RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_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 15.97 13.6574 0.308815
2 to 25 15.72 26.5590 0.935139
3 to 26 15.97 27.3605 0.947011
4 to 27 16.00 12.6391 0.240006
5 to 28 15.83 19.2160 0.683726
6 to 29 15.77 12.4684 0.229019
7 to 30 15.49 36.5731 0.996157
8 to 31 15.76 14.5824 0.374466
9 to 32 15.77 17.9823 0.610044
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.260120
Tough bday spacings test for dh-ranFile-2018-06-17_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 6 37 64 95 107 78 56 29 20 4 4
(O-E)^2/E 1.1 0.0 1.2 0.1 0.9 0.0 0.3 0.0 1.8 1.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 6.331, p= 0.213
RESULTS OF GCD FOR dh-ranFile-2018-06-17_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.021327
p-value, dist. of gcd's: 0.056132
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.320 0.167 0.364 0.442 0.317 0.233 0.959 0.983
Bits 8 to 15---> 0.019 0.881 0.590 0.948 0.056 0.362 0.380 0.006
Bits 16 to 23---> 0.215 0.192 0.021 0.638 0.090 0.583 0.945 0.284
Bits 24 to 31---> 0.415 0.068 0.184 0.214 0.232 0.844 0.030 0.734
KS test for the above 32 p values: 0.970
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_16:31,
p-values for 5 runs: 0.4111, 0.6727, 0.6891, 0.6680, 0.5398
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5103 5134.0 0.187 1.488
r= 30 23264 23103.0 1.121 2.609
r= 31 11405 11551.5 1.859 4.468
chi-square = 4.468 with df = 3; p-value = 0.785
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5167 5134.0 0.212 0.221
r= 31 23201 23103.0 0.415 0.637
r= 32 11422 11551.5 1.452 2.089
chi-square = 2.089 with df = 3; p-value = 0.446
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_16:31
b-rank test for bits 1 to 8, p=0.87445
b-rank test for bits 2 to 9, p=0.78653
b-rank test for bits 3 to 10, p=0.45608
b-rank test for bits 4 to 11, p=0.23208
b-rank test for bits 5 to 12, p=0.64428
b-rank test for bits 6 to 13, p=0.48586
b-rank test for bits 7 to 14, p=0.46380
b-rank test for bits 8 to 15, p=0.83968
b-rank test for bits 9 to 16, p=0.06609
b-rank test for bits 10 to 17, p=0.71742
b-rank test for bits 11 to 18, p=0.96093
b-rank test for bits 12 to 19, p=0.94204
b-rank test for bits 13 to 20, p=0.20471
b-rank test for bits 14 to 21, p=0.57035
b-rank test for bits 15 to 22, p=0.76492
b-rank test for bits 16 to 23, p=0.57280
b-rank test for bits 17 to 24, p=0.91782
b-rank test for bits 18 to 25, p=0.53637
b-rank test for bits 19 to 26, p=0.97924
b-rank test for bits 20 to 27, p=0.09966
b-rank test for bits 21 to 28, p=0.91739
b-rank test for bits 22 to 29, p=0.94412
b-rank test for bits 23 to 30, p=0.07994
b-rank test for bits 24 to 31, p=0.64480
b-rank test for bits 25 to 32, p=0.92598
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 = 0.031391
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_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 142858 2.22 0.986672
2 142589 1.59 0.943858
3 142174 0.62 0.731840
4 141963 0.13 0.549895
5 142097 0.44 0.669481
6 141825 -0.20 0.421901
7 142067 0.37 0.643708
8 141513 -0.93 0.177222
9 141765 -0.34 0.367976
10 141393 -1.21 0.113836
11 142878 2.26 0.988190
12 142218 0.72 0.764604
13 142003 0.22 0.586619
14 142016 0.25 0.598408
15 141703 -0.48 0.314875
16 142534 1.46 0.927788
17 142000 0.21 0.583886
18 142093 0.43 0.666088
19 142011 0.24 0.593884
20 141321 -1.37 0.084627
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_16:31
Bits used No. missing words z-score p-value
23 to 32 141748 -0.5563 0.288999
22 to 31 141829 -0.2770 0.390890
21 to 30 141666 -0.8391 0.200715
20 to 29 142206 1.0230 0.846846
19 to 28 142404 1.7058 0.955973
18 to 27 141825 -0.2908 0.385605
17 to 26 141306 -2.0804 0.018742
16 to 25 141703 -0.7115 0.238393
15 to 24 141242 -2.3011 0.010692
14 to 23 141663 -0.8494 0.197826
13 to 22 142257 1.1989 0.884709
12 to 21 141614 -1.0184 0.154249
11 to 20 141599 -1.0701 0.142286
10 to 19 141623 -0.9873 0.161737
9 to 18 142336 1.4713 0.929392
8 to 17 142325 1.4333 0.924120
7 to 16 142472 1.9402 0.973825
6 to 15 141895 -0.0494 0.480295
5 to 14 142218 1.0644 0.856422
4 to 13 142060 0.5196 0.698312
3 to 12 142002 0.3196 0.625346
2 to 11 142407 1.7161 0.956928
1 to 10 141903 -0.0218 0.491293
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_16:31
Bits used No. missing words z-score p-value
28 to 32 141648 -0.8859 0.187845
27 to 31 141962 0.1785 0.570852
26 to 30 141421 -1.6554 0.048926
25 to 29 141988 0.2667 0.605141
24 to 28 142087 0.6023 0.726503
23 to 27 142127 0.7379 0.769702
22 to 26 141864 -0.1537 0.438939
21 to 25 141251 -2.2316 0.012820
20 to 24 141774 -0.4587 0.323208
19 to 23 141989 0.2701 0.606446
18 to 22 141484 -1.4418 0.074680
17 to 21 142431 1.7684 0.961501
16 to 20 141359 -1.8655 0.031054
15 to 19 142091 0.6158 0.730997
14 to 18 141607 -1.0248 0.152718
13 to 17 141463 -1.5130 0.065142
12 to 16 142398 1.6565 0.951191
11 to 15 141535 -1.2689 0.102236
10 to 14 141119 -2.6791 0.003691
9 to 13 141992 0.2802 0.610352
8 to 12 142100 0.6463 0.740970
7 to 11 142058 0.5040 0.692857
6 to 10 141795 -0.3876 0.349171
5 to 9 141956 0.1582 0.562852
4 to 8 142032 0.4158 0.661233
3 to 7 141617 -0.9909 0.160855
2 to 6 142139 0.7785 0.781875
1 to 5 141934 0.0836 0.533324
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_16:31
Bits used No. missing words z-score p-value
31 to 32 141815 -0.2783 0.390407
30 to 31 141893 -0.0482 0.480790
29 to 30 142046 0.4032 0.656583
28 to 29 142092 0.5388 0.705005
27 to 28 142013 0.3058 0.620126
26 to 27 142094 0.5447 0.707037
25 to 26 141986 0.2262 0.589464
24 to 25 141585 -0.9567 0.169353
23 to 24 141891 -0.0541 0.478439
22 to 23 142101 0.5654 0.714099
21 to 22 141986 0.2262 0.589464
20 to 21 141739 -0.5024 0.307676
19 to 20 141986 0.2262 0.589464
18 to 19 141589 -0.9449 0.172348
17 to 18 141769 -0.4140 0.339454
16 to 17 142017 0.3176 0.624610
15 to 16 141911 0.0049 0.501965
14 to 15 142461 1.6273 0.948168
13 to 14 142159 0.7365 0.769284
12 to 13 142134 0.6627 0.746253
11 to 12 141997 0.2586 0.602033
10 to 11 141734 -0.5172 0.302509
9 to 10 142467 1.6450 0.950020
8 to 9 141971 0.1819 0.572176
7 to 8 142411 1.4799 0.930544
6 to 7 142099 0.5595 0.712089
5 to 6 141665 -0.7207 0.235536
4 to 5 142422 1.5123 0.934771
3 to 4 141496 -1.2193 0.111372
2 to 3 142065 0.4592 0.676956
1 to 2 141772 -0.4051 0.342701
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2478.71 -0.301 0.381679
Test results for specific bytes for dh-ranFile-2018-06-17_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2509.21 0.130 0.551797
2 to 9 2489.12 -0.154 0.438879
3 to 10 2434.54 -0.926 0.177305
4 to 11 2378.09 -1.724 0.042350
5 to 12 2601.19 1.431 0.923785
6 to 13 2409.52 -1.280 0.100348
7 to 14 2589.71 1.269 0.897725
8 to 15 2550.32 0.712 0.761656
9 to 16 2556.59 0.800 0.788250
10 to 17 2604.03 1.471 0.929390
11 to 18 2492.06 -0.112 0.455289
12 to 19 2469.87 -0.426 0.335006
13 to 20 2514.02 0.198 0.578610
14 to 21 2565.92 0.932 0.824389
15 to 22 2430.85 -0.978 0.164051
16 to 23 2468.47 -0.446 0.327818
17 to 24 2547.05 0.665 0.747089
18 to 25 2452.39 -0.673 0.250376
19 to 26 2512.74 0.180 0.571512
20 to 27 2551.51 0.728 0.766834
21 to 28 2574.63 1.055 0.854369
22 to 29 2641.86 2.006 0.977584
23 to 30 2542.33 0.599 0.725306
24 to 31 2420.92 -1.118 0.131707
25 to 32 2671.63 2.427 0.992393
CDPARK for dh-ranFile-2018-06-17_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
3527 0.1826 0.572463
3566 1.9635 0.975204
3567 2.0091 0.977738
3513 -0.4566 0.323972
3491 -1.4612 0.071982
3492 -1.4155 0.078457
3508 -0.6849 0.246694
3550 1.2329 0.891189
3536 0.5936 0.723613
3504 -0.8676 0.192812
Square side=100, avg. no. parked=3525.40 sample std.=27.04
p-value of the KSTEST for those 10 p-values: 0.480309
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_16:31
0.0894,0.7887,0.2100,0.9865,0.5256,0.3311,0.2551,0.8854,0.3292,0.4546,
The KS test for those 10 p-values: 0.883221
The 3DSPHERES test for dh-ranFile-2018-06-17_16:31
sample no r^3 equiv. uni.
1 57.993 0.855300
2 12.455 0.339768
3 0.146 0.004859
4 20.524 0.495469
5 13.894 0.370686
6 8.079 0.236082
7 9.927 0.281715
8 31.857 0.654203
9 20.841 0.500773
10 46.639 0.788733
11 0.099 0.003298
12 48.473 0.801264
13 4.799 0.147818
14 9.731 0.277019
15 3.926 0.122663
16 5.542 0.168685
17 52.613 0.826879
18 7.150 0.212070
19 19.777 0.482748
20 23.318 0.540339
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.172421
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 0.1 0.9 -1.8 -0.3
1.0 -0.1 1.1 -0.4 -1.7 -1.2
-0.2 0.2 -0.3 -0.8 1.3 -1.5
-0.6 0.2 1.1 1.7 -0.2 0.2
0.9 0.5 0.2 1.4 -0.5 0.3
0.0 -0.8 0.7 -2.1 -2.4 0.8
-0.2 0.5 1.7 -0.1 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:40.956552
z-score=-0.113850, p-value=0.483315
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_16:31
Test no p-value
1 0.202775
2 0.010120
3 0.024371
4 0.540381
5 0.011694
6 0.892496
7 0.007143
8 0.614750
9 0.122681
10 0.007497
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000081
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_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 66624 0.03 66520 0.32
3 25000.00 25021 0.02 25100 0.40
4 6666.67 6697 0.14 6721 0.44
5 1388.89 1392 0.01 1388 0.00
6 238.10 228 0.43 239 0.00
7 34.72 35 0.00 27 1.72
8 4.96 2 1.77 4 0.19
p=0.11907 p=0.20022
Number of rngs required: 687624, p-value: 0.184
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_16:31
No. of wins: Observed Expected
98662 98585.9
z-score= 0.341, pvalue=0.63328
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66450 66666.7 0.704 0.704
2 37569 37654.3 0.193 0.897
3 27093 26954.7 0.709 1.607
4 19293 19313.5 0.022 1.628
5 13964 13851.4 0.915 2.543
6 9945 9943.5 0.000 2.544
7 7109 7145.0 0.182 2.725
8 5152 5139.1 0.033 2.758
9 3719 3699.9 0.099 2.857
10 2677 2666.3 0.043 2.900
11 1939 1923.3 0.128 3.027
12 1433 1388.7 1.411 4.438
13 1021 1003.7 0.298 4.736
14 694 726.1 1.423 6.158
15 535 525.8 0.160 6.318
16 370 381.2 0.326 6.644
17 284 276.5 0.201 6.845
18 213 200.8 0.737 7.583
19 157 146.0 0.831 8.414
20 119 106.2 1.539 9.953
21 264 287.1 1.861 11.814
Chisq= 11.81 for 20 degrees of freedom, p= 0.07767
SUMMARY of craptest
p-value for no. of wins: 0.633278
p-value for throws/game: 0.077665
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_16:31
No. of wins: Observed Expected
98494 98585.9
z-score=-0.411, pvalue=0.34059
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66872 66666.7 0.632 0.632
2 37686 37654.3 0.027 0.659
3 26627 26954.7 3.985 4.644
4 19413 19313.5 0.513 5.157
5 13836 13851.4 0.017 5.174
6 9914 9943.5 0.088 5.262
7 7194 7145.0 0.336 5.597
8 5144 5139.1 0.005 5.602
9 3669 3699.9 0.257 5.860
10 2711 2666.3 0.749 6.609
11 1946 1923.3 0.267 6.876
12 1382 1388.7 0.033 6.909
13 1006 1003.7 0.005 6.914
14 707 726.1 0.505 7.419
15 490 525.8 2.442 9.861
16 371 381.2 0.270 10.131
17 296 276.5 1.369 11.501
18 177 200.8 2.828 14.328
19 162 146.0 1.757 16.085
20 118 106.2 1.308 17.393
21 279 287.1 0.229 17.622
Chisq= 17.62 for 20 degrees of freedom, p= 0.38773
SUMMARY of craptest
p-value for no. of wins: 0.340593
p-value for throws/game: 0.387729
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0033,0.0037,0.0049,0.0064,0.0071,0.0075,0.0101,0.0107,0.0117,
0.0128,0.0187,0.0191,0.0208,0.0213,0.0244,0.0296,0.0311,0.0314,0.0424,
0.0489,0.0561,0.0562,0.0651,0.0661,0.0683,0.0720,0.0747,0.0777,0.0785,
0.0799,0.0846,0.0894,0.0903,0.0997,0.1003,0.1022,0.1114,0.1138,0.1191,
0.1227,0.1227,0.1317,0.1423,0.1478,0.1527,0.1542,0.1609,0.1617,0.1641,
0.1666,0.1687,0.1694,0.1723,0.1724,0.1772,0.1773,0.1837,0.1844,0.1878,
0.1921,0.1928,0.1978,0.2002,0.2007,0.2028,0.2047,0.2100,0.2121,0.2133,
0.2144,0.2147,0.2290,0.2315,0.2321,0.2326,0.2355,0.2361,0.2384,0.2400,
0.2467,0.2504,0.2551,0.2601,0.2770,0.2817,0.2844,0.2890,0.3025,0.3077,
0.3088,0.3149,0.3170,0.3199,0.3232,0.3240,0.3278,0.3292,0.3311,0.3350,
0.3395,0.3398,0.3406,0.3427,0.3492,0.3617,0.3640,0.3680,0.3707,0.3745,
0.3796,0.3817,0.3856,0.3877,0.3904,0.3909,0.4111,0.4153,0.4219,0.4389,
0.4389,0.4417,0.4459,0.4546,0.4553,0.4561,0.4638,0.4784,0.4803,0.4803,
0.4808,0.4827,0.4833,0.4859,0.4913,0.4955,0.5008,0.5020,0.5256,0.5333,
0.5364,0.5398,0.5403,0.5404,0.5499,0.5518,0.5629,0.5703,0.5709,0.5715,
0.5722,0.5725,0.5728,0.5786,0.5825,0.5839,0.5866,0.5895,0.5895,0.5895,
0.5896,0.5939,0.5984,0.6020,0.6051,0.6064,0.6100,0.6104,0.6148,0.6201,
0.6246,0.6253,0.6333,0.6380,0.6437,0.6443,0.6448,0.6542,0.6566,0.6612,
0.6661,0.6680,0.6695,0.6727,0.6770,0.6837,0.6891,0.6929,0.6983,0.7050,
0.7070,0.7121,0.7141,0.7174,0.7236,0.7253,0.7265,0.7310,0.7318,0.7337,
0.7410,0.7463,0.7471,0.7617,0.7646,0.7649,0.7668,0.7693,0.7697,0.7819,
0.7848,0.7865,0.7883,0.7887,0.7887,0.8013,0.8244,0.8269,0.8397,0.8435,
0.8468,0.8544,0.8553,0.8564,0.8745,0.8806,0.8832,0.8847,0.8854,0.8912,
0.8925,0.8977,0.9174,0.9178,0.9238,0.9241,0.9260,0.9278,0.9294,0.9294,
0.9305,0.9348,0.9351,0.9420,0.9439,0.9441,0.9452,0.9470,0.9478,0.9482,
0.9500,0.9512,0.9560,0.9569,0.9591,0.9609,0.9615,0.9703,0.9738,0.9752,
0.9776,0.9777,0.9792,0.9832,0.9865,0.9867,0.9882,0.9924,0.9962,
Overall p-value after applying KStest on 269 p-values = 0.119326
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.