RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.52 18.5360 0.644196
2 to 25 15.77 11.3401 0.161653
3 to 26 15.82 14.6340 0.378178
4 to 27 15.49 17.6031 0.585717
5 to 28 15.72 20.5859 0.754640
6 to 29 15.87 19.5755 0.703486
7 to 30 15.59 20.3301 0.742305
8 to 31 15.56 17.8052 0.598770
9 to 32 15.81 21.4057 0.791335
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.225054
Tough bday spacings test for dh-ranFile-2018-07-03_02:31: 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 7 36 87 94 95 76 45 35 15 6 4
(O-E)^2/E 0.5 0.0 2.6 0.1 0.1 0.1 1.0 0.9 0.0 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.312, p= 0.131
RESULTS OF GCD FOR dh-ranFile-2018-07-03_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.786774
p-value, dist. of gcd's: 0.545065
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.733 0.545 0.218 0.889 0.887 0.416 0.058 0.350
Bits 8 to 15---> 0.701 0.864 0.376 0.769 0.553 0.752 0.539 0.464
Bits 16 to 23---> 0.236 0.387 0.540 0.418 0.269 0.775 1.000 0.120
Bits 24 to 31---> 0.609 0.128 0.356 0.084 0.390 0.445 0.810 0.871
KS test for the above 32 p values: 0.314
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_02:31,
p-values for 5 runs: 0.9349, 0.0809, 0.5844, 0.6678, 0.1621
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 229 211.4 1.462 1.462
r= 29 5012 5134.0 2.900 4.362
r= 30 23094 23103.0 0.004 4.365
r= 31 11665 11551.5 1.115 5.480
chi-square = 5.480 with df = 3; p-value = 0.860
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 185 211.4 3.301 3.301
r= 30 5229 5134.0 1.757 5.059
r= 31 22956 23103.0 0.936 5.995
r= 32 11630 11551.5 0.533 6.528
chi-square = 6.528 with df = 3; p-value = 0.911
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_02:31
b-rank test for bits 1 to 8, p=0.37167
b-rank test for bits 2 to 9, p=0.84770
b-rank test for bits 3 to 10, p=0.27672
b-rank test for bits 4 to 11, p=0.66146
b-rank test for bits 5 to 12, p=0.99998
b-rank test for bits 6 to 13, p=0.99960
b-rank test for bits 7 to 14, p=0.70425
b-rank test for bits 8 to 15, p=0.92899
b-rank test for bits 9 to 16, p=0.84653
b-rank test for bits 10 to 17, p=0.50662
b-rank test for bits 11 to 18, p=0.00919
b-rank test for bits 12 to 19, p=0.09424
b-rank test for bits 13 to 20, p=0.28865
b-rank test for bits 14 to 21, p=0.40901
b-rank test for bits 15 to 22, p=0.08585
b-rank test for bits 16 to 23, p=0.73822
b-rank test for bits 17 to 24, p=0.27918
b-rank test for bits 18 to 25, p=0.67344
b-rank test for bits 19 to 26, p=0.28019
b-rank test for bits 20 to 27, p=0.06004
b-rank test for bits 21 to 28, p=0.69798
b-rank test for bits 22 to 29, p=0.46540
b-rank test for bits 23 to 30, p=0.57409
b-rank test for bits 24 to 31, p=0.79650
b-rank test for bits 25 to 32, p=0.94427
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 = 0.267267
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_02:31
(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 141701 -0.49 0.313217
2 141586 -0.76 0.224991
3 142067 0.37 0.643708
4 142186 0.65 0.740998
5 141806 -0.24 0.404613
6 142724 1.90 0.971508
7 141879 -0.07 0.471753
8 141458 -1.05 0.145825
9 141868 -0.10 0.461536
10 142216 0.72 0.763164
11 142557 1.51 0.934892
12 141898 -0.03 0.489440
13 142551 1.50 0.933093
14 141793 -0.27 0.392888
15 141417 -1.15 0.125009
16 141734 -0.41 0.341032
17 142914 2.35 0.990547
18 141872 -0.09 0.465249
19 141841 -0.16 0.436579
20 141657 -0.59 0.277744
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_02:31
Bits used No. missing words z-score p-value
23 to 32 141751 -0.5460 0.292545
22 to 31 141829 -0.2770 0.390890
21 to 30 141670 -0.8253 0.204608
20 to 29 141622 -0.9908 0.160893
19 to 28 142410 1.7264 0.957867
18 to 27 142433 1.8058 0.964522
17 to 26 142108 0.6851 0.753350
16 to 25 141999 0.3092 0.621418
15 to 24 142237 1.1299 0.870740
14 to 23 142013 0.3575 0.639635
13 to 22 142094 0.6368 0.737870
12 to 21 141856 -0.1839 0.427047
11 to 20 141933 0.0816 0.532526
10 to 19 142131 0.7644 0.777679
9 to 18 142019 0.3782 0.647349
8 to 17 142177 0.9230 0.821996
7 to 16 141888 -0.0736 0.470684
6 to 15 141876 -0.1149 0.454250
5 to 14 142351 1.5230 0.936121
4 to 13 141546 -1.2529 0.105128
3 to 12 141840 -0.2391 0.405526
2 to 11 142140 0.7954 0.786814
1 to 10 141830 -0.2736 0.392215
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_02:31
Bits used No. missing words z-score p-value
28 to 32 141716 -0.6554 0.256119
27 to 31 142366 1.5480 0.939193
26 to 30 141283 -2.1232 0.016871
25 to 29 141734 -0.5943 0.276143
24 to 28 142223 1.0633 0.856174
23 to 27 141565 -1.1672 0.121561
22 to 26 141863 -0.1571 0.437602
21 to 25 142013 0.3514 0.637365
20 to 24 142218 1.0463 0.852298
19 to 23 141902 -0.0248 0.490088
18 to 22 141784 -0.4248 0.335474
17 to 21 141576 -1.1299 0.129252
16 to 20 142001 0.3107 0.622003
15 to 19 141370 -1.8282 0.033757
14 to 18 142285 1.2735 0.898572
13 to 17 142036 0.4294 0.666180
12 to 16 142003 0.3175 0.624578
11 to 15 141669 -0.8147 0.207628
10 to 14 141498 -1.3943 0.081608
9 to 13 142082 0.5853 0.720834
8 to 12 141275 -2.1503 0.015767
7 to 11 142004 0.3209 0.625863
6 to 10 142044 0.4565 0.675988
5 to 9 141759 -0.5096 0.305168
4 to 8 141563 -1.1740 0.120198
3 to 7 141944 0.1175 0.546778
2 to 6 141951 0.1413 0.556166
1 to 5 141614 -1.0011 0.158385
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_02:31
Bits used No. missing words z-score p-value
31 to 32 142116 0.6096 0.728952
30 to 31 142300 1.1524 0.875426
29 to 30 142148 0.7040 0.759297
28 to 29 142090 0.5329 0.702966
27 to 28 141949 0.1170 0.546578
26 to 27 142368 1.3530 0.911974
25 to 26 142018 0.3206 0.625728
24 to 25 141858 -0.1514 0.439824
23 to 24 141941 0.0934 0.537216
22 to 23 141762 -0.4346 0.331926
21 to 22 141407 -1.4818 0.069197
20 to 21 142049 0.4120 0.659832
19 to 20 141592 -0.9361 0.174617
18 to 19 141503 -1.1986 0.115339
17 to 18 141421 -1.4405 0.074863
16 to 17 141665 -0.7207 0.235536
15 to 16 141495 -1.2222 0.110814
14 to 15 142429 1.5329 0.937356
13 to 14 142044 0.3973 0.654411
12 to 13 141719 -0.5614 0.287247
11 to 12 141943 0.0993 0.539559
10 to 11 142184 0.8102 0.791098
9 to 10 142343 1.2793 0.899598
8 to 9 141626 -0.8358 0.201639
7 to 8 141602 -0.9066 0.182315
6 to 7 142181 0.8014 0.788546
5 to 6 141528 -1.1249 0.130323
4 to 5 142196 0.8456 0.801122
3 to 4 141178 -2.1573 0.015491
2 to 3 142394 1.4297 0.923599
1 to 2 141701 -0.6145 0.269428
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2448.08 -0.734 0.231411
Test results for specific bytes for dh-ranFile-2018-07-03_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2655.71 2.202 0.986172
2 to 9 2347.93 -2.151 0.015755
3 to 10 2462.26 -0.534 0.296759
4 to 11 2497.20 -0.040 0.484211
5 to 12 2551.77 0.732 0.767960
6 to 13 2547.74 0.675 0.750229
7 to 14 2509.16 0.130 0.551555
8 to 15 2415.35 -1.197 0.115616
9 to 16 2584.30 1.192 0.883392
10 to 17 2482.69 -0.245 0.403312
11 to 18 2385.20 -1.623 0.052245
12 to 19 2458.30 -0.590 0.277678
13 to 20 2476.27 -0.336 0.368589
14 to 21 2503.87 0.055 0.521838
15 to 22 2476.66 -0.330 0.370659
16 to 23 2466.28 -0.477 0.316710
17 to 24 2523.83 0.337 0.631957
18 to 25 2448.87 -0.723 0.234834
19 to 26 2519.51 0.276 0.608696
20 to 27 2408.46 -1.295 0.097741
21 to 28 2412.88 -1.232 0.108964
22 to 29 2483.63 -0.231 0.408466
23 to 30 2483.53 -0.233 0.407908
24 to 31 2429.10 -1.003 0.158024
25 to 32 2428.70 -1.008 0.156661
CDPARK for dh-ranFile-2018-07-03_02:31: 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
3570 2.1461 0.984068
3559 1.6438 0.949895
3537 0.6393 0.738676
3501 -1.0046 0.157553
3499 -1.0959 0.136563
3523 0.0000 0.500000
3541 0.8219 0.794438
3504 -0.8676 0.192812
3530 0.3196 0.625377
3507 -0.7306 0.232514
Square side=100, avg. no. parked=3527.10 sample std.=23.63
p-value of the KSTEST for those 10 p-values: 0.727449
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_02:31
0.8095,0.0401,0.7975,0.4899,0.6817,0.3882,0.4331,0.8462,0.1970,0.2605,
The KS test for those 10 p-values: 0.968855
The 3DSPHERES test for dh-ranFile-2018-07-03_02:31
sample no r^3 equiv. uni.
1 22.947 0.534624
2 24.327 0.555537
3 10.602 0.297699
4 16.266 0.418532
5 1.908 0.061616
6 90.970 0.951797
7 11.175 0.310987
8 31.444 0.649411
9 49.304 0.806688
10 89.810 0.949896
11 38.442 0.722347
12 35.454 0.693270
13 2.348 0.075297
14 0.940 0.030842
15 0.400 0.013260
16 106.808 0.971569
17 9.640 0.274826
18 2.465 0.078881
19 49.911 0.810565
20 48.304 0.800138
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.559221
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 -2.3 -0.4 0.2 -1.0
-0.9 -0.3 -1.2 -0.7 -1.3 -1.7
0.8 -1.9 -1.2 0.7 -0.7 -0.2
0.2 2.2 -0.4 0.8 0.7 -0.8
1.8 1.3 0.4 1.2 1.2 -0.2
1.2 1.3 -0.2 0.1 0.9 -1.4
-0.9 0.5 -0.4 -0.7 2.4 -1.0
-1.1
Chi-square with 42 degrees of freedom:52.502282
z-score=1.145893, p-value=0.871538
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_02:31
Test no p-value
1 0.506609
2 0.284221
3 0.037421
4 0.063888
5 0.218923
6 0.898541
7 0.339260
8 0.693993
9 0.199840
10 0.838871
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.541017
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_02:31:
(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 66874 0.64 66664 0.00
3 25000.00 24856 0.83 24954 0.08
4 6666.67 6552 1.97 6701 0.18
5 1388.89 1458 3.44 1401 0.11
6 238.10 224 0.83 241 0.04
7 34.72 30 0.64 35 0.00
8 4.96 5 0.00 3 0.77
p=0.78723 p=0.02211
Number of rngs required: 687246, p-value: 0.089
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_02:31
No. of wins: Observed Expected
98300 98585.9
z-score=-1.279, pvalue=0.10053
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66765 66666.7 0.145 0.145
2 37849 37654.3 1.007 1.152
3 26991 26954.7 0.049 1.200
4 19154 19313.5 1.317 2.517
5 13849 13851.4 0.000 2.517
6 9902 9943.5 0.174 2.691
7 7201 7145.0 0.439 3.129
8 5194 5139.1 0.587 3.717
9 3616 3699.9 1.901 5.618
10 2593 2666.3 2.015 7.632
11 1921 1923.3 0.003 7.635
12 1386 1388.7 0.005 7.641
13 971 1003.7 1.066 8.707
14 725 726.1 0.002 8.709
15 520 525.8 0.065 8.774
16 401 381.2 1.034 9.807
17 239 276.5 5.096 14.903
18 200 200.8 0.003 14.907
19 141 146.0 0.170 15.077
20 102 106.2 0.167 15.244
21 280 287.1 0.176 15.420
Chisq= 15.42 for 20 degrees of freedom, p= 0.24813
SUMMARY of craptest
p-value for no. of wins: 0.100532
p-value for throws/game: 0.248128
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_02:31
No. of wins: Observed Expected
98284 98585.9
z-score=-1.350, pvalue=0.08849
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66635 66666.7 0.015 0.015
2 37578 37654.3 0.155 0.170
3 26963 26954.7 0.003 0.172
4 19333 19313.5 0.020 0.192
5 13962 13851.4 0.883 1.075
6 9894 9943.5 0.247 1.322
7 7139 7145.0 0.005 1.327
8 5148 5139.1 0.016 1.342
9 3661 3699.9 0.408 1.751
10 2586 2666.3 2.418 4.169
11 1928 1923.3 0.011 4.180
12 1386 1388.7 0.005 4.185
13 1065 1003.7 3.742 7.927
14 764 726.1 1.974 9.901
15 530 525.8 0.033 9.934
16 384 381.2 0.021 9.956
17 277 276.5 0.001 9.956
18 182 200.8 1.765 11.722
19 168 146.0 3.320 15.042
20 102 106.2 0.167 15.209
21 315 287.1 2.708 17.918
Chisq= 17.92 for 20 degrees of freedom, p= 0.40717
SUMMARY of craptest
p-value for no. of wins: 0.088494
p-value for throws/game: 0.407171
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0092,0.0133,0.0155,0.0158,0.0158,0.0169,0.0221,0.0308,0.0338,0.0374,
0.0401,0.0522,0.0583,0.0600,0.0616,0.0639,0.0692,0.0749,0.0753,0.0789,
0.0809,0.0816,0.0844,0.0858,0.0885,0.0888,0.0942,0.0977,0.1005,0.1051,
0.1090,0.1108,0.1153,0.1156,0.1196,0.1202,0.1216,0.1250,0.1283,0.1293,
0.1303,0.1306,0.1366,0.1458,0.1567,0.1576,0.1580,0.1584,0.1609,0.1617,
0.1621,0.1746,0.1823,0.1928,0.1970,0.1998,0.2016,0.2046,0.2076,0.2180,
0.2189,0.2250,0.2251,0.2314,0.2325,0.2348,0.2355,0.2362,0.2481,0.2561,
0.2605,0.2673,0.2688,0.2694,0.2748,0.2761,0.2767,0.2777,0.2777,0.2792,
0.2802,0.2842,0.2872,0.2887,0.2925,0.2968,0.2977,0.3052,0.3110,0.3132,
0.3137,0.3167,0.3319,0.3355,0.3393,0.3410,0.3499,0.3565,0.3686,0.3707,
0.3717,0.3756,0.3782,0.3867,0.3882,0.3904,0.3909,0.3922,0.3929,0.4033,
0.4046,0.4055,0.4072,0.4079,0.4085,0.4090,0.4158,0.4178,0.4185,0.4270,
0.4331,0.4366,0.4376,0.4398,0.4452,0.4542,0.4615,0.4643,0.4652,0.4654,
0.4707,0.4718,0.4842,0.4894,0.4899,0.4901,0.5000,0.5066,0.5066,0.5218,
0.5325,0.5346,0.5372,0.5385,0.5396,0.5403,0.5410,0.5449,0.5451,0.5466,
0.5468,0.5516,0.5534,0.5555,0.5562,0.5592,0.5741,0.5844,0.5857,0.5988,
0.6087,0.6088,0.6214,0.6220,0.6246,0.6254,0.6257,0.6259,0.6320,0.6374,
0.6396,0.6437,0.6442,0.6473,0.6494,0.6544,0.6598,0.6615,0.6662,0.6678,
0.6734,0.6760,0.6817,0.6933,0.6940,0.6980,0.7008,0.7030,0.7035,0.7042,
0.7208,0.7223,0.7274,0.7290,0.7334,0.7379,0.7382,0.7387,0.7410,0.7423,
0.7502,0.7516,0.7533,0.7546,0.7593,0.7632,0.7680,0.7693,0.7750,0.7777,
0.7868,0.7868,0.7872,0.7885,0.7911,0.7913,0.7944,0.7965,0.7975,0.8001,
0.8011,0.8067,0.8095,0.8101,0.8106,0.8220,0.8389,0.8462,0.8465,0.8477,
0.8523,0.8562,0.8602,0.8638,0.8707,0.8711,0.8715,0.8754,0.8834,0.8870,
0.8891,0.8985,0.8986,0.8996,0.9114,0.9120,0.9236,0.9290,0.9331,0.9349,
0.9349,0.9361,0.9374,0.9392,0.9443,0.9499,0.9499,0.9518,0.9579,0.9645,
0.9689,0.9715,0.9716,0.9841,0.9862,0.9905,0.9996,0.9997,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.956398
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.