RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_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 15.83 15.7892 0.461173
2 to 25 15.93 18.5346 0.644112
3 to 26 15.85 12.4197 0.225915
4 to 27 16.06 10.8712 0.136820
5 to 28 15.87 22.5125 0.834197
6 to 29 15.89 6.7140 0.013041
7 to 30 15.49 23.0585 0.852643
8 to 31 15.62 14.6868 0.381974
9 to 32 15.78 22.0401 0.816818
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.912325
Tough bday spacings test for dh-ranFile-2018-07-07_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 12 45 67 115 107 70 43 25 9 3 4
(O-E)^2/E 0.9 1.9 0.5 3.1 0.9 0.8 1.6 0.8 2.3 2.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 14.794, p= 0.860
RESULTS OF GCD FOR dh-ranFile-2018-07-07_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.232380
p-value, dist. of gcd's: 0.688104
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.097 0.913 0.804 0.236 0.003 0.723 0.181 0.343
Bits 8 to 15---> 0.476 0.810 0.263 0.824 0.187 0.726 0.597 0.218
Bits 16 to 23---> 0.094 0.783 0.587 0.125 0.373 0.784 0.472 0.384
Bits 24 to 31---> 0.317 0.959 0.118 0.774 0.552 0.421 0.847 0.267
KS test for the above 32 p values: 0.164
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_03:31,
p-values for 5 runs: 0.4541, 0.6927, 0.7032, 0.4365, 0.9780
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5148 5134.0 0.038 1.044
r= 30 22941 23103.0 1.137 2.180
r= 31 11685 11551.5 1.542 3.723
chi-square = 3.723 with df = 3; p-value = 0.707
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5068 5134.0 0.849 2.821
r= 31 23276 23103.0 1.295 4.115
r= 32 11465 11551.5 0.648 4.763
chi-square = 4.763 with df = 3; p-value = 0.810
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_03:31
b-rank test for bits 1 to 8, p=0.77724
b-rank test for bits 2 to 9, p=0.20221
b-rank test for bits 3 to 10, p=0.15714
b-rank test for bits 4 to 11, p=0.48298
b-rank test for bits 5 to 12, p=0.16618
b-rank test for bits 6 to 13, p=0.49828
b-rank test for bits 7 to 14, p=0.57003
b-rank test for bits 8 to 15, p=0.12520
b-rank test for bits 9 to 16, p=0.01938
b-rank test for bits 10 to 17, p=0.46463
b-rank test for bits 11 to 18, p=0.11330
b-rank test for bits 12 to 19, p=0.58271
b-rank test for bits 13 to 20, p=0.84941
b-rank test for bits 14 to 21, p=0.38219
b-rank test for bits 15 to 22, p=0.34367
b-rank test for bits 16 to 23, p=0.24103
b-rank test for bits 17 to 24, p=0.84907
b-rank test for bits 18 to 25, p=0.49068
b-rank test for bits 19 to 26, p=0.62449
b-rank test for bits 20 to 27, p=0.11283
b-rank test for bits 21 to 28, p=0.01026
b-rank test for bits 22 to 29, p=0.53616
b-rank test for bits 23 to 30, p=0.01814
b-rank test for bits 24 to 31, p=0.83238
b-rank test for bits 25 to 32, p=0.15579
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 = 0.056291
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_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 142106 0.46 0.677066
2 142435 1.23 0.890314
3 142624 1.67 0.952520
4 141557 -0.82 0.205197
5 141141 -1.80 0.036314
6 142710 1.87 0.969308
7 142586 1.58 0.943062
8 142280 0.87 0.806769
9 141746 -0.38 0.351375
10 141599 -0.73 0.234205
11 141382 -1.23 0.108960
12 141729 -0.42 0.336756
13 141486 -0.99 0.161310
14 142156 0.58 0.717805
15 142044 0.31 0.623486
16 142169 0.61 0.727977
17 141603 -0.72 0.237081
18 141875 -0.08 0.468035
19 142018 0.25 0.600214
20 142316 0.95 0.828985
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_03:31
Bits used No. missing words z-score p-value
23 to 32 141703 -0.7115 0.238393
22 to 31 142388 1.6506 0.950588
21 to 30 142022 0.3885 0.651183
20 to 29 141535 -1.2908 0.098388
19 to 28 142109 0.6885 0.754436
18 to 27 142229 1.1023 0.864837
17 to 26 141740 -0.5839 0.279645
16 to 25 141974 0.2230 0.588232
15 to 24 141977 0.2333 0.592253
14 to 23 141874 -0.1218 0.451518
13 to 22 141691 -0.7529 0.225766
12 to 21 142578 2.3058 0.989438
11 to 20 142397 1.6816 0.953679
10 to 19 142114 0.7058 0.759831
9 to 18 141946 0.1264 0.550312
8 to 17 142024 0.3954 0.653731
7 to 16 141709 -0.6908 0.244848
6 to 15 141824 -0.2942 0.384287
5 to 14 141737 -0.5942 0.276175
4 to 13 141994 0.2920 0.614844
3 to 12 142157 0.8540 0.803457
2 to 11 141687 -0.7667 0.221643
1 to 10 141624 -0.9839 0.162583
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_03:31
Bits used No. missing words z-score p-value
28 to 32 142247 1.1446 0.873822
27 to 31 141783 -0.4282 0.334239
26 to 30 141692 -0.7367 0.230649
25 to 29 141669 -0.8147 0.207628
24 to 28 142082 0.5853 0.720834
23 to 27 141705 -0.6926 0.244267
22 to 26 141931 0.0735 0.529279
21 to 25 141595 -1.0655 0.143319
20 to 24 142231 1.0904 0.862233
19 to 23 141558 -1.1909 0.116837
18 to 22 141815 -0.3198 0.374574
17 to 21 141893 -0.0554 0.477928
16 to 20 141746 -0.5537 0.289905
15 to 19 141825 -0.2859 0.387491
14 to 18 141968 0.1989 0.578822
13 to 17 141567 -1.1604 0.122935
12 to 16 141575 -1.1333 0.128540
11 to 15 141360 -1.8621 0.031292
10 to 14 142630 2.4429 0.992716
9 to 13 141511 -1.3503 0.088465
8 to 12 141608 -1.0215 0.153519
7 to 11 141846 -0.2147 0.415009
6 to 10 141906 -0.0113 0.495497
5 to 9 141780 -0.4384 0.330546
4 to 8 141899 -0.0350 0.486033
3 to 7 141795 -0.3876 0.349171
2 to 6 141995 0.2904 0.614248
1 to 5 141408 -1.6994 0.044620
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_03:31
Bits used No. missing words z-score p-value
31 to 32 141936 0.0787 0.531354
30 to 31 141502 -1.2016 0.114766
29 to 30 141344 -1.6676 0.047694
28 to 29 141906 -0.0098 0.496081
27 to 28 142009 0.2940 0.615626
26 to 27 141726 -0.5408 0.294324
25 to 26 141947 0.1111 0.544240
24 to 25 141526 -1.1308 0.129077
23 to 24 141792 -0.3461 0.364632
22 to 23 141985 0.2232 0.588316
21 to 22 141536 -1.1013 0.135390
20 to 21 142188 0.8220 0.794472
19 to 20 141718 -0.5644 0.286243
18 to 19 142174 0.7807 0.782522
17 to 18 142187 0.8191 0.793631
16 to 17 141754 -0.4582 0.323404
15 to 16 141918 0.0256 0.510202
14 to 15 142239 0.9725 0.834594
13 to 14 142341 1.2734 0.898555
12 to 13 141789 -0.3550 0.361311
11 to 12 141396 -1.5142 0.064982
10 to 11 141570 -1.0010 0.158420
9 to 10 142056 0.4327 0.667367
8 to 9 141966 0.1672 0.566381
7 to 8 142166 0.7571 0.775517
6 to 7 141602 -0.9066 0.182315
5 to 6 141646 -0.7768 0.218643
4 to 5 141481 -1.2635 0.103203
3 to 4 141554 -1.0482 0.147280
2 to 3 142261 1.0374 0.850219
1 to 2 142322 1.2173 0.888258
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2514.48 0.205 0.581132
Test results for specific bytes for dh-ranFile-2018-07-07_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2462.96 -0.524 0.300184
2 to 9 2532.37 0.458 0.676429
3 to 10 2558.54 0.828 0.796128
4 to 11 2513.60 0.192 0.576279
5 to 12 2529.16 0.412 0.659989
6 to 13 2513.68 0.193 0.576696
7 to 14 2475.01 -0.353 0.361878
8 to 15 2418.86 -1.148 0.125578
9 to 16 2405.20 -1.341 0.090011
10 to 17 2547.66 0.674 0.749861
11 to 18 2515.84 0.224 0.588621
12 to 19 2418.76 -1.149 0.125304
13 to 20 2501.01 0.014 0.505705
14 to 21 2594.98 1.343 0.910391
15 to 22 2549.58 0.701 0.758416
16 to 23 2516.37 0.231 0.591514
17 to 24 2450.41 -0.701 0.241554
18 to 25 2405.49 -1.337 0.090674
19 to 26 2460.47 -0.559 0.288059
20 to 27 2399.25 -1.425 0.077108
21 to 28 2433.85 -0.936 0.174749
22 to 29 2483.59 -0.232 0.408218
23 to 30 2502.53 0.036 0.514244
24 to 31 2470.11 -0.423 0.336273
25 to 32 2529.06 0.411 0.659449
CDPARK for dh-ranFile-2018-07-07_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
3559 1.6438 0.949895
3541 0.8219 0.794438
3547 1.0959 0.863437
3527 0.1826 0.572463
3491 -1.4612 0.071982
3533 0.4566 0.676028
3516 -0.3196 0.374623
3518 -0.2283 0.409702
3550 1.2329 0.891189
3529 0.2740 0.607947
Square side=100, avg. no. parked=3531.10 sample std.=18.76
p-value of the KSTEST for those 10 p-values: 0.340263
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_03:31
0.5836,0.1092,0.9251,0.3456,0.9056,0.0548,0.7050,0.7395,0.4343,0.3713,
The KS test for those 10 p-values: 0.990761
The 3DSPHERES test for dh-ranFile-2018-07-07_03:31
sample no r^3 equiv. uni.
1 58.994 0.860051
2 41.206 0.746786
3 6.785 0.202419
4 1.307 0.042639
5 3.278 0.103521
6 12.909 0.349683
7 69.499 0.901395
8 4.231 0.131549
9 0.513 0.016962
10 47.028 0.791456
11 5.220 0.159709
12 54.454 0.837182
13 17.005 0.432680
14 19.746 0.482216
15 80.130 0.930816
16 13.364 0.359482
17 11.170 0.310874
18 6.634 0.198403
19 4.425 0.137138
20 24.819 0.562772
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.366076
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 1.1 -0.1 0.4 -2.4
0.5 0.8 0.3 -0.2 -0.8 0.5
-1.2 3.3 0.2 0.2 -0.9 -0.6
0.9 -0.2 0.5 -0.6 -1.0 0.9
-1.0 -0.8 -0.9 -1.0 1.4 -0.3
1.0 0.3 -0.1 -1.3 0.1 1.3
0.7 0.5 -1.2 -1.8 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:44.494051
z-score=0.272123, p-value=0.632840
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_03:31
Test no p-value
1 0.140047
2 0.331149
3 0.836202
4 0.735260
5 0.091970
6 0.032770
7 0.028301
8 0.855855
9 0.086541
10 0.543530
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.095769
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_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 66638 0.01 66894 0.78
3 25000.00 25154 0.95 24646 5.01
4 6666.67 6560 1.71 6755 1.17
5 1388.89 1403 0.14 1421 0.74
6 238.10 207 4.06 246 0.26
7 34.72 36 0.05 32 0.21
8 4.96 1 3.16 5 0.00
p=0.87871 p=0.77453
Number of rngs required: 688630, p-value: 0.603
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_03:31
No. of wins: Observed Expected
98762 98585.9
z-score= 0.788, pvalue=0.78460
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66470 66666.7 0.580 0.580
2 37563 37654.3 0.221 0.802
3 27169 26954.7 1.703 2.505
4 19263 19313.5 0.132 2.637
5 13823 13851.4 0.058 2.695
6 10155 9943.5 4.497 7.192
7 7106 7145.0 0.213 7.405
8 5129 5139.1 0.020 7.425
9 3614 3699.9 1.993 9.417
10 2714 2666.3 0.853 10.271
11 1942 1923.3 0.181 10.452
12 1370 1388.7 0.253 10.705
13 1005 1003.7 0.002 10.707
14 698 726.1 1.091 11.797
15 528 525.8 0.009 11.806
16 398 381.2 0.745 12.551
17 294 276.5 1.102 13.653
18 207 200.8 0.190 13.843
19 139 146.0 0.334 14.177
20 113 106.2 0.433 14.611
21 300 287.1 0.578 15.189
Chisq= 15.19 for 20 degrees of freedom, p= 0.23450
SUMMARY of craptest
p-value for no. of wins: 0.784595
p-value for throws/game: 0.234501
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_03:31
No. of wins: Observed Expected
98760 98585.9
z-score= 0.779, pvalue=0.78197
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66465 66666.7 0.610 0.610
2 37507 37654.3 0.576 1.186
3 27188 26954.7 2.019 3.205
4 19229 19313.5 0.369 3.575
5 13979 13851.4 1.175 4.750
6 10018 9943.5 0.558 5.307
7 6987 7145.0 3.495 8.802
8 5207 5139.1 0.898 9.700
9 3768 3699.9 1.255 10.955
10 2637 2666.3 0.322 11.277
11 1953 1923.3 0.458 11.734
12 1445 1388.7 2.279 14.014
13 980 1003.7 0.560 14.574
14 707 726.1 0.505 15.078
15 547 525.8 0.852 15.930
16 367 381.2 0.525 16.456
17 287 276.5 0.396 16.851
18 175 200.8 3.322 20.173
19 127 146.0 2.469 22.642
20 123 106.2 2.652 25.295
21 304 287.1 0.993 26.288
Chisq= 26.29 for 20 degrees of freedom, p= 0.84348
SUMMARY of craptest
p-value for no. of wins: 0.781969
p-value for throws/game: 0.843484
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0028,0.0103,0.0130,0.0170,0.0181,0.0194,0.0283,0.0313,0.0328,0.0363,
0.0426,0.0446,0.0477,0.0548,0.0563,0.0650,0.0720,0.0771,0.0865,0.0885,
0.0900,0.0907,0.0920,0.0941,0.0958,0.0967,0.0984,0.1032,0.1035,0.1090,
0.1092,0.1128,0.1133,0.1148,0.1168,0.1185,0.1229,0.1250,0.1252,0.1253,
0.1256,0.1285,0.1291,0.1315,0.1354,0.1368,0.1371,0.1400,0.1433,0.1473,
0.1535,0.1558,0.1571,0.1584,0.1597,0.1613,0.1626,0.1641,0.1662,0.1747,
0.1805,0.1823,0.1874,0.1984,0.2022,0.2024,0.2052,0.2076,0.2181,0.2186,
0.2216,0.2258,0.2259,0.2306,0.2324,0.2342,0.2345,0.2364,0.2371,0.2384,
0.2410,0.2416,0.2443,0.2448,0.2627,0.2669,0.2762,0.2796,0.2862,0.2881,
0.2899,0.2943,0.3002,0.3109,0.3174,0.3234,0.3305,0.3311,0.3342,0.3363,
0.3368,0.3403,0.3431,0.3437,0.3456,0.3492,0.3497,0.3514,0.3595,0.3613,
0.3619,0.3646,0.3661,0.3713,0.3731,0.3746,0.3746,0.3820,0.3822,0.3843,
0.3843,0.3875,0.4082,0.4097,0.4150,0.4212,0.4327,0.4343,0.4365,0.4515,
0.4541,0.4612,0.4646,0.4680,0.4722,0.4761,0.4779,0.4822,0.4830,0.4860,
0.4907,0.4955,0.4961,0.4983,0.5057,0.5102,0.5142,0.5293,0.5314,0.5362,
0.5435,0.5442,0.5503,0.5517,0.5628,0.5664,0.5700,0.5725,0.5763,0.5767,
0.5788,0.5811,0.5827,0.5836,0.5871,0.5882,0.5883,0.5886,0.5915,0.5923,
0.5973,0.6002,0.6030,0.6079,0.6142,0.6148,0.6156,0.6235,0.6245,0.6328,
0.6441,0.6512,0.6537,0.6594,0.6600,0.6674,0.6760,0.6764,0.6771,0.6881,
0.6927,0.7032,0.7050,0.7070,0.7178,0.7208,0.7228,0.7256,0.7280,0.7353,
0.7395,0.7468,0.7499,0.7544,0.7584,0.7598,0.7742,0.7745,0.7755,0.7772,
0.7820,0.7825,0.7832,0.7842,0.7846,0.7915,0.7936,0.7944,0.7945,0.7961,
0.8035,0.8039,0.8068,0.8100,0.8101,0.8168,0.8237,0.8290,0.8324,0.8342,
0.8346,0.8362,0.8372,0.8435,0.8474,0.8491,0.8494,0.8502,0.8526,0.8559,
0.8601,0.8602,0.8622,0.8634,0.8648,0.8738,0.8787,0.8883,0.8903,0.8912,
0.8986,0.9014,0.9056,0.9104,0.9123,0.9127,0.9251,0.9308,0.9431,0.9499,
0.9506,0.9525,0.9537,0.9587,0.9693,0.9780,0.9894,0.9908,0.9927,
Overall p-value after applying KStest on 269 p-values = 0.151115
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.