RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.14 20.0032 0.725934
2 to 25 16.11 8.9843 0.059248
3 to 26 15.96 10.3676 0.112506
4 to 27 15.69 22.7012 0.840768
5 to 28 15.80 10.9456 0.140621
6 to 29 15.61 28.1656 0.956960
7 to 30 15.35 26.3704 0.932028
8 to 31 15.50 14.7497 0.386495
9 to 32 15.75 18.5681 0.646120
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.654559
Tough bday spacings test for dh-ranFile-2018-06-15_09:31: 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 3 50 75 107 100 66 48 26 15 8 2
(O-E)^2/E 4.1 4.9 0.0 0.9 0.1 1.9 0.3 0.5 0.0 0.3 1.0
Birthday Spacings: Sum(O-E)^2/E= 14.033, p= 0.828
RESULTS OF GCD FOR dh-ranFile-2018-06-15_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.244933
p-value, dist. of gcd's: 0.369929
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.059 0.927 0.800 0.157 0.377 0.978 0.739 0.715
Bits 8 to 15---> 0.288 0.768 0.030 0.428 0.623 0.278 0.282 0.567
Bits 16 to 23---> 0.815 0.322 0.084 0.994 0.287 0.377 0.500 0.868
Bits 24 to 31---> 0.845 0.895 0.370 0.182 0.432 0.312 0.629 0.729
KS test for the above 32 p values: 0.078
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_09:31,
p-values for 5 runs: 0.6756, 0.5013, 0.3083, 0.5570, 0.6437
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5075 5134.0 0.678 0.778
r= 30 23069 23103.0 0.050 0.828
r= 31 11640 11551.5 0.678 1.505
chi-square = 1.505 with df = 3; p-value = 0.319
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 233 211.4 2.203 2.203
r= 30 5137 5134.0 0.002 2.205
r= 31 23155 23103.0 0.117 2.322
r= 32 11475 11551.5 0.507 2.829
chi-square = 2.829 with df = 3; p-value = 0.581
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_09:31
b-rank test for bits 1 to 8, p=0.80522
b-rank test for bits 2 to 9, p=0.54662
b-rank test for bits 3 to 10, p=0.64568
b-rank test for bits 4 to 11, p=0.40668
b-rank test for bits 5 to 12, p=0.55692
b-rank test for bits 6 to 13, p=0.49272
b-rank test for bits 7 to 14, p=0.11194
b-rank test for bits 8 to 15, p=0.05962
b-rank test for bits 9 to 16, p=0.76542
b-rank test for bits 10 to 17, p=0.07144
b-rank test for bits 11 to 18, p=0.48422
b-rank test for bits 12 to 19, p=0.57063
b-rank test for bits 13 to 20, p=0.93803
b-rank test for bits 14 to 21, p=0.80220
b-rank test for bits 15 to 22, p=0.75562
b-rank test for bits 16 to 23, p=0.37647
b-rank test for bits 17 to 24, p=0.53140
b-rank test for bits 18 to 25, p=0.24407
b-rank test for bits 19 to 26, p=0.78020
b-rank test for bits 20 to 27, p=0.31602
b-rank test for bits 21 to 28, p=0.67979
b-rank test for bits 22 to 29, p=0.08664
b-rank test for bits 23 to 30, p=0.99363
b-rank test for bits 24 to 31, p=0.46035
b-rank test for bits 25 to 32, p=0.85284
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 = 0.740905
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_09:31
(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 141538 -0.87 0.192808
2 142474 1.32 0.906469
3 141965 0.13 0.551745
4 141206 -1.64 0.050161
5 141362 -1.28 0.100482
6 141361 -1.28 0.100071
7 142179 0.63 0.735676
8 141195 -1.67 0.047559
9 141690 -0.51 0.304167
10 142577 1.56 0.940617
11 141879 -0.07 0.471753
12 141132 -1.82 0.034671
13 142281 0.87 0.807409
14 142309 0.93 0.824799
15 141359 -1.29 0.099253
16 141880 -0.07 0.472683
17 142382 1.10 0.865284
18 141901 -0.02 0.492236
19 141957 0.11 0.544342
20 141402 -1.19 0.117939
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_09:31
Bits used No. missing words z-score p-value
23 to 32 142215 1.0540 0.854066
22 to 31 142015 0.3644 0.642213
21 to 30 142242 1.1471 0.874338
20 to 29 142124 0.7402 0.770423
19 to 28 141623 -0.9873 0.161737
18 to 27 141878 -0.1080 0.456984
17 to 26 142029 0.4127 0.660070
16 to 25 141684 -0.7770 0.218579
15 to 24 142512 2.0782 0.981153
14 to 23 142138 0.7885 0.784803
13 to 22 142131 0.7644 0.777679
12 to 21 142441 1.8333 0.966624
11 to 20 142342 1.4920 0.932146
10 to 19 141999 0.3092 0.621418
9 to 18 141498 -1.4184 0.078040
8 to 17 141910 0.0023 0.500922
7 to 16 142613 2.4264 0.992376
6 to 15 141631 -0.9598 0.168588
5 to 14 142075 0.5713 0.716094
4 to 13 141927 0.0609 0.524293
3 to 12 141792 -0.4046 0.342891
2 to 11 141899 -0.0356 0.485792
1 to 10 141464 -1.5356 0.062316
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_09:31
Bits used No. missing words z-score p-value
28 to 32 141765 -0.4893 0.312331
27 to 31 142089 0.6091 0.728755
26 to 30 142265 1.2057 0.886026
25 to 29 142026 0.3955 0.653760
24 to 28 142075 0.5616 0.712803
23 to 27 142584 2.2870 0.988903
22 to 26 141588 -1.0893 0.138021
21 to 25 141757 -0.5164 0.302797
20 to 24 141729 -0.6113 0.270504
19 to 23 141818 -0.3096 0.378435
18 to 22 141618 -0.9876 0.161684
17 to 21 141350 -1.8960 0.028978
16 to 20 142511 2.0396 0.979303
15 to 19 141829 -0.2723 0.392694
14 to 18 141987 0.2633 0.603836
13 to 17 142057 0.5006 0.691665
12 to 16 142103 0.6565 0.744252
11 to 15 141757 -0.5164 0.302797
10 to 14 142123 0.7243 0.765561
9 to 13 141691 -0.7401 0.229619
8 to 12 141376 -1.8079 0.035311
7 to 11 142103 0.6565 0.744252
6 to 10 141766 -0.4859 0.313532
5 to 9 141830 -0.2689 0.393998
4 to 8 141589 -1.0859 0.138770
3 to 7 142384 1.6091 0.946197
2 to 6 141914 0.0158 0.506315
1 to 5 141419 -1.6621 0.048243
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_09:31
Bits used No. missing words z-score p-value
31 to 32 142126 0.6391 0.738636
30 to 31 142166 0.7571 0.775517
29 to 30 142321 1.2144 0.887696
28 to 29 141584 -0.9597 0.168609
27 to 28 142004 0.2793 0.609978
26 to 27 142149 0.7070 0.760214
25 to 26 141994 0.2498 0.598615
24 to 25 142059 0.4415 0.670576
23 to 24 142308 1.1760 0.880206
22 to 23 142148 0.7040 0.759297
21 to 22 142416 1.4946 0.932491
20 to 21 142297 1.1436 0.873599
19 to 20 142168 0.7630 0.777280
18 to 19 141346 -1.6617 0.048282
17 to 18 142298 1.1465 0.874210
16 to 17 141357 -1.6293 0.051626
15 to 16 142613 2.0757 0.981040
14 to 15 141334 -1.6971 0.044835
13 to 14 141800 -0.3225 0.373534
12 to 13 141746 -0.4818 0.314974
11 to 12 141575 -0.9862 0.162012
10 to 11 142187 0.8191 0.793631
9 to 10 142225 0.9312 0.824120
8 to 9 141817 -0.2724 0.392673
7 to 8 141734 -0.5172 0.302509
6 to 7 141935 0.0757 0.530180
5 to 6 142005 0.2822 0.611110
4 to 5 141879 -0.0895 0.464355
3 to 4 141706 -0.5998 0.274322
2 to 3 141804 -0.3107 0.378011
1 to 2 142216 0.9046 0.817170
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2488.86 -0.157 0.437429
Test results for specific bytes for dh-ranFile-2018-06-15_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2478.98 -0.297 0.383128
2 to 9 2594.89 1.342 0.910197
3 to 10 2430.78 -0.979 0.163811
4 to 11 2433.80 -0.936 0.174578
5 to 12 2596.99 1.372 0.914914
6 to 13 2483.35 -0.235 0.406931
7 to 14 2397.42 -1.451 0.073427
8 to 15 2559.09 0.836 0.798330
9 to 16 2572.22 1.021 0.846446
10 to 17 2440.37 -0.843 0.199533
11 to 18 2502.02 0.029 0.511413
12 to 19 2574.94 1.060 0.855375
13 to 20 2486.29 -0.194 0.423129
14 to 21 2460.78 -0.555 0.289550
15 to 22 2437.02 -0.891 0.186571
16 to 23 2396.75 -1.460 0.072120
17 to 24 2414.81 -1.205 0.114137
18 to 25 2324.11 -2.487 0.006433
19 to 26 2318.54 -2.566 0.005140
20 to 27 2602.90 1.455 0.927192
21 to 28 2574.53 1.054 0.854071
22 to 29 2423.49 -1.082 0.139631
23 to 30 2475.33 -0.349 0.363588
24 to 31 2476.05 -0.339 0.367414
25 to 32 2566.12 0.935 0.825134
CDPARK for dh-ranFile-2018-06-15_09:31: 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
3512 -0.5023 0.307734
3564 1.8721 0.969407
3530 0.3196 0.625377
3510 -0.5936 0.276387
3531 0.3653 0.642555
3518 -0.2283 0.409702
3504 -0.8676 0.192812
3524 0.0457 0.518210
3531 0.3653 0.642555
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3524.30 sample std.=15.92
p-value of the KSTEST for those 10 p-values: 0.592705
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_09:31
0.9231,0.6449,0.2722,0.6281,0.6592,0.0419,0.6436,0.6568,0.8626,0.0326,
The KS test for those 10 p-values: 0.461085
The 3DSPHERES test for dh-ranFile-2018-06-15_09:31
sample no r^3 equiv. uni.
1 8.697 0.251672
2 0.923 0.030311
3 17.197 0.436305
4 51.927 0.822872
5 40.694 0.742433
6 13.161 0.355118
7 26.151 0.581759
8 5.161 0.158041
9 11.630 0.321357
10 18.689 0.463654
11 24.500 0.558099
12 1.715 0.055559
13 3.844 0.120262
14 17.042 0.433388
15 5.202 0.159201
16 42.048 0.753799
17 49.232 0.806226
18 96.804 0.960316
19 35.025 0.688854
20 37.632 0.714755
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.950697
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.9 0.8 -1.1 0.2 1.8
-0.9 -2.0 0.8 -0.1 2.2 -1.8
-0.6 -1.6 0.7 0.3 0.4 0.2
0.0 2.2 -0.3 0.4 -1.1 -1.8
1.1 1.0 0.1 -0.5 -0.5 -1.7
2.0 0.2 -0.1 -0.6 -0.6 -1.6
-0.7 -1.0 -0.4 -0.7 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:50.201295
z-score=0.894835, p-value=0.819681
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_09:31
Test no p-value
1 0.413233
2 0.041977
3 0.828711
4 0.229728
5 0.518783
6 0.444663
7 0.103456
8 0.562908
9 0.369027
10 0.527630
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.385311
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_09:31:
(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 66978 1.45 66962 1.31
3 25000.00 24751 2.48 24760 2.30
4 6666.67 6638 0.12 6723 0.48
5 1388.89 1359 0.64 1287 7.47
6 238.10 231 0.21 224 0.83
7 34.72 34 0.01 34 0.01
8 4.96 8 1.86 9 3.29
p=0.65930 p=0.98456
Number of rngs required: 686748, p-value: 0.026
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_09:31
No. of wins: Observed Expected
98318 98585.9
z-score=-1.198, pvalue=0.11545
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67042 66666.7 2.113 2.113
2 37552 37654.3 0.278 2.391
3 26754 26954.7 1.495 3.886
4 19629 19313.5 5.155 9.041
5 13674 13851.4 2.273 11.314
6 9868 9943.5 0.574 11.888
7 7201 7145.0 0.439 12.326
8 5079 5139.1 0.702 13.028
9 3706 3699.9 0.010 13.039
10 2654 2666.3 0.057 13.095
11 1938 1923.3 0.112 13.207
12 1385 1388.7 0.010 13.217
13 983 1003.7 0.428 13.645
14 730 726.1 0.021 13.665
15 495 525.8 1.808 15.474
16 373 381.2 0.174 15.648
17 266 276.5 0.402 16.050
18 180 200.8 2.160 18.210
19 126 146.0 2.736 20.946
20 97 106.2 0.800 21.745
21 268 287.1 1.272 23.018
Chisq= 23.02 for 20 degrees of freedom, p= 0.71207
SUMMARY of craptest
p-value for no. of wins: 0.115455
p-value for throws/game: 0.712074
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_09:31
No. of wins: Observed Expected
98548 98585.9
z-score=-0.169, pvalue=0.43277
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66604 66666.7 0.059 0.059
2 37803 37654.3 0.587 0.646
3 26853 26954.7 0.384 1.030
4 19370 19313.5 0.166 1.195
5 13843 13851.4 0.005 1.201
6 9743 9943.5 4.045 5.245
7 7126 7145.0 0.051 5.296
8 5205 5139.1 0.846 6.142
9 3684 3699.9 0.068 6.210
10 2719 2666.3 1.042 7.251
11 1910 1923.3 0.092 7.344
12 1353 1388.7 0.920 8.264
13 1042 1003.7 1.460 9.724
14 752 726.1 0.921 10.645
15 545 525.8 0.698 11.343
16 415 381.2 3.006 14.349
17 301 276.5 2.164 16.513
18 191 200.8 0.481 16.994
19 143 146.0 0.061 17.055
20 101 106.2 0.256 17.311
21 297 287.1 0.340 17.651
Chisq= 17.65 for 20 degrees of freedom, p= 0.38965
SUMMARY of craptest
p-value for no. of wins: 0.432770
p-value for throws/game: 0.389645
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0051,0.0064,0.0255,0.0290,0.0297,0.0303,0.0326,0.0347,0.0353,0.0419,
0.0420,0.0448,0.0476,0.0482,0.0483,0.0502,0.0516,0.0556,0.0586,0.0592,
0.0596,0.0623,0.0714,0.0721,0.0734,0.0775,0.0780,0.0835,0.0866,0.0993,
0.1001,0.1005,0.1035,0.1119,0.1125,0.1141,0.1155,0.1179,0.1203,0.1380,
0.1388,0.1396,0.1406,0.1573,0.1580,0.1592,0.1617,0.1617,0.1620,0.1638,
0.1686,0.1686,0.1746,0.1824,0.1866,0.1928,0.1928,0.1995,0.2186,0.2296,
0.2297,0.2441,0.2449,0.2517,0.2705,0.2722,0.2743,0.2764,0.2775,0.2820,
0.2869,0.2884,0.2895,0.3025,0.3028,0.3028,0.3042,0.3077,0.3083,0.3122,
0.3123,0.3135,0.3150,0.3160,0.3190,0.3214,0.3223,0.3429,0.3551,0.3636,
0.3674,0.3690,0.3699,0.3702,0.3735,0.3765,0.3766,0.3771,0.3780,0.3784,
0.3831,0.3853,0.3865,0.3896,0.3927,0.3927,0.3940,0.4067,0.4069,0.4097,
0.4132,0.4231,0.4275,0.4281,0.4322,0.4328,0.4334,0.4363,0.4374,0.4447,
0.4570,0.4604,0.4611,0.4637,0.4644,0.4718,0.4727,0.4842,0.4858,0.4922,
0.4927,0.5002,0.5009,0.5013,0.5063,0.5114,0.5182,0.5188,0.5243,0.5276,
0.5302,0.5314,0.5443,0.5466,0.5517,0.5569,0.5570,0.5581,0.5629,0.5667,
0.5706,0.5812,0.5818,0.5927,0.5986,0.6038,0.6100,0.6111,0.6214,0.6227,
0.6254,0.6281,0.6287,0.6422,0.6426,0.6426,0.6436,0.6437,0.6449,0.6457,
0.6461,0.6538,0.6546,0.6568,0.6592,0.6593,0.6601,0.6706,0.6756,0.6798,
0.6889,0.6917,0.7121,0.7128,0.7145,0.7148,0.7161,0.7259,0.7288,0.7288,
0.7357,0.7386,0.7388,0.7409,0.7424,0.7443,0.7443,0.7538,0.7556,0.7593,
0.7602,0.7654,0.7656,0.7677,0.7704,0.7755,0.7773,0.7777,0.7802,0.7848,
0.7936,0.7983,0.7996,0.8022,0.8052,0.8062,0.8074,0.8152,0.8172,0.8197,
0.8229,0.8241,0.8248,0.8251,0.8285,0.8287,0.8408,0.8449,0.8464,0.8528,
0.8541,0.8541,0.8554,0.8626,0.8653,0.8676,0.8736,0.8742,0.8743,0.8802,
0.8860,0.8877,0.8946,0.9065,0.9102,0.9149,0.9231,0.9269,0.9272,0.9320,
0.9321,0.9325,0.9380,0.9406,0.9462,0.9507,0.9570,0.9603,0.9666,0.9694,
0.9778,0.9793,0.9810,0.9812,0.9846,0.9889,0.9924,0.9936,0.9941,
Overall p-value after applying KStest on 269 p-values = 0.847807
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.