RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-09-20_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.76 30.6596 0.978038
2 to 25 15.70 26.5468 0.934942
3 to 26 15.78 18.9049 0.665979
4 to 27 15.95 22.6913 0.840428
5 to 28 15.68 22.1684 0.821671
6 to 29 15.91 16.1611 0.487553
7 to 30 15.86 15.1922 0.418363
8 to 31 15.66 20.4851 0.749831
9 to 32 15.55 18.4114 0.636657
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.032320
Tough bday spacings test for dh-ranFile-2018-09-20_12:31: 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 13 37 74 115 78 74 58 28 9 6 8
(O-E)^2/E 1.6 0.0 0.0 3.1 4.0 0.2 0.7 0.1 2.3 0.1 3.8
Birthday Spacings: Sum(O-E)^2/E= 15.843, p= 0.896
RESULTS OF GCD FOR dh-ranFile-2018-09-20_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.249353
p-value, dist. of gcd's: 0.721625
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-09-20_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.050 0.429 0.144 0.425 0.767 0.250 0.764 0.630
Bits 8 to 15---> 0.618 0.300 0.363 0.130 0.600 0.255 0.954 0.329
Bits 16 to 23---> 0.279 0.743 0.598 0.465 0.930 0.910 0.341 0.255
Bits 24 to 31---> 0.642 0.382 0.716 0.862 0.184 0.107 0.809 0.238
KS test for the above 32 p values: 0.210
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-09-20_12:31,
p-values for 5 runs: 0.1582, 0.0189, 0.5267, 0.3688, 0.7086
Rank test for binary matrices (31x31) for dh-ranFile-2018-09-20_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5189 5134.0 0.589 1.206
r= 30 22982 23103.0 0.634 1.840
r= 31 11629 11551.5 0.520 2.359
chi-square = 2.359 with df = 3; p-value = 0.499
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-09-20_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5204 5134.0 0.954 1.093
r= 31 23115 23103.0 0.006 1.099
r= 32 11475 11551.5 0.507 1.606
chi-square = 1.606 with df = 3; p-value = 0.342
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-09-20_12:31
b-rank test for bits 1 to 8, p=0.62422
b-rank test for bits 2 to 9, p=0.88230
b-rank test for bits 3 to 10, p=0.71209
b-rank test for bits 4 to 11, p=0.86463
b-rank test for bits 5 to 12, p=0.24480
b-rank test for bits 6 to 13, p=0.57257
b-rank test for bits 7 to 14, p=0.72671
b-rank test for bits 8 to 15, p=0.31277
b-rank test for bits 9 to 16, p=0.53306
b-rank test for bits 10 to 17, p=0.33236
b-rank test for bits 11 to 18, p=0.91595
b-rank test for bits 12 to 19, p=0.99442
b-rank test for bits 13 to 20, p=0.06451
b-rank test for bits 14 to 21, p=0.70144
b-rank test for bits 15 to 22, p=0.59793
b-rank test for bits 16 to 23, p=0.67766
b-rank test for bits 17 to 24, p=0.82267
b-rank test for bits 18 to 25, p=0.01561
b-rank test for bits 19 to 26, p=0.48426
b-rank test for bits 20 to 27, p=0.67450
b-rank test for bits 21 to 28, p=0.21919
b-rank test for bits 22 to 29, p=0.32941
b-rank test for bits 23 to 30, p=0.07196
b-rank test for bits 24 to 31, p=0.55288
b-rank test for bits 25 to 32, p=0.30058
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 = 0.843719
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-09-20_12:31
(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 142080 0.40 0.654966
2 141015 -2.09 0.018329
3 142039 0.30 0.619043
4 141888 -0.05 0.480126
5 142030 0.28 0.611005
6 141871 -0.09 0.464320
7 142037 0.30 0.617261
8 141640 -0.63 0.264584
9 141619 -0.68 0.248778
10 142906 2.33 0.990062
11 141495 -0.97 0.166507
12 141979 0.16 0.564654
13 141127 -1.83 0.033784
14 141598 -0.73 0.233489
15 142317 0.95 0.829578
16 142117 0.49 0.686236
17 142321 0.96 0.831936
18 141631 -0.65 0.257748
19 142023 0.27 0.604720
20 142393 1.13 0.870777
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-09-20_12:31
Bits used No. missing words z-score p-value
23 to 32 141599 -1.0701 0.142286
22 to 31 141646 -0.9080 0.181930
21 to 30 141830 -0.2736 0.392215
20 to 29 141793 -0.4011 0.344159
19 to 28 141937 0.0954 0.538007
18 to 27 141887 -0.0770 0.469312
17 to 26 141846 -0.2184 0.413567
16 to 25 141496 -1.4253 0.077039
15 to 24 142099 0.6540 0.743455
14 to 23 141922 0.0437 0.517424
13 to 22 141715 -0.6701 0.251396
12 to 21 141484 -1.4667 0.071235
11 to 20 142413 1.7368 0.958788
10 to 19 141785 -0.4287 0.334062
9 to 18 141888 -0.0736 0.470684
8 to 17 141912 0.0092 0.503673
7 to 16 141859 -0.1736 0.431109
6 to 15 142345 1.5023 0.933492
5 to 14 142065 0.5368 0.704295
4 to 13 142248 1.1678 0.878562
3 to 12 142255 1.1920 0.883363
2 to 11 141737 -0.5942 0.276175
1 to 10 142678 2.6506 0.995982
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-09-20_12:31
Bits used No. missing words z-score p-value
28 to 32 142138 0.7752 0.780875
27 to 31 141277 -2.1435 0.016037
26 to 30 140856 -3.5706 0.000178
25 to 29 141595 -1.0655 0.143319
24 to 28 141671 -0.8079 0.209575
23 to 27 141866 -0.1469 0.441613
22 to 26 142047 0.4667 0.679635
21 to 25 142179 0.9141 0.819677
20 to 24 141043 -2.9367 0.001659
19 to 23 142135 0.7650 0.777859
18 to 22 141886 -0.0791 0.468483
17 to 21 141910 0.0023 0.500906
16 to 20 141946 0.1243 0.549463
15 to 19 141216 -2.3503 0.009380
14 to 18 142461 1.8701 0.969263
13 to 17 142050 0.4768 0.683265
12 to 16 141829 -0.2723 0.392694
11 to 15 141712 -0.6689 0.251775
10 to 14 141727 -0.6181 0.268265
9 to 13 141489 -1.4248 0.077101
8 to 12 142076 0.5650 0.713957
7 to 11 141834 -0.2554 0.399224
6 to 10 140856 -3.5706 0.000178
5 to 9 141623 -0.9706 0.165871
4 to 8 141881 -0.0960 0.461747
3 to 7 141793 -0.3943 0.346665
2 to 6 142201 0.9887 0.838598
1 to 5 141917 0.0260 0.510371
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-09-20_12:31
Bits used No. missing words z-score p-value
31 to 32 142080 0.5035 0.692677
30 to 31 142151 0.7129 0.762043
29 to 30 141757 -0.4494 0.326589
28 to 29 141473 -1.2871 0.099028
27 to 28 141660 -0.7355 0.231022
26 to 27 142300 1.1524 0.875426
25 to 26 141666 -0.7178 0.236444
24 to 25 142174 0.7807 0.782522
23 to 24 142347 1.2911 0.901659
22 to 23 141108 -2.3638 0.009044
21 to 22 141362 -1.6145 0.053205
20 to 21 141944 0.1023 0.540729
19 to 20 141960 0.1495 0.559408
18 to 19 141763 -0.4317 0.332997
17 to 18 142032 0.3619 0.641271
16 to 17 141343 -1.6706 0.047401
15 to 16 142132 0.6568 0.744359
14 to 15 141523 -1.1396 0.127223
13 to 14 141585 -0.9567 0.169353
12 to 13 141218 -2.0393 0.020709
11 to 12 141736 -0.5113 0.304571
10 to 11 142335 1.2557 0.895381
9 to 10 141708 -0.5939 0.276292
8 to 9 141972 0.1849 0.573333
7 to 8 141721 -0.5555 0.289261
6 to 7 141589 -0.9449 0.172348
5 to 6 140808 -3.2488 0.000580
4 to 5 141591 -0.9390 0.173859
3 to 4 141936 0.0787 0.531354
2 to 3 141598 -0.9184 0.179211
1 to 2 142297 1.1436 0.873599
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-09-20_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2418.76 -1.149 0.125292
Test results for specific bytes for dh-ranFile-2018-09-20_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2483.94 -0.227 0.410176
2 to 9 2472.48 -0.389 0.348565
3 to 10 2552.54 0.743 0.771286
4 to 11 2525.38 0.359 0.640166
5 to 12 2413.62 -1.222 0.110921
6 to 13 2408.89 -1.288 0.098799
7 to 14 2557.72 0.816 0.792823
8 to 15 2415.29 -1.198 0.115470
9 to 16 2498.59 -0.020 0.492063
10 to 17 2621.58 1.719 0.957228
11 to 18 2506.62 0.094 0.537292
12 to 19 2636.76 1.934 0.973445
13 to 20 2494.83 -0.073 0.470858
14 to 21 2516.19 0.229 0.590568
15 to 22 2579.88 1.130 0.870706
16 to 23 2580.19 1.134 0.871619
17 to 24 2491.55 -0.120 0.452423
18 to 25 2465.36 -0.490 0.312097
19 to 26 2457.62 -0.599 0.274494
20 to 27 2597.18 1.374 0.915328
21 to 28 2486.11 -0.196 0.422124
22 to 29 2532.94 0.466 0.679346
23 to 30 2529.59 0.418 0.662194
24 to 31 2406.09 -1.328 0.092069
25 to 32 2559.06 0.835 0.798199
CDPARK for dh-ranFile-2018-09-20_12:31: 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
3510 -0.5936 0.276387
3554 1.4155 0.921543
3513 -0.4566 0.323972
3531 0.3653 0.642555
3475 -2.1918 0.014198
3572 2.2374 0.987371
3536 0.5936 0.723613
3510 -0.5936 0.276387
3518 -0.2283 0.409702
3553 1.3699 0.914635
Square side=100, avg. no. parked=3527.20 sample std.=26.62
p-value of the KSTEST for those 10 p-values: 0.594272
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-09-20_12:31
0.0188,0.0311,0.7195,0.7001,0.4686,0.6663,0.6846,0.4722,0.0612,0.8381,
The KS test for those 10 p-values: 0.317575
The 3DSPHERES test for dh-ranFile-2018-09-20_12:31
sample no r^3 equiv. uni.
1 29.175 0.621859
2 20.290 0.491530
3 35.342 0.692123
4 61.163 0.869810
5 8.269 0.240913
6 19.503 0.478006
7 2.102 0.067683
8 34.439 0.682724
9 12.299 0.336338
10 21.214 0.506948
11 7.604 0.223882
12 21.588 0.513051
13 5.330 0.162770
14 7.677 0.225781
15 61.452 0.871058
16 26.542 0.587169
17 24.097 0.552123
18 6.376 0.191463
19 26.821 0.590999
20 50.461 0.814002
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.572645
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-09-20_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.9 0.3 -1.0 1.0 -1.4
0.9 -1.5 0.7 0.1 0.3 -0.9
-1.0 1.9 1.1 -0.5 0.3 -0.5
1.0 -0.4 -0.7 -0.0 -0.7 -0.9
-0.5 1.9 0.0 -0.5 -0.5 0.0
0.1 0.3 -0.9 0.8 2.0 1.0
-1.2 -1.3 0.5 1.0 -1.3 2.0
-0.1
Chi-square with 42 degrees of freedom:40.761161
z-score=-0.135168, p-value=0.474676
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-09-20_12:31
Test no p-value
1 0.560929
2 0.048678
3 0.450321
4 0.052455
5 0.151759
6 0.219441
7 0.111273
8 0.118030
9 0.087307
10 0.243037
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001168
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-09-20_12:31:
(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 66455 0.67 66600 0.07
3 25000.00 25104 0.43 25043 0.07
4 6666.67 6717 0.38 6672 0.00
5 1388.89 1412 0.38 1410 0.32
6 238.10 273 5.12 237 0.01
7 34.72 31 0.40 32 0.21
8 4.96 7 0.84 5 0.00
p=0.77784 p=0.00517
Number of rngs required: 689653, p-value: 0.928
RESULTS OF CRAPS TEST for dh-ranFile-2018-09-20_12:31
No. of wins: Observed Expected
98411 98585.9
z-score=-0.782, pvalue=0.21709
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66722 66666.7 0.046 0.046
2 37536 37654.3 0.372 0.418
3 26770 26954.7 1.266 1.684
4 19339 19313.5 0.034 1.718
5 13866 13851.4 0.015 1.733
6 9981 9943.5 0.141 1.874
7 7105 7145.0 0.224 2.098
8 5101 5139.1 0.282 2.380
9 3691 3699.9 0.021 2.402
10 2667 2666.3 0.000 2.402
11 2032 1923.3 6.140 8.542
12 1422 1388.7 0.797 9.338
13 993 1003.7 0.114 9.453
14 802 726.1 7.925 17.378
15 563 525.8 2.627 20.004
16 367 381.2 0.525 20.530
17 282 276.5 0.108 20.637
18 205 200.8 0.087 20.724
19 142 146.0 0.109 20.833
20 115 106.2 0.727 21.559
21 299 287.1 0.492 22.051
Chisq= 22.05 for 20 degrees of freedom, p= 0.66227
SUMMARY of craptest
p-value for no. of wins: 0.217087
p-value for throws/game: 0.662274
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-09-20_12:31
No. of wins: Observed Expected
98639 98585.9
z-score= 0.238, pvalue=0.59394
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66672 66666.7 0.000 0.000
2 37563 37654.3 0.221 0.222
3 27078 26954.7 0.564 0.786
4 19386 19313.5 0.272 1.058
5 13712 13851.4 1.403 2.461
6 9917 9943.5 0.071 2.532
7 7066 7145.0 0.874 3.406
8 5175 5139.1 0.251 3.657
9 3748 3699.9 0.626 4.284
10 2691 2666.3 0.229 4.513
11 1839 1923.3 3.697 8.210
12 1424 1388.7 0.895 9.105
13 957 1003.7 2.174 11.279
14 765 726.1 2.080 13.359
15 609 525.8 13.153 26.512
16 403 381.2 1.253 27.764
17 284 276.5 0.201 27.966
18 172 200.8 4.139 32.104
19 140 146.0 0.245 32.350
20 105 106.2 0.014 32.364
21 294 287.1 0.165 32.529
Chisq= 32.53 for 20 degrees of freedom, p= 0.96202
SUMMARY of craptest
p-value for no. of wins: 0.593935
p-value for throws/game: 0.962020
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0002,0.0006,0.0012,0.0017,0.0052,0.0090,0.0094,0.0142,0.0156,
0.0160,0.0183,0.0188,0.0189,0.0207,0.0311,0.0323,0.0338,0.0474,0.0487,
0.0503,0.0525,0.0532,0.0612,0.0645,0.0677,0.0712,0.0720,0.0770,0.0771,
0.0873,0.0921,0.0988,0.0990,0.1070,0.1109,0.1113,0.1155,0.1180,0.1253,
0.1272,0.1302,0.1423,0.1433,0.1444,0.1518,0.1582,0.1628,0.1659,0.1665,
0.1694,0.1723,0.1739,0.1792,0.1819,0.1840,0.1915,0.2096,0.2104,0.2171,
0.2192,0.2194,0.2239,0.2258,0.2310,0.2335,0.2364,0.2382,0.2409,0.2430,
0.2448,0.2488,0.2494,0.2504,0.2514,0.2518,0.2553,0.2554,0.2577,0.2646,
0.2683,0.2745,0.2762,0.2763,0.2764,0.2764,0.2792,0.2893,0.3001,0.3006,
0.3046,0.3121,0.3128,0.3176,0.3240,0.3266,0.3293,0.3294,0.3324,0.3330,
0.3341,0.3363,0.3413,0.3420,0.3442,0.3467,0.3486,0.3631,0.3688,0.3816,
0.3922,0.3927,0.3992,0.4097,0.4102,0.4136,0.4184,0.4221,0.4253,0.4285,
0.4311,0.4416,0.4503,0.4524,0.4617,0.4643,0.4648,0.4685,0.4686,0.4693,
0.4707,0.4709,0.4722,0.4747,0.4780,0.4801,0.4843,0.4876,0.4915,0.4921,
0.4988,0.5009,0.5037,0.5069,0.5104,0.5131,0.5174,0.5267,0.5314,0.5331,
0.5373,0.5380,0.5407,0.5495,0.5521,0.5529,0.5594,0.5609,0.5647,0.5726,
0.5726,0.5733,0.5872,0.5906,0.5910,0.5939,0.5943,0.5978,0.5979,0.6001,
0.6047,0.6110,0.6173,0.6176,0.6190,0.6219,0.6242,0.6302,0.6367,0.6402,
0.6413,0.6415,0.6426,0.6550,0.6622,0.6623,0.6660,0.6663,0.6745,0.6777,
0.6793,0.6796,0.6827,0.6833,0.6846,0.6862,0.6921,0.6927,0.7001,0.7014,
0.7043,0.7086,0.7121,0.7140,0.7157,0.7195,0.7216,0.7236,0.7267,0.7434,
0.7435,0.7444,0.7498,0.7620,0.7635,0.7673,0.7713,0.7778,0.7779,0.7809,
0.7825,0.7928,0.7982,0.8089,0.8140,0.8197,0.8217,0.8227,0.8296,0.8319,
0.8381,0.8386,0.8404,0.8437,0.8616,0.8646,0.8698,0.8707,0.8708,0.8711,
0.8716,0.8736,0.8754,0.8786,0.8823,0.8834,0.8954,0.8958,0.9017,0.9096,
0.9146,0.9153,0.9159,0.9215,0.9277,0.9296,0.9335,0.9349,0.9544,0.9572,
0.9588,0.9620,0.9693,0.9734,0.9780,0.9874,0.9901,0.9944,0.9960,
Overall p-value after applying KStest on 269 p-values = 0.167695
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.