RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.68 15.5313 0.442731
2 to 25 15.65 13.3560 0.287956
3 to 26 15.37 29.9514 0.973302
4 to 27 15.66 14.9065 0.397783
5 to 28 15.71 22.6987 0.840681
6 to 29 15.76 13.5595 0.301996
7 to 30 15.71 19.6579 0.707899
8 to 31 15.96 22.0813 0.818386
9 to 32 15.57 21.8369 0.808927
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.314958
Tough bday spacings test for dh-ranFile-2018-07-08_16:31: 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 11 34 72 116 92 67 47 40 9 7 5
(O-E)^2/E 0.4 0.2 0.0 3.4 0.3 1.6 0.5 3.5 2.3 0.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 12.514, p= 0.748
RESULTS OF GCD FOR dh-ranFile-2018-07-08_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.171360
p-value, dist. of gcd's: 0.109071
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.481 0.745 0.684 0.411 0.573 0.210 0.935 0.954
Bits 8 to 15---> 0.390 0.091 0.028 0.379 0.752 0.587 0.210 0.610
Bits 16 to 23---> 0.913 0.651 0.570 0.885 0.202 0.703 0.101 0.366
Bits 24 to 31---> 0.700 0.957 0.794 0.088 0.219 0.159 0.714 0.452
KS test for the above 32 p values: 0.040
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_16:31,
p-values for 5 runs: 0.5200, 0.7458, 0.7746, 0.7920, 0.0365
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 234 211.4 2.412 2.412
r= 29 5081 5134.0 0.547 2.959
r= 30 23339 23103.0 2.410 5.369
r= 31 11346 11551.5 3.657 9.026
chi-square = 9.026 with df = 3; p-value = 0.971
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 229 211.4 1.462 1.462
r= 30 5082 5134.0 0.527 1.989
r= 31 23261 23103.0 1.080 3.069
r= 32 11428 11551.5 1.321 4.390
chi-square = 4.390 with df = 3; p-value = 0.778
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_16:31
b-rank test for bits 1 to 8, p=0.12880
b-rank test for bits 2 to 9, p=0.89636
b-rank test for bits 3 to 10, p=0.58999
b-rank test for bits 4 to 11, p=0.67907
b-rank test for bits 5 to 12, p=0.10059
b-rank test for bits 6 to 13, p=0.19335
b-rank test for bits 7 to 14, p=0.13377
b-rank test for bits 8 to 15, p=0.59356
b-rank test for bits 9 to 16, p=0.23069
b-rank test for bits 10 to 17, p=0.40649
b-rank test for bits 11 to 18, p=0.27942
b-rank test for bits 12 to 19, p=0.91759
b-rank test for bits 13 to 20, p=0.16033
b-rank test for bits 14 to 21, p=0.02139
b-rank test for bits 15 to 22, p=0.42331
b-rank test for bits 16 to 23, p=0.32348
b-rank test for bits 17 to 24, p=0.10948
b-rank test for bits 18 to 25, p=0.61341
b-rank test for bits 19 to 26, p=0.45341
b-rank test for bits 20 to 27, p=0.23397
b-rank test for bits 21 to 28, p=0.52433
b-rank test for bits 22 to 29, p=0.62270
b-rank test for bits 23 to 30, p=0.72051
b-rank test for bits 24 to 31, p=0.97482
b-rank test for bits 25 to 32, p=0.98094
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 = 0.602097
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_16:31
(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 141626 -0.66 0.253990
2 141881 -0.07 0.473613
3 142195 0.67 0.747759
4 141816 -0.22 0.413691
5 142668 1.77 0.961852
6 141988 0.18 0.572918
7 141637 -0.64 0.262295
8 141873 -0.08 0.466177
9 141634 -0.64 0.260017
10 141333 -1.35 0.089060
11 141741 -0.39 0.347051
12 141584 -0.76 0.223592
13 142067 0.37 0.643708
14 141994 0.20 0.578410
15 141212 -1.63 0.051627
16 141047 -2.01 0.021963
17 142071 0.38 0.647186
18 142097 0.44 0.669481
19 141667 -0.57 0.285632
20 142402 1.15 0.875154
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_16:31
Bits used No. missing words z-score p-value
23 to 32 142072 0.5609 0.712578
22 to 31 142129 0.7575 0.775620
21 to 30 142153 0.8402 0.799614
20 to 29 141912 0.0092 0.503673
19 to 28 141679 -0.7942 0.213528
18 to 27 141799 -0.3804 0.351806
17 to 26 141984 0.2575 0.601597
16 to 25 142237 1.1299 0.870740
15 to 24 142208 1.0299 0.848471
14 to 23 141800 -0.3770 0.353087
13 to 22 141923 0.0471 0.518798
12 to 21 142104 0.6713 0.748978
11 to 20 142258 1.2023 0.885378
10 to 19 141721 -0.6494 0.258036
9 to 18 142103 0.6678 0.747878
8 to 17 141983 0.2540 0.600266
7 to 16 142486 1.9885 0.976623
6 to 15 141512 -1.3701 0.085327
5 to 14 142081 0.5920 0.723063
4 to 13 141788 -0.4184 0.337835
3 to 12 141624 -0.9839 0.162583
2 to 11 141880 -0.1011 0.459721
1 to 10 142060 0.5196 0.698312
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_16:31
Bits used No. missing words z-score p-value
28 to 32 142420 1.7311 0.958282
27 to 31 141608 -1.0215 0.153519
26 to 30 141981 0.2429 0.595978
25 to 29 141842 -0.2282 0.409731
24 to 28 141408 -1.6994 0.044620
23 to 27 141492 -1.4147 0.078581
22 to 26 142364 1.5413 0.938373
21 to 25 141844 -0.2215 0.412368
20 to 24 141647 -0.8893 0.186933
19 to 23 142067 0.5345 0.703493
18 to 22 142312 1.3650 0.913871
17 to 21 142249 1.1514 0.875221
16 to 20 141976 0.2260 0.589399
15 to 19 141043 -2.9367 0.001659
14 to 18 141791 -0.4011 0.344166
13 to 17 141690 -0.7435 0.228592
12 to 16 141637 -0.9232 0.177964
11 to 15 141877 -0.1096 0.456366
10 to 14 141810 -0.3367 0.368167
9 to 13 142107 0.6701 0.748593
8 to 12 142005 0.3243 0.627147
7 to 11 141781 -0.4350 0.331775
6 to 10 141776 -0.4520 0.325647
5 to 9 141793 -0.3943 0.346665
4 to 8 141676 -0.7909 0.214487
3 to 7 141827 -0.2791 0.390090
2 to 6 141489 -1.4248 0.077101
1 to 5 142152 0.8226 0.794635
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_16:31
Bits used No. missing words z-score p-value
31 to 32 141676 -0.6883 0.245635
30 to 31 142023 0.3353 0.631304
29 to 30 141828 -0.2399 0.405199
28 to 29 142048 0.4091 0.658751
27 to 28 142249 1.0020 0.841823
26 to 27 142122 0.6273 0.734784
25 to 26 141806 -0.3048 0.380256
24 to 25 141290 -1.8269 0.033855
23 to 24 141999 0.2645 0.604308
22 to 23 141584 -0.9597 0.168609
21 to 22 142424 1.5182 0.935518
20 to 21 141244 -1.9626 0.024845
19 to 20 142413 1.4858 0.931328
18 to 19 141476 -1.2783 0.100579
17 to 18 141900 -0.0275 0.489022
16 to 17 141543 -1.0806 0.139933
15 to 16 142403 1.4563 0.927339
14 to 15 142163 0.7483 0.772857
13 to 14 141699 -0.6204 0.267483
12 to 13 141958 0.1436 0.557080
11 to 12 141939 0.0875 0.534872
10 to 11 141934 0.0728 0.529007
9 to 10 142426 1.5241 0.936258
8 to 9 141973 0.1878 0.574490
7 to 8 141949 0.1170 0.546578
6 to 7 141655 -0.7502 0.226556
5 to 6 141761 -0.4376 0.330856
4 to 5 141447 -1.3638 0.086314
3 to 4 142181 0.8014 0.788546
2 to 3 142385 1.4032 0.919715
1 to 2 142231 0.9489 0.828659
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2529.49 0.417 0.661698
Test results for specific bytes for dh-ranFile-2018-07-08_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2514.74 0.209 0.582587
2 to 9 2514.61 0.207 0.581849
3 to 10 2587.95 1.244 0.893201
4 to 11 2668.60 2.384 0.991446
5 to 12 2464.13 -0.507 0.305971
6 to 13 2415.80 -1.191 0.116871
7 to 14 2477.69 -0.316 0.376189
8 to 15 2530.23 0.428 0.665495
9 to 16 2563.79 0.902 0.816493
10 to 17 2483.49 -0.233 0.407713
11 to 18 2424.71 -1.065 0.143490
12 to 19 2410.56 -1.265 0.102950
13 to 20 2494.04 -0.084 0.466391
14 to 21 2628.61 1.819 0.965534
15 to 22 2530.98 0.438 0.669364
16 to 23 2507.06 0.100 0.539791
17 to 24 2405.91 -1.331 0.091656
18 to 25 2458.42 -0.588 0.278245
19 to 26 2539.74 0.562 0.712950
20 to 27 2451.32 -0.688 0.245595
21 to 28 2640.74 1.990 0.976721
22 to 29 2628.81 1.822 0.965751
23 to 30 2495.94 -0.057 0.477084
24 to 31 2384.79 -1.629 0.051623
25 to 32 2481.03 -0.268 0.394245
CDPARK for dh-ranFile-2018-07-08_16:31: 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
3520 -0.1370 0.445521
3532 0.4110 0.659449
3506 -0.7763 0.218799
3506 -0.7763 0.218799
3571 2.1918 0.985802
3514 -0.4110 0.340551
3497 -1.1872 0.117571
3516 -0.3196 0.374623
3544 0.9589 0.831196
3538 0.6849 0.753306
Square side=100, avg. no. parked=3524.40 sample std.=21.03
p-value of the KSTEST for those 10 p-values: 0.942862
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_16:31
0.6591,0.5098,0.9720,0.2027,0.9261,0.8575,0.9047,0.1703,0.5421,0.7962,
The KS test for those 10 p-values: 0.135014
The 3DSPHERES test for dh-ranFile-2018-07-08_16:31
sample no r^3 equiv. uni.
1 60.765 0.868072
2 55.432 0.842404
3 16.339 0.419945
4 11.461 0.317521
5 131.258 0.987415
6 52.080 0.823775
7 11.393 0.315978
8 6.073 0.183257
9 10.399 0.292940
10 3.290 0.103866
11 5.393 0.164536
12 17.213 0.436601
13 25.594 0.573926
14 36.424 0.703036
15 37.440 0.712925
16 40.491 0.740684
17 6.753 0.201552
18 12.525 0.341301
19 46.811 0.789941
20 67.902 0.896005
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.765406
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 1.5 0.9 1.1 1.6
-2.1 -0.9 0.2 -1.1 -0.5 0.5
-1.1 -0.9 -1.1 0.1 0.7 0.3
1.0 -1.0 -1.2 1.1 1.5 1.2
-0.8 1.0 -0.2 0.3 0.0 0.3
1.1 1.2 -1.4 1.3 -0.5 -1.9
0.0 0.8 0.1 1.0 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:41.591337
z-score=-0.044589, p-value=0.511227
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_16:31
Test no p-value
1 0.536231
2 0.617198
3 0.001725
4 0.003682
5 0.173202
6 0.868791
7 0.397194
8 0.577670
9 0.036415
10 0.193355
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.031460
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_16:31:
(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 67020 1.87 66725 0.05
3 25000.00 24741 2.68 25040 0.06
4 6666.67 6522 3.14 6562 1.64
5 1388.89 1424 0.89 1397 0.05
6 238.10 251 0.70 231 0.21
7 34.72 39 0.53 41 1.14
8 4.96 2 1.77 3 0.77
p=0.92788 p=0.31353
Number of rngs required: 687962, p-value: 0.306
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_16:31
No. of wins: Observed Expected
98521 98585.9
z-score=-0.290, pvalue=0.38588
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66470 66666.7 0.580 0.580
2 37717 37654.3 0.104 0.685
3 26829 26954.7 0.586 1.271
4 19308 19313.5 0.002 1.273
5 14028 13851.4 2.251 3.524
6 10033 9943.5 0.805 4.328
7 7209 7145.0 0.573 4.901
8 5138 5139.1 0.000 4.901
9 3611 3699.9 2.134 7.036
10 2661 2666.3 0.011 7.046
11 1964 1923.3 0.860 7.906
12 1438 1388.7 1.747 9.654
13 986 1003.7 0.313 9.966
14 691 726.1 1.701 11.667
15 546 525.8 0.773 12.440
16 361 381.2 1.065 13.505
17 262 276.5 0.764 14.270
18 220 200.8 1.830 16.100
19 139 146.0 0.334 16.434
20 107 106.2 0.006 16.440
21 282 287.1 0.091 16.531
Chisq= 16.53 for 20 degrees of freedom, p= 0.31680
SUMMARY of craptest
p-value for no. of wins: 0.385875
p-value for throws/game: 0.316804
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_16:31
No. of wins: Observed Expected
98863 98585.9
z-score= 1.240, pvalue=0.89243
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66685 66666.7 0.005 0.005
2 37726 37654.3 0.136 0.141
3 26893 26954.7 0.141 0.283
4 19171 19313.5 1.051 1.334
5 13916 13851.4 0.301 1.635
6 10007 9943.5 0.405 2.040
7 7194 7145.0 0.336 2.375
8 5149 5139.1 0.019 2.395
9 3724 3699.9 0.157 2.552
10 2639 2666.3 0.279 2.832
11 1947 1923.3 0.291 3.123
12 1362 1388.7 0.515 3.638
13 992 1003.7 0.137 3.774
14 707 726.1 0.505 4.279
15 480 525.8 3.995 8.274
16 382 381.2 0.002 8.276
17 297 276.5 1.514 9.790
18 229 200.8 3.951 13.742
19 146 146.0 0.000 13.742
20 96 106.2 0.982 14.724
21 258 287.1 2.952 17.676
Chisq= 17.68 for 20 degrees of freedom, p= 0.39127
SUMMARY of craptest
p-value for no. of wins: 0.892427
p-value for throws/game: 0.391271
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0017,0.0037,0.0214,0.0220,0.0248,0.0281,0.0315,0.0339,0.0364,
0.0365,0.0400,0.0446,0.0516,0.0516,0.0771,0.0786,0.0853,0.0863,0.0876,
0.0891,0.0906,0.0917,0.1006,0.1006,0.1006,0.1029,0.1039,0.1091,0.1095,
0.1169,0.1176,0.1288,0.1338,0.1350,0.1399,0.1435,0.1535,0.1591,0.1603,
0.1626,0.1645,0.1686,0.1703,0.1714,0.1732,0.1780,0.1833,0.1869,0.1933,
0.1934,0.2016,0.2018,0.2027,0.2099,0.2105,0.2135,0.2145,0.2185,0.2188,
0.2188,0.2236,0.2266,0.2286,0.2307,0.2340,0.2456,0.2456,0.2540,0.2580,
0.2600,0.2623,0.2675,0.2782,0.2794,0.2856,0.2880,0.2929,0.3020,0.3056,
0.3060,0.3135,0.3150,0.3160,0.3168,0.3175,0.3235,0.3256,0.3309,0.3318,
0.3378,0.3406,0.3413,0.3442,0.3467,0.3471,0.3518,0.3531,0.3660,0.3682,
0.3746,0.3762,0.3791,0.3803,0.3859,0.3901,0.3903,0.3913,0.3942,0.3972,
0.3978,0.4052,0.4065,0.4077,0.4097,0.4112,0.4124,0.4137,0.4199,0.4233,
0.4366,0.4427,0.4455,0.4523,0.4534,0.4564,0.4597,0.4662,0.4664,0.4736,
0.4771,0.4806,0.4890,0.5037,0.5098,0.5112,0.5188,0.5200,0.5243,0.5290,
0.5349,0.5362,0.5398,0.5421,0.5466,0.5571,0.5696,0.5729,0.5732,0.5739,
0.5745,0.5777,0.5784,0.5818,0.5826,0.5873,0.5894,0.5900,0.5936,0.5960,
0.6003,0.6016,0.6021,0.6043,0.6099,0.6134,0.6172,0.6227,0.6271,0.6313,
0.6437,0.6472,0.6512,0.6588,0.6591,0.6594,0.6617,0.6655,0.6694,0.6695,
0.6791,0.6836,0.6983,0.6997,0.7028,0.7030,0.7035,0.7079,0.7126,0.7129,
0.7130,0.7141,0.7205,0.7231,0.7348,0.7407,0.7454,0.7458,0.7478,0.7479,
0.7479,0.7486,0.7490,0.7516,0.7533,0.7654,0.7729,0.7746,0.7756,0.7777,
0.7885,0.7899,0.7920,0.7939,0.7946,0.7962,0.7996,0.8089,0.8165,0.8184,
0.8238,0.8287,0.8312,0.8407,0.8418,0.8424,0.8485,0.8575,0.8681,0.8688,
0.8707,0.8752,0.8752,0.8853,0.8854,0.8924,0.8932,0.8960,0.8964,0.9047,
0.9127,0.9139,0.9176,0.9197,0.9261,0.9273,0.9279,0.9313,0.9347,0.9355,
0.9363,0.9384,0.9429,0.9543,0.9574,0.9583,0.9619,0.9655,0.9658,0.9711,
0.9720,0.9733,0.9748,0.9766,0.9767,0.9809,0.9858,0.9874,0.9914,
Overall p-value after applying KStest on 269 p-values = 0.984837
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.