RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.62 21.7305 0.804692
2 to 25 15.37 23.9784 0.879976
3 to 26 15.87 10.6975 0.128150
4 to 27 15.67 11.1739 0.152617
5 to 28 15.74 18.0841 0.616447
6 to 29 15.97 12.9834 0.262700
7 to 30 15.75 18.0798 0.616176
8 to 31 15.63 15.4352 0.435833
9 to 32 16.19 17.8430 0.601192
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.939756
Tough bday spacings test for dh-ranFile-2018-06-21_03:31: 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 5 45 63 89 94 77 64 36 17 7 3
(O-E)^2/E 1.9 1.9 1.4 0.8 0.1 0.0 2.7 1.3 0.3 0.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.790, p= 0.626
RESULTS OF GCD FOR dh-ranFile-2018-06-21_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.261341
p-value, dist. of gcd's: 0.687851
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.978 0.703 0.524 0.587 0.620 0.488 0.979 0.648
Bits 8 to 15---> 0.931 0.203 0.117 0.023 0.218 0.635 0.158 0.897
Bits 16 to 23---> 0.865 0.229 0.423 0.890 0.702 0.040 0.228 0.791
Bits 24 to 31---> 0.507 0.908 0.413 0.505 0.975 0.832 0.358 0.399
KS test for the above 32 p values: 0.554
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_03:31,
p-values for 5 runs: 0.6662, 0.8986, 0.1955, 0.8405, 0.3015
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5234 5134.0 1.947 3.222
r= 30 22965 23103.0 0.825 4.047
r= 31 11606 11551.5 0.257 4.304
chi-square = 4.304 with df = 3; p-value = 0.770
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5136 5134.0 0.001 0.206
r= 31 23077 23103.0 0.029 0.235
r= 32 11569 11551.5 0.026 0.261
chi-square = 0.261 with df = 3; p-value = 0.033
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_03:31
b-rank test for bits 1 to 8, p=0.73804
b-rank test for bits 2 to 9, p=0.88354
b-rank test for bits 3 to 10, p=0.50041
b-rank test for bits 4 to 11, p=0.47816
b-rank test for bits 5 to 12, p=0.20815
b-rank test for bits 6 to 13, p=0.69715
b-rank test for bits 7 to 14, p=0.38805
b-rank test for bits 8 to 15, p=0.50321
b-rank test for bits 9 to 16, p=0.69709
b-rank test for bits 10 to 17, p=0.03293
b-rank test for bits 11 to 18, p=0.31467
b-rank test for bits 12 to 19, p=0.91701
b-rank test for bits 13 to 20, p=0.67622
b-rank test for bits 14 to 21, p=0.08662
b-rank test for bits 15 to 22, p=0.04010
b-rank test for bits 16 to 23, p=0.65792
b-rank test for bits 17 to 24, p=0.95329
b-rank test for bits 18 to 25, p=0.99028
b-rank test for bits 19 to 26, p=0.72604
b-rank test for bits 20 to 27, p=0.62386
b-rank test for bits 21 to 28, p=0.60959
b-rank test for bits 22 to 29, p=0.76091
b-rank test for bits 23 to 30, p=0.88822
b-rank test for bits 24 to 31, p=0.42558
b-rank test for bits 25 to 32, p=0.37810
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 = 0.385537
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_03:31
(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 141859 -0.12 0.453195
3 141589 -0.75 0.227099
4 141593 -0.74 0.229927
5 142277 0.86 0.804841
6 141807 -0.24 0.405518
7 141775 -0.31 0.376816
8 141384 -1.23 0.109835
9 142138 0.53 0.703425
10 141402 -1.19 0.117939
11 142035 0.29 0.615476
12 141607 -0.71 0.239976
13 141028 -2.06 0.019738
14 142359 1.05 0.853286
15 142505 1.39 0.918001
16 141683 -0.53 0.298469
17 142513 1.41 0.920796
18 141871 -0.09 0.464320
19 141265 -1.51 0.066105
20 141546 -0.85 0.197968
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_03:31
Bits used No. missing words z-score p-value
23 to 32 141617 -1.0080 0.156719
22 to 31 141733 -0.6080 0.271582
21 to 30 141595 -1.0839 0.139205
20 to 29 142433 1.8058 0.964522
19 to 28 142234 1.1196 0.868548
18 to 27 141375 -1.8425 0.032700
17 to 26 141433 -1.6425 0.050241
16 to 25 141874 -0.1218 0.451518
15 to 24 142181 0.9368 0.825568
14 to 23 141888 -0.0736 0.470684
13 to 22 141521 -1.3391 0.090274
12 to 21 142108 0.6851 0.753350
11 to 20 141692 -0.7494 0.226804
10 to 19 141747 -0.5598 0.287822
9 to 18 141182 -2.5080 0.006070
8 to 17 142308 1.3747 0.915392
7 to 16 141973 0.2196 0.586890
6 to 15 141627 -0.9736 0.165140
5 to 14 141793 -0.4011 0.344159
4 to 13 141669 -0.8287 0.203630
3 to 12 141989 0.2747 0.608236
2 to 11 141844 -0.2253 0.410882
1 to 10 141826 -0.2873 0.386924
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_03:31
Bits used No. missing words z-score p-value
28 to 32 141596 -1.0621 0.144087
27 to 31 142104 0.6599 0.745341
26 to 30 141908 -0.0045 0.498201
25 to 29 142210 1.0192 0.845951
24 to 28 141505 -1.3706 0.085248
23 to 27 141358 -1.8689 0.030817
22 to 26 142153 0.8260 0.795598
21 to 25 141837 -0.2452 0.403156
20 to 24 141514 -1.3401 0.090106
19 to 23 142322 1.3989 0.919076
18 to 22 142433 1.7752 0.962064
17 to 21 141944 0.1175 0.546778
16 to 20 141941 0.1074 0.542747
15 to 19 142212 1.0260 0.847554
14 to 18 142084 0.5921 0.723109
13 to 17 142283 1.2667 0.897365
12 to 16 142232 1.0938 0.862978
11 to 15 142112 0.6870 0.753964
10 to 14 141981 0.2429 0.595978
9 to 13 141791 -0.4011 0.344166
8 to 12 141896 -0.0452 0.481979
7 to 11 141586 -1.0960 0.136532
6 to 10 141376 -1.8079 0.035311
5 to 9 141875 -0.1164 0.453679
4 to 8 142059 0.5074 0.694048
3 to 7 142230 1.0870 0.861485
2 to 6 141627 -0.9571 0.169271
1 to 5 141863 -0.1571 0.437602
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_03:31
Bits used No. missing words z-score p-value
31 to 32 142116 0.6096 0.728952
30 to 31 141047 -2.5437 0.005484
29 to 30 142091 0.5359 0.703986
28 to 29 142105 0.5772 0.718097
27 to 28 142047 0.4061 0.657668
26 to 27 141286 -1.8387 0.032977
25 to 26 142112 0.5978 0.725029
24 to 25 142068 0.4681 0.680127
23 to 24 142054 0.4268 0.665221
22 to 23 142320 1.2114 0.887132
21 to 22 141850 -0.1750 0.430534
20 to 21 142325 1.2262 0.889932
19 to 20 141811 -0.2901 0.385886
18 to 19 142091 0.5359 0.703986
17 to 18 141763 -0.4317 0.332997
16 to 17 142027 0.3471 0.635745
15 to 16 142309 1.1790 0.880794
14 to 15 141718 -0.5644 0.286243
13 to 14 141799 -0.3255 0.372418
12 to 13 142064 0.4563 0.675896
11 to 12 141539 -1.0924 0.137325
10 to 11 141825 -0.2488 0.401773
9 to 10 142000 0.2675 0.605444
8 to 9 141940 0.0905 0.536044
7 to 8 141957 0.1406 0.555915
6 to 7 142475 1.6686 0.952406
5 to 6 142188 0.8220 0.794472
4 to 5 141596 -0.9243 0.177671
3 to 4 141617 -0.8623 0.194253
2 to 3 141919 0.0285 0.511378
1 to 2 141839 -0.2075 0.417824
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2427.63 -1.023 0.153052
Test results for specific bytes for dh-ranFile-2018-06-21_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2292.15 -2.939 0.001644
2 to 9 2463.33 -0.519 0.302042
3 to 10 2593.67 1.325 0.907354
4 to 11 2596.53 1.365 0.913892
5 to 12 2664.10 2.321 0.989849
6 to 13 2434.31 -0.929 0.176443
7 to 14 2689.99 2.687 0.996394
8 to 15 2540.18 0.568 0.715045
9 to 16 2509.35 0.132 0.552571
10 to 17 2563.56 0.899 0.815632
11 to 18 2468.40 -0.447 0.327478
12 to 19 2536.62 0.518 0.697730
13 to 20 2617.91 1.667 0.952289
14 to 21 2623.99 1.754 0.960242
15 to 22 2456.53 -0.615 0.269338
16 to 23 2492.37 -0.108 0.457062
17 to 24 2437.93 -0.878 0.190038
18 to 25 2407.04 -1.315 0.094305
19 to 26 2463.96 -0.510 0.305135
20 to 27 2556.27 0.796 0.786918
21 to 28 2536.33 0.514 0.696285
22 to 29 2547.68 0.674 0.749955
23 to 30 2588.79 1.256 0.895386
24 to 31 2475.92 -0.341 0.366718
25 to 32 2601.26 1.432 0.923937
CDPARK for dh-ranFile-2018-06-21_03:31: 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
3490 -1.5068 0.065925
3531 0.3653 0.642555
3500 -1.0502 0.146807
3532 0.4110 0.659449
3528 0.2283 0.590298
3517 -0.2740 0.392053
3514 -0.4110 0.340551
3526 0.1370 0.554479
3499 -1.0959 0.136563
3526 0.1370 0.554479
Square side=100, avg. no. parked=3516.30 sample std.=14.32
p-value of the KSTEST for those 10 p-values: 0.338596
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_03:31
0.2719,0.3798,0.8882,0.0225,0.7751,0.2365,0.9843,0.5867,0.8359,0.8786,
The KS test for those 10 p-values: 0.435926
The 3DSPHERES test for dh-ranFile-2018-06-21_03:31
sample no r^3 equiv. uni.
1 27.266 0.597025
2 6.676 0.199520
3 9.159 0.263099
4 6.684 0.199713
5 63.816 0.880828
6 35.327 0.691977
7 18.303 0.456711
8 156.396 0.994556
9 28.767 0.616684
10 102.753 0.967454
11 13.596 0.364413
12 30.433 0.637394
13 33.102 0.668263
14 1.288 0.042039
15 91.527 0.952684
16 14.170 0.376456
17 21.863 0.517491
18 3.248 0.102603
19 7.225 0.214018
20 1.809 0.058528
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.868804
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 1.8 0.6 -0.5 -0.4 0.9
1.4 -1.0 -0.3 0.6 0.1 -0.6
-1.5 1.7 -0.2 -1.0 0.0 -0.9
1.1 0.7 0.3 -0.1 1.3 -2.0
0.4 1.4 -0.9 -0.8 -0.6 -0.7
0.3 -0.4 1.3 0.3 -0.9 0.8
0.3 0.8 -1.2 1.0 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:36.490384
z-score=-0.601148, p-value=0.289104
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_03:31
Test no p-value
1 0.073571
2 0.036578
3 0.694996
4 0.002691
5 0.003350
6 0.982256
7 0.065258
8 0.060320
9 0.272411
10 0.578297
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000852
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_03:31:
(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 66687 0.01 66722 0.05
3 25000.00 24813 1.40 25042 0.07
4 6666.67 6798 2.59 6603 0.61
5 1388.89 1401 0.11 1376 0.12
6 238.10 253 0.93 225 0.72
7 34.72 41 1.14 29 0.94
8 4.96 6 0.22 2 1.77
p=0.61850 p=0.36025
Number of rngs required: 687665, p-value: 0.197
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_03:31
No. of wins: Observed Expected
98673 98585.9
z-score= 0.390, pvalue=0.65164
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67376 66666.7 7.547 7.547
2 37664 37654.3 0.002 7.550
3 26648 26954.7 3.490 11.040
4 19120 19313.5 1.938 12.978
5 13874 13851.4 0.037 13.015
6 9799 9943.5 2.101 15.116
7 7075 7145.0 0.686 15.802
8 5049 5139.1 1.579 17.381
9 3742 3699.9 0.480 17.861
10 2615 2666.3 0.987 18.848
11 1930 1923.3 0.023 18.871
12 1424 1388.7 0.895 19.766
13 938 1003.7 4.302 24.069
14 767 726.1 2.299 26.368
15 513 525.8 0.313 26.681
16 386 381.2 0.062 26.743
17 302 276.5 2.344 29.087
18 214 200.8 0.864 29.951
19 159 146.0 1.160 31.111
20 96 106.2 0.982 32.094
21 309 287.1 1.668 33.762
Chisq= 33.76 for 20 degrees of freedom, p= 0.97222
SUMMARY of craptest
p-value for no. of wins: 0.651638
p-value for throws/game: 0.972219
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_03:31
No. of wins: Observed Expected
98650 98585.9
z-score= 0.287, pvalue=0.61290
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66780 66666.7 0.193 0.193
2 37559 37654.3 0.241 0.434
3 26688 26954.7 2.639 3.073
4 19659 19313.5 6.182 9.255
5 13997 13851.4 1.530 10.786
6 9927 9943.5 0.028 10.813
7 7066 7145.0 0.874 11.687
8 5064 5139.1 1.097 12.784
9 3707 3699.9 0.014 12.798
10 2644 2666.3 0.186 12.984
11 1919 1923.3 0.010 12.994
12 1390 1388.7 0.001 12.995
13 1001 1003.7 0.007 13.002
14 715 726.1 0.171 13.173
15 483 525.8 3.490 16.663
16 400 381.2 0.932 17.595
17 276 276.5 0.001 17.596
18 186 200.8 1.095 18.691
19 152 146.0 0.248 18.939
20 102 106.2 0.167 19.106
21 285 287.1 0.016 19.122
Chisq= 19.12 for 20 degrees of freedom, p= 0.48607
SUMMARY of craptest
p-value for no. of wins: 0.612897
p-value for throws/game: 0.486072
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0009,0.0016,0.0027,0.0034,0.0055,0.0061,0.0197,0.0225,0.0229,0.0308,
0.0327,0.0329,0.0329,0.0330,0.0353,0.0366,0.0401,0.0405,0.0420,0.0502,
0.0585,0.0603,0.0653,0.0659,0.0661,0.0736,0.0852,0.0866,0.0901,0.0903,
0.0943,0.1026,0.1098,0.1168,0.1179,0.1282,0.1365,0.1366,0.1373,0.1392,
0.1441,0.1468,0.1526,0.1531,0.1567,0.1579,0.1651,0.1693,0.1764,0.1777,
0.1900,0.1943,0.1955,0.1967,0.1980,0.1995,0.1997,0.2031,0.2036,0.2082,
0.2140,0.2177,0.2268,0.2271,0.2279,0.2286,0.2299,0.2365,0.2400,0.2613,
0.2627,0.2631,0.2693,0.2716,0.2719,0.2724,0.2862,0.2878,0.2891,0.2985,
0.3015,0.3020,0.3051,0.3147,0.3275,0.3330,0.3386,0.3406,0.3442,0.3442,
0.3578,0.3602,0.3644,0.3667,0.3724,0.3765,0.3768,0.3781,0.3798,0.3855,
0.3859,0.3869,0.3881,0.3921,0.3987,0.4018,0.4032,0.4055,0.4109,0.4134,
0.4178,0.4229,0.4256,0.4305,0.4358,0.4359,0.4376,0.4515,0.4532,0.4537,
0.4567,0.4571,0.4643,0.4707,0.4782,0.4820,0.4861,0.4878,0.4982,0.5004,
0.5032,0.5052,0.5071,0.5114,0.5175,0.5243,0.5360,0.5427,0.5468,0.5526,
0.5541,0.5545,0.5545,0.5559,0.5783,0.5867,0.5867,0.5869,0.5903,0.5960,
0.5970,0.6012,0.6054,0.6082,0.6096,0.6129,0.6155,0.6162,0.6164,0.6167,
0.6185,0.6199,0.6239,0.6259,0.6352,0.6357,0.6374,0.6426,0.6479,0.6516,
0.6577,0.6579,0.6594,0.6652,0.6662,0.6683,0.6759,0.6762,0.6801,0.6879,
0.6920,0.6940,0.6950,0.6963,0.6971,0.6972,0.6977,0.7023,0.7025,0.7034,
0.7040,0.7040,0.7150,0.7181,0.7231,0.7250,0.7260,0.7290,0.7380,0.7453,
0.7500,0.7533,0.7540,0.7609,0.7696,0.7751,0.7801,0.7869,0.7913,0.7945,
0.7956,0.8047,0.8048,0.8156,0.8256,0.8324,0.8359,0.8405,0.8460,0.8476,
0.8533,0.8615,0.8630,0.8653,0.8685,0.8688,0.8786,0.8800,0.8808,0.8808,
0.8835,0.8871,0.8882,0.8882,0.8898,0.8899,0.8954,0.8972,0.8974,0.8986,
0.9074,0.9082,0.9139,0.9154,0.9170,0.9180,0.9191,0.9208,0.9239,0.9311,
0.9398,0.9523,0.9524,0.9527,0.9533,0.9602,0.9621,0.9645,0.9675,0.9722,
0.9749,0.9778,0.9793,0.9823,0.9843,0.9898,0.9903,0.9946,0.9964,
Overall p-value after applying KStest on 269 p-values = 0.587903
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.