RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.80 32.7186 0.987766
2 to 25 15.60 25.2538 0.910828
3 to 26 15.89 21.4693 0.794002
4 to 27 15.65 21.3269 0.787993
5 to 28 15.88 13.7456 0.314978
6 to 29 15.60 23.3461 0.861681
7 to 30 15.78 25.4440 0.914797
8 to 31 15.38 29.0403 0.965843
9 to 32 15.99 20.5555 0.753194
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000900
Tough bday spacings test for dh-ranFile-2018-07-08_04:31: 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 40 64 104 100 78 62 20 12 11 3
(O-E)^2/E 1.1 0.3 1.2 0.4 0.1 0.0 1.9 3.2 0.6 2.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 11.866, p= 0.706
RESULTS OF GCD FOR dh-ranFile-2018-07-08_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.254934
p-value, dist. of gcd's: 0.715572
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.688 0.817 0.283 0.088 0.843 0.319 0.729 0.897
Bits 8 to 15---> 0.043 0.355 0.197 0.707 0.185 0.875 0.710 0.234
Bits 16 to 23---> 0.219 0.732 0.478 0.219 0.169 0.852 0.824 0.786
Bits 24 to 31---> 0.746 0.499 0.407 0.923 0.050 0.336 0.220 0.229
KS test for the above 32 p values: 0.399
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_04:31,
p-values for 5 runs: 0.0004, 0.3490, 0.7847, 0.6935, 0.6065
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5125 5134.0 0.016 0.047
r= 30 23186 23103.0 0.298 0.345
r= 31 11475 11551.5 0.507 0.852
chi-square = 0.852 with df = 3; p-value = 0.163
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 202 211.4 0.420 0.420
r= 30 5211 5134.0 1.155 1.574
r= 31 23074 23103.0 0.037 1.611
r= 32 11513 11551.5 0.128 1.739
chi-square = 1.739 with df = 3; p-value = 0.372
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_04:31
b-rank test for bits 1 to 8, p=0.79373
b-rank test for bits 2 to 9, p=0.38022
b-rank test for bits 3 to 10, p=0.49709
b-rank test for bits 4 to 11, p=0.75534
b-rank test for bits 5 to 12, p=0.63491
b-rank test for bits 6 to 13, p=0.38070
b-rank test for bits 7 to 14, p=0.32073
b-rank test for bits 8 to 15, p=0.15104
b-rank test for bits 9 to 16, p=0.90439
b-rank test for bits 10 to 17, p=0.79608
b-rank test for bits 11 to 18, p=0.96363
b-rank test for bits 12 to 19, p=0.39917
b-rank test for bits 13 to 20, p=0.53933
b-rank test for bits 14 to 21, p=0.93404
b-rank test for bits 15 to 22, p=0.40637
b-rank test for bits 16 to 23, p=0.34086
b-rank test for bits 17 to 24, p=0.33669
b-rank test for bits 18 to 25, p=0.10448
b-rank test for bits 19 to 26, p=0.28757
b-rank test for bits 20 to 27, p=0.63199
b-rank test for bits 21 to 28, p=0.72066
b-rank test for bits 22 to 29, p=0.41811
b-rank test for bits 23 to 30, p=0.39227
b-rank test for bits 24 to 31, p=0.55588
b-rank test for bits 25 to 32, p=0.67550
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 = 0.371415
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_04:31
(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 141907 -0.01 0.497828
2 141361 -1.28 0.100071
3 142051 0.33 0.629680
4 141443 -1.09 0.137954
5 141277 -1.48 0.069783
6 141777 -0.31 0.378591
7 141893 -0.04 0.484782
8 140990 -2.15 0.015858
9 142539 1.47 0.929380
10 141601 -0.72 0.235640
11 141628 -0.66 0.255490
12 141606 -0.71 0.239251
13 142251 0.80 0.787650
14 142117 0.49 0.686236
15 142429 1.21 0.887661
16 142281 0.87 0.807409
17 141375 -1.25 0.105936
18 141874 -0.08 0.467106
19 141624 -0.67 0.252495
20 141975 0.15 0.560972
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_04:31
Bits used No. missing words z-score p-value
23 to 32 141780 -0.4460 0.327811
22 to 31 142169 0.8954 0.814717
21 to 30 141579 -1.1391 0.127337
20 to 29 141532 -1.3011 0.096606
19 to 28 142220 1.0713 0.857977
18 to 27 141685 -0.7736 0.219598
17 to 26 142457 1.8885 0.970522
16 to 25 141997 0.3023 0.618792
15 to 24 142555 2.2264 0.987008
14 to 23 141908 -0.0046 0.498170
13 to 22 142327 1.4402 0.925100
12 to 21 142236 1.1264 0.870012
11 to 20 141830 -0.2736 0.392215
10 to 19 142165 0.8816 0.811009
9 to 18 141497 -1.4218 0.077538
8 to 17 142103 0.6678 0.747878
7 to 16 141151 -2.6149 0.004462
6 to 15 141762 -0.5080 0.305715
5 to 14 141623 -0.9873 0.161737
4 to 13 142139 0.7920 0.785810
3 to 12 141335 -1.9804 0.023827
2 to 11 141997 0.3023 0.618792
1 to 10 142129 0.7575 0.775620
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_04:31
Bits used No. missing words z-score p-value
28 to 32 141703 -0.6994 0.242144
27 to 31 142145 0.7989 0.787820
26 to 30 141926 0.0565 0.522532
25 to 29 141912 0.0091 0.503611
24 to 28 142160 0.8497 0.802262
23 to 27 142059 0.5074 0.694048
22 to 26 141568 -1.1571 0.123626
21 to 25 141460 -1.5232 0.063860
20 to 24 141994 0.2870 0.612950
19 to 23 142066 0.5311 0.702320
18 to 22 142048 0.4701 0.680847
17 to 21 141998 0.3006 0.618131
16 to 20 142134 0.7616 0.776849
15 to 19 142197 0.9752 0.835258
14 to 18 141627 -0.9571 0.169271
13 to 17 141919 0.0328 0.513075
12 to 16 141629 -0.9503 0.170987
11 to 15 142029 0.4057 0.657504
10 to 14 141573 -1.1401 0.127122
9 to 13 141611 -1.0113 0.155939
8 to 12 142210 1.0192 0.845951
7 to 11 142352 1.5006 0.933267
6 to 10 141435 -1.6079 0.053929
5 to 9 141863 -0.1571 0.437602
4 to 8 141862 -0.1604 0.436267
3 to 7 141684 -0.7638 0.222484
2 to 6 141493 -1.4113 0.079080
1 to 5 141776 -0.4520 0.325647
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_04:31
Bits used No. missing words z-score p-value
31 to 32 141854 -0.1632 0.435174
30 to 31 142360 1.3294 0.908144
29 to 30 142386 1.4061 0.920154
28 to 29 142409 1.4740 0.929753
27 to 28 142149 0.7070 0.760214
26 to 27 142141 0.6834 0.752821
25 to 26 142497 1.7335 0.958500
24 to 25 141962 0.1554 0.561735
23 to 24 142107 0.5831 0.720086
22 to 23 141797 -0.3314 0.370187
21 to 22 141494 -1.2252 0.110257
20 to 21 142077 0.4946 0.689559
19 to 20 141984 0.2203 0.587168
18 to 19 141352 -1.6440 0.050084
17 to 18 141441 -1.3815 0.083562
16 to 17 141940 0.0905 0.536044
15 to 16 142099 0.5595 0.712089
14 to 15 142308 1.1760 0.880206
13 to 14 142035 0.3707 0.644573
12 to 13 142169 0.7660 0.778158
11 to 12 141889 -0.0600 0.476090
10 to 11 141238 -1.9803 0.023834
9 to 10 141517 -1.1573 0.123572
8 to 9 141657 -0.7443 0.228337
7 to 8 141562 -1.0246 0.152783
6 to 7 141709 -0.5909 0.277279
5 to 6 141483 -1.2576 0.104266
4 to 5 141509 -1.1809 0.118818
3 to 4 142045 0.4002 0.655498
2 to 3 142077 0.4946 0.689559
1 to 2 142222 0.9223 0.821822
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2614.04 1.613 0.946603
Test results for specific bytes for dh-ranFile-2018-07-08_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2521.29 0.301 0.618347
2 to 9 2513.25 0.187 0.574327
3 to 10 2499.26 -0.010 0.495847
4 to 11 2523.87 0.338 0.632153
5 to 12 2431.14 -0.974 0.165065
6 to 13 2617.31 1.659 0.951443
7 to 14 2500.88 0.012 0.504983
8 to 15 2525.34 0.358 0.639953
9 to 16 2390.53 -1.548 0.060794
10 to 17 2532.48 0.459 0.676991
11 to 18 2509.33 0.132 0.552463
12 to 19 2523.92 0.338 0.632417
13 to 20 2472.31 -0.392 0.347673
14 to 21 2573.80 1.044 0.851676
15 to 22 2440.54 -0.841 0.200186
16 to 23 2556.82 0.804 0.789162
17 to 24 2582.02 1.160 0.876953
18 to 25 2420.36 -1.126 0.130032
19 to 26 2492.32 -0.109 0.456776
20 to 27 2466.42 -0.475 0.317415
21 to 28 2425.87 -1.048 0.147247
22 to 29 2506.32 0.089 0.535617
23 to 30 2487.85 -0.172 0.431778
24 to 31 2455.25 -0.633 0.263417
25 to 32 2550.40 0.713 0.761995
CDPARK for dh-ranFile-2018-07-08_04:31: 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
3512 -0.5023 0.307734
3540 0.7763 0.781201
3523 0.0000 0.500000
3505 -0.8219 0.205562
3526 0.1370 0.554479
3540 0.7763 0.781201
3506 -0.7763 0.218799
3497 -1.1872 0.117571
3513 -0.4566 0.323972
3505 -0.8219 0.205562
Square side=100, avg. no. parked=3516.70 sample std.=14.23
p-value of the KSTEST for those 10 p-values: 0.323509
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_04:31
0.2047,0.7472,0.5229,0.8972,0.3069,0.3288,0.1225,0.4309,0.4295,0.1175,
The KS test for those 10 p-values: 0.487141
The 3DSPHERES test for dh-ranFile-2018-07-08_04:31
sample no r^3 equiv. uni.
1 13.437 0.361041
2 3.279 0.103525
3 20.795 0.500005
4 22.758 0.531679
5 150.016 0.993266
6 0.020 0.000650
7 4.280 0.132959
8 7.330 0.216780
9 8.834 0.255071
10 0.119 0.003964
11 16.066 0.414643
12 64.328 0.882846
13 12.712 0.345402
14 15.745 0.408353
15 14.378 0.380760
16 16.199 0.417234
17 31.943 0.655196
18 99.241 0.963412
19 28.999 0.619643
20 36.252 0.701322
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.312585
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.8 0.0 0.0 0.8
-0.3 -0.0 -1.5 0.8 -0.9 1.7
-0.6 -1.2 -0.2 -0.1 0.4 0.0
1.0 -0.9 1.4 -0.4 1.3 -1.5
-0.8 0.3 0.1 0.2 0.3 0.4
-1.6 -0.6 0.4 -0.9 1.6 0.6
2.1 0.8 2.5 0.4 1.6 1.0
0.8
Chi-square with 42 degrees of freedom:41.998419
z-score=-0.000173, p-value=0.528957
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_04:31
Test no p-value
1 0.542754
2 0.334413
3 0.532920
4 0.763292
5 0.494885
6 0.866399
7 0.087811
8 0.116709
9 0.002184
10 0.643174
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.554159
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_04:31:
(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 66619 0.03 66867 0.60
3 25000.00 25049 0.10 24837 1.06
4 6666.67 6715 0.35 6650 0.04
5 1388.89 1344 1.45 1368 0.31
6 238.10 240 0.02 239 0.00
7 34.72 29 0.94 32 0.21
8 4.96 3 0.77 6 0.22
p=0.27789 p=0.12655
Number of rngs required: 688848, p-value: 0.696
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_04:31
No. of wins: Observed Expected
98894 98585.9
z-score= 1.378, pvalue=0.91593
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66767 66666.7 0.151 0.151
2 37678 37654.3 0.015 0.166
3 26871 26954.7 0.260 0.426
4 19253 19313.5 0.189 0.615
5 14005 13851.4 1.703 2.318
6 9909 9943.5 0.120 2.438
7 7057 7145.0 1.084 3.523
8 5110 5139.1 0.164 3.687
9 3672 3699.9 0.210 3.897
10 2647 2666.3 0.140 4.037
11 1922 1923.3 0.001 4.037
12 1413 1388.7 0.424 4.461
13 979 1003.7 0.609 5.070
14 753 726.1 0.994 6.063
15 529 525.8 0.019 6.082
16 410 381.2 2.184 8.266
17 284 276.5 0.201 8.467
18 190 200.8 0.584 9.051
19 151 146.0 0.172 9.224
20 116 106.2 0.901 10.125
21 284 287.1 0.034 10.159
Chisq= 10.16 for 20 degrees of freedom, p= 0.03480
SUMMARY of craptest
p-value for no. of wins: 0.915927
p-value for throws/game: 0.034800
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_04:31
No. of wins: Observed Expected
98612 98585.9
z-score= 0.117, pvalue=0.54654
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66556 66666.7 0.184 0.184
2 37596 37654.3 0.090 0.274
3 26906 26954.7 0.088 0.362
4 19405 19313.5 0.434 0.796
5 13708 13851.4 1.485 2.281
6 10015 9943.5 0.514 2.794
7 7228 7145.0 0.964 3.758
8 5141 5139.1 0.001 3.759
9 3757 3699.9 0.882 4.641
10 2711 2666.3 0.749 5.391
11 1953 1923.3 0.458 5.848
12 1389 1388.7 0.000 5.848
13 953 1003.7 2.562 8.411
14 716 726.1 0.142 8.552
15 497 525.8 1.581 10.134
16 375 381.2 0.099 10.233
17 280 276.5 0.043 10.276
18 222 200.8 2.232 12.508
19 148 146.0 0.028 12.536
20 112 106.2 0.315 12.851
21 332 287.1 7.017 19.868
Chisq= 19.87 for 20 degrees of freedom, p= 0.53379
SUMMARY of craptest
p-value for no. of wins: 0.546538
p-value for throws/game: 0.533791
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0006,0.0009,0.0022,0.0040,0.0045,0.0159,0.0238,0.0238,0.0348,
0.0431,0.0501,0.0501,0.0539,0.0608,0.0639,0.0698,0.0775,0.0791,0.0836,
0.0878,0.0883,0.0966,0.1001,0.1035,0.1043,0.1045,0.1059,0.1103,0.1167,
0.1175,0.1176,0.1188,0.1225,0.1236,0.1236,0.1266,0.1271,0.1273,0.1300,
0.1330,0.1380,0.1472,0.1510,0.1528,0.1559,0.1617,0.1630,0.1651,0.1686,
0.1693,0.1710,0.1852,0.1968,0.2002,0.2047,0.2056,0.2056,0.2168,0.2186,
0.2188,0.2189,0.2196,0.2199,0.2225,0.2283,0.2291,0.2338,0.2356,0.2393,
0.2421,0.2525,0.2549,0.2551,0.2555,0.2634,0.2773,0.2779,0.2830,0.2876,
0.3057,0.3069,0.3077,0.3126,0.3150,0.3174,0.3188,0.3207,0.3235,0.3240,
0.3256,0.3278,0.3288,0.3344,0.3357,0.3367,0.3409,0.3454,0.3477,0.3490,
0.3547,0.3610,0.3702,0.3714,0.3717,0.3786,0.3802,0.3807,0.3808,0.3922,
0.3923,0.3992,0.3993,0.4064,0.4071,0.4084,0.4146,0.4172,0.4181,0.4295,
0.4309,0.4318,0.4352,0.4363,0.4376,0.4568,0.4671,0.4761,0.4785,0.4848,
0.4871,0.4949,0.4958,0.4971,0.4978,0.4982,0.4993,0.5000,0.5000,0.5036,
0.5050,0.5131,0.5225,0.5229,0.5290,0.5317,0.5329,0.5338,0.5356,0.5360,
0.5393,0.5428,0.5465,0.5525,0.5542,0.5545,0.5559,0.5610,0.5617,0.5743,
0.5872,0.6065,0.6130,0.6181,0.6183,0.6188,0.6188,0.6196,0.6297,0.6320,
0.6322,0.6324,0.6349,0.6400,0.6432,0.6446,0.6552,0.6555,0.6575,0.6755,
0.6770,0.6808,0.6862,0.6877,0.6896,0.6896,0.6935,0.6940,0.6960,0.7013,
0.7023,0.7059,0.7075,0.7096,0.7121,0.7156,0.7201,0.7207,0.7288,0.7321,
0.7456,0.7472,0.7479,0.7528,0.7532,0.7553,0.7602,0.7620,0.7633,0.7756,
0.7768,0.7782,0.7812,0.7812,0.7847,0.7858,0.7859,0.7877,0.7878,0.7880,
0.7892,0.7937,0.7940,0.7961,0.8023,0.8074,0.8110,0.8147,0.8173,0.8218,
0.8239,0.8353,0.8435,0.8460,0.8517,0.8517,0.8580,0.8617,0.8664,0.8700,
0.8746,0.8770,0.8802,0.8828,0.8877,0.8970,0.8972,0.9044,0.9081,0.9108,
0.9148,0.9159,0.9202,0.9233,0.9251,0.9294,0.9298,0.9333,0.9340,0.9466,
0.9514,0.9585,0.9634,0.9636,0.9658,0.9705,0.9870,0.9878,0.9933,
Overall p-value after applying KStest on 269 p-values = 0.649345
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.