RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.71 17.1022 0.552536
2 to 25 15.82 25.6707 0.919327
3 to 26 15.61 20.9305 0.770586
4 to 27 15.40 42.7919 0.999485
5 to 28 15.60 18.6657 0.651946
6 to 29 15.63 24.2219 0.886471
7 to 30 15.68 11.2643 0.157501
8 to 31 15.75 22.5009 0.833784
9 to 32 15.82 12.3891 0.223975
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.079065
Tough bday spacings test for dh-ranFile-2018-07-08_23:31: 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 35 74 99 102 72 54 27 9 9 7
(O-E)^2/E 0.9 0.1 0.0 0.0 0.2 0.5 0.1 0.3 2.3 0.9 2.1
Birthday Spacings: Sum(O-E)^2/E= 7.284, p= 0.302
RESULTS OF GCD FOR dh-ranFile-2018-07-08_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.919069
p-value, dist. of gcd's: 0.017128
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.264 0.897 0.923 0.053 0.946 0.519 0.455 0.067
Bits 8 to 15---> 0.937 0.477 0.123 0.974 0.537 0.507 0.026 0.837
Bits 16 to 23---> 0.110 0.144 0.669 0.009 0.184 0.916 0.440 0.220
Bits 24 to 31---> 0.986 0.678 0.273 0.686 0.999 0.083 0.896 0.544
KS test for the above 32 p values: 0.803
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_23:31,
p-values for 5 runs: 0.7589, 0.3795, 0.2207, 0.7644, 0.6127
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5165 5134.0 0.187 0.717
r= 30 22990 23103.0 0.553 1.270
r= 31 11623 11551.5 0.442 1.712
chi-square = 1.712 with df = 3; p-value = 0.366
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 193 211.4 1.605 1.605
r= 30 5147 5134.0 0.033 1.637
r= 31 23185 23103.0 0.291 1.928
r= 32 11475 11551.5 0.507 2.435
chi-square = 2.435 with df = 3; p-value = 0.513
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_23:31
b-rank test for bits 1 to 8, p=0.24350
b-rank test for bits 2 to 9, p=0.23951
b-rank test for bits 3 to 10, p=0.27936
b-rank test for bits 4 to 11, p=0.98576
b-rank test for bits 5 to 12, p=0.90381
b-rank test for bits 6 to 13, p=0.39058
b-rank test for bits 7 to 14, p=0.27217
b-rank test for bits 8 to 15, p=0.75621
b-rank test for bits 9 to 16, p=0.04511
b-rank test for bits 10 to 17, p=0.84294
b-rank test for bits 11 to 18, p=0.17235
b-rank test for bits 12 to 19, p=0.62778
b-rank test for bits 13 to 20, p=0.89842
b-rank test for bits 14 to 21, p=0.24249
b-rank test for bits 15 to 22, p=0.04686
b-rank test for bits 16 to 23, p=0.18249
b-rank test for bits 17 to 24, p=0.90297
b-rank test for bits 18 to 25, p=0.09103
b-rank test for bits 19 to 26, p=0.75738
b-rank test for bits 20 to 27, p=0.91268
b-rank test for bits 21 to 28, p=0.76482
b-rank test for bits 22 to 29, p=0.05204
b-rank test for bits 23 to 30, p=0.53229
b-rank test for bits 24 to 31, p=0.89067
b-rank test for bits 25 to 32, p=0.60481
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 = 0.472475
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_23:31
(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 141793 -0.27 0.392888
2 141447 -1.08 0.140024
3 141809 -0.23 0.407331
4 141372 -1.26 0.104659
5 141668 -0.56 0.286426
6 142311 0.94 0.826001
7 142060 0.35 0.637593
8 142190 0.66 0.744014
9 142126 0.51 0.693655
10 142655 1.74 0.959265
11 141494 -0.97 0.165924
12 141340 -1.33 0.091725
13 142152 0.57 0.714638
14 141243 -1.56 0.059754
15 142417 1.19 0.882217
16 141633 -0.65 0.259259
17 141832 -0.18 0.428310
18 142334 0.99 0.839455
19 141933 0.06 0.522052
20 141977 0.16 0.562814
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_23:31
Bits used No. missing words z-score p-value
23 to 32 141789 -0.4149 0.339096
22 to 31 142019 0.3782 0.647349
21 to 30 142115 0.7092 0.760902
20 to 29 141622 -0.9908 0.160893
19 to 28 141860 -0.1701 0.432464
18 to 27 141320 -2.0322 0.021068
17 to 26 141318 -2.0391 0.020722
16 to 25 141718 -0.6598 0.254704
15 to 24 141550 -1.2391 0.107660
14 to 23 141858 -0.1770 0.429754
13 to 22 142061 0.5230 0.699513
12 to 21 142291 1.3161 0.905930
11 to 20 141586 -1.1149 0.132440
10 to 19 142171 0.9023 0.816554
9 to 18 141940 0.1058 0.542113
8 to 17 141744 -0.5701 0.284304
7 to 16 142084 0.6023 0.726516
6 to 15 142334 1.4644 0.928455
5 to 14 142425 1.7782 0.962312
4 to 13 141814 -0.3287 0.371182
3 to 12 142173 0.9092 0.818380
2 to 11 141839 -0.2425 0.404190
1 to 10 141733 -0.6080 0.271582
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_23:31
Bits used No. missing words z-score p-value
28 to 32 141450 -1.5571 0.059729
27 to 31 142027 0.3989 0.655010
26 to 30 141411 -1.6893 0.045585
25 to 29 141789 -0.4079 0.341674
24 to 28 142139 0.7785 0.781875
23 to 27 142030 0.4091 0.658749
22 to 26 141785 -0.4215 0.336711
21 to 25 141818 -0.3096 0.378435
20 to 24 141168 -2.5130 0.005986
19 to 23 141663 -0.8350 0.201854
18 to 22 141480 -1.4554 0.072785
17 to 21 141513 -1.3435 0.089556
16 to 20 141565 -1.1672 0.121561
15 to 19 142304 1.3379 0.909530
14 to 18 141542 -1.2452 0.106532
13 to 17 141136 -2.6215 0.004378
12 to 16 141663 -0.8350 0.201854
11 to 15 142198 0.9785 0.836097
10 to 14 141748 -0.5469 0.292230
9 to 13 141783 -0.4282 0.334239
8 to 12 142324 1.4057 0.920088
7 to 11 141940 0.1040 0.541402
6 to 10 141569 -1.1537 0.124320
5 to 9 142066 0.5311 0.702320
4 to 8 141695 -0.7265 0.233753
3 to 7 141682 -0.7706 0.220469
2 to 6 142035 0.4260 0.664946
1 to 5 142282 1.2633 0.896757
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_23:31
Bits used No. missing words z-score p-value
31 to 32 141470 -1.2960 0.097495
30 to 31 141770 -0.4110 0.340535
29 to 30 141962 0.1554 0.561735
28 to 29 141653 -0.7561 0.224784
27 to 28 141840 -0.2045 0.418976
26 to 27 141369 -1.5939 0.055480
25 to 26 141654 -0.7532 0.225669
24 to 25 141982 0.2144 0.584869
23 to 24 141586 -0.9538 0.170099
22 to 23 142502 1.7483 0.959793
21 to 22 141665 -0.7207 0.235536
20 to 21 141950 0.1200 0.547747
19 to 20 142088 0.5271 0.700921
18 to 19 141014 -2.6411 0.004132
17 to 18 142196 0.8456 0.801122
16 to 17 141913 0.0108 0.504319
15 to 16 141558 -1.0364 0.150014
14 to 15 141439 -1.3874 0.082659
13 to 14 141764 -0.4287 0.334070
12 to 13 141229 -2.0069 0.022382
11 to 12 142319 1.2085 0.886566
10 to 11 141507 -1.1868 0.117650
9 to 10 141739 -0.5024 0.307676
8 to 9 141663 -0.7266 0.233724
7 to 8 141679 -0.6794 0.248430
6 to 7 142113 0.6008 0.726012
5 to 6 142088 0.5271 0.700921
4 to 5 141542 -1.0836 0.139278
3 to 4 141659 -0.7384 0.230125
2 to 3 141518 -1.1544 0.124175
1 to 2 141780 -0.3815 0.351415
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2538.49 0.544 0.706896
Test results for specific bytes for dh-ranFile-2018-07-08_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2498.38 -0.023 0.490833
2 to 9 2539.54 0.559 0.711959
3 to 10 2401.05 -1.399 0.080857
4 to 11 2458.38 -0.589 0.278083
5 to 12 2531.26 0.442 0.670783
6 to 13 2518.92 0.268 0.605473
7 to 14 2484.99 -0.212 0.415969
8 to 15 2462.01 -0.537 0.295528
9 to 16 2397.08 -1.455 0.072770
10 to 17 2455.28 -0.632 0.263551
11 to 18 2556.29 0.796 0.786994
12 to 19 2410.91 -1.260 0.103844
13 to 20 2515.49 0.219 0.586694
14 to 21 2515.24 0.215 0.585307
15 to 22 2531.96 0.452 0.674384
16 to 23 2424.93 -1.062 0.144211
17 to 24 2417.98 -1.160 0.123041
18 to 25 2408.65 -1.292 0.098190
19 to 26 2573.03 1.033 0.849160
20 to 27 2457.28 -0.604 0.272885
21 to 28 2485.79 -0.201 0.420339
22 to 29 2447.46 -0.743 0.228729
23 to 30 2557.49 0.813 0.791896
24 to 31 2543.37 0.613 0.730155
25 to 32 2473.41 -0.376 0.353469
CDPARK for dh-ranFile-2018-07-08_23:31: 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
3548 1.1416 0.873180
3515 -0.3653 0.357445
3537 0.6393 0.738676
3512 -0.5023 0.307734
3546 1.0502 0.853193
3558 1.5982 0.944998
3522 -0.0457 0.481790
3506 -0.7763 0.218799
3515 -0.3653 0.357445
3499 -1.0959 0.136563
Square side=100, avg. no. parked=3525.80 sample std.=19.00
p-value of the KSTEST for those 10 p-values: 0.872780
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_23:31
0.6085,0.1904,0.8147,0.2547,0.7432,0.9104,0.4127,0.6023,0.3558,0.8177,
The KS test for those 10 p-values: 0.661132
The 3DSPHERES test for dh-ranFile-2018-07-08_23:31
sample no r^3 equiv. uni.
1 0.133 0.004428
2 22.144 0.521997
3 28.296 0.610624
4 11.575 0.320124
5 69.127 0.900166
6 12.557 0.342008
7 37.392 0.712464
8 62.472 0.875369
9 12.818 0.347713
10 67.933 0.896110
11 10.473 0.294688
12 60.574 0.867227
13 24.538 0.558657
14 40.878 0.744006
15 17.345 0.439074
16 81.468 0.933834
17 3.502 0.110168
18 14.668 0.386724
19 16.463 0.422338
20 32.235 0.658536
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.598078
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.9 0.8 -0.3 -0.2 1.6
-1.8 1.1 -0.5 0.5 -0.9 -0.4
0.5 0.3 1.1 -2.0 0.6 0.5
-0.7 0.2 -1.1 0.3 0.1 2.2
-0.3 0.2 -0.1 0.1 -0.7 -0.3
1.0 -0.1 -1.5 -0.6 -0.2 0.4
1.0 -0.4 0.5 -1.3 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:33.249179
z-score=-0.954793, p-value=0.169438
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_23:31
Test no p-value
1 0.070699
2 0.094036
3 0.059483
4 0.484793
5 0.610713
6 0.030884
7 0.000938
8 0.361096
9 0.580154
10 0.636256
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.011611
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_23:31:
(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 66867 0.60 66733 0.07
3 25000.00 24739 2.72 24954 0.08
4 6666.67 6688 0.07 6700 0.17
5 1388.89 1405 0.19 1360 0.60
6 238.10 251 0.70 212 2.86
7 34.72 38 0.31 32 0.21
8 4.96 11 7.36 8 1.86
p=0.93682 p=0.56032
Number of rngs required: 687801, p-value: 0.244
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_23:31
No. of wins: Observed Expected
99020 98585.9
z-score= 1.942, pvalue=0.97392
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66834 66666.7 0.420 0.420
2 37547 37654.3 0.306 0.726
3 27060 26954.7 0.411 1.137
4 19305 19313.5 0.004 1.141
5 13796 13851.4 0.222 1.362
6 10070 9943.5 1.608 2.971
7 7154 7145.0 0.011 2.982
8 5159 5139.1 0.077 3.059
9 3711 3699.9 0.034 3.093
10 2595 2666.3 1.907 4.999
11 1842 1923.3 3.439 8.438
12 1325 1388.7 2.926 11.364
13 949 1003.7 2.983 14.346
14 726 726.1 0.000 14.347
15 500 525.8 1.269 15.616
16 404 381.2 1.370 16.986
17 280 276.5 0.043 17.029
18 187 200.8 0.952 17.981
19 162 146.0 1.757 19.738
20 111 106.2 0.216 19.954
21 283 287.1 0.059 20.013
Chisq= 20.01 for 20 degrees of freedom, p= 0.54288
SUMMARY of craptest
p-value for no. of wins: 0.973915
p-value for throws/game: 0.542877
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_23:31
No. of wins: Observed Expected
98911 98585.9
z-score= 1.454, pvalue=0.92706
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66896 66666.7 0.789 0.789
2 37491 37654.3 0.708 1.497
3 27059 26954.7 0.403 1.901
4 19225 19313.5 0.405 2.306
5 13852 13851.4 0.000 2.306
6 9879 9943.5 0.419 2.725
7 7146 7145.0 0.000 2.725
8 4985 5139.1 4.619 7.344
9 3739 3699.9 0.414 7.758
10 2748 2666.3 2.504 10.262
11 1962 1923.3 0.778 11.039
12 1338 1388.7 1.854 12.893
13 988 1003.7 0.246 13.139
14 699 726.1 1.014 14.154
15 577 525.8 4.978 19.132
16 372 381.2 0.220 19.352
17 269 276.5 0.206 19.557
18 212 200.8 0.621 20.178
19 143 146.0 0.061 20.239
20 114 106.2 0.571 20.810
21 306 287.1 1.242 22.052
Chisq= 22.05 for 20 degrees of freedom, p= 0.66232
SUMMARY of craptest
p-value for no. of wins: 0.927058
p-value for throws/game: 0.662315
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0009,0.0041,0.0044,0.0044,0.0060,0.0091,0.0116,0.0171,0.0207,0.0211,
0.0224,0.0260,0.0309,0.0451,0.0456,0.0469,0.0520,0.0527,0.0555,0.0595,
0.0597,0.0598,0.0666,0.0707,0.0728,0.0728,0.0791,0.0809,0.0827,0.0828,
0.0896,0.0910,0.0917,0.0940,0.0975,0.0982,0.1038,0.1047,0.1065,0.1077,
0.1099,0.1102,0.1177,0.1216,0.1227,0.1230,0.1242,0.1243,0.1324,0.1366,
0.1393,0.1400,0.1436,0.1442,0.1500,0.1575,0.1609,0.1659,0.1694,0.1701,
0.1723,0.1825,0.1837,0.1904,0.2019,0.2019,0.2188,0.2201,0.2205,0.2207,
0.2240,0.2248,0.2257,0.2287,0.2301,0.2337,0.2338,0.2355,0.2395,0.2425,
0.2435,0.2435,0.2484,0.2547,0.2547,0.2593,0.2636,0.2641,0.2716,0.2722,
0.2729,0.2733,0.2781,0.2794,0.2843,0.2864,0.2922,0.2947,0.2955,0.3017,
0.3077,0.3077,0.3201,0.3341,0.3342,0.3367,0.3391,0.3405,0.3417,0.3420,
0.3477,0.3514,0.3535,0.3558,0.3574,0.3574,0.3611,0.3658,0.3712,0.3784,
0.3795,0.3867,0.3906,0.3929,0.4042,0.4073,0.4127,0.4160,0.4190,0.4203,
0.4223,0.4283,0.4298,0.4325,0.4391,0.4397,0.4549,0.4725,0.4773,0.4818,
0.4848,0.4908,0.5043,0.5074,0.5129,0.5194,0.5220,0.5221,0.5323,0.5367,
0.5414,0.5421,0.5429,0.5441,0.5477,0.5525,0.5587,0.5603,0.5617,0.5628,
0.5802,0.5849,0.5853,0.5867,0.5981,0.6023,0.6048,0.6055,0.6085,0.6106,
0.6107,0.6127,0.6278,0.6363,0.6376,0.6473,0.6519,0.6550,0.6585,0.6587,
0.6611,0.6623,0.6649,0.6688,0.6708,0.6744,0.6780,0.6855,0.6937,0.6995,
0.7009,0.7009,0.7023,0.7069,0.7120,0.7125,0.7146,0.7260,0.7265,0.7302,
0.7387,0.7432,0.7440,0.7440,0.7562,0.7574,0.7589,0.7609,0.7644,0.7648,
0.7706,0.7819,0.7870,0.7919,0.8011,0.8028,0.8147,0.8166,0.8177,0.8184,
0.8260,0.8338,0.8361,0.8374,0.8395,0.8429,0.8492,0.8532,0.8672,0.8728,
0.8732,0.8754,0.8822,0.8865,0.8866,0.8907,0.8956,0.8961,0.8968,0.8972,
0.8984,0.9002,0.9030,0.9038,0.9059,0.9095,0.9104,0.9127,0.9158,0.9191,
0.9193,0.9201,0.9227,0.9271,0.9285,0.9338,0.9368,0.9374,0.9450,0.9455,
0.9593,0.9598,0.9623,0.9737,0.9739,0.9856,0.9858,0.9985,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.083607
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.