RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.42 32.0944 0.985353
2 to 25 16.20 17.3584 0.569650
3 to 26 15.96 25.9207 0.924082
4 to 27 16.13 18.7216 0.655258
5 to 28 15.86 16.3036 0.497579
6 to 29 16.00 8.9236 0.057373
7 to 30 15.91 7.0395 0.016969
8 to 31 15.90 15.7774 0.460331
9 to 32 15.59 20.8248 0.765776
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.581401
Tough bday spacings test for dh-ranFile-2018-06-15_12:31: 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 38 79 93 83 80 57 30 18 8 8
(O-E)^2/E 1.1 0.1 0.4 0.2 2.2 0.0 0.5 0.0 0.7 0.3 3.8
Birthday Spacings: Sum(O-E)^2/E= 9.276, p= 0.494
RESULTS OF GCD FOR dh-ranFile-2018-06-15_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.129366
p-value, dist. of gcd's: 0.174351
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.217 0.655 0.450 0.801 0.060 0.372 0.162 0.242
Bits 8 to 15---> 0.151 0.935 0.972 0.470 0.481 0.372 0.811 0.076
Bits 16 to 23---> 0.408 0.387 0.238 0.748 0.883 0.015 0.593 0.303
Bits 24 to 31---> 0.113 0.504 0.333 0.561 0.857 0.400 0.775 0.933
KS test for the above 32 p values: 0.053
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_12:31,
p-values for 5 runs: 0.2206, 0.2295, 0.3137, 0.7811, 0.6888
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5073 5134.0 0.725 0.817
r= 30 23190 23103.0 0.327 1.145
r= 31 11530 11551.5 0.040 1.185
chi-square = 1.185 with df = 3; p-value = 0.243
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5109 5134.0 0.122 0.134
r= 31 23195 23103.0 0.366 0.500
r= 32 11483 11551.5 0.406 0.906
chi-square = 0.906 with df = 3; p-value = 0.176
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_12:31
b-rank test for bits 1 to 8, p=0.78470
b-rank test for bits 2 to 9, p=0.77144
b-rank test for bits 3 to 10, p=0.66735
b-rank test for bits 4 to 11, p=0.48939
b-rank test for bits 5 to 12, p=0.38619
b-rank test for bits 6 to 13, p=0.72779
b-rank test for bits 7 to 14, p=0.44116
b-rank test for bits 8 to 15, p=0.17478
b-rank test for bits 9 to 16, p=0.80993
b-rank test for bits 10 to 17, p=0.22468
b-rank test for bits 11 to 18, p=0.51017
b-rank test for bits 12 to 19, p=0.66467
b-rank test for bits 13 to 20, p=0.37493
b-rank test for bits 14 to 21, p=0.52954
b-rank test for bits 15 to 22, p=0.79474
b-rank test for bits 16 to 23, p=0.93738
b-rank test for bits 17 to 24, p=0.42017
b-rank test for bits 18 to 25, p=0.10767
b-rank test for bits 19 to 26, p=0.37432
b-rank test for bits 20 to 27, p=0.21040
b-rank test for bits 21 to 28, p=0.66352
b-rank test for bits 22 to 29, p=0.49641
b-rank test for bits 23 to 30, p=0.24157
b-rank test for bits 24 to 31, p=0.42614
b-rank test for bits 25 to 32, p=0.94415
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 = 0.462931
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_12:31
(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 141728 -0.42 0.335904
2 142310 0.94 0.825401
3 142015 0.25 0.597504
4 141475 -1.01 0.155103
5 142163 0.59 0.723305
6 141591 -0.74 0.228510
7 141768 -0.33 0.370621
8 141957 0.11 0.544342
9 142045 0.32 0.624373
10 141868 -0.10 0.461536
11 141890 -0.05 0.481989
12 141541 -0.86 0.194734
13 141988 0.18 0.572918
14 142239 0.77 0.779426
15 142066 0.37 0.642837
16 141518 -0.91 0.180274
17 140727 -2.76 0.002868
18 141553 -0.83 0.202550
19 141443 -1.09 0.137954
20 141763 -0.34 0.366216
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_12:31
Bits used No. missing words z-score p-value
23 to 32 142108 0.6851 0.753350
22 to 31 141847 -0.2149 0.414911
21 to 30 142027 0.4058 0.657540
20 to 29 142526 2.1264 0.983267
19 to 28 141660 -0.8598 0.194961
18 to 27 142279 1.2747 0.898797
17 to 26 142565 2.2609 0.988118
16 to 25 141919 0.0333 0.513300
15 to 24 141825 -0.2908 0.385605
14 to 23 142081 0.5920 0.723063
13 to 22 142567 2.2678 0.988330
12 to 21 142219 1.0678 0.857201
11 to 20 141928 0.0644 0.525666
10 to 19 141302 -2.0942 0.018119
9 to 18 141570 -1.1701 0.120980
8 to 17 142240 1.1402 0.872907
7 to 16 141933 0.0816 0.532526
6 to 15 141773 -0.4701 0.319141
5 to 14 141882 -0.0942 0.462459
4 to 13 142282 1.2851 0.900616
3 to 12 142267 1.2333 0.891276
2 to 11 141992 0.2851 0.612204
1 to 10 141939 0.1023 0.540745
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_12:31
Bits used No. missing words z-score p-value
28 to 32 142162 0.8565 0.804142
27 to 31 141991 0.2768 0.609051
26 to 30 141994 0.2870 0.612950
25 to 29 141462 -1.5164 0.064713
24 to 28 142217 1.0429 0.851514
23 to 27 142141 0.7853 0.783868
22 to 26 141668 -0.8181 0.206659
21 to 25 141616 -0.9943 0.160029
20 to 24 141720 -0.6418 0.260503
19 to 23 141800 -0.3706 0.355464
18 to 22 142127 0.7379 0.769702
17 to 21 141540 -1.2520 0.105291
16 to 20 142395 1.6463 0.950153
15 to 19 141656 -0.8587 0.195240
14 to 18 142080 0.5785 0.718551
13 to 17 141863 -0.1571 0.437602
12 to 16 142321 1.3955 0.918566
11 to 15 141466 -1.5028 0.066444
10 to 14 141874 -0.1198 0.452336
9 to 13 141759 -0.5096 0.305168
8 to 12 141821 -0.2994 0.382308
7 to 11 141761 -0.5028 0.307548
6 to 10 141609 -1.0181 0.154323
5 to 9 141994 0.2870 0.612950
4 to 8 141591 -1.0791 0.140275
3 to 7 141426 -1.6384 0.050668
2 to 6 141863 -0.1571 0.437602
1 to 5 142114 0.6938 0.756095
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_12:31
Bits used No. missing words z-score p-value
31 to 32 142002 0.2734 0.607713
30 to 31 142054 0.4268 0.665221
29 to 30 141782 -0.3756 0.353605
28 to 29 142186 0.8161 0.792789
27 to 28 142153 0.7188 0.763865
26 to 27 142532 1.8368 0.966879
25 to 26 141425 -1.4287 0.076545
24 to 25 141690 -0.6470 0.258819
23 to 24 141466 -1.3078 0.095478
22 to 23 142748 2.4740 0.993319
21 to 22 141530 -1.1190 0.131577
20 to 21 141267 -1.8948 0.029061
19 to 20 141776 -0.3933 0.347048
18 to 19 141948 0.1141 0.545409
17 to 18 141178 -2.1573 0.015491
16 to 17 142170 0.7689 0.779035
15 to 16 141939 0.0875 0.534872
14 to 15 141907 -0.0069 0.497258
13 to 14 141881 -0.0836 0.466699
12 to 13 141914 0.0138 0.505496
11 to 12 141659 -0.7384 0.230125
10 to 11 142134 0.6627 0.746253
9 to 10 141574 -0.9892 0.161289
8 to 9 141442 -1.3786 0.084016
7 to 8 142248 0.9990 0.841109
6 to 7 141360 -1.6204 0.052569
5 to 6 141456 -1.3373 0.090569
4 to 5 141881 -0.0836 0.466699
3 to 4 141520 -1.1485 0.125388
2 to 3 142024 0.3383 0.632416
1 to 2 142740 2.4504 0.992864
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2483.21 -0.237 0.406140
Test results for specific bytes for dh-ranFile-2018-06-15_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2476.17 -0.337 0.368049
2 to 9 2551.72 0.731 0.767740
3 to 10 2514.31 0.202 0.580201
4 to 11 2540.80 0.577 0.718034
5 to 12 2562.03 0.877 0.809812
6 to 13 2496.43 -0.051 0.479853
7 to 14 2557.04 0.807 0.790062
8 to 15 2571.91 1.017 0.845429
9 to 16 2357.59 -2.014 0.022006
10 to 17 2459.16 -0.578 0.281762
11 to 18 2541.47 0.587 0.721242
12 to 19 2496.77 -0.046 0.481787
13 to 20 2475.01 -0.353 0.361876
14 to 21 2475.81 -0.342 0.366124
15 to 22 2538.40 0.543 0.706474
16 to 23 2489.32 -0.151 0.439978
17 to 24 2517.20 0.243 0.596092
18 to 25 2606.11 1.501 0.933268
19 to 26 2615.13 1.628 0.948258
20 to 27 2544.78 0.633 0.736747
21 to 28 2474.45 -0.361 0.358921
22 to 29 2498.86 -0.016 0.493580
23 to 30 2430.28 -0.986 0.162071
24 to 31 2481.55 -0.261 0.397098
25 to 32 2570.55 0.998 0.840781
CDPARK for dh-ranFile-2018-06-15_12:31: 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
3481 -1.9178 0.027568
3508 -0.6849 0.246694
3509 -0.6393 0.261324
3547 1.0959 0.863437
3550 1.2329 0.891189
3496 -1.2329 0.108811
3509 -0.6393 0.261324
3496 -1.2329 0.108811
3537 0.6393 0.738676
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3514.90 sample std.=21.76
p-value of the KSTEST for those 10 p-values: 0.263282
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_12:31
0.3121,0.7915,0.4799,0.8181,0.7036,0.2046,0.1727,0.1239,0.8850,0.6747,
The KS test for those 10 p-values: 0.926648
The 3DSPHERES test for dh-ranFile-2018-06-15_12:31
sample no r^3 equiv. uni.
1 1.749 0.056641
2 81.806 0.934577
3 10.315 0.290960
4 17.606 0.443929
5 1.166 0.038127
6 4.115 0.128176
7 28.013 0.606932
8 12.385 0.338231
9 125.983 0.984996
10 8.996 0.259086
11 105.642 0.970442
12 4.576 0.141463
13 20.682 0.498129
14 71.926 0.909057
15 1.819 0.058845
16 36.293 0.701729
17 0.307 0.010192
18 1.477 0.048056
19 35.873 0.697523
20 8.156 0.238038
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.103983
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.8 -0.6 1.4 -0.2 1.0
0.5 1.2 -1.6 -1.4 -0.4 0.8
-1.2 0.4 1.9 0.6 -0.5 0.2
1.2 0.3 -2.3 1.9 -0.2 -2.3
-0.8 -1.2 0.4 1.0 0.6 0.0
0.5 -1.6 0.9 -1.5 1.6 -1.0
1.2 -1.7 0.9 -0.7 -0.6 0.0
2.7
Chi-square with 42 degrees of freedom:61.528446
z-score=2.130728, p-value=0.973745
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_12:31
Test no p-value
1 0.581899
2 0.590508
3 0.068983
4 0.260132
5 0.001838
6 0.047845
7 0.364616
8 0.042667
9 0.022682
10 0.532721
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002558
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_12:31:
(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 66872 0.63 66574 0.13
3 25000.00 25006 0.00 25009 0.00
4 6666.67 6493 4.52 6787 2.17
5 1388.89 1344 1.45 1383 0.02
6 238.10 239 0.00 212 2.86
7 34.72 37 0.15 28 1.30
8 4.96 8 1.86 6 0.22
p=0.80423 p=0.65127
Number of rngs required: 687253, p-value: 0.090
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_12:31
No. of wins: Observed Expected
98667 98585.9
z-score= 0.363, pvalue=0.64166
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66483 66666.7 0.506 0.506
2 37813 37654.3 0.669 1.175
3 26695 26954.7 2.503 3.677
4 19375 19313.5 0.196 3.874
5 13851 13851.4 0.000 3.874
6 9933 9943.5 0.011 3.885
7 7223 7145.0 0.851 4.736
8 5142 5139.1 0.002 4.737
9 3746 3699.9 0.575 5.313
10 2689 2666.3 0.193 5.506
11 1943 1923.3 0.201 5.707
12 1443 1388.7 2.120 7.827
13 979 1003.7 0.609 8.436
14 767 726.1 2.299 10.735
15 541 525.8 0.437 11.172
16 388 381.2 0.123 11.295
17 294 276.5 1.102 12.398
18 186 200.8 1.095 13.493
19 137 146.0 0.553 14.046
20 119 106.2 1.539 15.584
21 253 287.1 4.053 19.638
Chisq= 19.64 for 20 degrees of freedom, p= 0.51922
SUMMARY of craptest
p-value for no. of wins: 0.641665
p-value for throws/game: 0.519218
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_12:31
No. of wins: Observed Expected
98835 98585.9
z-score= 1.114, pvalue=0.86743
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66712 66666.7 0.031 0.031
2 37602 37654.3 0.073 0.104
3 26879 26954.7 0.213 0.316
4 19370 19313.5 0.166 0.482
5 13824 13851.4 0.054 0.536
6 10077 9943.5 1.791 2.327
7 7085 7145.0 0.504 2.832
8 5113 5139.1 0.132 2.964
9 3710 3699.9 0.028 2.992
10 2681 2666.3 0.081 3.073
11 1953 1923.3 0.458 3.530
12 1375 1388.7 0.136 3.666
13 959 1003.7 1.992 5.658
14 738 726.1 0.194 5.852
15 534 525.8 0.127 5.979
16 375 381.2 0.099 6.078
17 283 276.5 0.151 6.229
18 196 200.8 0.116 6.345
19 164 146.0 2.223 8.568
20 96 106.2 0.982 9.551
21 274 287.1 0.599 10.150
Chisq= 10.15 for 20 degrees of freedom, p= 0.03463
SUMMARY of craptest
p-value for no. of wins: 0.867426
p-value for throws/game: 0.034628
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0026,0.0029,0.0102,0.0154,0.0155,0.0170,0.0181,0.0220,0.0227,
0.0276,0.0291,0.0346,0.0381,0.0427,0.0478,0.0481,0.0507,0.0526,0.0526,
0.0566,0.0574,0.0588,0.0600,0.0647,0.0664,0.0690,0.0759,0.0765,0.0840,
0.0902,0.0906,0.0955,0.1040,0.1053,0.1077,0.1088,0.1088,0.1131,0.1210,
0.1239,0.1254,0.1282,0.1294,0.1316,0.1380,0.1403,0.1415,0.1512,0.1543,
0.1551,0.1600,0.1613,0.1616,0.1621,0.1727,0.1744,0.1748,0.1761,0.1803,
0.1947,0.1950,0.1952,0.2026,0.2046,0.2067,0.2104,0.2168,0.2206,0.2247,
0.2285,0.2295,0.2301,0.2380,0.2384,0.2416,0.2420,0.2433,0.2467,0.2588,
0.2591,0.2601,0.2605,0.2613,0.2613,0.2633,0.2818,0.2910,0.3034,0.3052,
0.3075,0.3121,0.3137,0.3191,0.3332,0.3359,0.3382,0.3470,0.3536,0.3555,
0.3589,0.3619,0.3646,0.3661,0.3662,0.3680,0.3706,0.3718,0.3723,0.3743,
0.3746,0.3749,0.3823,0.3856,0.3862,0.3874,0.3971,0.4000,0.4061,0.4079,
0.4149,0.4202,0.4261,0.4376,0.4376,0.4400,0.4412,0.4439,0.4501,0.4523,
0.4603,0.4615,0.4625,0.4629,0.4667,0.4667,0.4699,0.4799,0.4799,0.4813,
0.4818,0.4820,0.4894,0.4936,0.4938,0.4964,0.4973,0.4976,0.4981,0.5044,
0.5055,0.5102,0.5133,0.5192,0.5257,0.5295,0.5325,0.5327,0.5349,0.5407,
0.5443,0.5454,0.5605,0.5697,0.5729,0.5802,0.5814,0.5819,0.5905,0.5932,
0.5961,0.5975,0.6069,0.6077,0.6091,0.6122,0.6130,0.6130,0.6244,0.6324,
0.6417,0.6428,0.6513,0.6553,0.6553,0.6575,0.6635,0.6647,0.6652,0.6674,
0.6747,0.6888,0.6975,0.7017,0.7036,0.7065,0.7180,0.7186,0.7212,0.7231,
0.7233,0.7278,0.7367,0.7387,0.7463,0.7480,0.7533,0.7561,0.7639,0.7658,
0.7677,0.7697,0.7714,0.7753,0.7790,0.7794,0.7811,0.7839,0.7847,0.7901,
0.7915,0.7928,0.7947,0.8010,0.8041,0.8042,0.8098,0.8099,0.8106,0.8181,
0.8254,0.8408,0.8411,0.8454,0.8515,0.8566,0.8572,0.8634,0.8674,0.8729,
0.8828,0.8850,0.8912,0.8913,0.8988,0.9006,0.9091,0.9186,0.9241,0.9266,
0.9333,0.9333,0.9346,0.9350,0.9374,0.9441,0.9483,0.9502,0.9669,0.9704,
0.9725,0.9737,0.9833,0.9850,0.9854,0.9881,0.9883,0.9929,0.9933,
Overall p-value after applying KStest on 269 p-values = 0.199419
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.