value
28 to 32 141729 -0.6113 0.270504
27 to 31 141878 -0.1062 0.457711
26 to 30 142532 2.1107 0.982603
25 to 29 141792 -0.3977 0.345415
24 to 28 141672 -0.8045 0.210552
23 to 27 142245 1.1379 0.872411
22 to 26 142017 0.3650 0.642438
21 to 25 141840 -0.2350 0.407098
20 to 24 141887 -0.0757 0.469831
19 to 23 141692 -0.7367 0.230649
18 to 22 141774 -0.4587 0.323208
17 to 21 141887 -0.0757 0.469831
16 to 20 142019 0.3718 0.644965
15 to 19 141952 0.1446 0.557504
14 to 18 141917 0.0260 0.510371
13 to 17 142233 1.0972 0.863720
12 to 16 141356 -1.8757 0.030349
11 to 15 141587 -1.0926 0.137275
10 to 14 141823 -0.2926 0.384897
9 to 13 141847 -0.2113 0.416331
8 to 12 142314 1.3718 0.914931
7 to 11 142443 1.8091 0.964778
6 to 10 141736 -0.5876 0.278414
5 to 9 141357 -1.8723 0.030582
4 to 8 142290 1.2904 0.901545
3 to 7 142127 0.7379 0.769702
2 to 6 142065 0.5277 0.701145
1 to 5 141709 -0.6791 0.248542
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_13:31
Bits used No. missing words z-score p-value
31 to 32 141909 -0.0010 0.499612
30 to 31 141448 -1.3609 0.086780
29 to 30 141781 -0.3786 0.352509
28 to 29 141552 -1.0541 0.145925
27 to 28 141960 0.1495 0.559408
26 to 27 141654 -0.7532 0.225669
25 to 26 142095 0.5477 0.708051
24 to 25 142275 1.0787 0.859633
23 to 24 142471 1.6568 0.951224
22 to 23 142139 0.6775 0.750953
21 to 22 141595 -0.9272 0.176904
20 to 21 141979 0.2055 0.581416
19 to 20 142567 1.9400 0.973812
18 to 19 141829 -0.2370 0.406343
17 to 18 141873 -0.1072 0.457328
16 to 17 142475 1.6686 0.952406
15 to 16 141653 -0.7561 0.224784
14 to 15 141939 0.0875 0.534872
13 to 14 141899 -0.0305 0.487845
12 to 13 142224 0.9282 0.823356
11 to 12 141925 0.0462 0.518434
10 to 11 141640 -0.7945 0.213457
9 to 10 142320 1.2114 0.887132
8 to 9 141366 -1.6027 0.054496
7 to 8 141892 -0.0511 0.479615
6 to 7 142104 0.5742 0.717100
5 to 6 142009 0.2940 0.615626
4 to 5 141877 -0.0954 0.462011
3 to 4 142228 0.9400 0.826399
2 to 3 141665 -0.7207 0.235536
1 to 2 142367 1.3501 0.911501
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2550.77 0.718 0.763631
Test results for specific bytes for dh-ranFile-2018-06-16_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2493.56 -0.091 0.463719
2 to 9 2475.39 -0.348 0.363902
3 to 10 2582.11 1.161 0.877218
4 to 11 2394.62 -1.490 0.068071
5 to 12 2523.46 0.332 0.629979
6 to 13 2514.91 0.211 0.583490
7 to 14 2518.23 0.258 0.601697
8 to 15 2457.61 -0.599 0.274440
9 to 16 2549.40 0.699 0.757610
10 to 17 2522.09 0.312 0.622652
11 to 18 2438.08 -0.876 0.190585
12 to 19 2457.79 -0.597 0.275280
13 to 20 2529.17 0.413 0.660045
14 to 21 2406.47 -1.323 0.092962
15 to 22 2451.29 -0.689 0.245438
16 to 23 2424.42 -1.069 0.142580
17 to 24 2481.70 -0.259 0.397884
18 to 25 2407.63 -1.306 0.095720
19 to 26 2512.55 0.177 0.570438
20 to 27 2472.61 -0.387 0.349253
21 to 28 2505.03 0.071 0.528368
22 to 29 2421.48 -1.110 0.133409
23 to 30 2485.82 -0.201 0.420515
24 to 31 2456.76 -0.612 0.270417
25 to 32 2387.08 -1.597 0.055140
CDPARK for dh-ranFile-2018-06-16_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
3522 -0.0457 0.481790
3488 -1.5982 0.055002
3515 -0.3653 0.357445
3507 -0.7306 0.232514
3537 0.6393 0.738676
3506 -0.7763 0.218799
3528 0.2283 0.590298
3540 0.7763 0.781201
3473 -2.2831 0.011212
3540 0.7763 0.781201
Square side=100, avg. no. parked=3515.60 sample std.=21.42
p-value of the KSTEST for those 10 p-values: 0.583033
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_13:31
0.2189,0.7014,0.9239,0.4225,0.8164,0.3753,0.7755,0.5567,0.0919,0.1587,
The KS test for those 10 p-values: 0.998714
The 3DSPHERES test for dh-ranFile-2018-06-16_13:31
sample no r^3 equiv. uni.
1 19.344 0.475226
2 41.668 0.750659
3 14.272 0.378573
4 10.541 0.296267
5 53.638 0.832695
6 43.093 0.762227
7 104.188 0.968974
8 5.575 0.169595
9 57.013 0.850496
10 7.398 0.218542
11 9.167 0.263285
12 39.285 0.730046
13 109.836 0.974298
14 17.736 0.446341
15 8.226 0.239816
16 4.323 0.134188
17 1.504 0.048910
18 9.432 0.269763
19 13.032 0.352350
20 55.474 0.842626
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.791577
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 1.1 0.8 -0.4 0.0
-0.6 -0.4 -1.0 0.5 -1.6 -0.1
1.5 0.7 -1.8 -0.1 0.7 -0.1
-1.5 1.3 0.4 0.1 0.3 -1.9
2.2 -0.1 -0.1 -0.8 1.3 0.7
-1.0 1.8 0.7 -0.4 -1.5 0.6
0.7 0.2 0.1 1.5 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:40.650194
z-score=-0.147276, p-value=0.469762
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_13:31
Test no p-value
1 0.771668
2 0.234063
3 0.797047
4 0.002661
5 0.019142
6 0.204648
7 0.043098
8 0.041278
9 0.259353
10 0.328466
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004681
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_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 66618 0.04 66634 0.02
3 25000.00 24893 0.46 24972 0.03
4 6666.67 6817 3.39 6706 0.23
5 1388.89 1418 0.61 1386 0.01
6 238.10 215 2.24 264 2.82
7 34.72 36 0.05 36 0.05
8 4.96 2 1.77 1 3.16
p=0.79932 p=0.61091
Number of rngs required: 687779, p-value: 0.236
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_13:31
No. of wins: Observed Expected
98862 98585.9
z-score= 1.235, pvalue=0.89160
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66946 66666.7 1.170 1.170
2 37429 37654.3 1.348 2.519
3 26697 26954.7 2.464 4.983
4 19413 19313.5 0.513 5.496
5 13693 13851.4 1.812 7.308
6 10187 9943.5 5.961 13.269
7 7088 7145.0 0.455 13.724
8 5240 5139.1 1.982 15.706
9 3784 3699.9 1.913 17.619
10 2681 2666.3 0.081 17.700
11 1920 1923.3 0.006 17.706
12 1349 1388.7 1.137 18.843
13 995 1003.7 0.076 18.919
14 691 726.1 1.701 20.620
15 558 525.8 1.967 22.587
16 370 381.2 0.326 22.913
17 263 276.5 0.663 23.576
18 189 200.8 0.697 24.273
19 143 146.0 0.061 24.334
20 98 106.2 0.635 24.969
21 266 287.1 1.553 26.522
Chisq= 26.52 for 20 degrees of freedom, p= 0.85074
SUMMARY of craptest
p-value for no. of wins: 0.891597
p-value for throws/game: 0.850745
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_13:31
No. of wins: Observed Expected
98877 98585.9
z-score= 1.302, pvalue=0.90357
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66718 66666.7 0.040 0.040
2 37619 37654.3 0.033 0.073
3 26882 26954.7 0.196 0.269
4 19174 19313.5 1.007 1.276
5 14123 13851.4 5.325 6.601
6 9884 9943.5 0.357 6.957
7 7204 7145.0 0.487 7.444
8 5033 5139.1 2.189 9.633
9 3723 3699.9 0.145 9.778
10 2691 2666.3 0.229 10.007
11 1865 1923.3 1.769 11.776
12 1411 1388.7 0.357 12.133
13 993 1003.7 0.114 12.247
14 745 726.1 0.490 12.737
15 485 525.8 3.171 15.908
16 374 381.2 0.134 16.042
17 302 276.5 2.344 18.386
18 211 200.8 0.515 18.901
19 144 146.0 0.027 18.928
20 110 106.2 0.135 19.063
21 309 287.1 1.668 20.732
Chisq= 20.73 for 20 degrees of freedom, p= 0.58692
SUMMARY of craptest
p-value for no. of wins: 0.903568
p-value for throws/game: 0.586921
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0027,0.0047,0.0112,0.0142,0.0167,0.0191,0.0223,0.0258,0.0265,0.0300,
0.0303,0.0306,0.0352,0.0363,0.0413,0.0431,0.0472,0.0489,0.0545,0.0550,
0.0551,0.0560,0.0681,0.0806,0.0868,0.0919,0.0930,0.0957,0.0982,0.1240,
0.1250,0.1256,0.1332,0.1334,0.1342,0.1373,0.1401,0.1426,0.1426,0.1459,
0.1474,0.1580,0.1587,0.1666,0.1696,0.1744,0.1769,0.1778,0.1906,0.2019,
0.2039,0.2046,0.2059,0.2106,0.2135,0.2185,0.2188,0.2189,0.2248,0.2257,
0.2291,0.2292,0.2304,0.2306,0.2324,0.2325,0.2341,0.2355,0.2356,0.2373,
0.2398,0.2454,0.2480,0.2485,0.2554,0.2594,0.2616,0.2633,0.2698,0.2704,
0.2705,0.2717,0.2744,0.2753,0.2784,0.2788,0.2796,0.2963,0.3142,0.3216,
0.3232,0.3233,0.3285,0.3331,0.3366,0.3368,0.3445,0.3454,0.3493,0.3524,
0.3525,0.3574,0.3639,0.3753,0.3783,0.3786,0.3792,0.3849,0.3868,0.3979,
0.4037,0.4037,0.4063,0.4071,0.4162,0.4163,0.4197,0.4205,0.4225,0.4312,
0.4352,0.4413,0.4449,0.4463,0.4573,0.4577,0.4585,0.4620,0.4625,0.4637,
0.4652,0.4698,0.4698,0.4698,0.4734,0.4752,0.4796,0.4818,0.4839,0.4878,
0.4927,0.4957,0.4996,0.5062,0.5104,0.5184,0.5284,0.5349,0.5391,0.5440,
0.5567,0.5575,0.5594,0.5637,0.5651,0.5680,0.5702,0.5704,0.5810,0.5814,
0.5829,0.5830,0.5835,0.5869,0.5903,0.5939,0.5972,0.6000,0.6017,0.6109,
0.6156,0.6175,0.6217,0.6227,0.6253,0.6300,0.6424,0.6433,0.6450,0.6520,
0.6600,0.6601,0.6630,0.6661,0.6775,0.6935,0.7011,0.7014,0.7079,0.7081,
0.7171,0.7182,0.7254,0.7272,0.7300,0.7315,0.7360,0.7368,0.7387,0.7490,
0.7507,0.7510,0.7576,0.7599,0.7620,0.7622,0.7636,0.7673,0.7697,0.7717,
0.7734,0.7755,0.7812,0.7812,0.7916,0.7920,0.7970,0.7993,0.8005,0.8090,
0.8097,0.8147,0.8164,0.8181,0.8234,0.8264,0.8327,0.8410,0.8426,0.8505,
0.8507,0.8596,0.8596,0.8612,0.8634,0.8637,0.8663,0.8724,0.8772,0.8871,
0.8880,0.8909,0.8916,0.8946,0.8966,0.8982,0.9015,0.9030,0.9036,0.9115,
0.9149,0.9179,0.9239,0.9261,0.9297,0.9415,0.9512,0.9524,0.9648,0.9690,
0.9738,0.9743,0.9760,0.9803,0.9826,0.9908,0.9950,0.9982,0.9987,
Overall p-value after applying KStest on 269 p-values = 0.873209
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.