RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.75 17.4274 0.574207
2 to 25 15.67 17.1560 0.556154
3 to 26 15.94 19.4997 0.699388
4 to 27 16.06 13.1037 0.270785
5 to 28 15.88 12.1015 0.206047
6 to 29 15.94 9.9043 0.092426
7 to 30 15.81 25.7558 0.920974
8 to 31 15.23 24.3208 0.889024
9 to 32 15.62 15.6549 0.451584
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.993960
Tough bday spacings test for dh-ranFile-2018-07-06_00:31: 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 12 43 61 87 102 87 57 27 11 10 3
(O-E)^2/E 0.9 1.1 2.1 1.2 0.2 1.0 0.5 0.3 1.0 1.7 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.148, p= 0.572
RESULTS OF GCD FOR dh-ranFile-2018-07-06_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.246457
p-value, dist. of gcd's: 0.357433
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.204 0.049 0.720 0.490 0.916 0.640 0.121 0.595
Bits 8 to 15---> 0.182 0.613 0.490 0.789 0.694 0.977 0.093 0.950
Bits 16 to 23---> 0.941 0.746 0.225 0.917 0.945 0.392 0.367 0.317
Bits 24 to 31---> 0.230 0.511 0.948 0.276 0.210 0.997 0.304 0.245
KS test for the above 32 p values: 0.642
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_00:31,
p-values for 5 runs: 0.3471, 0.3359, 0.3176, 0.7686, 0.8247
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5116 5134.0 0.063 0.065
r= 30 23068 23103.0 0.053 0.118
r= 31 11604 11551.5 0.238 0.356
chi-square = 0.356 with df = 3; p-value = 0.051
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 198 211.4 0.852 0.852
r= 30 5227 5134.0 1.684 2.536
r= 31 22911 23103.0 1.596 4.132
r= 32 11664 11551.5 1.095 5.227
chi-square = 5.227 with df = 3; p-value = 0.844
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_00:31
b-rank test for bits 1 to 8, p=0.33697
b-rank test for bits 2 to 9, p=0.34689
b-rank test for bits 3 to 10, p=0.81277
b-rank test for bits 4 to 11, p=0.97082
b-rank test for bits 5 to 12, p=0.80061
b-rank test for bits 6 to 13, p=0.37085
b-rank test for bits 7 to 14, p=0.46042
b-rank test for bits 8 to 15, p=0.82368
b-rank test for bits 9 to 16, p=0.74946
b-rank test for bits 10 to 17, p=0.62842
b-rank test for bits 11 to 18, p=0.19802
b-rank test for bits 12 to 19, p=0.21777
b-rank test for bits 13 to 20, p=0.31958
b-rank test for bits 14 to 21, p=0.25002
b-rank test for bits 15 to 22, p=0.10374
b-rank test for bits 16 to 23, p=0.48693
b-rank test for bits 17 to 24, p=0.07682
b-rank test for bits 18 to 25, p=0.66176
b-rank test for bits 19 to 26, p=0.82061
b-rank test for bits 20 to 27, p=0.59897
b-rank test for bits 21 to 28, p=0.31145
b-rank test for bits 22 to 29, p=0.35189
b-rank test for bits 23 to 30, p=0.25252
b-rank test for bits 24 to 31, p=0.48859
b-rank test for bits 25 to 32, p=0.43080
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 = 0.517298
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_00:31
(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 142613 1.64 0.949921
2 142160 0.59 0.720954
3 142267 0.84 0.798332
4 141963 0.13 0.549895
5 141567 -0.80 0.211903
6 142001 0.21 0.584798
7 142199 0.68 0.750733
8 141213 -1.63 0.051875
9 141123 -1.84 0.033089
10 141840 -0.16 0.435658
11 141846 -0.15 0.441184
12 141472 -1.02 0.153438
13 141818 -0.21 0.415512
14 142402 1.15 0.875154
15 141863 -0.11 0.456900
16 141413 -1.16 0.123096
17 141362 -1.28 0.100482
18 141319 -1.38 0.083905
19 141644 -0.62 0.267652
20 142193 0.66 0.746264
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_00:31
Bits used No. missing words z-score p-value
23 to 32 141957 0.1644 0.565284
22 to 31 142129 0.7575 0.775620
21 to 30 141490 -1.4460 0.074093
20 to 29 142075 0.5713 0.716094
19 to 28 142065 0.5368 0.704295
18 to 27 142106 0.6782 0.751169
17 to 26 141774 -0.4667 0.320373
16 to 25 141856 -0.1839 0.427047
15 to 24 141650 -0.8942 0.185596
14 to 23 141887 -0.0770 0.469312
13 to 22 141279 -2.1736 0.014869
12 to 21 141623 -0.9873 0.161737
11 to 20 141853 -0.1942 0.422994
10 to 19 141890 -0.0667 0.473428
9 to 18 142410 1.7264 0.957867
8 to 17 141735 -0.6011 0.273874
7 to 16 141857 -0.1804 0.428400
6 to 15 142160 0.8644 0.806310
5 to 14 141459 -1.5529 0.060228
4 to 13 142150 0.8299 0.796701
3 to 12 142034 0.4299 0.666365
2 to 11 141806 -0.3563 0.360804
1 to 10 141711 -0.6839 0.247020
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_00:31
Bits used No. missing words z-score p-value
28 to 32 141816 -0.3164 0.375860
27 to 31 142332 1.4328 0.924040
26 to 30 142155 0.8328 0.797516
25 to 29 141704 -0.6960 0.243204
24 to 28 142090 0.6124 0.729877
23 to 27 141469 -1.4926 0.067765
22 to 26 142133 0.7582 0.775835
21 to 25 141593 -1.0723 0.141792
20 to 24 142193 0.9616 0.831873
19 to 23 141869 -0.1367 0.445629
18 to 22 141880 -0.0994 0.460401
17 to 21 141078 -2.8181 0.002416
16 to 20 141977 0.2294 0.590717
15 to 19 141819 -0.3062 0.379725
14 to 18 141680 -0.7774 0.218464
13 to 17 141444 -1.5774 0.057353
12 to 16 141756 -0.5198 0.301615
11 to 15 141328 -1.9706 0.024384
10 to 14 142078 0.5718 0.716259
9 to 13 142084 0.5921 0.723109
8 to 12 141897 -0.0418 0.483330
7 to 11 142190 0.9514 0.829305
6 to 10 142180 0.9175 0.820566
5 to 9 141517 -1.3299 0.091770
4 to 8 141600 -1.0486 0.147187
3 to 7 142244 1.1345 0.871702
2 to 6 141389 -1.7638 0.038880
1 to 5 141588 -1.0893 0.138021
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_00:31
Bits used No. missing words z-score p-value
31 to 32 141723 -0.5496 0.291281
30 to 31 141986 0.2262 0.589464
29 to 30 141735 -0.5142 0.303539
28 to 29 141462 -1.3196 0.093491
27 to 28 141650 -0.7650 0.222140
26 to 27 141950 0.1200 0.547747
25 to 26 141636 -0.8063 0.210040
24 to 25 141421 -1.4405 0.074863
23 to 24 142033 0.3648 0.642373
22 to 23 142089 0.5300 0.701944
21 to 22 141615 -0.8682 0.192634
20 to 21 142426 1.5241 0.936258
19 to 20 142386 1.4061 0.920154
18 to 19 141704 -0.6057 0.272359
17 to 18 142021 0.3294 0.629077
16 to 17 141816 -0.2753 0.391539
15 to 16 141291 -1.8240 0.034077
14 to 15 141865 -0.1308 0.447980
13 to 14 141775 -0.3963 0.345959
12 to 13 142006 0.2852 0.612240
11 to 12 141980 0.2085 0.582568
10 to 11 142124 0.6332 0.736713
9 to 10 142130 0.6509 0.742459
8 to 9 142556 1.9076 0.971777
7 to 8 142150 0.7099 0.761130
6 to 7 141884 -0.0747 0.470219
5 to 6 141382 -1.5555 0.059908
4 to 5 141689 -0.6499 0.257865
3 to 4 141541 -1.0865 0.138625
2 to 3 141832 -0.2281 0.409780
1 to 2 141450 -1.3550 0.087716
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2569.87 0.988 0.838440
Test results for specific bytes for dh-ranFile-2018-07-06_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2551.46 0.728 0.766623
2 to 9 2461.64 -0.543 0.293723
3 to 10 2531.93 0.452 0.674228
4 to 11 2604.86 1.483 0.930957
5 to 12 2593.27 1.319 0.906433
6 to 13 2428.95 -1.005 0.157501
7 to 14 2526.37 0.373 0.645399
8 to 15 2473.56 -0.374 0.354244
9 to 16 2532.14 0.454 0.675260
10 to 17 2524.28 0.343 0.634317
11 to 18 2470.69 -0.414 0.339260
12 to 19 2542.11 0.596 0.724249
13 to 20 2618.47 1.675 0.953080
14 to 21 2544.56 0.630 0.735727
15 to 22 2442.95 -0.807 0.209901
16 to 23 2464.19 -0.506 0.306284
17 to 24 2430.70 -0.980 0.163542
18 to 25 2463.08 -0.522 0.300768
19 to 26 2484.22 -0.223 0.411715
20 to 27 2523.92 0.338 0.632442
21 to 28 2590.68 1.282 0.900139
22 to 29 2473.10 -0.380 0.351821
23 to 30 2349.20 -2.133 0.016475
24 to 31 2343.27 -2.216 0.013331
25 to 32 2467.84 -0.455 0.324643
CDPARK for dh-ranFile-2018-07-06_00:31: 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
3550 1.2329 0.891189
3529 0.2740 0.607947
3514 -0.4110 0.340551
3544 0.9589 0.831196
3526 0.1370 0.554479
3531 0.3653 0.642555
3561 1.7352 0.958644
3501 -1.0046 0.157553
3548 1.1416 0.873180
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3531.70 sample std.=18.04
p-value of the KSTEST for those 10 p-values: 0.350313
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_00:31
0.5222,0.6686,0.4632,0.1383,0.0566,0.7611,0.4126,0.5966,0.8979,0.6711,
The KS test for those 10 p-values: 0.856441
The 3DSPHERES test for dh-ranFile-2018-07-06_00:31
sample no r^3 equiv. uni.
1 49.192 0.805968
2 0.893 0.029319
3 1.250 0.040815
4 23.718 0.546428
5 12.379 0.338092
6 6.012 0.181586
7 16.755 0.427925
8 10.097 0.285792
9 110.893 0.975188
10 15.201 0.397529
11 148.500 0.992917
12 29.806 0.629736
13 34.172 0.679884
14 48.505 0.801471
15 24.631 0.560023
16 7.472 0.220482
17 10.817 0.302721
18 0.606 0.019988
19 6.826 0.203506
20 39.066 0.728066
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.700508
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 2.2 -0.8 0.0 -0.7 1.6
0.3 1.5 -0.4 -0.7 -0.1 -0.6
0.6 0.3 1.9 0.1 -0.3 -1.0
-1.1 0.4 0.3 0.1 -0.0 -0.9
0.2 -0.8 -0.8 0.4 1.5 -0.6
0.7 -0.3 -0.8 1.1 1.5 -0.8
1.0 0.8 0.5 -0.7 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:34.044107
z-score=-0.868059, p-value=0.196048
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_00:31
Test no p-value
1 0.018959
2 0.912442
3 0.207330
4 0.320159
5 0.396813
6 0.009016
7 0.605952
8 0.014597
9 0.300051
10 0.326874
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.021921
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_00:31:
(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 66905 0.85 66483 0.51
3 25000.00 24959 0.07 25074 0.22
4 6666.67 6475 5.51 6788 2.21
5 1388.89 1370 0.26 1394 0.02
6 238.10 248 0.41 220 1.38
7 34.72 39 0.53 37 0.15
8 4.96 3 0.77 3 0.77
p=0.78982 p=0.48801
Number of rngs required: 688633, p-value: 0.604
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_00:31
No. of wins: Observed Expected
98410 98585.9
z-score=-0.787, pvalue=0.21577
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67049 66666.7 2.193 2.193
2 37391 37654.3 1.841 4.034
3 26720 26954.7 2.044 6.078
4 19162 19313.5 1.188 7.266
5 14078 13851.4 3.706 10.972
6 10030 9943.5 0.752 11.724
7 6996 7145.0 3.108 14.832
8 5155 5139.1 0.049 14.882
9 3776 3699.9 1.567 16.448
10 2663 2666.3 0.004 16.453
11 1918 1923.3 0.015 16.467
12 1407 1388.7 0.240 16.707
13 974 1003.7 0.880 17.587
14 738 726.1 0.194 17.781
15 516 525.8 0.184 17.965
16 373 381.2 0.174 18.139
17 283 276.5 0.151 18.290
18 203 200.8 0.023 18.313
19 155 146.0 0.557 18.870
20 109 106.2 0.073 18.943
21 304 287.1 0.993 19.936
Chisq= 19.94 for 20 degrees of freedom, p= 0.53808
SUMMARY of craptest
p-value for no. of wins: 0.215775
p-value for throws/game: 0.538085
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_00:31
No. of wins: Observed Expected
98611 98585.9
z-score= 0.112, pvalue=0.54477
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66732 66666.7 0.064 0.064
2 37723 37654.3 0.125 0.189
3 26967 26954.7 0.006 0.195
4 19235 19313.5 0.319 0.514
5 13733 13851.4 1.012 1.526
6 9985 9943.5 0.173 1.699
7 7183 7145.0 0.202 1.901
8 5149 5139.1 0.019 1.920
9 3640 3699.9 0.969 2.889
10 2629 2666.3 0.522 3.410
11 1935 1923.3 0.071 3.481
12 1454 1388.7 3.067 6.548
13 987 1003.7 0.278 6.826
14 715 726.1 0.171 6.997
15 535 525.8 0.160 7.157
16 403 381.2 1.253 8.409
17 265 276.5 0.482 8.891
18 197 200.8 0.073 8.964
19 151 146.0 0.172 9.136
20 95 106.2 1.184 10.320
21 287 287.1 0.000 10.320
Chisq= 10.32 for 20 degrees of freedom, p= 0.03802
SUMMARY of craptest
p-value for no. of wins: 0.544766
p-value for throws/game: 0.038017
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0024,0.0090,0.0133,0.0146,0.0149,0.0165,0.0190,0.0200,0.0219,0.0244,
0.0293,0.0331,0.0341,0.0380,0.0389,0.0408,0.0495,0.0509,0.0519,0.0566,
0.0574,0.0599,0.0602,0.0678,0.0741,0.0749,0.0768,0.0839,0.0877,0.0918,
0.0924,0.0933,0.0935,0.1005,0.1037,0.1208,0.1231,0.1380,0.1383,0.1386,
0.1418,0.1472,0.1534,0.1575,0.1576,0.1617,0.1635,0.1816,0.1822,0.1856,
0.1926,0.1960,0.1980,0.2035,0.2044,0.2060,0.2073,0.2095,0.2099,0.2100,
0.2119,0.2158,0.2178,0.2185,0.2205,0.2221,0.2254,0.2299,0.2432,0.2448,
0.2465,0.2470,0.2500,0.2525,0.2579,0.2677,0.2708,0.2724,0.2739,0.2761,
0.2858,0.2913,0.2937,0.3001,0.3008,0.3016,0.3027,0.3035,0.3043,0.3063,
0.3115,0.3170,0.3176,0.3196,0.3202,0.3204,0.3240,0.3246,0.3269,0.3359,
0.3370,0.3381,0.3393,0.3406,0.3460,0.3469,0.3471,0.3503,0.3518,0.3519,
0.3542,0.3574,0.3608,0.3669,0.3708,0.3759,0.3797,0.3915,0.3922,0.3968,
0.3975,0.4098,0.4117,0.4126,0.4155,0.4230,0.4270,0.4279,0.4284,0.4308,
0.4357,0.4412,0.4456,0.4480,0.4516,0.4569,0.4604,0.4604,0.4632,0.4693,
0.4702,0.4734,0.4833,0.4869,0.4880,0.4886,0.4899,0.4904,0.5111,0.5173,
0.5222,0.5381,0.5448,0.5464,0.5477,0.5499,0.5545,0.5562,0.5600,0.5653,
0.5724,0.5742,0.5826,0.5848,0.5895,0.5907,0.5949,0.5966,0.5990,0.6044,
0.6060,0.6079,0.6122,0.6126,0.6284,0.6291,0.6297,0.6324,0.6343,0.6398,
0.6424,0.6424,0.6426,0.6454,0.6618,0.6664,0.6686,0.6711,0.6742,0.6753,
0.6799,0.6937,0.6994,0.7005,0.7019,0.7043,0.7161,0.7163,0.7195,0.7210,
0.7231,0.7242,0.7281,0.7299,0.7357,0.7367,0.7425,0.7457,0.7463,0.7495,
0.7507,0.7512,0.7611,0.7611,0.7666,0.7686,0.7756,0.7758,0.7890,0.7898,
0.7967,0.7975,0.7983,0.8006,0.8015,0.8060,0.8063,0.8128,0.8206,0.8206,
0.8237,0.8247,0.8293,0.8312,0.8319,0.8384,0.8441,0.8564,0.8717,0.8732,
0.8752,0.8890,0.8912,0.8979,0.9001,0.9064,0.9124,0.9162,0.9168,0.9202,
0.9210,0.9240,0.9310,0.9363,0.9406,0.9450,0.9477,0.9498,0.9499,0.9531,
0.9579,0.9586,0.9708,0.9718,0.9752,0.9775,0.9929,0.9940,0.9966,
Overall p-value after applying KStest on 269 p-values = 0.281974
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.