RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_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 15.61 15.9487 0.472525
2 to 25 15.63 19.5247 0.700743
3 to 26 15.55 18.6646 0.651880
4 to 27 15.79 10.2722 0.108189
5 to 28 15.63 26.3590 0.931836
6 to 29 15.67 20.3895 0.745205
7 to 30 15.64 12.9190 0.258411
8 to 31 15.68 17.8428 0.601181
9 to 32 15.43 24.0906 0.883006
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.586679
Tough bday spacings test for dh-ranFile-2018-07-04_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 8 39 81 90 98 80 57 19 13 9 6
(O-E)^2/E 0.1 0.2 0.8 0.6 0.0 0.0 0.5 3.9 0.2 0.9 0.9
Birthday Spacings: Sum(O-E)^2/E= 8.142, p= 0.385
RESULTS OF GCD FOR dh-ranFile-2018-07-04_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.728771
p-value, dist. of gcd's: 0.801706
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.749 0.638 0.780 0.980 0.914 0.452 0.817 0.137
Bits 8 to 15---> 0.741 0.561 0.665 0.140 0.093 0.909 0.152 0.368
Bits 16 to 23---> 0.222 0.389 0.273 0.178 0.710 0.956 0.023 0.032
Bits 24 to 31---> 0.933 0.124 0.381 0.923 0.437 0.676 0.129 0.054
KS test for the above 32 p values: 0.398
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_23:31,
p-values for 5 runs: 0.8286, 0.0676, 0.7976, 0.1307, 0.4043
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5098 5134.0 0.253 0.982
r= 30 23021 23103.0 0.291 1.273
r= 31 11682 11551.5 1.474 2.747
chi-square = 2.747 with df = 3; p-value = 0.568
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 5050 5134.0 1.375 1.570
r= 31 22954 23103.0 0.962 2.531
r= 32 11791 11551.5 4.965 7.496
chi-square = 7.496 with df = 3; p-value = 0.942
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_23:31
b-rank test for bits 1 to 8, p=0.91714
b-rank test for bits 2 to 9, p=0.13796
b-rank test for bits 3 to 10, p=0.33719
b-rank test for bits 4 to 11, p=0.78659
b-rank test for bits 5 to 12, p=0.19618
b-rank test for bits 6 to 13, p=0.60917
b-rank test for bits 7 to 14, p=0.48594
b-rank test for bits 8 to 15, p=0.21535
b-rank test for bits 9 to 16, p=0.26780
b-rank test for bits 10 to 17, p=0.14952
b-rank test for bits 11 to 18, p=0.56203
b-rank test for bits 12 to 19, p=0.56453
b-rank test for bits 13 to 20, p=0.97914
b-rank test for bits 14 to 21, p=0.28094
b-rank test for bits 15 to 22, p=0.55581
b-rank test for bits 16 to 23, p=0.34311
b-rank test for bits 17 to 24, p=0.76758
b-rank test for bits 18 to 25, p=0.91274
b-rank test for bits 19 to 26, p=0.51430
b-rank test for bits 20 to 27, p=0.73721
b-rank test for bits 21 to 28, p=0.80755
b-rank test for bits 22 to 29, p=0.86692
b-rank test for bits 23 to 30, p=0.85048
b-rank test for bits 24 to 31, p=0.57796
b-rank test for bits 25 to 32, p=0.69595
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 = 0.408752
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_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 141795 -0.27 0.394686
2 142731 1.92 0.972558
3 141278 -1.48 0.070097
4 141928 0.04 0.517397
5 142571 1.55 0.938943
6 141843 -0.15 0.438420
7 142056 0.34 0.634083
8 141752 -0.37 0.356588
9 141911 0.00 0.501557
10 142281 0.87 0.807409
11 142365 1.06 0.856483
12 141642 -0.62 0.266116
13 141958 0.11 0.545268
14 141728 -0.42 0.335904
15 142030 0.28 0.611005
16 141824 -0.20 0.420987
17 142044 0.31 0.623486
18 141347 -1.31 0.094447
19 141795 -0.27 0.394686
20 142149 0.56 0.712252
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_23:31
Bits used No. missing words z-score p-value
23 to 32 142118 0.7196 0.764100
22 to 31 142174 0.9127 0.819288
21 to 30 141939 0.1023 0.540745
20 to 29 141884 -0.0873 0.465199
19 to 28 141693 -0.7460 0.227844
18 to 27 141180 -2.5149 0.005953
17 to 26 142050 0.4851 0.686186
16 to 25 142101 0.6609 0.745672
15 to 24 141813 -0.3322 0.369880
14 to 23 141860 -0.1701 0.432464
13 to 22 141720 -0.6529 0.256923
12 to 21 141884 -0.0873 0.465199
11 to 20 142058 0.5127 0.695904
10 to 19 141533 -1.2977 0.097197
9 to 18 141722 -0.6460 0.259151
8 to 17 141917 0.0264 0.510550
7 to 16 142225 1.0885 0.861817
6 to 15 142298 1.3402 0.909917
5 to 14 142060 0.5196 0.698312
4 to 13 142101 0.6609 0.745672
3 to 12 142027 0.4058 0.657540
2 to 11 141563 -1.1942 0.116192
1 to 10 141598 -1.0736 0.141512
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_23:31
Bits used No. missing words z-score p-value
28 to 32 142113 0.6904 0.755031
27 to 31 141621 -0.9774 0.164188
26 to 30 141917 0.0260 0.510371
25 to 29 142291 1.2938 0.902132
24 to 28 141816 -0.3164 0.375860
23 to 27 141874 -0.1198 0.452336
22 to 26 141657 -0.8554 0.196177
21 to 25 142244 1.1345 0.871702
20 to 24 141903 -0.0215 0.491440
19 to 23 142121 0.7175 0.763475
18 to 22 142151 0.8192 0.793670
17 to 21 141888 -0.0723 0.471180
16 to 20 142004 0.3209 0.625863
15 to 19 141809 -0.3401 0.366890
14 to 18 141782 -0.4316 0.333006
13 to 17 142063 0.5209 0.698787
12 to 16 142257 1.1785 0.880710
11 to 15 141645 -0.8960 0.185117
10 to 14 141681 -0.7740 0.219465
9 to 13 142028 0.4023 0.656258
8 to 12 141798 -0.3774 0.352942
7 to 11 141651 -0.8757 0.190598
6 to 10 142038 0.4362 0.668643
5 to 9 142006 0.3277 0.628429
4 to 8 141942 0.1107 0.544091
3 to 7 141968 0.1989 0.578822
2 to 6 141682 -0.7706 0.220469
1 to 5 141915 0.0192 0.507667
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_23:31
Bits used No. missing words z-score p-value
31 to 32 142029 0.3530 0.637959
30 to 31 142125 0.6362 0.737675
29 to 30 142183 0.8073 0.790249
28 to 29 142556 1.9076 0.971777
27 to 28 142381 1.3914 0.917941
26 to 27 142148 0.7040 0.759297
25 to 26 142034 0.3678 0.643473
24 to 25 141644 -0.7827 0.216906
23 to 24 141636 -0.8063 0.210040
22 to 23 141818 -0.2694 0.393807
21 to 22 141886 -0.0688 0.472566
20 to 21 141545 -1.0747 0.141250
19 to 20 142189 0.8250 0.795310
18 to 19 140995 -2.6971 0.003497
17 to 18 141835 -0.2193 0.413223
16 to 17 141694 -0.6352 0.262652
15 to 16 141037 -2.5732 0.005037
14 to 15 142305 1.1672 0.878429
13 to 14 142364 1.3412 0.910074
12 to 13 142014 0.3088 0.621248
11 to 12 141558 -1.0364 0.150014
10 to 11 142310 1.1819 0.881381
9 to 10 141585 -0.9567 0.169353
8 to 9 142104 0.5742 0.717100
7 to 8 142332 1.2468 0.893767
6 to 7 142112 0.5978 0.725029
5 to 6 141605 -0.8977 0.184665
4 to 5 141592 -0.9361 0.174617
3 to 4 142732 2.4268 0.992383
2 to 3 141084 -2.4346 0.007454
1 to 2 142438 1.5595 0.940561
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2472.11 -0.394 0.346611
Test results for specific bytes for dh-ranFile-2018-07-04_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2511.68 0.165 0.565595
2 to 9 2483.43 -0.234 0.407352
3 to 10 2564.72 0.915 0.819981
4 to 11 2497.90 -0.030 0.488135
5 to 12 2461.65 -0.542 0.293796
6 to 13 2457.21 -0.605 0.272537
7 to 14 2516.69 0.236 0.593323
8 to 15 2496.34 -0.052 0.479367
9 to 16 2676.30 2.493 0.993670
10 to 17 2466.55 -0.473 0.318097
11 to 18 2525.65 0.363 0.641602
12 to 19 2607.79 1.524 0.936300
13 to 20 2515.66 0.221 0.587622
14 to 21 2622.08 1.726 0.957866
15 to 22 2504.81 0.068 0.527094
16 to 23 2530.61 0.433 0.667443
17 to 24 2524.74 0.350 0.636809
18 to 25 2498.89 -0.016 0.493760
19 to 26 2615.16 1.629 0.948295
20 to 27 2310.43 -2.681 0.003670
21 to 28 2577.56 1.097 0.863649
22 to 29 2503.99 0.056 0.522507
23 to 30 2513.72 0.194 0.576906
24 to 31 2670.06 2.405 0.991913
25 to 32 2327.65 -2.437 0.007397
CDPARK for dh-ranFile-2018-07-04_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
3537 0.6393 0.738676
3542 0.8676 0.807188
3532 0.4110 0.659449
3552 1.3242 0.907282
3498 -1.1416 0.126820
3544 0.9589 0.831196
3540 0.7763 0.781201
3512 -0.5023 0.307734
3550 1.2329 0.891189
3508 -0.6849 0.246694
Square side=100, avg. no. parked=3531.50 sample std.=17.85
p-value of the KSTEST for those 10 p-values: 0.184215
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_23:31
0.8515,0.3955,0.2573,0.3950,0.2647,0.4361,0.5466,0.6114,0.8044,0.0144,
The KS test for those 10 p-values: 0.730689
The 3DSPHERES test for dh-ranFile-2018-07-04_23:31
sample no r^3 equiv. uni.
1 11.607 0.320835
2 26.843 0.591302
3 35.320 0.691901
4 3.482 0.109599
5 5.330 0.162787
6 5.357 0.163541
7 39.490 0.731881
8 15.882 0.411033
9 11.910 0.327656
10 30.651 0.640020
11 28.009 0.606879
12 5.027 0.154287
13 11.720 0.323384
14 3.595 0.112925
15 174.082 0.996981
16 45.053 0.777265
17 7.154 0.212165
18 22.951 0.534681
19 7.400 0.218611
20 42.060 0.753892
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.389380
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 0.6 0.2 -1.6 0.4
-0.2 -0.9 0.2 -1.7 0.4 -1.1
0.9 0.5 0.8 -0.3 1.7 0.3
-0.5 0.0 0.3 -0.7 0.1 -0.9
-0.3 -0.6 0.5 -0.2 -0.4 0.2
-1.0 1.4 0.5 0.9 -0.6 -0.3
-0.9 -0.7 -0.8 0.4 0.1 -1.0
0.8
Chi-square with 42 degrees of freedom:24.135230
z-score=-1.949206, p-value=0.012267
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_23:31
Test no p-value
1 0.110267
2 0.143322
3 0.941510
4 0.008005
5 0.736275
6 0.971552
7 0.764606
8 0.052245
9 0.035124
10 0.977835
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.039834
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_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 66786 0.21 66684 0.00
3 25000.00 25035 0.05 24868 0.70
4 6666.67 6583 1.05 6763 1.39
5 1388.89 1336 2.01 1414 0.45
6 238.10 214 2.44 236 0.02
7 34.72 38 0.31 31 0.40
8 4.96 7 0.84 3 0.77
p=0.67114 p=0.28804
Number of rngs required: 688850, p-value: 0.697
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_23:31
No. of wins: Observed Expected
98465 98585.9
z-score=-0.541, pvalue=0.29441
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66397 66666.7 1.091 1.091
2 38005 37654.3 3.266 4.357
3 26988 26954.7 0.041 4.398
4 19292 19313.5 0.024 4.422
5 13722 13851.4 1.209 5.631
6 9929 9943.5 0.021 5.652
7 7074 7145.0 0.706 6.358
8 5126 5139.1 0.033 6.391
9 3841 3699.9 5.384 11.775
10 2749 2666.3 2.565 14.340
11 1892 1923.3 0.510 14.851
12 1326 1388.7 2.834 17.685
13 1062 1003.7 3.385 21.070
14 742 726.1 0.346 21.416
15 502 525.8 1.080 22.497
16 375 381.2 0.099 22.596
17 275 276.5 0.009 22.604
18 195 200.8 0.169 22.774
19 127 146.0 2.469 25.242
20 97 106.2 0.800 26.042
21 284 287.1 0.034 26.076
Chisq= 26.08 for 20 degrees of freedom, p= 0.83668
SUMMARY of craptest
p-value for no. of wins: 0.294409
p-value for throws/game: 0.836675
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_23:31
No. of wins: Observed Expected
98333 98585.9
z-score=-1.131, pvalue=0.12904
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66357 66666.7 1.438 1.438
2 37832 37654.3 0.838 2.277
3 26879 26954.7 0.213 2.490
4 19376 19313.5 0.203 2.692
5 13880 13851.4 0.059 2.751
6 9956 9943.5 0.016 2.767
7 7259 7145.0 1.818 4.585
8 5222 5139.1 1.338 5.923
9 3716 3699.9 0.070 5.993
10 2580 2666.3 2.793 8.786
11 1890 1923.3 0.578 9.364
12 1382 1388.7 0.033 9.397
13 997 1003.7 0.045 9.442
14 704 726.1 0.675 10.117
15 531 525.8 0.051 10.167
16 395 381.2 0.503 10.671
17 288 276.5 0.475 11.146
18 222 200.8 2.232 13.377
19 141 146.0 0.170 13.547
20 100 106.2 0.364 13.911
21 293 287.1 0.121 14.032
Chisq= 14.03 for 20 degrees of freedom, p= 0.17112
SUMMARY of craptest
p-value for no. of wins: 0.129042
p-value for throws/game: 0.171115
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0035,0.0037,0.0050,0.0060,0.0074,0.0075,0.0080,0.0123,0.0144,0.0226,
0.0325,0.0351,0.0398,0.0522,0.0537,0.0676,0.0701,0.0925,0.0944,0.0972,
0.1082,0.1096,0.1103,0.1129,0.1162,0.1239,0.1268,0.1289,0.1290,0.1307,
0.1373,0.1380,0.1395,0.1413,0.1415,0.1433,0.1495,0.1500,0.1522,0.1543,
0.1628,0.1635,0.1642,0.1694,0.1711,0.1746,0.1782,0.1842,0.1847,0.1851,
0.1906,0.1962,0.1962,0.2100,0.2122,0.2153,0.2169,0.2186,0.2195,0.2205,
0.2221,0.2278,0.2467,0.2569,0.2573,0.2584,0.2592,0.2627,0.2647,0.2661,
0.2678,0.2725,0.2732,0.2809,0.2880,0.2938,0.2944,0.3077,0.3181,0.3208,
0.3234,0.3277,0.3330,0.3359,0.3372,0.3431,0.3466,0.3529,0.3566,0.3669,
0.3678,0.3699,0.3759,0.3811,0.3850,0.3888,0.3894,0.3938,0.3947,0.3947,
0.3950,0.3955,0.3981,0.4043,0.4074,0.4088,0.4110,0.4132,0.4210,0.4325,
0.4361,0.4369,0.4384,0.4523,0.4525,0.4652,0.4652,0.4712,0.4725,0.4726,
0.4794,0.4859,0.4881,0.4914,0.4938,0.5016,0.5077,0.5104,0.5106,0.5143,
0.5174,0.5225,0.5271,0.5347,0.5407,0.5441,0.5453,0.5466,0.5558,0.5609,
0.5620,0.5645,0.5656,0.5677,0.5769,0.5780,0.5788,0.5867,0.5876,0.5913,
0.5933,0.6012,0.6069,0.6092,0.6110,0.6114,0.6212,0.6235,0.6259,0.6284,
0.6341,0.6368,0.6377,0.6380,0.6400,0.6416,0.6435,0.6519,0.6563,0.6575,
0.6594,0.6648,0.6674,0.6686,0.6711,0.6761,0.6862,0.6919,0.6959,0.6960,
0.6968,0.6983,0.6988,0.7007,0.7095,0.7123,0.7171,0.7250,0.7288,0.7307,
0.7319,0.7363,0.7372,0.7377,0.7387,0.7406,0.7452,0.7457,0.7457,0.7489,
0.7539,0.7550,0.7593,0.7635,0.7641,0.7646,0.7676,0.7773,0.7799,0.7812,
0.7866,0.7902,0.7937,0.7953,0.7976,0.8017,0.8044,0.8072,0.8074,0.8075,
0.8166,0.8193,0.8200,0.8286,0.8312,0.8367,0.8505,0.8515,0.8565,0.8618,
0.8636,0.8669,0.8717,0.8784,0.8807,0.8814,0.8830,0.8912,0.8938,0.9021,
0.9073,0.9092,0.9099,0.9101,0.9127,0.9145,0.9171,0.9179,0.9231,0.9318,
0.9333,0.9363,0.9389,0.9406,0.9415,0.9423,0.9483,0.9565,0.9579,0.9716,
0.9718,0.9726,0.9778,0.9791,0.9802,0.9919,0.9924,0.9937,0.9970,
Overall p-value after applying KStest on 269 p-values = 0.533314
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.