RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_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 15.93 6.4633 0.010508
2 to 25 15.66 19.9123 0.721262
3 to 26 15.62 21.0654 0.776622
4 to 27 16.08 15.6491 0.451170
5 to 28 15.97 15.5222 0.442080
6 to 29 15.60 20.4332 0.747328
7 to 30 15.21 28.2016 0.957363
8 to 31 15.62 15.7106 0.455561
9 to 32 15.79 26.3499 0.931683
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.305355
Tough bday spacings test for dh-ranFile-2018-06-27_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 9 32 73 97 96 76 54 35 24 2 2
(O-E)^2/E 0.0 0.6 0.0 0.0 0.0 0.1 0.1 0.9 5.6 3.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 11.522, p= 0.682
RESULTS OF GCD FOR dh-ranFile-2018-06-27_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.254871
p-value, dist. of gcd's: 0.466455
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.090 0.047 0.654 0.514 0.555 0.338 0.625 0.515
Bits 8 to 15---> 0.149 0.256 0.316 0.517 0.201 0.069 0.382 0.337
Bits 16 to 23---> 0.952 0.008 0.745 0.945 0.526 0.213 0.537 0.532
Bits 24 to 31---> 0.831 0.317 0.838 0.457 0.221 0.419 0.702 0.039
KS test for the above 32 p values: 0.716
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_14:31,
p-values for 5 runs: 0.1014, 0.6475, 0.7224, 0.7710, 0.3628
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5058 5134.0 1.125 1.157
r= 30 23164 23103.0 0.161 1.318
r= 31 11564 11551.5 0.013 1.331
chi-square = 1.331 with df = 3; p-value = 0.278
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5124 5134.0 0.020 0.636
r= 31 23101 23103.0 0.000 0.636
r= 32 11575 11551.5 0.048 0.684
chi-square = 0.684 with df = 3; p-value = 0.123
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_14:31
b-rank test for bits 1 to 8, p=0.92837
b-rank test for bits 2 to 9, p=0.65990
b-rank test for bits 3 to 10, p=0.89360
b-rank test for bits 4 to 11, p=0.55332
b-rank test for bits 5 to 12, p=0.75117
b-rank test for bits 6 to 13, p=0.55296
b-rank test for bits 7 to 14, p=0.92186
b-rank test for bits 8 to 15, p=0.27760
b-rank test for bits 9 to 16, p=0.25765
b-rank test for bits 10 to 17, p=0.56402
b-rank test for bits 11 to 18, p=0.37434
b-rank test for bits 12 to 19, p=0.44114
b-rank test for bits 13 to 20, p=0.67746
b-rank test for bits 14 to 21, p=0.86752
b-rank test for bits 15 to 22, p=0.81903
b-rank test for bits 16 to 23, p=0.00358
b-rank test for bits 17 to 24, p=0.16684
b-rank test for bits 18 to 25, p=0.36924
b-rank test for bits 19 to 26, p=0.84226
b-rank test for bits 20 to 27, p=0.15352
b-rank test for bits 21 to 28, p=0.28256
b-rank test for bits 22 to 29, p=0.93321
b-rank test for bits 23 to 30, p=0.36982
b-rank test for bits 24 to 31, p=0.18300
b-rank test for bits 25 to 32, p=0.38033
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 = 0.768647
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_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 141606 -0.71 0.239251
2 142041 0.31 0.620822
3 142166 0.60 0.725646
4 141800 -0.26 0.399190
5 141752 -0.37 0.356588
6 141959 0.12 0.546194
7 141610 -0.70 0.242161
8 141660 -0.58 0.280099
9 142128 0.51 0.695293
10 141894 -0.04 0.485714
11 142103 0.45 0.674546
12 141582 -0.76 0.222198
13 141458 -1.05 0.145825
14 142183 0.64 0.738724
15 141788 -0.28 0.388404
16 141986 0.18 0.571084
17 142117 0.49 0.686236
18 142069 0.37 0.645448
19 142070 0.38 0.646317
20 141955 0.11 0.542489
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_14:31
Bits used No. missing words z-score p-value
23 to 32 141493 -1.4356 0.075555
22 to 31 141916 0.0230 0.509175
21 to 30 142109 0.6885 0.754436
20 to 29 141763 -0.5046 0.306925
19 to 28 142315 1.3989 0.919073
18 to 27 141748 -0.5563 0.288999
17 to 26 141551 -1.2356 0.108300
16 to 25 142041 0.4540 0.675098
15 to 24 141813 -0.3322 0.369880
14 to 23 141729 -0.6218 0.267028
13 to 22 141746 -0.5632 0.286647
12 to 21 141309 -2.0701 0.019221
11 to 20 141429 -1.6563 0.048830
10 to 19 141381 -1.8218 0.034241
9 to 18 141291 -2.1322 0.016496
8 to 17 142154 0.8437 0.800579
7 to 16 141921 0.0402 0.516050
6 to 15 141750 -0.5494 0.291361
5 to 14 141645 -0.9115 0.181021
4 to 13 141456 -1.5632 0.059002
3 to 12 141686 -0.7701 0.220619
2 to 11 141967 0.1989 0.578815
1 to 10 141742 -0.5770 0.281970
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_14:31
Bits used No. missing words z-score p-value
28 to 32 141456 -1.5367 0.062182
27 to 31 141825 -0.2859 0.387491
26 to 30 142186 0.9379 0.825843
25 to 29 141752 -0.5333 0.296905
24 to 28 141873 -0.1232 0.450993
23 to 27 141467 -1.4994 0.066882
22 to 26 142361 1.5311 0.937126
21 to 25 141602 -1.0418 0.148753
20 to 24 142072 0.5514 0.709328
19 to 23 142233 1.0972 0.863720
18 to 22 141543 -1.2418 0.107156
17 to 21 142161 0.8531 0.803203
16 to 20 141863 -0.1571 0.437602
15 to 19 142142 0.7887 0.784860
14 to 18 141702 -0.7028 0.241086
13 to 17 141806 -0.3503 0.363068
12 to 16 141914 0.0158 0.506315
11 to 15 141822 -0.2960 0.383602
10 to 14 142079 0.5752 0.717406
9 to 13 142351 1.4972 0.932828
8 to 12 141505 -1.3706 0.085248
7 to 11 141539 -1.2554 0.104675
6 to 10 141727 -0.6181 0.268265
5 to 9 142125 0.7311 0.767636
4 to 8 141602 -1.0418 0.148753
3 to 7 141779 -0.4418 0.329318
2 to 6 141976 0.2260 0.589399
1 to 5 142025 0.3921 0.652509
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_14:31
Bits used No. missing words z-score p-value
31 to 32 141246 -1.9567 0.025190
30 to 31 142143 0.6893 0.754680
29 to 30 142441 1.5683 0.941600
28 to 29 142396 1.4356 0.924443
27 to 28 141699 -0.6204 0.267483
26 to 27 142232 0.9518 0.829408
25 to 26 142182 0.8043 0.789399
24 to 25 141373 -1.5821 0.056814
23 to 24 141506 -1.1898 0.117070
22 to 23 141694 -0.6352 0.262652
21 to 22 142127 0.6421 0.739594
20 to 21 141844 -0.1927 0.423592
19 to 20 142027 0.3471 0.635745
18 to 19 141608 -0.8889 0.187034
17 to 18 142419 1.5035 0.933639
16 to 17 142190 0.8279 0.796146
15 to 16 142007 0.2881 0.613370
14 to 15 141471 -1.2930 0.098004
13 to 14 141674 -0.6942 0.243782
12 to 13 142294 1.1347 0.871754
11 to 12 142169 0.7660 0.778158
10 to 11 141906 -0.0098 0.496081
9 to 10 142013 0.3058 0.620126
8 to 9 142013 0.3058 0.620126
7 to 8 141977 0.1996 0.579110
6 to 7 141649 -0.7679 0.221263
5 to 6 141313 -1.7591 0.039282
4 to 5 141271 -1.8830 0.029852
3 to 4 141355 -1.6352 0.051004
2 to 3 141797 -0.3314 0.370187
1 to 2 141761 -0.4376 0.330856
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2501.69 0.024 0.509536
Test results for specific bytes for dh-ranFile-2018-06-27_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2520.86 0.295 0.615998
2 to 9 2520.42 0.289 0.613608
3 to 10 2486.92 -0.185 0.426622
4 to 11 2361.18 -1.963 0.024814
5 to 12 2620.43 1.703 0.955726
6 to 13 2529.21 0.413 0.660222
7 to 14 2420.81 -1.120 0.131385
8 to 15 2379.83 -1.699 0.044615
9 to 16 2463.36 -0.518 0.302189
10 to 17 2529.78 0.421 0.663188
11 to 18 2449.14 -0.719 0.235980
12 to 19 2534.56 0.489 0.687473
13 to 20 2626.97 1.796 0.963725
14 to 21 2471.08 -0.409 0.341275
15 to 22 2418.78 -1.149 0.125356
16 to 23 2568.22 0.965 0.832688
17 to 24 2471.87 -0.398 0.345405
18 to 25 2586.35 1.221 0.888993
19 to 26 2476.45 -0.333 0.369550
20 to 27 2501.99 0.028 0.511217
21 to 28 2533.72 0.477 0.683292
22 to 29 2495.97 -0.057 0.477302
23 to 30 2548.78 0.690 0.754854
24 to 31 2531.96 0.452 0.674374
25 to 32 2532.33 0.457 0.676247
CDPARK for dh-ranFile-2018-06-27_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
3514 -0.4110 0.340551
3504 -0.8676 0.192812
3530 0.3196 0.625377
3520 -0.1370 0.445521
3501 -1.0046 0.157553
3503 -0.9132 0.180558
3516 -0.3196 0.374623
3500 -1.0502 0.146807
3487 -1.6438 0.050105
3527 0.1826 0.572463
Square side=100, avg. no. parked=3510.20 sample std.=12.79
p-value of the KSTEST for those 10 p-values: 0.051801
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_14:31
0.8311,0.0047,0.6829,0.5119,0.8068,0.1083,0.4125,0.0197,0.2879,0.8292,
The KS test for those 10 p-values: 0.390273
The 3DSPHERES test for dh-ranFile-2018-06-27_14:31
sample no r^3 equiv. uni.
1 59.985 0.864596
2 4.500 0.139300
3 30.923 0.643261
4 23.776 0.547302
5 4.726 0.145748
6 4.453 0.137945
7 54.506 0.837464
8 4.081 0.127181
9 15.949 0.412356
10 6.662 0.199150
11 3.113 0.098574
12 31.892 0.654602
13 17.691 0.445515
14 12.435 0.339326
15 12.774 0.346762
16 66.831 0.892225
17 34.904 0.687597
18 18.059 0.452268
19 12.284 0.335995
20 5.771 0.175001
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.299891
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 1.5 -0.5 2.0 2.7
-1.2 -1.6 0.3 0.4 2.0 1.2
1.1 0.7 -1.4 0.7 -1.0 -1.4
0.6 1.1 0.2 -0.9 -0.4 -1.1
0.5 -0.4 -0.6 0.6 -0.8 -0.9
-0.6 0.2 -0.5 -1.6 -0.8 1.0
-0.5 -1.7 0.9 0.4 0.9 2.0
1.8
Chi-square with 42 degrees of freedom:55.099272
z-score=1.429248, p-value=0.915286
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_14:31
Test no p-value
1 0.392807
2 0.014216
3 0.132623
4 0.688589
5 0.005820
6 0.217292
7 0.346545
8 0.058938
9 0.049496
10 0.038723
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000276
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_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 66710 0.03 66837 0.44
3 25000.00 24947 0.11 24887 0.51
4 6666.67 6687 0.06 6633 0.17
5 1388.89 1391 0.00 1366 0.38
6 238.10 229 0.35 229 0.35
7 34.72 32 0.21 39 0.53
8 4.96 3 0.77 8 1.86
p=0.04326 p=0.35462
Number of rngs required: 690374, p-value: 0.990
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_14:31
No. of wins: Observed Expected
98129 98585.9
z-score=-2.043, pvalue=0.02051
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66791 66666.7 0.232 0.232
2 37618 37654.3 0.035 0.267
3 27032 26954.7 0.221 0.488
4 19344 19313.5 0.048 0.537
5 13737 13851.4 0.945 1.482
6 9987 9943.5 0.190 1.672
7 7063 7145.0 0.942 2.613
8 5151 5139.1 0.028 2.641
9 3740 3699.9 0.435 3.077
10 2622 2666.3 0.736 3.812
11 1945 1923.3 0.244 4.057
12 1309 1388.7 4.579 8.635
13 964 1003.7 1.571 10.207
14 734 726.1 0.085 10.292
15 525 525.8 0.001 10.293
16 371 381.2 0.270 10.563
17 283 276.5 0.151 10.714
18 189 200.8 0.697 11.411
19 158 146.0 0.989 12.400
20 116 106.2 0.901 13.302
21 321 287.1 3.999 17.301
Chisq= 17.30 for 20 degrees of freedom, p= 0.36664
SUMMARY of craptest
p-value for no. of wins: 0.020509
p-value for throws/game: 0.366642
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_14:31
No. of wins: Observed Expected
98559 98585.9
z-score=-0.120, pvalue=0.45219
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66864 66666.7 0.584 0.584
2 37443 37654.3 1.186 1.770
3 26826 26954.7 0.615 2.385
4 19382 19313.5 0.243 2.628
5 13900 13851.4 0.170 2.798
6 9893 9943.5 0.257 3.055
7 7161 7145.0 0.036 3.091
8 5259 5139.1 2.799 5.890
9 3722 3699.9 0.132 6.022
10 2600 2666.3 1.648 7.671
11 1915 1923.3 0.036 7.707
12 1393 1388.7 0.013 7.720
13 995 1003.7 0.076 7.796
14 723 726.1 0.014 7.809
15 518 525.8 0.117 7.926
16 351 381.2 2.385 10.311
17 280 276.5 0.043 10.354
18 238 200.8 6.880 17.234
19 161 146.0 1.544 18.778
20 97 106.2 0.800 19.578
21 279 287.1 0.229 19.807
Chisq= 19.81 for 20 degrees of freedom, p= 0.52994
SUMMARY of craptest
p-value for no. of wins: 0.452191
p-value for throws/game: 0.529943
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0036,0.0047,0.0058,0.0075,0.0105,0.0142,0.0165,0.0192,0.0197,
0.0205,0.0248,0.0252,0.0299,0.0342,0.0387,0.0388,0.0393,0.0433,0.0446,
0.0468,0.0488,0.0495,0.0501,0.0510,0.0518,0.0568,0.0589,0.0590,0.0622,
0.0669,0.0694,0.0756,0.0852,0.0897,0.0980,0.0986,0.1014,0.1047,0.1072,
0.1083,0.1083,0.1171,0.1231,0.1254,0.1272,0.1314,0.1326,0.1379,0.1393,
0.1457,0.1458,0.1468,0.1488,0.1488,0.1488,0.1535,0.1576,0.1668,0.1750,
0.1806,0.1810,0.1830,0.1870,0.1928,0.1991,0.2013,0.2132,0.2173,0.2206,
0.2213,0.2214,0.2222,0.2360,0.2393,0.2411,0.2422,0.2438,0.2549,0.2557,
0.2577,0.2627,0.2670,0.2675,0.2683,0.2776,0.2783,0.2801,0.2820,0.2826,
0.2866,0.2879,0.2890,0.2914,0.2969,0.2999,0.3022,0.3054,0.3069,0.3158,
0.3170,0.3293,0.3309,0.3360,0.3367,0.3380,0.3393,0.3406,0.3413,0.3454,
0.3465,0.3468,0.3546,0.3566,0.3628,0.3631,0.3666,0.3692,0.3696,0.3698,
0.3699,0.3702,0.3743,0.3746,0.3803,0.3816,0.3836,0.3875,0.3884,0.3903,
0.3928,0.3992,0.4124,0.4125,0.4190,0.4236,0.4266,0.4376,0.4411,0.4421,
0.4455,0.4455,0.4510,0.4512,0.4522,0.4523,0.4556,0.4569,0.4665,0.4773,
0.4857,0.4961,0.5063,0.5092,0.5095,0.5112,0.5119,0.5143,0.5147,0.5160,
0.5166,0.5259,0.5299,0.5318,0.5375,0.5425,0.5462,0.5473,0.5530,0.5533,
0.5552,0.5640,0.5711,0.5725,0.5788,0.5791,0.5894,0.6134,0.6136,0.6160,
0.6201,0.6201,0.6208,0.6254,0.6255,0.6357,0.6433,0.6454,0.6463,0.6475,
0.6525,0.6542,0.6546,0.6599,0.6602,0.6632,0.6744,0.6745,0.6751,0.6762,
0.6775,0.6817,0.6829,0.6833,0.6862,0.6875,0.6876,0.6886,0.6953,0.7022,
0.7093,0.7163,0.7174,0.7213,0.7224,0.7256,0.7387,0.7396,0.7445,0.7473,
0.7512,0.7544,0.7547,0.7549,0.7676,0.7686,0.7710,0.7766,0.7782,0.7849,
0.7894,0.7961,0.8006,0.8032,0.8068,0.8190,0.8258,0.8292,0.8294,0.8309,
0.8311,0.8327,0.8375,0.8381,0.8423,0.8637,0.8646,0.8675,0.8718,0.8890,
0.8922,0.8936,0.9153,0.9191,0.9219,0.9244,0.9284,0.9317,0.9328,0.9332,
0.9336,0.9371,0.9416,0.9450,0.9517,0.9557,0.9574,0.9637,0.9904,
Overall p-value after applying KStest on 269 p-values = 0.002101
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.