RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.35 13.1056 0.270913
2 to 25 15.85 18.6641 0.651850
3 to 26 15.93 10.1460 0.102625
4 to 27 16.03 8.5044 0.045459
5 to 28 15.90 12.6998 0.243964
6 to 29 15.97 17.1469 0.555542
7 to 30 15.80 10.1912 0.104598
8 to 31 15.73 16.1411 0.486148
9 to 32 15.66 13.9840 0.331763
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.081527
Tough bday spacings test for dh-ranFile-2018-07-04_17:31: 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 19 40 85 80 83 95 52 21 16 4 5
(O-E)^2/E 10.6 0.3 1.9 3.2 2.2 3.6 0.0 2.6 0.1 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 25.727, p= 0.996
RESULTS OF GCD FOR dh-ranFile-2018-07-04_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.534220
p-value, dist. of gcd's: 0.349666
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.313 0.933 0.471 0.085 0.507 0.384 0.051 0.248
Bits 8 to 15---> 0.707 0.191 0.106 0.574 0.543 0.599 0.715 0.216
Bits 16 to 23---> 0.509 0.847 0.935 0.924 0.419 0.774 0.126 0.292
Bits 24 to 31---> 0.348 0.224 0.209 0.806 0.161 0.883 0.675 0.950
KS test for the above 32 p values: 0.032
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_17:31,
p-values for 5 runs: 0.8164, 0.0110, 0.8427, 0.6843, 0.4277
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5197 5134.0 0.773 0.834
r= 30 23051 23103.0 0.117 0.951
r= 31 11537 11551.5 0.018 0.969
chi-square = 0.969 with df = 3; p-value = 0.191
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 192 211.4 1.783 1.783
r= 30 5162 5134.0 0.153 1.936
r= 31 23134 23103.0 0.041 1.978
r= 32 11512 11551.5 0.135 2.113
chi-square = 2.113 with df = 3; p-value = 0.451
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_17:31
b-rank test for bits 1 to 8, p=0.27745
b-rank test for bits 2 to 9, p=0.82175
b-rank test for bits 3 to 10, p=0.56229
b-rank test for bits 4 to 11, p=0.87181
b-rank test for bits 5 to 12, p=0.77668
b-rank test for bits 6 to 13, p=0.96359
b-rank test for bits 7 to 14, p=0.07328
b-rank test for bits 8 to 15, p=0.01769
b-rank test for bits 9 to 16, p=0.23894
b-rank test for bits 10 to 17, p=0.38195
b-rank test for bits 11 to 18, p=0.79505
b-rank test for bits 12 to 19, p=0.63293
b-rank test for bits 13 to 20, p=0.13329
b-rank test for bits 14 to 21, p=0.49361
b-rank test for bits 15 to 22, p=0.45095
b-rank test for bits 16 to 23, p=0.55572
b-rank test for bits 17 to 24, p=0.77847
b-rank test for bits 18 to 25, p=0.85559
b-rank test for bits 19 to 26, p=0.06832
b-rank test for bits 20 to 27, p=0.83861
b-rank test for bits 21 to 28, p=0.86010
b-rank test for bits 22 to 29, p=0.67069
b-rank test for bits 23 to 30, p=0.47405
b-rank test for bits 24 to 31, p=0.31776
b-rank test for bits 25 to 32, p=0.65716
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 = 0.672012
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_17:31
(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 141889 -0.05 0.481057
2 142670 1.78 0.962238
3 141478 -1.01 0.156780
4 141653 -0.60 0.274619
5 141739 -0.40 0.345327
6 141781 -0.30 0.382151
7 141933 0.06 0.522052
8 141990 0.19 0.574750
9 142234 0.76 0.775947
10 142168 0.60 0.727201
11 141765 -0.34 0.367976
12 141543 -0.86 0.196023
13 142161 0.59 0.721739
14 141833 -0.18 0.429228
15 141857 -0.12 0.451344
16 141838 -0.17 0.433819
17 142543 1.48 0.930635
18 141509 -0.94 0.174804
19 141415 -1.15 0.124050
20 141596 -0.73 0.232060
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_17:31
Bits used No. missing words z-score p-value
23 to 32 142335 1.4678 0.928924
22 to 31 142625 2.4678 0.993203
21 to 30 142370 1.5885 0.943915
20 to 29 142013 0.3575 0.639635
19 to 28 141779 -0.4494 0.326567
18 to 27 141927 0.0609 0.524293
17 to 26 141729 -0.6218 0.267028
16 to 25 141963 0.1851 0.573413
15 to 24 141522 -1.3356 0.090837
14 to 23 141629 -0.9667 0.166858
13 to 22 141829 -0.2770 0.390890
12 to 21 142000 0.3127 0.622729
11 to 20 141470 -1.5149 0.064895
10 to 19 141953 0.1506 0.559849
9 to 18 142070 0.5540 0.710222
8 to 17 141703 -0.7115 0.238393
7 to 16 142400 1.6920 0.954674
6 to 15 141623 -0.9873 0.161737
5 to 14 141830 -0.2736 0.392215
4 to 13 141860 -0.1701 0.432464
3 to 12 142013 0.3575 0.639635
2 to 11 141499 -1.4149 0.078544
1 to 10 141824 -0.2942 0.384287
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_17:31
Bits used No. missing words z-score p-value
28 to 32 141399 -1.7299 0.041821
27 to 31 141661 -0.8418 0.199951
26 to 30 142318 1.3853 0.917023
25 to 29 142253 1.1650 0.877987
24 to 28 141566 -1.1638 0.122246
23 to 27 141607 -1.0248 0.152718
22 to 26 142241 1.1243 0.869558
21 to 25 141092 -2.7706 0.002798
20 to 24 141798 -0.3774 0.352942
19 to 23 142319 1.3887 0.917540
18 to 22 142057 0.5006 0.691665
17 to 21 141559 -1.1876 0.117504
16 to 20 141342 -1.9232 0.027230
15 to 19 141849 -0.2045 0.418978
14 to 18 141588 -1.0893 0.138021
13 to 17 141556 -1.1977 0.115511
12 to 16 141583 -1.1062 0.134319
11 to 15 142001 0.3107 0.622003
10 to 14 142060 0.5107 0.695236
9 to 13 142229 1.0836 0.860735
8 to 12 141502 -1.3808 0.083673
7 to 11 141430 -1.6248 0.052098
6 to 10 141681 -0.7740 0.219465
5 to 9 141685 -0.7604 0.223496
4 to 8 141612 -1.0079 0.156752
3 to 7 142150 0.8158 0.792702
2 to 6 141779 -0.4418 0.329318
1 to 5 141858 -0.1740 0.430933
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_17:31
Bits used No. missing words z-score p-value
31 to 32 140791 -3.2989 0.000485
30 to 31 142055 0.4297 0.666295
29 to 30 141853 -0.1662 0.434014
28 to 29 141377 -1.5703 0.058173
27 to 28 142376 1.3766 0.915683
26 to 27 141251 -1.9420 0.026070
25 to 26 141631 -0.8210 0.205814
24 to 25 141329 -1.7119 0.043459
23 to 24 141951 0.1229 0.548915
22 to 23 141825 -0.2488 0.401773
21 to 22 142159 0.7365 0.769284
20 to 21 142010 0.2970 0.616752
19 to 20 142211 0.8899 0.813235
18 to 19 141306 -1.7797 0.037560
17 to 18 142058 0.4386 0.669508
16 to 17 141978 0.2026 0.580263
15 to 16 142119 0.6185 0.731876
14 to 15 141951 0.1229 0.548915
13 to 14 141882 -0.0806 0.467872
12 to 13 141427 -1.4228 0.077397
11 to 12 141945 0.1052 0.541900
10 to 11 142377 1.3796 0.916139
9 to 10 141626 -0.8358 0.201639
8 to 9 141344 -1.6676 0.047694
7 to 8 141675 -0.6912 0.244708
6 to 7 142022 0.3324 0.630191
5 to 6 141485 -1.2517 0.105338
4 to 5 141178 -2.1573 0.015491
3 to 4 141713 -0.5791 0.281246
2 to 3 141379 -1.5644 0.058862
1 to 2 141568 -1.0069 0.156998
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2468.85 -0.441 0.329785
Test results for specific bytes for dh-ranFile-2018-07-04_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2576.93 1.088 0.861705
2 to 9 2496.23 -0.053 0.478729
3 to 10 2450.77 -0.696 0.243151
4 to 11 2492.60 -0.105 0.458320
5 to 12 2577.50 1.096 0.863452
6 to 13 2499.52 -0.007 0.497314
7 to 14 2535.54 0.503 0.692372
8 to 15 2492.10 -0.112 0.455532
9 to 16 2619.30 1.687 0.954216
10 to 17 2500.85 0.012 0.504824
11 to 18 2476.09 -0.338 0.367626
12 to 19 2609.32 1.546 0.938946
13 to 20 2494.23 -0.082 0.467503
14 to 21 2511.70 0.165 0.565690
15 to 22 2568.55 0.969 0.833824
16 to 23 2548.37 0.684 0.753033
17 to 24 2434.12 -0.932 0.175745
18 to 25 2608.62 1.536 0.937739
19 to 26 2489.94 -0.142 0.443445
20 to 27 2375.88 -1.755 0.039596
21 to 28 2421.11 -1.116 0.132277
22 to 29 2602.13 1.444 0.925679
23 to 30 2509.62 0.136 0.554090
24 to 31 2415.94 -1.189 0.117267
25 to 32 2415.94 -1.189 0.117254
CDPARK for dh-ranFile-2018-07-04_17:31: 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
3478 -2.0548 0.019949
3583 2.7397 0.996925
3545 1.0046 0.842447
3515 -0.3653 0.357445
3515 -0.3653 0.357445
3561 1.7352 0.958644
3506 -0.7763 0.218799
3508 -0.6849 0.246694
3491 -1.4612 0.071982
3501 -1.0046 0.157553
Square side=100, avg. no. parked=3520.30 sample std.=31.03
p-value of the KSTEST for those 10 p-values: 0.188010
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_17:31
0.1521,0.1614,0.3114,0.7898,0.9641,0.3115,0.6817,0.9537,0.9517,0.9895,
The KS test for those 10 p-values: 0.056708
The 3DSPHERES test for dh-ranFile-2018-07-04_17:31
sample no r^3 equiv. uni.
1 23.639 0.545233
2 67.571 0.894850
3 10.439 0.293872
4 7.058 0.209647
5 68.549 0.898224
6 18.228 0.455338
7 29.857 0.630357
8 27.138 0.595300
9 10.645 0.298716
10 10.065 0.285014
11 1.913 0.061774
12 36.915 0.707850
13 23.418 0.541870
14 24.992 0.565280
15 26.704 0.589398
16 14.797 0.389356
17 17.988 0.450961
18 40.362 0.739565
19 97.975 0.961835
20 2.881 0.091559
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.810287
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 -0.4 1.5 -0.7 0.3
-2.2 -0.2 -1.2 -0.2 -0.1 -0.6
-1.0 0.8 0.9 0.5 -0.3 1.3
-1.4 -0.2 0.3 -0.5 0.6 -0.3
1.0 -0.1 -0.2 0.2 0.2 0.4
0.7 0.8 -0.5 -0.3 0.5 1.1
-1.2 -0.1 0.5 -1.3 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:24.631421
z-score=-1.895067, p-value=0.014992
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_17:31
Test no p-value
1 0.504720
2 0.047035
3 0.117969
4 0.468618
5 0.696033
6 0.886279
7 0.876080
8 0.104835
9 0.798498
10 0.105036
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.543862
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_17:31:
(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 66639 0.01 66548 0.21
3 25000.00 24938 0.15 25060 0.14
4 6666.67 6665 0.00 6676 0.01
5 1388.89 1481 6.11 1425 0.94
6 238.10 241 0.04 239 0.00
7 34.72 30 0.64 44 2.48
8 4.96 5 0.00 7 0.84
p=0.67467 p=0.40793
Number of rngs required: 688426, p-value: 0.511
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_17:31
No. of wins: Observed Expected
98512 98585.9
z-score=-0.330, pvalue=0.37057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66323 66666.7 1.772 1.772
2 37329 37654.3 2.811 4.582
3 27220 26954.7 2.611 7.193
4 19554 19313.5 2.996 10.189
5 13839 13851.4 0.011 10.200
6 10081 9943.5 1.900 12.100
7 7154 7145.0 0.011 12.111
8 5126 5139.1 0.033 12.144
9 3692 3699.9 0.017 12.161
10 2640 2666.3 0.259 12.420
11 1966 1923.3 0.947 13.367
12 1382 1388.7 0.033 13.400
13 1004 1003.7 0.000 13.400
14 732 726.1 0.047 13.447
15 521 525.8 0.044 13.492
16 406 381.2 1.620 15.112
17 257 276.5 1.381 16.492
18 221 200.8 2.026 18.518
19 149 146.0 0.062 18.580
20 92 106.2 1.902 20.483
21 312 287.1 2.157 22.640
Chisq= 22.64 for 20 degrees of freedom, p= 0.69318
SUMMARY of craptest
p-value for no. of wins: 0.370572
p-value for throws/game: 0.693184
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_17:31
No. of wins: Observed Expected
98882 98585.9
z-score= 1.325, pvalue=0.90733
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66939 66666.7 1.112 1.112
2 37727 37654.3 0.140 1.253
3 27031 26954.7 0.216 1.469
4 19361 19313.5 0.117 1.586
5 13671 13851.4 2.350 3.936
6 9793 9943.5 2.279 6.215
7 7084 7145.0 0.521 6.736
8 5136 5139.1 0.002 6.738
9 3713 3699.9 0.047 6.784
10 2645 2666.3 0.170 6.955
11 1900 1923.3 0.283 7.238
12 1381 1388.7 0.043 7.281
13 996 1003.7 0.059 7.340
14 754 726.1 1.069 8.409
15 521 525.8 0.044 8.453
16 340 381.2 4.443 12.896
17 294 276.5 1.102 13.999
18 195 200.8 0.169 14.168
19 144 146.0 0.027 14.195
20 101 106.2 0.256 14.451
21 274 287.1 0.599 15.050
Chisq= 15.05 for 20 degrees of freedom, p= 0.22645
SUMMARY of craptest
p-value for no. of wins: 0.907334
p-value for throws/game: 0.226452
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0028,0.0110,0.0150,0.0155,0.0177,0.0199,0.0261,0.0272,0.0318,
0.0376,0.0396,0.0418,0.0435,0.0455,0.0470,0.0477,0.0506,0.0521,0.0567,
0.0582,0.0589,0.0618,0.0649,0.0683,0.0720,0.0733,0.0774,0.0785,0.0815,
0.0837,0.0854,0.0908,0.0916,0.1026,0.1046,0.1048,0.1050,0.1053,0.1065,
0.1155,0.1173,0.1173,0.1175,0.1180,0.1222,0.1241,0.1257,0.1323,0.1333,
0.1343,0.1380,0.1521,0.1527,0.1568,0.1568,0.1570,0.1576,0.1614,0.1614,
0.1617,0.1669,0.1748,0.1757,0.1880,0.1905,0.1913,0.1960,0.2000,0.2016,
0.2058,0.2087,0.2096,0.2163,0.2188,0.2195,0.2235,0.2243,0.2265,0.2321,
0.2384,0.2389,0.2432,0.2440,0.2447,0.2467,0.2482,0.2670,0.2709,0.2746,
0.2774,0.2812,0.2850,0.2921,0.2939,0.2987,0.3114,0.3115,0.3130,0.3178,
0.3266,0.3293,0.3298,0.3318,0.3453,0.3476,0.3497,0.3529,0.3574,0.3574,
0.3676,0.3680,0.3706,0.3820,0.3822,0.3839,0.3843,0.3894,0.3909,0.3922,
0.4018,0.4079,0.4189,0.4190,0.4277,0.4292,0.4309,0.4325,0.4338,0.4340,
0.4434,0.4507,0.4509,0.4510,0.4513,0.4553,0.4555,0.4583,0.4675,0.4679,
0.4686,0.4713,0.4741,0.4787,0.4811,0.4861,0.4936,0.4973,0.5047,0.5048,
0.5067,0.5087,0.5106,0.5221,0.5243,0.5342,0.5419,0.5419,0.5429,0.5439,
0.5452,0.5489,0.5489,0.5541,0.5555,0.5557,0.5598,0.5623,0.5653,0.5657,
0.5734,0.5744,0.5748,0.5803,0.5894,0.5953,0.5987,0.6168,0.6220,0.6227,
0.6302,0.6304,0.6329,0.6396,0.6396,0.6518,0.6572,0.6663,0.6695,0.6707,
0.6720,0.6747,0.6751,0.6817,0.6843,0.6917,0.6924,0.6932,0.6952,0.6960,
0.7069,0.7078,0.7102,0.7153,0.7217,0.7272,0.7319,0.7396,0.7530,0.7693,
0.7743,0.7759,0.7767,0.7785,0.7898,0.7927,0.7951,0.7985,0.8061,0.8103,
0.8132,0.8164,0.8217,0.8338,0.8386,0.8424,0.8427,0.8473,0.8556,0.8601,
0.8607,0.8617,0.8635,0.8696,0.8718,0.8761,0.8780,0.8832,0.8863,0.8949,
0.8982,0.9073,0.9157,0.9161,0.9170,0.9175,0.9236,0.9257,0.9289,0.9306,
0.9333,0.9352,0.9377,0.9389,0.9439,0.9495,0.9517,0.9537,0.9542,0.9547,
0.9586,0.9618,0.9622,0.9636,0.9641,0.9895,0.9932,0.9959,0.9969,
Overall p-value after applying KStest on 269 p-values = 0.053939
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.