RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.05 11.3826 0.164002
2 to 25 15.80 14.1189 0.341329
3 to 26 15.88 17.5291 0.580889
4 to 27 16.11 15.0465 0.407865
5 to 28 15.83 10.2660 0.107914
6 to 29 15.68 14.6699 0.380752
7 to 30 15.77 26.1697 0.928576
8 to 31 15.54 19.3506 0.691215
9 to 32 15.60 16.8440 0.535016
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.858250
Tough bday spacings test for dh-ranFile-2018-07-10_04:31: 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 6 41 67 109 105 70 56 22 13 7 4
(O-E)^2/E 1.1 0.5 0.5 1.3 0.5 0.8 0.3 2.0 0.2 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.436, p= 0.316
RESULTS OF GCD FOR dh-ranFile-2018-07-10_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.873879
p-value, dist. of gcd's: 0.183167
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.685 0.894 0.677 0.808 0.587 0.029 0.247 0.147
Bits 8 to 15---> 0.909 0.219 0.721 0.816 0.923 0.174 0.370 0.676
Bits 16 to 23---> 0.091 0.521 0.869 0.725 0.560 0.509 0.173 0.557
Bits 24 to 31---> 0.073 0.199 0.901 0.025 0.705 0.126 0.191 0.456
KS test for the above 32 p values: 0.232
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_04:31,
p-values for 5 runs: 0.5919, 0.7694, 0.5686, 0.3229, 0.2518
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5102 5134.0 0.200 3.058
r= 30 23113 23103.0 0.004 3.062
r= 31 11549 11551.5 0.001 3.063
chi-square = 3.063 with df = 3; p-value = 0.618
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5121 5134.0 0.033 0.061
r= 31 23026 23103.0 0.257 0.318
r= 32 11644 11551.5 0.740 1.058
chi-square = 1.058 with df = 3; p-value = 0.213
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_04:31
b-rank test for bits 1 to 8, p=0.23117
b-rank test for bits 2 to 9, p=0.17556
b-rank test for bits 3 to 10, p=0.05206
b-rank test for bits 4 to 11, p=0.62532
b-rank test for bits 5 to 12, p=0.00614
b-rank test for bits 6 to 13, p=0.28132
b-rank test for bits 7 to 14, p=0.76220
b-rank test for bits 8 to 15, p=0.92114
b-rank test for bits 9 to 16, p=0.59021
b-rank test for bits 10 to 17, p=0.16624
b-rank test for bits 11 to 18, p=0.54214
b-rank test for bits 12 to 19, p=0.75082
b-rank test for bits 13 to 20, p=0.39871
b-rank test for bits 14 to 21, p=0.04415
b-rank test for bits 15 to 22, p=0.30704
b-rank test for bits 16 to 23, p=0.10525
b-rank test for bits 17 to 24, p=0.07224
b-rank test for bits 18 to 25, p=0.10170
b-rank test for bits 19 to 26, p=0.69985
b-rank test for bits 20 to 27, p=0.15159
b-rank test for bits 21 to 28, p=0.50523
b-rank test for bits 22 to 29, p=0.43804
b-rank test for bits 23 to 30, p=0.81926
b-rank test for bits 24 to 31, p=0.64764
b-rank test for bits 25 to 32, p=0.07851
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 = 0.047557
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_04:31
(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 142080 0.40 0.654966
2 141306 -1.41 0.079322
3 141984 0.17 0.569249
4 142417 1.19 0.882217
5 141850 -0.14 0.444875
6 141553 -0.83 0.202550
7 141926 0.04 0.515534
8 142342 1.01 0.843971
9 142687 1.82 0.965390
10 141934 0.06 0.522982
11 141633 -0.65 0.259259
12 142499 1.38 0.915857
13 141435 -1.11 0.133877
14 141754 -0.36 0.358332
15 141865 -0.10 0.458753
16 141505 -0.94 0.172407
17 142021 0.26 0.602920
18 141812 -0.23 0.410054
19 142599 1.61 0.946451
20 142281 0.87 0.807409
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_04:31
Bits used No. missing words z-score p-value
23 to 32 141894 -0.0529 0.478921
22 to 31 142158 0.8575 0.804411
21 to 30 142252 1.1816 0.881322
20 to 29 142089 0.6196 0.732224
19 to 28 142762 2.9402 0.998360
18 to 27 141313 -2.0563 0.019876
17 to 26 141714 -0.6736 0.250298
16 to 25 141323 -2.0218 0.021597
15 to 24 141814 -0.3287 0.371182
14 to 23 141982 0.2506 0.598933
13 to 22 141902 -0.0253 0.489918
12 to 21 141779 -0.4494 0.326567
11 to 20 142396 1.6782 0.953343
10 to 19 141526 -1.3218 0.093113
9 to 18 141596 -1.0804 0.139971
8 to 17 141817 -0.3184 0.375099
7 to 16 141383 -1.8149 0.034767
6 to 15 141412 -1.7149 0.043179
5 to 14 141625 -0.9804 0.163432
4 to 13 141692 -0.7494 0.226804
3 to 12 141890 -0.0667 0.473428
2 to 11 141930 0.0713 0.528411
1 to 10 141789 -0.4149 0.339096
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_04:31
Bits used No. missing words z-score p-value
28 to 32 142190 0.9514 0.829305
27 to 31 141645 -0.8960 0.185117
26 to 30 141820 -0.3028 0.381016
25 to 29 141929 0.0667 0.526581
24 to 28 141609 -1.0181 0.154323
23 to 27 141918 0.0294 0.511723
22 to 26 141683 -0.7672 0.221475
21 to 25 141832 -0.2621 0.396609
20 to 24 142144 0.7955 0.786836
19 to 23 141548 -1.2248 0.110316
18 to 22 141418 -1.6655 0.047904
17 to 21 142148 0.8091 0.790757
16 to 20 141607 -1.0248 0.152718
15 to 19 141840 -0.2350 0.407098
14 to 18 142169 0.8802 0.810635
13 to 17 142028 0.4023 0.656258
12 to 16 141493 -1.4113 0.079080
11 to 15 141995 0.2904 0.614248
10 to 14 142245 1.1379 0.872411
9 to 13 142043 0.4531 0.674768
8 to 12 141616 -0.9943 0.160029
7 to 11 141715 -0.6587 0.255030
6 to 10 141560 -1.1842 0.118173
5 to 9 142130 0.7480 0.772780
4 to 8 141764 -0.4926 0.311132
3 to 7 142187 0.9413 0.826713
2 to 6 141553 -1.2079 0.113543
1 to 5 142194 0.9650 0.832723
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_04:31
Bits used No. missing words z-score p-value
31 to 32 142022 0.3324 0.630191
30 to 31 142426 1.5241 0.936258
29 to 30 142026 0.3442 0.634637
28 to 29 142717 2.3825 0.991402
27 to 28 141638 -0.8004 0.211744
26 to 27 142057 0.4356 0.668438
25 to 26 142299 1.1495 0.874819
24 to 25 140786 -3.3137 0.000460
23 to 24 142320 1.2114 0.887132
22 to 23 141528 -1.1249 0.130323
21 to 22 142571 1.9518 0.974521
20 to 21 142308 1.1760 0.880206
19 to 20 141423 -1.4346 0.075700
18 to 19 141582 -0.9656 0.167128
17 to 18 141762 -0.4346 0.331926
16 to 17 142144 0.6922 0.755607
15 to 16 141683 -0.6676 0.252182
14 to 15 141983 0.2173 0.586019
13 to 14 141561 -1.0275 0.152087
12 to 13 141875 -0.1013 0.459669
11 to 12 141908 -0.0039 0.498435
10 to 11 141761 -0.4376 0.330856
9 to 10 142161 0.7424 0.771074
8 to 9 141865 -0.1308 0.447980
7 to 8 142135 0.6657 0.747196
6 to 7 142395 1.4327 0.924022
5 to 6 142517 1.7925 0.963477
4 to 5 142080 0.5035 0.692677
3 to 4 141940 0.0905 0.536044
2 to 3 142113 0.6008 0.726012
1 to 2 142166 0.7571 0.775517
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2550.45 0.713 0.762214
Test results for specific bytes for dh-ranFile-2018-07-10_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2554.76 0.774 0.780644
2 to 9 2470.25 -0.421 0.336989
3 to 10 2488.72 -0.159 0.436642
4 to 11 2429.82 -0.993 0.160473
5 to 12 2482.24 -0.251 0.400832
6 to 13 2577.44 1.095 0.863270
7 to 14 2311.13 -2.671 0.003780
8 to 15 2458.83 -0.582 0.280195
9 to 16 2478.16 -0.309 0.378700
10 to 17 2386.64 -1.603 0.054444
11 to 18 2539.18 0.554 0.710260
12 to 19 2482.68 -0.245 0.403252
13 to 20 2628.88 1.823 0.965817
14 to 21 2554.16 0.766 0.778157
15 to 22 2539.48 0.558 0.711708
16 to 23 2419.61 -1.137 0.127789
17 to 24 2494.92 -0.072 0.471342
18 to 25 2344.44 -2.200 0.013906
19 to 26 2516.62 0.235 0.592900
20 to 27 2529.46 0.417 0.661513
21 to 28 2536.45 0.515 0.696871
22 to 29 2510.06 0.142 0.556557
23 to 30 2503.01 0.043 0.516962
24 to 31 2568.71 0.972 0.834402
25 to 32 2382.64 -1.660 0.048487
CDPARK for dh-ranFile-2018-07-10_04:31: 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
3521 -0.0913 0.463617
3521 -0.0913 0.463617
3526 0.1370 0.554479
3456 -3.0594 0.001109
3521 -0.0913 0.463617
3521 -0.0913 0.463617
3527 0.1826 0.572463
3528 0.2283 0.590298
3518 -0.2283 0.409702
3487 -1.6438 0.050105
Square side=100, avg. no. parked=3512.60 sample std.=21.90
p-value of the KSTEST for those 10 p-values: 0.085794
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_04:31
0.5468,0.7763,0.5402,0.0103,0.7760,0.4736,0.2889,0.6224,0.3786,0.9388,
The KS test for those 10 p-values: 0.770093
The 3DSPHERES test for dh-ranFile-2018-07-10_04:31
sample no r^3 equiv. uni.
1 44.038 0.769597
2 3.675 0.115299
3 8.732 0.252532
4 29.532 0.626336
5 33.680 0.674594
6 32.741 0.664242
7 42.469 0.757225
8 30.076 0.633049
9 61.556 0.871505
10 21.726 0.515291
11 15.363 0.400755
12 3.260 0.102965
13 4.416 0.136882
14 2.269 0.072837
15 9.627 0.274494
16 20.728 0.498886
17 37.330 0.711863
18 112.592 0.976554
19 87.250 0.945434
20 0.854 0.028077
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.955456
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 1.8 -0.1 -1.0 -0.7 -1.0
-0.0 -0.8 -0.2 0.7 0.5 0.5
0.1 -0.3 1.8 0.5 -0.6 -0.1
0.8 -0.5 -1.1 -0.8 0.6 -0.3
0.2 -1.1 -1.3 1.5 -1.3 0.8
-0.3 1.6 -0.9 -1.9 0.9 -1.2
1.4 2.1 1.3 1.0 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:43.737757
z-score=0.189605, p-value=0.602424
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_04:31
Test no p-value
1 0.898615
2 0.549125
3 0.435288
4 0.588050
5 0.075122
6 0.513285
7 0.077803
8 0.318713
9 0.790966
10 0.097100
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.681319
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_04:31:
(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 67021 1.88 66636 0.01
3 25000.00 24733 2.85 25059 0.14
4 6666.67 6595 0.77 6643 0.08
5 1388.89 1399 0.07 1404 0.16
6 238.10 219 1.53 218 1.70
7 34.72 28 1.30 35 0.00
8 4.96 4 0.19 4 0.19
p=0.80244 p=0.10838
Number of rngs required: 687229, p-value: 0.086
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_04:31
No. of wins: Observed Expected
98651 98585.9
z-score= 0.291, pvalue=0.61461
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66563 66666.7 0.161 0.161
2 37732 37654.3 0.160 0.321
3 27084 26954.7 0.620 0.941
4 19144 19313.5 1.487 2.428
5 13943 13851.4 0.605 3.034
6 9877 9943.5 0.445 3.479
7 7021 7145.0 2.153 5.632
8 5255 5139.1 2.615 8.247
9 3710 3699.9 0.028 8.275
10 2688 2666.3 0.177 8.451
11 1913 1923.3 0.055 8.507
12 1363 1388.7 0.477 8.984
13 1018 1003.7 0.203 9.187
14 739 726.1 0.228 9.415
15 510 525.8 0.477 9.892
16 389 381.2 0.162 10.054
17 293 276.5 0.980 11.033
18 221 200.8 2.026 13.059
19 146 146.0 0.000 13.059
20 106 106.2 0.000 13.060
21 285 287.1 0.016 13.075
Chisq= 13.08 for 20 degrees of freedom, p= 0.12587
SUMMARY of craptest
p-value for no. of wins: 0.614608
p-value for throws/game: 0.125866
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_04:31
No. of wins: Observed Expected
98463 98585.9
z-score=-0.549, pvalue=0.29133
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66545 66666.7 0.222 0.222
2 37782 37654.3 0.433 0.655
3 26981 26954.7 0.026 0.681
4 19469 19313.5 1.253 1.933
5 13965 13851.4 0.931 2.865
6 9988 9943.5 0.199 3.063
7 7010 7145.0 2.552 5.615
8 5113 5139.1 0.132 5.747
9 3686 3699.9 0.052 5.799
10 2631 2666.3 0.467 6.266
11 1897 1923.3 0.360 6.627
12 1374 1388.7 0.156 6.783
13 944 1003.7 3.553 10.336
14 724 726.1 0.006 10.342
15 562 525.8 2.487 12.830
16 329 381.2 7.135 19.965
17 301 276.5 2.164 22.129
18 209 200.8 0.332 22.461
19 136 146.0 0.683 23.144
20 87 106.2 3.476 26.620
21 267 287.1 1.409 28.029
Chisq= 28.03 for 20 degrees of freedom, p= 0.89129
SUMMARY of craptest
p-value for no. of wins: 0.291333
p-value for throws/game: 0.891289
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0011,0.0038,0.0061,0.0103,0.0139,0.0199,0.0216,0.0249,0.0281,
0.0292,0.0348,0.0432,0.0442,0.0476,0.0479,0.0485,0.0501,0.0521,0.0544,
0.0722,0.0727,0.0728,0.0751,0.0757,0.0778,0.0785,0.0791,0.0793,0.0856,
0.0858,0.0907,0.0931,0.0971,0.1017,0.1030,0.1053,0.1079,0.1084,0.1103,
0.1135,0.1153,0.1182,0.1259,0.1263,0.1278,0.1303,0.1339,0.1369,0.1400,
0.1467,0.1516,0.1521,0.1527,0.1543,0.1600,0.1605,0.1634,0.1640,0.1662,
0.1671,0.1724,0.1733,0.1738,0.1756,0.1832,0.1851,0.1912,0.1988,0.2026,
0.2117,0.2128,0.2189,0.2215,0.2268,0.2312,0.2316,0.2474,0.2503,0.2518,
0.2522,0.2525,0.2550,0.2593,0.2745,0.2802,0.2813,0.2889,0.2913,0.3070,
0.3111,0.3163,0.3187,0.3229,0.3266,0.3309,0.3319,0.3370,0.3391,0.3413,
0.3583,0.3703,0.3712,0.3751,0.3786,0.3787,0.3808,0.3810,0.3966,0.3987,
0.4008,0.4008,0.4033,0.4071,0.4079,0.4097,0.4101,0.4353,0.4366,0.4380,
0.4449,0.4480,0.4561,0.4588,0.4597,0.4636,0.4636,0.4636,0.4636,0.4713,
0.4734,0.4736,0.4789,0.4899,0.4984,0.4989,0.5052,0.5095,0.5117,0.5133,
0.5153,0.5155,0.5170,0.5206,0.5230,0.5266,0.5284,0.5350,0.5360,0.5402,
0.5421,0.5468,0.5491,0.5545,0.5566,0.5572,0.5601,0.5686,0.5692,0.5725,
0.5809,0.5860,0.5875,0.5880,0.5902,0.5903,0.5919,0.5929,0.5989,0.6024,
0.6029,0.6142,0.6146,0.6179,0.6224,0.6253,0.6263,0.6302,0.6330,0.6346,
0.6476,0.6550,0.6563,0.6615,0.6642,0.6684,0.6746,0.6748,0.6764,0.6774,
0.6813,0.6846,0.6912,0.6927,0.6969,0.6998,0.7052,0.7103,0.7117,0.7119,
0.7208,0.7254,0.7260,0.7322,0.7472,0.7508,0.7556,0.7572,0.7622,0.7622,
0.7694,0.7696,0.7701,0.7711,0.7728,0.7755,0.7760,0.7763,0.7782,0.7806,
0.7868,0.7908,0.7910,0.8024,0.8044,0.8074,0.8084,0.8106,0.8163,0.8193,
0.8267,0.8293,0.8327,0.8344,0.8440,0.8582,0.8633,0.8689,0.8715,0.8724,
0.8739,0.8748,0.8802,0.8813,0.8822,0.8871,0.8913,0.8935,0.8986,0.9014,
0.9092,0.9159,0.9211,0.9230,0.9240,0.9286,0.9363,0.9388,0.9454,0.9465,
0.9533,0.9555,0.9635,0.9654,0.9658,0.9745,0.9766,0.9914,0.9984,
Overall p-value after applying KStest on 269 p-values = 0.182124
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.