RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 15.5692 0.445448
2 to 25 15.56 13.5620 0.302171
3 to 26 15.78 26.1988 0.929086
4 to 27 15.79 31.9246 0.984624
5 to 28 15.88 13.6903 0.311111
6 to 29 15.94 22.9427 0.848873
7 to 30 15.68 15.7975 0.461768
8 to 31 15.49 23.3189 0.860847
9 to 32 15.63 23.5498 0.867809
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.083129
Tough bday spacings test for dh-ranFile-2018-07-05_18:31: 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 7 33 59 111 87 79 53 39 21 7 4
(O-E)^2/E 0.5 0.4 2.8 1.8 1.2 0.0 0.0 2.9 2.5 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 12.051, p= 0.718
RESULTS OF GCD FOR dh-ranFile-2018-07-05_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.113848
p-value, dist. of gcd's: 0.117793
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.673 0.456 0.469 0.464 0.427 0.790 0.144 0.665
Bits 8 to 15---> 0.252 0.515 0.802 0.002 0.081 0.061 0.701 0.470
Bits 16 to 23---> 0.221 0.557 0.578 0.028 0.963 0.155 0.070 0.322
Bits 24 to 31---> 0.519 0.545 0.258 0.268 0.629 0.625 0.720 0.038
KS test for the above 32 p values: 0.867
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_18:31,
p-values for 5 runs: 0.2808, 0.5028, 0.7678, 0.1750, 0.5949
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5191 5134.0 0.633 0.725
r= 30 23087 23103.0 0.011 0.736
r= 31 11515 11551.5 0.115 0.852
chi-square = 0.852 with df = 3; p-value = 0.163
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 195 211.4 1.275 1.275
r= 30 5128 5134.0 0.007 1.282
r= 31 23123 23103.0 0.017 1.299
r= 32 11554 11551.5 0.001 1.300
chi-square = 1.300 with df = 3; p-value = 0.271
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_18:31
b-rank test for bits 1 to 8, p=0.45223
b-rank test for bits 2 to 9, p=0.76585
b-rank test for bits 3 to 10, p=0.59915
b-rank test for bits 4 to 11, p=0.78642
b-rank test for bits 5 to 12, p=0.36416
b-rank test for bits 6 to 13, p=0.33665
b-rank test for bits 7 to 14, p=0.50734
b-rank test for bits 8 to 15, p=0.39579
b-rank test for bits 9 to 16, p=0.61758
b-rank test for bits 10 to 17, p=0.95365
b-rank test for bits 11 to 18, p=0.91172
b-rank test for bits 12 to 19, p=0.77780
b-rank test for bits 13 to 20, p=0.79240
b-rank test for bits 14 to 21, p=0.10955
b-rank test for bits 15 to 22, p=0.32761
b-rank test for bits 16 to 23, p=0.60335
b-rank test for bits 17 to 24, p=0.28061
b-rank test for bits 18 to 25, p=0.75777
b-rank test for bits 19 to 26, p=0.36636
b-rank test for bits 20 to 27, p=0.69385
b-rank test for bits 21 to 28, p=0.81013
b-rank test for bits 22 to 29, p=0.61878
b-rank test for bits 23 to 30, p=0.92151
b-rank test for bits 24 to 31, p=0.54949
b-rank test for bits 25 to 32, p=0.86112
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 = 0.070486
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_18:31
(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 141391 -1.21 0.112938
2 142779 2.03 0.978920
3 141685 -0.52 0.300092
4 142468 1.31 0.904105
5 142121 0.49 0.689543
6 142214 0.71 0.761720
7 141686 -0.52 0.300905
8 141791 -0.28 0.391093
9 142502 1.38 0.916934
10 141679 -0.54 0.295235
11 141636 -0.64 0.261535
12 141594 -0.74 0.230637
13 141835 -0.17 0.431063
14 141909 -0.00 0.499692
15 142399 1.14 0.873707
16 141542 -0.86 0.195378
17 142328 0.98 0.836013
18 141847 -0.15 0.442106
19 141900 -0.02 0.491304
20 141662 -0.58 0.281675
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_18:31
Bits used No. missing words z-score p-value
23 to 32 141774 -0.4667 0.320373
22 to 31 141758 -0.5218 0.300895
21 to 30 142127 0.7506 0.773549
20 to 29 142253 1.1851 0.882005
19 to 28 141420 -1.6873 0.045769
18 to 27 141780 -0.4460 0.327811
17 to 26 141690 -0.7563 0.224732
16 to 25 142274 1.2575 0.895711
15 to 24 141952 0.1471 0.558488
14 to 23 141904 -0.0184 0.492668
13 to 22 141650 -0.8942 0.185596
12 to 21 141672 -0.8184 0.206570
11 to 20 141941 0.1092 0.543481
10 to 19 141869 -0.1391 0.444698
9 to 18 141704 -0.7080 0.239462
8 to 17 141856 -0.1839 0.427047
7 to 16 141943 0.1161 0.546215
6 to 15 142080 0.5885 0.721907
5 to 14 142137 0.7851 0.783793
4 to 13 142211 1.0402 0.850886
3 to 12 141524 -1.3287 0.091970
2 to 11 142373 1.5989 0.945074
1 to 10 141793 -0.4011 0.344159
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_18:31
Bits used No. missing words z-score p-value
28 to 32 142082 0.5853 0.720834
27 to 31 142016 0.3616 0.641172
26 to 30 142138 0.7752 0.780875
25 to 29 141718 -0.6486 0.258306
24 to 28 142195 0.9684 0.833571
23 to 27 141767 -0.4825 0.314734
22 to 26 142207 1.0091 0.843525
21 to 25 141966 0.1921 0.576169
20 to 24 141922 0.0429 0.517129
19 to 23 142050 0.4768 0.683265
18 to 22 142170 0.8836 0.811551
17 to 21 141962 0.1785 0.570852
16 to 20 142032 0.4158 0.661233
15 to 19 141645 -0.8960 0.185117
14 to 18 141791 -0.4011 0.344166
13 to 17 142220 1.0531 0.853857
12 to 16 141887 -0.0757 0.469831
11 to 15 141860 -0.1672 0.433598
10 to 14 142409 1.6938 0.954848
9 to 13 142036 0.4294 0.666180
8 to 12 142556 2.1921 0.985814
7 to 11 141613 -1.0045 0.157567
6 to 10 142318 1.3853 0.917023
5 to 9 141972 0.2124 0.584118
4 to 8 142132 0.7548 0.774820
3 to 7 142042 0.4497 0.673547
2 to 6 141367 -1.8384 0.033001
1 to 5 141688 -0.7503 0.226546
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_18:31
Bits used No. missing words z-score p-value
31 to 32 142026 0.3442 0.634637
30 to 31 141851 -0.1721 0.431693
29 to 30 142288 1.1170 0.868007
28 to 29 141447 -1.3638 0.086314
27 to 28 142186 0.8161 0.792789
26 to 27 141764 -0.4287 0.334070
25 to 26 141686 -0.6588 0.255015
24 to 25 142162 0.7453 0.771967
23 to 24 142486 1.7011 0.955537
22 to 23 141734 -0.5172 0.302509
21 to 22 141615 -0.8682 0.192634
20 to 21 141886 -0.0688 0.472566
19 to 20 142160 0.7394 0.770180
18 to 19 141415 -1.4582 0.072393
17 to 18 141986 0.2262 0.589464
16 to 17 142015 0.3117 0.622370
15 to 16 141621 -0.8505 0.197515
14 to 15 142431 1.5388 0.938080
13 to 14 142185 0.8132 0.791944
12 to 13 142170 0.7689 0.779035
11 to 12 141678 -0.6824 0.247496
10 to 11 142151 0.7129 0.762043
9 to 10 141835 -0.2193 0.413223
8 to 9 141675 -0.6912 0.244708
7 to 8 141563 -1.0216 0.153480
6 to 7 141958 0.1436 0.557080
5 to 6 141579 -0.9744 0.164923
4 to 5 141908 -0.0039 0.498435
3 to 4 142397 1.4386 0.924862
2 to 3 141973 0.1878 0.574490
1 to 2 141317 -1.7473 0.040294
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2514.75 0.209 0.582628
Test results for specific bytes for dh-ranFile-2018-07-05_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2540.16 0.568 0.714965
2 to 9 2363.90 -1.925 0.027128
3 to 10 2440.66 -0.839 0.200685
4 to 11 2363.96 -1.924 0.027182
5 to 12 2379.64 -1.702 0.044365
6 to 13 2436.19 -0.902 0.183420
7 to 14 2407.57 -1.307 0.095575
8 to 15 2519.72 0.279 0.609851
9 to 16 2521.81 0.308 0.621140
10 to 17 2484.46 -0.220 0.413050
11 to 18 2563.40 0.897 0.815019
12 to 19 2475.22 -0.350 0.362995
13 to 20 2589.40 1.264 0.896929
14 to 21 2510.80 0.153 0.560688
15 to 22 2467.69 -0.457 0.323836
16 to 23 2520.91 0.296 0.616291
17 to 24 2470.46 -0.418 0.338072
18 to 25 2383.29 -1.651 0.049417
19 to 26 2496.15 -0.054 0.478297
20 to 27 2600.78 1.425 0.922948
21 to 28 2553.75 0.760 0.776415
22 to 29 2439.45 -0.856 0.195925
23 to 30 2540.43 0.572 0.716259
24 to 31 2445.90 -0.765 0.222113
25 to 32 2461.86 -0.539 0.294811
CDPARK for dh-ranFile-2018-07-05_18:31: 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
3533 0.4566 0.676028
3531 0.3653 0.642555
3510 -0.5936 0.276387
3541 0.8219 0.794438
3539 0.7306 0.767486
3517 -0.2740 0.392053
3529 0.2740 0.607947
3511 -0.5479 0.291865
3514 -0.4110 0.340551
3568 2.0548 0.980051
Square side=100, avg. no. parked=3529.30 sample std.=16.85
p-value of the KSTEST for those 10 p-values: 0.499262
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_18:31
0.4584,0.3412,0.4185,0.6713,0.3847,0.2369,0.4590,0.6420,0.3912,0.0444,
The KS test for those 10 p-values: 0.191811
The 3DSPHERES test for dh-ranFile-2018-07-05_18:31
sample no r^3 equiv. uni.
1 130.760 0.987204
2 33.621 0.673947
3 22.813 0.532543
4 42.346 0.756234
5 30.065 0.632918
6 24.971 0.564978
7 149.552 0.993161
8 88.785 0.948155
9 215.700 0.999246
10 8.044 0.235183
11 62.479 0.875400
12 86.217 0.943522
13 5.379 0.164132
14 13.445 0.361199
15 59.895 0.864191
16 36.575 0.704522
17 0.927 0.030417
18 6.035 0.182214
19 52.213 0.824556
20 5.991 0.181022
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.027876
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -0.6 -0.4 -0.7 -2.3
1.4 -1.6 1.4 1.0 0.6 0.5
-0.9 -0.8 -1.3 -0.8 -1.1 0.5
0.7 0.5 0.2 1.4 -1.4 0.2
0.9 -0.6 0.6 2.4 0.4 -0.4
-0.0 0.1 0.6 -1.0 1.3 -0.5
0.5 -0.4 -1.6 2.6 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:46.477434
z-score=0.488528, p-value=0.706907
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_18:31
Test no p-value
1 0.589991
2 0.324301
3 0.347688
4 0.472205
5 0.259612
6 0.138578
7 0.096052
8 0.000340
9 0.013517
10 0.201555
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004709
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_18:31:
(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 66705 0.02 66580 0.11
3 25000.00 24878 0.60 25096 0.37
4 6666.67 6806 2.91 6687 0.06
5 1388.89 1310 4.48 1372 0.21
6 238.10 261 2.20 235 0.04
7 34.72 32 0.21 25 2.72
8 4.96 7 0.84 4 0.19
p=0.91950 p=0.28225
Number of rngs required: 688480, p-value: 0.535
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_18:31
No. of wins: Observed Expected
98732 98585.9
z-score= 0.654, pvalue=0.74332
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66920 66666.7 0.963 0.963
2 37381 37654.3 1.984 2.947
3 26866 26954.7 0.292 3.239
4 19216 19313.5 0.492 3.731
5 13937 13851.4 0.529 4.259
6 10040 9943.5 0.936 5.195
7 7135 7145.0 0.014 5.209
8 5183 5139.1 0.375 5.585
9 3668 3699.9 0.274 5.859
10 2719 2666.3 1.042 6.901
11 1955 1923.3 0.522 7.422
12 1373 1388.7 0.178 7.601
13 957 1003.7 2.174 9.775
14 746 726.1 0.543 10.318
15 483 525.8 3.490 13.807
16 375 381.2 0.099 13.907
17 302 276.5 2.344 16.251
18 203 200.8 0.023 16.274
19 130 146.0 1.750 18.024
20 99 106.2 0.490 18.515
21 312 287.1 2.157 20.672
Chisq= 20.67 for 20 degrees of freedom, p= 0.58332
SUMMARY of craptest
p-value for no. of wins: 0.743325
p-value for throws/game: 0.583319
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_18:31
No. of wins: Observed Expected
98502 98585.9
z-score=-0.375, pvalue=0.35381
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66859 66666.7 0.555 0.555
2 37492 37654.3 0.700 1.255
3 27065 26954.7 0.451 1.706
4 19275 19313.5 0.077 1.782
5 13999 13851.4 1.572 3.355
6 9876 9943.5 0.459 3.813
7 7021 7145.0 2.153 5.966
8 5209 5139.1 0.952 6.918
9 3632 3699.9 1.245 8.163
10 2693 2666.3 0.267 8.430
11 1914 1923.3 0.045 8.475
12 1399 1388.7 0.076 8.551
13 972 1003.7 1.002 9.553
14 711 726.1 0.316 9.869
15 508 525.8 0.605 10.474
16 386 381.2 0.062 10.536
17 273 276.5 0.045 10.581
18 187 200.8 0.952 11.533
19 130 146.0 1.750 13.284
20 103 106.2 0.097 13.381
21 296 287.1 0.275 13.656
Chisq= 13.66 for 20 degrees of freedom, p= 0.15249
SUMMARY of craptest
p-value for no. of wins: 0.353806
p-value for throws/game: 0.152493
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0017,0.0047,0.0135,0.0271,0.0272,0.0275,0.0279,0.0304,0.0330,
0.0384,0.0403,0.0444,0.0444,0.0458,0.0494,0.0614,0.0697,0.0705,0.0724,
0.0809,0.0831,0.0863,0.0920,0.0956,0.0961,0.1096,0.1129,0.1138,0.1178,
0.1386,0.1444,0.1525,0.1535,0.1546,0.1576,0.1629,0.1641,0.1649,0.1750,
0.1810,0.1822,0.1834,0.1851,0.1856,0.1918,0.1926,0.1954,0.1959,0.1975,
0.2007,0.2016,0.2066,0.2207,0.2221,0.2247,0.2265,0.2306,0.2352,0.2369,
0.2395,0.2447,0.2475,0.2521,0.2550,0.2575,0.2583,0.2596,0.2615,0.2682,
0.2708,0.2764,0.2806,0.2808,0.2817,0.2823,0.2919,0.2948,0.2952,0.3001,
0.3009,0.3009,0.3022,0.3025,0.3111,0.3147,0.3204,0.3217,0.3238,0.3243,
0.3276,0.3278,0.3341,0.3366,0.3381,0.3406,0.3412,0.3442,0.3442,0.3477,
0.3538,0.3612,0.3630,0.3642,0.3664,0.3847,0.3911,0.3912,0.3921,0.3958,
0.4131,0.4132,0.4185,0.4270,0.4273,0.4311,0.4317,0.4336,0.4421,0.4447,
0.4454,0.4522,0.4562,0.4584,0.4590,0.4618,0.4636,0.4691,0.4698,0.4700,
0.4722,0.4726,0.4783,0.4913,0.4927,0.4984,0.4993,0.4997,0.5028,0.5073,
0.5149,0.5171,0.5188,0.5325,0.5353,0.5435,0.5446,0.5462,0.5495,0.5571,
0.5574,0.5585,0.5607,0.5650,0.5709,0.5745,0.5762,0.5777,0.5826,0.5833,
0.5841,0.5895,0.5900,0.5949,0.5991,0.6033,0.6079,0.6099,0.6163,0.6176,
0.6188,0.6211,0.6224,0.6250,0.6292,0.6329,0.6346,0.6412,0.6420,0.6426,
0.6612,0.6653,0.6662,0.6713,0.6732,0.6735,0.6739,0.6760,0.6833,0.6895,
0.6939,0.7007,0.7045,0.7069,0.7150,0.7163,0.7183,0.7195,0.7208,0.7219,
0.7433,0.7562,0.7578,0.7617,0.7620,0.7658,0.7675,0.7678,0.7702,0.7720,
0.7735,0.7748,0.7764,0.7778,0.7790,0.7809,0.7838,0.7864,0.7903,0.7919,
0.7924,0.7928,0.7944,0.8018,0.8101,0.8116,0.8150,0.8246,0.8336,0.8360,
0.8435,0.8489,0.8509,0.8539,0.8608,0.8611,0.8642,0.8671,0.8678,0.8680,
0.8737,0.8754,0.8820,0.8957,0.8969,0.9041,0.9117,0.9169,0.9170,0.9195,
0.9215,0.9229,0.9249,0.9291,0.9381,0.9435,0.9451,0.9482,0.9537,0.9548,
0.9555,0.9630,0.9789,0.9801,0.9846,0.9858,0.9872,0.9932,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.888967
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.