RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.56 15.1258 0.413581
2 to 25 15.93 8.8654 0.055610
3 to 26 15.87 23.4215 0.863975
4 to 27 16.08 10.1692 0.103633
5 to 28 15.77 15.1379 0.414448
6 to 29 15.77 22.0856 0.818550
7 to 30 15.85 20.9731 0.772506
8 to 31 15.70 17.1542 0.556032
9 to 32 15.96 11.3443 0.161884
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.910941
Tough bday spacings test for dh-ranFile-2018-06-29_20:31: 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 82 100 93 64 58 33 12 10 4
(O-E)^2/E 1.1 0.1 1.0 0.1 0.2 2.6 0.7 0.4 0.6 1.7 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.333, p= 0.404
RESULTS OF GCD FOR dh-ranFile-2018-06-29_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.701895
p-value, dist. of gcd's: 0.648894
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.270 0.124 0.325 0.357 0.411 0.022 0.001 0.931
Bits 8 to 15---> 0.722 0.312 0.479 0.951 0.320 0.470 0.045 0.783
Bits 16 to 23---> 0.535 0.987 0.261 0.874 0.373 0.279 0.629 0.946
Bits 24 to 31---> 0.442 0.948 0.733 0.627 0.094 0.201 0.560 0.162
KS test for the above 32 p values: 0.312
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_20:31,
p-values for 5 runs: 0.3870, 0.0989, 0.1220, 0.4106, 0.9797
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 190 211.4 2.170 2.170
r= 29 5008 5134.0 3.093 5.263
r= 30 23287 23103.0 1.465 6.727
r= 31 11515 11551.5 0.115 6.843
chi-square = 6.843 with df = 3; p-value = 0.923
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 216 211.4 0.099 0.099
r= 30 5077 5134.0 0.633 0.732
r= 31 23261 23103.0 1.080 1.812
r= 32 11446 11551.5 0.964 2.776
chi-square = 2.776 with df = 3; p-value = 0.573
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_20:31
b-rank test for bits 1 to 8, p=0.20646
b-rank test for bits 2 to 9, p=0.55938
b-rank test for bits 3 to 10, p=0.13215
b-rank test for bits 4 to 11, p=0.33308
b-rank test for bits 5 to 12, p=0.49781
b-rank test for bits 6 to 13, p=0.28423
b-rank test for bits 7 to 14, p=0.51067
b-rank test for bits 8 to 15, p=0.09830
b-rank test for bits 9 to 16, p=0.18825
b-rank test for bits 10 to 17, p=0.77248
b-rank test for bits 11 to 18, p=0.49570
b-rank test for bits 12 to 19, p=0.80538
b-rank test for bits 13 to 20, p=0.69683
b-rank test for bits 14 to 21, p=0.61624
b-rank test for bits 15 to 22, p=0.63872
b-rank test for bits 16 to 23, p=0.73492
b-rank test for bits 17 to 24, p=0.04149
b-rank test for bits 18 to 25, p=0.51323
b-rank test for bits 19 to 26, p=0.06752
b-rank test for bits 20 to 27, p=0.16313
b-rank test for bits 21 to 28, p=0.56962
b-rank test for bits 22 to 29, p=0.66527
b-rank test for bits 23 to 30, p=0.02446
b-rank test for bits 24 to 31, p=0.36977
b-rank test for bits 25 to 32, p=0.85702
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 = 0.325315
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_20:31
(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 141741 -0.39 0.347051
2 141549 -0.84 0.199924
3 142264 0.83 0.796354
4 142151 0.56 0.713844
5 140529 -3.23 0.000630
6 141627 -0.66 0.254739
7 141193 -1.67 0.047098
8 142303 0.92 0.821159
9 141893 -0.04 0.484782
10 141709 -0.47 0.319871
11 141875 -0.08 0.468035
12 142052 0.33 0.630562
13 142066 0.37 0.642837
14 141642 -0.62 0.266116
15 141704 -0.48 0.315705
16 142109 0.47 0.679578
17 141220 -1.61 0.053635
18 141530 -0.89 0.187732
19 141027 -2.06 0.019627
20 142202 0.68 0.752952
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_20:31
Bits used No. missing words z-score p-value
23 to 32 141884 -0.0873 0.465199
22 to 31 142161 0.8678 0.807256
21 to 30 142076 0.5747 0.717261
20 to 29 142240 1.1402 0.872907
19 to 28 141957 0.1644 0.565284
18 to 27 142163 0.8747 0.809138
17 to 26 141600 -1.0667 0.143064
16 to 25 141784 -0.4322 0.332808
15 to 24 142141 0.7989 0.787815
14 to 23 141995 0.2954 0.616161
13 to 22 141805 -0.3598 0.359514
12 to 21 141595 -1.0839 0.139205
11 to 20 141858 -0.1770 0.429754
10 to 19 141732 -0.6115 0.270440
9 to 18 142112 0.6989 0.757681
8 to 17 141880 -0.1011 0.459721
7 to 16 142166 0.8851 0.811940
6 to 15 142110 0.6920 0.755521
5 to 14 141551 -1.2356 0.108300
4 to 13 142109 0.6885 0.754436
3 to 12 142499 2.0333 0.978991
2 to 11 142742 2.8713 0.997956
1 to 10 142274 1.2575 0.895711
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_20:31
Bits used No. missing words z-score p-value
28 to 32 141688 -0.7503 0.226546
27 to 31 141920 0.0362 0.514426
26 to 30 141862 -0.1604 0.436267
25 to 29 142122 0.7209 0.764519
24 to 28 141760 -0.5062 0.306357
23 to 27 141366 -1.8418 0.032752
22 to 26 141918 0.0294 0.511723
21 to 25 142049 0.4735 0.682057
20 to 24 141882 -0.0926 0.463093
19 to 23 142173 0.8938 0.814285
18 to 22 142373 1.5718 0.941997
17 to 21 141837 -0.2452 0.403156
16 to 20 142194 0.9650 0.832723
15 to 19 142246 1.1413 0.873118
14 to 18 141490 -1.4215 0.077592
13 to 17 142413 1.7074 0.956122
12 to 16 141822 -0.2960 0.383602
11 to 15 141402 -1.7198 0.042738
10 to 14 141534 -1.2723 0.101632
9 to 13 141791 -0.4011 0.344166
8 to 12 141919 0.0328 0.513075
7 to 11 141676 -0.7909 0.214487
6 to 10 141685 -0.7604 0.223496
5 to 9 141897 -0.0418 0.483330
4 to 8 141461 -1.5198 0.064285
3 to 7 142059 0.5074 0.694048
2 to 6 142390 1.6294 0.948385
1 to 5 141862 -0.1604 0.436267
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_20:31
Bits used No. missing words z-score p-value
31 to 32 141345 -1.6647 0.047987
30 to 31 142271 1.0669 0.856985
29 to 30 142050 0.4150 0.660913
28 to 29 142356 1.3176 0.906183
27 to 28 141509 -1.1809 0.118818
26 to 27 141990 0.2380 0.594046
25 to 26 142014 0.3088 0.621248
24 to 25 141805 -0.3078 0.379133
23 to 24 141418 -1.4494 0.073620
22 to 23 142196 0.8456 0.801122
21 to 22 141527 -1.1278 0.129699
20 to 21 141832 -0.2281 0.409780
19 to 20 141112 -2.3520 0.009336
18 to 19 142448 1.5890 0.943969
17 to 18 142152 0.7158 0.762955
16 to 17 142196 0.8456 0.801122
15 to 16 141971 0.1819 0.572176
14 to 15 141969 0.1760 0.569860
13 to 14 141965 0.1642 0.565220
12 to 13 142081 0.5064 0.693713
11 to 12 141559 -1.0334 0.150703
10 to 11 141785 -0.3668 0.356901
9 to 10 142156 0.7276 0.766583
8 to 9 142144 0.6922 0.755607
7 to 8 141952 0.1259 0.550083
6 to 7 141641 -0.7915 0.214316
5 to 6 142424 1.5182 0.935518
4 to 5 141973 0.1878 0.574490
3 to 4 141590 -0.9420 0.173102
2 to 3 142202 0.8633 0.806023
1 to 2 141717 -0.5673 0.285240
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2606.01 1.499 0.933093
Test results for specific bytes for dh-ranFile-2018-06-29_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2555.38 0.783 0.783249
2 to 9 2465.52 -0.488 0.312906
3 to 10 2551.02 0.721 0.764695
4 to 11 2512.84 0.182 0.572052
5 to 12 2422.86 -1.091 0.137646
6 to 13 2457.49 -0.601 0.273879
7 to 14 2402.53 -1.378 0.084033
8 to 15 2507.88 0.111 0.544387
9 to 16 2420.54 -1.124 0.130559
10 to 17 2541.55 0.588 0.721596
11 to 18 2485.03 -0.212 0.416150
12 to 19 2662.52 2.298 0.989230
13 to 20 2392.35 -1.522 0.063960
14 to 21 2565.46 0.926 0.822716
15 to 22 2524.99 0.353 0.638122
16 to 23 2579.38 1.123 0.869185
17 to 24 2445.73 -0.768 0.221377
18 to 25 2543.97 0.622 0.732960
19 to 26 2473.79 -0.371 0.355438
20 to 27 2500.94 0.013 0.505315
21 to 28 2397.66 -1.447 0.073897
22 to 29 2541.45 0.586 0.721149
23 to 30 2487.20 -0.181 0.428199
24 to 31 2488.76 -0.159 0.436838
25 to 32 2494.31 -0.080 0.467959
CDPARK for dh-ranFile-2018-06-29_20:31: 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
3522 -0.0457 0.481790
3536 0.5936 0.723613
3516 -0.3196 0.374623
3534 0.5023 0.692266
3527 0.1826 0.572463
3516 -0.3196 0.374623
3505 -0.8219 0.205562
3519 -0.1826 0.427537
3508 -0.6849 0.246694
Square side=100, avg. no. parked=3519.50 sample std.=9.84
p-value of the KSTEST for those 10 p-values: 0.281101
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_20:31
0.9415,0.4245,0.1645,0.8121,0.7771,0.2609,0.6668,0.2782,0.3136,0.1688,
The KS test for those 10 p-values: 0.857924
The 3DSPHERES test for dh-ranFile-2018-06-29_20:31
sample no r^3 equiv. uni.
1 13.620 0.364909
2 74.135 0.915515
3 85.675 0.942491
4 34.389 0.682189
5 1.164 0.038062
6 37.999 0.718226
7 25.580 0.573730
8 22.033 0.520230
9 6.344 0.190608
10 64.637 0.884045
11 3.078 0.097522
12 46.820 0.790006
13 20.743 0.499140
14 26.222 0.582747
15 17.662 0.444962
16 59.062 0.860367
17 4.403 0.136491
18 106.292 0.971075
19 15.963 0.412623
20 2.565 0.081944
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.886473
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 -2.0 -0.3 0.3 -0.2
-1.2 0.6 0.1 -0.1 1.1 -0.6
1.3 -0.6 0.0 -0.4 0.1 -0.7
-0.1 0.2 -1.1 0.7 -0.5 0.5
1.0 -1.6 1.5 1.1 0.1 -0.3
2.6 -1.8 -0.3 -1.0 -0.9 -0.5
0.0 -2.0 0.5 -0.1 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:38.682529
z-score=-0.361966, p-value=0.382603
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_20:31
Test no p-value
1 0.151736
2 0.290581
3 0.357720
4 0.197454
5 0.073612
6 0.167031
7 0.101463
8 0.268224
9 0.173803
10 0.525096
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.003370
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_20:31:
(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 66572 0.13 66730 0.06
3 25000.00 25034 0.05 24889 0.49
4 6666.67 6715 0.35 6754 1.14
5 1388.89 1394 0.02 1365 0.41
6 238.10 237 0.01 222 1.09
7 34.72 43 1.97 37 0.15
8 4.96 4 0.19 2 1.77
p=0.15636 p=0.47048
Number of rngs required: 687971, p-value: 0.309
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_20:31
No. of wins: Observed Expected
98664 98585.9
z-score= 0.349, pvalue=0.63664
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66188 66666.7 3.437 3.437
2 37605 37654.3 0.065 3.501
3 27227 26954.7 2.750 6.252
4 19385 19313.5 0.265 6.517
5 13766 13851.4 0.527 7.043
6 10193 9943.5 6.258 13.302
7 7090 7145.0 0.424 13.725
8 5132 5139.1 0.010 13.735
9 3743 3699.9 0.503 14.238
10 2732 2666.3 1.619 15.857
11 1871 1923.3 1.424 17.281
12 1403 1388.7 0.146 17.427
13 982 1003.7 0.470 17.897
14 702 726.1 0.803 18.699
15 549 525.8 1.020 19.720
16 399 381.2 0.836 20.556
17 269 276.5 0.206 20.761
18 207 200.8 0.190 20.951
19 152 146.0 0.248 21.199
20 110 106.2 0.135 21.334
21 295 287.1 0.217 21.550
Chisq= 21.55 for 20 degrees of freedom, p= 0.63460
SUMMARY of craptest
p-value for no. of wins: 0.636641
p-value for throws/game: 0.634597
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_20:31
No. of wins: Observed Expected
98663 98585.9
z-score= 0.345, pvalue=0.63496
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66766 66666.7 0.148 0.148
2 37707 37654.3 0.074 0.222
3 26838 26954.7 0.506 0.727
4 19019 19313.5 4.490 5.217
5 13933 13851.4 0.480 5.697
6 10066 9943.5 1.508 7.205
7 7093 7145.0 0.379 7.584
8 5190 5139.1 0.505 8.089
9 3693 3699.9 0.013 8.102
10 2704 2666.3 0.533 8.635
11 1894 1923.3 0.447 9.082
12 1346 1388.7 1.315 10.397
13 1036 1003.7 1.038 11.436
14 753 726.1 0.994 12.429
15 565 525.8 2.917 15.346
16 358 381.2 1.406 16.752
17 283 276.5 0.151 16.903
18 218 200.8 1.468 18.371
19 132 146.0 1.340 19.711
20 122 106.2 2.346 22.057
21 284 287.1 0.034 22.090
Chisq= 22.09 for 20 degrees of freedom, p= 0.66438
SUMMARY of craptest
p-value for no. of wins: 0.634961
p-value for throws/game: 0.664377
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0007,0.0034,0.0093,0.0196,0.0223,0.0245,0.0328,0.0381,0.0415,
0.0427,0.0450,0.0471,0.0480,0.0536,0.0556,0.0640,0.0643,0.0675,0.0736,
0.0736,0.0739,0.0776,0.0819,0.0840,0.0940,0.0975,0.0983,0.0989,0.1015,
0.1016,0.1036,0.1083,0.1188,0.1220,0.1238,0.1297,0.1306,0.1322,0.1365,
0.1376,0.1392,0.1431,0.1507,0.1517,0.1564,0.1619,0.1619,0.1631,0.1645,
0.1670,0.1688,0.1731,0.1738,0.1877,0.1882,0.1906,0.1975,0.1999,0.2007,
0.2056,0.2065,0.2143,0.2145,0.2214,0.2235,0.2265,0.2467,0.2547,0.2605,
0.2609,0.2661,0.2682,0.2696,0.2704,0.2739,0.2782,0.2790,0.2811,0.2842,
0.2852,0.2906,0.3064,0.3077,0.3093,0.3116,0.3125,0.3129,0.3136,0.3157,
0.3196,0.3199,0.3249,0.3253,0.3328,0.3331,0.3442,0.3471,0.3554,0.3568,
0.3569,0.3577,0.3595,0.3649,0.3698,0.3733,0.3746,0.3746,0.3791,0.3826,
0.3836,0.3870,0.4032,0.4037,0.4098,0.4106,0.4114,0.4126,0.4136,0.4144,
0.4162,0.4245,0.4275,0.4282,0.4298,0.4363,0.4363,0.4368,0.4417,0.4450,
0.4597,0.4631,0.4652,0.4680,0.4680,0.4697,0.4705,0.4793,0.4818,0.4833,
0.4848,0.4957,0.4978,0.4991,0.5053,0.5107,0.5117,0.5131,0.5132,0.5144,
0.5202,0.5251,0.5354,0.5444,0.5501,0.5560,0.5594,0.5597,0.5652,0.5653,
0.5696,0.5699,0.5721,0.5722,0.5725,0.5726,0.5737,0.5745,0.5827,0.5940,
0.6162,0.6162,0.6212,0.6266,0.6289,0.6306,0.6346,0.6350,0.6366,0.6381,
0.6387,0.6428,0.6489,0.6609,0.6644,0.6653,0.6668,0.6796,0.6821,0.6822,
0.6923,0.6937,0.6940,0.6968,0.7019,0.7138,0.7173,0.7182,0.7211,0.7216,
0.7216,0.7236,0.7330,0.7334,0.7349,0.7530,0.7544,0.7555,0.7556,0.7577,
0.7630,0.7645,0.7647,0.7666,0.7725,0.7725,0.7771,0.7832,0.7832,0.7878,
0.7900,0.7964,0.8011,0.8011,0.8054,0.8060,0.8073,0.8091,0.8119,0.8121,
0.8143,0.8185,0.8212,0.8227,0.8327,0.8570,0.8570,0.8579,0.8604,0.8640,
0.8692,0.8729,0.8731,0.8738,0.8840,0.8865,0.8957,0.9062,0.9109,0.9155,
0.9229,0.9306,0.9331,0.9355,0.9415,0.9420,0.9425,0.9440,0.9459,0.9480,
0.9484,0.9508,0.9561,0.9711,0.9790,0.9797,0.9872,0.9892,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.480718
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.