RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.91 13.7306 0.313928
2 to 25 15.98 19.3490 0.691130
3 to 26 15.62 23.6309 0.870184
4 to 27 15.45 14.9993 0.404470
5 to 28 15.66 20.6944 0.759741
6 to 29 15.44 21.8083 0.807795
7 to 30 15.66 13.4808 0.296549
8 to 31 15.72 15.2146 0.419973
9 to 32 15.68 22.0201 0.816054
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.350897
Tough bday spacings test for dh-ranFile-2018-06-18_14:31: 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 35 74 90 104 92 47 27 12 8 6
(O-E)^2/E 1.9 0.1 0.0 0.6 0.4 2.5 0.5 0.3 0.6 0.3 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.962, p= 0.367
RESULTS OF GCD FOR dh-ranFile-2018-06-18_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.337910
p-value, dist. of gcd's: 0.581978
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.472 0.169 0.378 0.517 0.482 0.366 0.148 0.965
Bits 8 to 15---> 0.892 0.757 0.233 0.052 0.696 0.218 0.587 0.618
Bits 16 to 23---> 0.671 0.027 0.774 0.422 0.387 0.274 0.061 0.011
Bits 24 to 31---> 0.579 0.928 0.191 0.360 0.080 0.401 0.221 0.845
KS test for the above 32 p values: 0.662
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_14:31,
p-values for 5 runs: 0.6522, 0.0322, 0.2665, 0.2426, 0.5503
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5214 5134.0 1.246 1.507
r= 30 22930 23103.0 1.296 2.803
r= 31 11652 11551.5 0.874 3.677
chi-square = 3.677 with df = 3; p-value = 0.701
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 201 211.4 0.513 0.513
r= 30 5214 5134.0 1.246 1.760
r= 31 23190 23103.0 0.327 2.087
r= 32 11395 11551.5 2.121 4.208
chi-square = 4.208 with df = 3; p-value = 0.760
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_14:31
b-rank test for bits 1 to 8, p=0.18412
b-rank test for bits 2 to 9, p=0.42714
b-rank test for bits 3 to 10, p=0.91139
b-rank test for bits 4 to 11, p=0.25903
b-rank test for bits 5 to 12, p=0.03010
b-rank test for bits 6 to 13, p=0.48213
b-rank test for bits 7 to 14, p=0.22455
b-rank test for bits 8 to 15, p=0.23355
b-rank test for bits 9 to 16, p=0.44447
b-rank test for bits 10 to 17, p=0.63781
b-rank test for bits 11 to 18, p=0.07178
b-rank test for bits 12 to 19, p=0.07892
b-rank test for bits 13 to 20, p=0.96955
b-rank test for bits 14 to 21, p=0.64694
b-rank test for bits 15 to 22, p=0.32635
b-rank test for bits 16 to 23, p=0.55003
b-rank test for bits 17 to 24, p=0.39127
b-rank test for bits 18 to 25, p=0.25330
b-rank test for bits 19 to 26, p=0.10932
b-rank test for bits 20 to 27, p=0.24004
b-rank test for bits 21 to 28, p=0.43700
b-rank test for bits 22 to 29, p=0.33686
b-rank test for bits 23 to 30, p=0.09201
b-rank test for bits 24 to 31, p=0.39400
b-rank test for bits 25 to 32, p=0.21714
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 = 0.016111
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_14:31
(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 141974 0.15 0.560051
2 142440 1.24 0.892491
3 141541 -0.86 0.194734
4 142078 0.39 0.653242
5 141716 -0.45 0.325741
6 142129 0.51 0.696111
7 142111 0.47 0.681248
8 141396 -1.20 0.115192
9 141816 -0.22 0.413691
10 141781 -0.30 0.382151
11 141830 -0.19 0.426477
12 142494 1.37 0.914039
13 142301 0.92 0.819935
14 141976 0.16 0.561893
15 141769 -0.33 0.371504
16 142635 1.70 0.955009
17 142139 0.54 0.704232
18 141681 -0.53 0.296850
19 141395 -1.20 0.114739
20 143070 2.71 0.996655
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_14:31
Bits used No. missing words z-score p-value
23 to 32 141432 -1.6460 0.049885
22 to 31 141423 -1.6770 0.046771
21 to 30 142164 0.8782 0.810075
20 to 29 141879 -0.1046 0.458352
19 to 28 142360 1.5540 0.939912
18 to 27 141761 -0.5115 0.304507
17 to 26 141666 -0.8391 0.200715
16 to 25 141720 -0.6529 0.256923
15 to 24 141676 -0.8046 0.210529
14 to 23 142072 0.5609 0.712578
13 to 22 141163 -2.5736 0.005033
12 to 21 141849 -0.2080 0.417601
11 to 20 141887 -0.0770 0.469312
10 to 19 142245 1.1575 0.876462
9 to 18 142134 0.7747 0.780749
8 to 17 141513 -1.3667 0.085867
7 to 16 141797 -0.3873 0.349251
6 to 15 141722 -0.6460 0.259151
5 to 14 141623 -0.9873 0.161737
4 to 13 141467 -1.5253 0.063595
3 to 12 141880 -0.1011 0.459721
2 to 11 141849 -0.2080 0.417601
1 to 10 141913 0.0127 0.505049
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_14:31
Bits used No. missing words z-score p-value
28 to 32 141970 0.2057 0.581472
27 to 31 141996 0.2938 0.615543
26 to 30 142338 1.4531 0.926905
25 to 29 141742 -0.5672 0.285282
24 to 28 142210 1.0192 0.845951
23 to 27 141817 -0.3130 0.377147
22 to 26 141571 -1.1469 0.125715
21 to 25 141968 0.1989 0.578822
20 to 24 141829 -0.2723 0.392694
19 to 23 141904 -0.0181 0.492792
18 to 22 141338 -1.9367 0.026390
17 to 21 141646 -0.8926 0.186024
16 to 20 141879 -0.1028 0.459056
15 to 19 142092 0.6192 0.732114
14 to 18 141770 -0.4723 0.318355
13 to 17 141459 -1.5265 0.063437
12 to 16 142187 0.9413 0.826713
11 to 15 142025 0.3921 0.652509
10 to 14 142294 1.3040 0.903877
9 to 13 141976 0.2260 0.589399
8 to 12 141294 -2.0859 0.018495
7 to 11 142186 0.9379 0.825843
6 to 10 141990 0.2735 0.607749
5 to 9 141860 -0.1672 0.433598
4 to 8 141812 -0.3299 0.370726
3 to 7 141449 -1.5604 0.059328
2 to 6 141558 -1.1909 0.116837
1 to 5 142177 0.9074 0.817891
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_14:31
Bits used No. missing words z-score p-value
31 to 32 141657 -0.7443 0.228337
30 to 31 142316 1.1996 0.884856
29 to 30 141615 -0.8682 0.192634
28 to 29 142463 1.6332 0.948791
27 to 28 141503 -1.1986 0.115339
26 to 27 141834 -0.2222 0.412074
25 to 26 141737 -0.5083 0.305605
24 to 25 142373 1.3678 0.914306
23 to 24 142129 0.6480 0.741506
22 to 23 142258 1.0285 0.848149
21 to 22 142627 2.1170 0.982871
20 to 21 142094 0.5447 0.707037
19 to 20 142025 0.3412 0.633527
18 to 19 142144 0.6922 0.755607
17 to 18 141757 -0.4494 0.326589
16 to 17 141906 -0.0098 0.496081
15 to 16 141274 -1.8741 0.030456
14 to 15 141531 -1.1160 0.132207
13 to 14 141484 -1.2547 0.104801
12 to 13 142436 1.5536 0.939860
11 to 12 142091 0.5359 0.703986
10 to 11 141706 -0.5998 0.274322
9 to 10 141910 0.0020 0.500789
8 to 9 142260 1.0344 0.849531
7 to 8 142235 0.9607 0.831643
6 to 7 141945 0.1052 0.541900
5 to 6 141565 -1.0157 0.154881
4 to 5 141965 0.1642 0.565220
3 to 4 141547 -1.0688 0.142575
2 to 3 142543 1.8692 0.969205
1 to 2 141782 -0.3756 0.353605
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2473.11 -0.380 0.351874
Test results for specific bytes for dh-ranFile-2018-06-18_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2626.95 1.795 0.963700
2 to 9 2447.79 -0.738 0.230143
3 to 10 2591.38 1.292 0.901864
4 to 11 2471.50 -0.403 0.343468
5 to 12 2628.82 1.822 0.965752
6 to 13 2449.60 -0.713 0.237998
7 to 14 2566.80 0.945 0.827587
8 to 15 2542.29 0.598 0.725101
9 to 16 2422.58 -1.095 0.136779
10 to 17 2350.22 -2.118 0.017079
11 to 18 2542.45 0.600 0.725842
12 to 19 2436.54 -0.898 0.184725
13 to 20 2316.26 -2.598 0.004682
14 to 21 2443.65 -0.797 0.212733
15 to 22 2393.38 -1.508 0.065793
16 to 23 2388.41 -1.578 0.057273
17 to 24 2526.55 0.376 0.646367
18 to 25 2548.21 0.682 0.752310
19 to 26 2536.65 0.518 0.697893
20 to 27 2513.87 0.196 0.577759
21 to 28 2609.32 1.546 0.938945
22 to 29 2438.15 -0.875 0.190889
23 to 30 2410.36 -1.268 0.102441
24 to 31 2436.91 -0.892 0.186132
25 to 32 2553.82 0.761 0.776689
CDPARK for dh-ranFile-2018-06-18_14:31: 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
3505 -0.8219 0.205562
3522 -0.0457 0.481790
3473 -2.2831 0.011212
3520 -0.1370 0.445521
3531 0.3653 0.642555
3561 1.7352 0.958644
3533 0.4566 0.676028
3532 0.4110 0.659449
3550 1.2329 0.891189
3575 2.3744 0.991212
Square side=100, avg. no. parked=3530.20 sample std.=27.27
p-value of the KSTEST for those 10 p-values: 0.334127
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_14:31
0.0009,0.4278,0.9543,0.8049,0.9514,0.2321,0.8086,0.4318,0.2139,0.1561,
The KS test for those 10 p-values: 0.466586
The 3DSPHERES test for dh-ranFile-2018-06-18_14:31
sample no r^3 equiv. uni.
1 31.353 0.648343
2 12.051 0.330826
3 1.147 0.037505
4 92.289 0.953870
5 0.685 0.022579
6 19.851 0.484023
7 18.063 0.452344
8 61.504 0.871281
9 19.251 0.473598
10 1.302 0.042466
11 28.328 0.611032
12 4.404 0.136524
13 11.382 0.315723
14 39.300 0.730177
15 51.328 0.819302
16 24.844 0.563129
17 134.769 0.988805
18 6.360 0.191034
19 39.762 0.734302
20 26.077 0.580723
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.940974
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 2.2 0.1 -0.8 2.4 -1.4
-1.3 -0.0 -2.0 -1.3 -0.4 -0.3
0.5 0.2 -1.1 0.5 -0.4 0.1
0.6 0.6 -1.2 1.5 1.2 -0.2
-0.1 1.3 -1.2 -0.9 0.3 1.3
0.5 -0.2 0.9 0.1 0.3 -0.7
0.0 1.8 1.3 0.4 -1.3 1.0
0.8
Chi-square with 42 degrees of freedom:46.256011
z-score=0.464369, p-value=0.699088
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_14:31
Test no p-value
1 0.001069
2 0.161366
3 0.911896
4 0.067242
5 0.003806
6 0.790820
7 0.248745
8 0.243333
9 0.486076
10 0.049605
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.006421
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_14:31:
(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 66792 0.24 66888 0.73
3 25000.00 24761 2.28 25003 0.00
4 6666.67 6713 0.32 6449 7.11
5 1388.89 1441 1.96 1391 0.00
6 238.10 251 0.70 220 1.38
7 34.72 33 0.09 43 1.97
8 4.96 8 1.86 5 0.00
p=0.71839 p=0.91748
Number of rngs required: 688767, p-value: 0.662
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_14:31
No. of wins: Observed Expected
98557 98585.9
z-score=-0.129, pvalue=0.44865
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66457 66666.7 0.659 0.659
2 37585 37654.3 0.128 0.787
3 27018 26954.7 0.148 0.936
4 19272 19313.5 0.089 1.025
5 14087 13851.4 4.007 5.031
6 10080 9943.5 1.873 6.904
7 7191 7145.0 0.296 7.200
8 5110 5139.1 0.164 7.364
9 3597 3699.9 2.860 10.224
10 2651 2666.3 0.088 10.312
11 1927 1923.3 0.007 10.319
12 1435 1388.7 1.541 11.860
13 964 1003.7 1.571 13.431
14 690 726.1 1.799 15.230
15 518 525.8 0.117 15.347
16 395 381.2 0.503 15.850
17 290 276.5 0.655 16.505
18 199 200.8 0.017 16.522
19 125 146.0 3.016 19.538
20 99 106.2 0.490 20.028
21 310 287.1 1.824 21.853
Chisq= 21.85 for 20 degrees of freedom, p= 0.65143
SUMMARY of craptest
p-value for no. of wins: 0.448650
p-value for throws/game: 0.651433
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_14:31
No. of wins: Observed Expected
98535 98585.9
z-score=-0.227, pvalue=0.41003
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66405 66666.7 1.027 1.027
2 37805 37654.3 0.603 1.630
3 27021 26954.7 0.163 1.793
4 19296 19313.5 0.016 1.809
5 14042 13851.4 2.622 4.431
6 9988 9943.5 0.199 4.630
7 7016 7145.0 2.330 6.960
8 5217 5139.1 1.182 8.141
9 3676 3699.9 0.154 8.295
10 2541 2666.3 5.888 14.183
11 1928 1923.3 0.011 14.195
12 1381 1388.7 0.043 14.238
13 1032 1003.7 0.797 15.035
14 739 726.1 0.228 15.263
15 536 525.8 0.196 15.459
16 388 381.2 0.123 15.582
17 242 276.5 4.314 19.896
18 227 200.8 3.410 23.306
19 136 146.0 0.683 23.989
20 100 106.2 0.364 24.353
21 284 287.1 0.034 24.387
Chisq= 24.39 for 20 degrees of freedom, p= 0.77409
SUMMARY of craptest
p-value for no. of wins: 0.410029
p-value for throws/game: 0.774090
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0009,0.0011,0.0038,0.0047,0.0050,0.0064,0.0107,0.0112,0.0161,0.0171,
0.0185,0.0226,0.0264,0.0271,0.0301,0.0305,0.0322,0.0375,0.0425,0.0468,
0.0496,0.0499,0.0520,0.0573,0.0593,0.0609,0.0634,0.0636,0.0658,0.0672,
0.0718,0.0789,0.0805,0.0859,0.0920,0.1024,0.1048,0.1093,0.1147,0.1152,
0.1153,0.1168,0.1257,0.1322,0.1365,0.1368,0.1426,0.1482,0.1549,0.1561,
0.1614,0.1617,0.1693,0.1841,0.1847,0.1860,0.1861,0.1906,0.1909,0.1910,
0.1926,0.1947,0.2007,0.2056,0.2105,0.2127,0.2139,0.2171,0.2177,0.2211,
0.2246,0.2283,0.2301,0.2321,0.2334,0.2335,0.2380,0.2400,0.2426,0.2433,
0.2487,0.2533,0.2569,0.2590,0.2592,0.2665,0.2737,0.2743,0.2853,0.2965,
0.2969,0.3045,0.3056,0.3139,0.3157,0.3184,0.3257,0.3263,0.3266,0.3308,
0.3341,0.3369,0.3379,0.3435,0.3493,0.3509,0.3519,0.3536,0.3603,0.3657,
0.3674,0.3707,0.3715,0.3771,0.3784,0.3822,0.3874,0.3913,0.3927,0.3940,
0.4010,0.4045,0.4100,0.4121,0.4137,0.4176,0.4176,0.4200,0.4217,0.4265,
0.4271,0.4278,0.4318,0.4336,0.4370,0.4445,0.4455,0.4487,0.4523,0.4584,
0.4591,0.4597,0.4666,0.4693,0.4718,0.4736,0.4818,0.4821,0.4825,0.4840,
0.4861,0.4928,0.4961,0.5008,0.5050,0.5166,0.5419,0.5500,0.5503,0.5601,
0.5619,0.5631,0.5652,0.5778,0.5786,0.5788,0.5807,0.5815,0.5820,0.5872,
0.5894,0.6077,0.6110,0.6155,0.6179,0.6335,0.6378,0.6426,0.6464,0.6469,
0.6483,0.6514,0.6522,0.6525,0.6532,0.6594,0.6615,0.6625,0.6711,0.6760,
0.6812,0.6911,0.6961,0.6962,0.6979,0.6991,0.7014,0.7040,0.7042,0.7070,
0.7126,0.7184,0.7251,0.7258,0.7302,0.7321,0.7343,0.7415,0.7523,0.7556,
0.7571,0.7597,0.7601,0.7741,0.7745,0.7767,0.7807,0.7908,0.8049,0.8078,
0.8086,0.8101,0.8161,0.8179,0.8193,0.8199,0.8258,0.8267,0.8276,0.8316,
0.8454,0.8460,0.8481,0.8495,0.8702,0.8713,0.8765,0.8849,0.8912,0.8916,
0.8925,0.9019,0.9039,0.9114,0.9119,0.9140,0.9143,0.9175,0.9269,0.9284,
0.9389,0.9399,0.9399,0.9410,0.9488,0.9514,0.9539,0.9543,0.9550,0.9586,
0.9637,0.9646,0.9658,0.9692,0.9696,0.9829,0.9888,0.9912,0.9967,
Overall p-value after applying KStest on 269 p-values = 0.081682
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.