RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_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 15.54 21.6614 0.801907
2 to 25 15.66 20.0456 0.728095
3 to 26 15.88 23.8111 0.875340
4 to 27 15.41 22.2327 0.824064
5 to 28 15.65 30.0837 0.974253
6 to 29 15.67 17.1098 0.553051
7 to 30 15.68 13.4678 0.295646
8 to 31 15.90 14.4527 0.365163
9 to 32 15.96 12.5664 0.235304
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.315879
Tough bday spacings test for dh-ranFile-2018-07-09_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 10 41 67 103 101 66 64 24 12 8 4
(O-E)^2/E 0.1 0.5 0.5 0.3 0.1 1.9 2.7 1.1 0.6 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.111, p= 0.382
RESULTS OF GCD FOR dh-ranFile-2018-07-09_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.818157
p-value, dist. of gcd's: 0.723018
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.898 0.095 0.235 0.791 0.064 0.483 0.009 0.722
Bits 8 to 15---> 0.905 0.250 0.301 0.985 0.458 0.521 0.865 0.665
Bits 16 to 23---> 0.209 0.225 0.384 0.758 0.090 0.926 0.459 0.737
Bits 24 to 31---> 0.225 0.943 0.437 0.693 0.546 0.143 0.586 0.458
KS test for the above 32 p values: 0.001
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_18:31,
p-values for 5 runs: 0.5638, 0.7096, 0.3306, 0.2676, 0.7445
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5110 5134.0 0.112 0.642
r= 30 23092 23103.0 0.005 0.647
r= 31 11576 11551.5 0.052 0.699
chi-square = 0.699 with df = 3; p-value = 0.127
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 193 211.4 1.605 1.605
r= 30 5189 5134.0 0.589 2.193
r= 31 23072 23103.0 0.042 2.235
r= 32 11546 11551.5 0.003 2.238
chi-square = 2.238 with df = 3; p-value = 0.475
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_18:31
b-rank test for bits 1 to 8, p=0.28607
b-rank test for bits 2 to 9, p=0.35603
b-rank test for bits 3 to 10, p=0.96929
b-rank test for bits 4 to 11, p=0.00869
b-rank test for bits 5 to 12, p=0.66460
b-rank test for bits 6 to 13, p=0.87442
b-rank test for bits 7 to 14, p=0.64932
b-rank test for bits 8 to 15, p=0.62539
b-rank test for bits 9 to 16, p=0.41999
b-rank test for bits 10 to 17, p=0.50611
b-rank test for bits 11 to 18, p=0.70887
b-rank test for bits 12 to 19, p=0.02520
b-rank test for bits 13 to 20, p=0.62973
b-rank test for bits 14 to 21, p=0.42194
b-rank test for bits 15 to 22, p=0.20479
b-rank test for bits 16 to 23, p=0.28881
b-rank test for bits 17 to 24, p=0.57504
b-rank test for bits 18 to 25, p=0.56817
b-rank test for bits 19 to 26, p=0.52812
b-rank test for bits 20 to 27, p=0.75517
b-rank test for bits 21 to 28, p=0.06818
b-rank test for bits 22 to 29, p=0.51380
b-rank test for bits 23 to 30, p=0.12776
b-rank test for bits 24 to 31, p=0.61404
b-rank test for bits 25 to 32, p=0.64264
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 = 0.471527
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_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 141630 -0.65 0.256994
2 142633 1.69 0.954564
3 142129 0.51 0.696111
4 142343 1.01 0.844529
5 141777 -0.31 0.378591
6 141608 -0.70 0.240703
7 141942 0.08 0.530422
8 142084 0.41 0.658403
9 142182 0.64 0.737963
10 142222 0.73 0.767469
11 141879 -0.07 0.471753
12 141451 -1.07 0.142115
13 142009 0.23 0.592070
14 141477 -1.01 0.156220
15 140890 -2.38 0.008619
16 141412 -1.16 0.122621
17 142496 1.37 0.914770
18 141643 -0.62 0.266883
19 141998 0.21 0.582063
20 142212 0.71 0.760271
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_18:31
Bits used No. missing words z-score p-value
23 to 32 142044 0.4644 0.678812
22 to 31 142051 0.4885 0.687408
21 to 30 141737 -0.5942 0.276175
20 to 29 141821 -0.3046 0.380341
19 to 28 142106 0.6782 0.751169
18 to 27 141917 0.0264 0.510550
17 to 26 141686 -0.7701 0.220619
16 to 25 141592 -1.0942 0.136925
15 to 24 142010 0.3471 0.635756
14 to 23 141855 -0.1873 0.425695
13 to 22 142188 0.9609 0.831707
12 to 21 141587 -1.1115 0.133180
11 to 20 141625 -0.9804 0.163432
10 to 19 141906 -0.0115 0.495419
9 to 18 141700 -0.7218 0.235200
8 to 17 141628 -0.9701 0.165998
7 to 16 142244 1.1540 0.875757
6 to 15 141984 0.2575 0.601597
5 to 14 141662 -0.8529 0.196868
4 to 13 142042 0.4575 0.676338
3 to 12 142342 1.4920 0.932146
2 to 11 141848 -0.2115 0.416255
1 to 10 141832 -0.2667 0.394867
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_18:31
Bits used No. missing words z-score p-value
28 to 32 142061 0.5141 0.696421
27 to 31 142277 1.2463 0.893680
26 to 30 141684 -0.7638 0.222484
25 to 29 142234 1.1006 0.864459
24 to 28 141783 -0.4282 0.334239
23 to 27 142070 0.5446 0.707001
22 to 26 141812 -0.3299 0.370726
21 to 25 141422 -1.6520 0.049271
20 to 24 141570 -1.1503 0.125016
19 to 23 141780 -0.4384 0.330546
18 to 22 141753 -0.5299 0.298080
17 to 21 141712 -0.6689 0.251775
16 to 20 141573 -1.1401 0.127122
15 to 19 142077 0.5684 0.715109
14 to 18 142001 0.3107 0.622003
13 to 17 142021 0.3785 0.647486
12 to 16 142145 0.7989 0.787820
11 to 15 142454 1.8463 0.967579
10 to 14 141936 0.0904 0.536018
9 to 13 141897 -0.0418 0.483330
8 to 12 141516 -1.3333 0.091213
7 to 11 142250 1.1548 0.875917
6 to 10 142200 0.9853 0.837767
5 to 9 141946 0.1243 0.549463
4 to 8 142137 0.7718 0.779873
3 to 7 142122 0.7209 0.764519
2 to 6 142168 0.8768 0.809715
1 to 5 142341 1.4633 0.928306
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_18:31
Bits used No. missing words z-score p-value
31 to 32 142303 1.1613 0.877234
30 to 31 142764 2.5212 0.994151
29 to 30 141927 0.0521 0.520785
28 to 29 142339 1.2675 0.897505
27 to 28 141531 -1.1160 0.132207
26 to 27 142455 1.6096 0.946262
25 to 26 141061 -2.5024 0.006167
24 to 25 141717 -0.5673 0.285240
23 to 24 141983 0.2173 0.586019
22 to 23 142122 0.6273 0.734784
21 to 22 142140 0.6804 0.751888
20 to 21 141758 -0.4464 0.327654
19 to 20 141874 -0.1042 0.458498
18 to 19 142499 1.7394 0.959021
17 to 18 142121 0.6244 0.733816
16 to 17 142395 1.4327 0.924022
15 to 16 141830 -0.2340 0.407488
14 to 15 142500 1.7424 0.959280
13 to 14 142121 0.6244 0.733816
12 to 13 141364 -1.6086 0.053847
11 to 12 142211 0.8899 0.813235
10 to 11 142126 0.6391 0.738636
9 to 10 141096 -2.3992 0.008215
8 to 9 142380 1.3884 0.917493
7 to 8 142569 1.9459 0.974168
6 to 7 142022 0.3324 0.630191
5 to 6 141747 -0.4788 0.316023
4 to 5 141226 -2.0157 0.021914
3 to 4 142268 1.0580 0.854978
2 to 3 141724 -0.5467 0.292294
1 to 2 141956 0.1377 0.554749
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2582.85 1.172 0.879343
Test results for specific bytes for dh-ranFile-2018-07-09_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2427.61 -1.024 0.152986
2 to 9 2502.08 0.029 0.511744
3 to 10 2500.71 0.010 0.504029
4 to 11 2526.19 0.370 0.644469
5 to 12 2365.40 -1.903 0.028489
6 to 13 2481.88 -0.256 0.398863
7 to 14 2573.44 1.039 0.850509
8 to 15 2542.22 0.597 0.724791
9 to 16 2424.10 -1.073 0.141546
10 to 17 2619.48 1.690 0.954452
11 to 18 2479.10 -0.296 0.383787
12 to 19 2546.30 0.655 0.743673
13 to 20 2502.02 0.029 0.511388
14 to 21 2519.91 0.282 0.610851
15 to 22 2567.73 0.958 0.830927
16 to 23 2498.85 -0.016 0.493518
17 to 24 2505.53 0.078 0.531145
18 to 25 2638.38 1.957 0.974829
19 to 26 2486.43 -0.192 0.423892
20 to 27 2608.36 1.532 0.937291
21 to 28 2518.56 0.262 0.603515
22 to 29 2460.36 -0.561 0.287552
23 to 30 2393.88 -1.501 0.066711
24 to 31 2612.51 1.591 0.944211
25 to 32 2473.65 -0.373 0.354708
CDPARK for dh-ranFile-2018-07-09_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
3518 -0.2283 0.409702
3531 0.3653 0.642555
3495 -1.2785 0.100530
3517 -0.2740 0.392053
3545 1.0046 0.842447
3526 0.1370 0.554479
3555 1.4612 0.928018
3510 -0.5936 0.276387
3545 1.0046 0.842447
3485 -1.7352 0.041356
Square side=100, avg. no. parked=3522.70 sample std.=21.27
p-value of the KSTEST for those 10 p-values: 0.993911
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_18:31
0.6822,0.5519,0.7193,0.7240,0.0801,0.3521,0.7870,0.0137,0.2031,0.6165,
The KS test for those 10 p-values: 0.673164
The 3DSPHERES test for dh-ranFile-2018-07-09_18:31
sample no r^3 equiv. uni.
1 2.324 0.074542
2 7.131 0.211558
3 10.059 0.284888
4 27.060 0.594246
5 28.705 0.615893
6 20.884 0.501491
7 12.870 0.348842
8 7.690 0.226103
9 4.798 0.147813
10 17.470 0.441397
11 28.613 0.614715
12 3.900 0.121912
13 77.012 0.923239
14 40.217 0.738306
15 80.218 0.931019
16 21.501 0.511636
17 0.415 0.013724
18 28.290 0.610538
19 21.729 0.515338
20 4.384 0.135958
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.429589
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.6 1.3 -0.3 -1.6 0.8
1.6 -0.4 1.0 0.1 0.5 0.6
1.1 -2.3 -0.1 -1.0 -1.1 -0.9
-0.0 1.3 -0.1 1.4 0.3 -0.3
0.9 -0.2 -1.5 1.6 -1.3 1.3
0.9 -0.5 0.9 1.1 -0.9 -0.5
-1.4 0.8 0.1 2.6 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:48.494535
z-score=0.708612, p-value=0.772467
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_18:31
Test no p-value
1 0.191210
2 0.639487
3 0.054638
4 0.044809
5 0.127485
6 0.125639
7 0.460581
8 0.465123
9 0.352008
10 0.217736
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.016904
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_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 66773 0.17 66725 0.05
3 25000.00 24915 0.29 24892 0.47
4 6666.67 6660 0.01 6735 0.70
5 1388.89 1346 1.32 1348 1.20
6 238.10 263 2.61 264 2.82
7 34.72 35 0.00 32 0.21
8 4.96 7 0.84 3 0.77
p=0.48609 p=0.60184
Number of rngs required: 688308, p-value: 0.456
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_18:31
No. of wins: Observed Expected
98951 98585.9
z-score= 1.633, pvalue=0.94878
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66709 66666.7 0.027 0.027
2 37715 37654.3 0.098 0.125
3 26833 26954.7 0.550 0.674
4 19344 19313.5 0.048 0.723
5 13908 13851.4 0.231 0.954
6 9847 9943.5 0.937 1.891
7 7043 7145.0 1.457 3.348
8 5070 5139.1 0.928 4.276
9 3694 3699.9 0.009 4.286
10 2721 2666.3 1.122 5.408
11 2016 1923.3 4.465 9.873
12 1442 1388.7 2.043 11.916
13 1038 1003.7 1.171 13.087
14 708 726.1 0.453 13.540
15 510 525.8 0.477 14.017
16 397 381.2 0.659 14.676
17 252 276.5 2.178 16.854
18 193 200.8 0.305 17.159
19 168 146.0 3.320 20.479
20 118 106.2 1.308 21.786
21 274 287.1 0.599 22.385
Chisq= 22.39 for 20 degrees of freedom, p= 0.68003
SUMMARY of craptest
p-value for no. of wins: 0.948779
p-value for throws/game: 0.680034
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_18:31
No. of wins: Observed Expected
98914 98585.9
z-score= 1.468, pvalue=0.92890
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66673 66666.7 0.001 0.001
2 37816 37654.3 0.694 0.695
3 26897 26954.7 0.124 0.818
4 19461 19313.5 1.127 1.946
5 13810 13851.4 0.124 2.069
6 9831 9943.5 1.274 3.343
7 7041 7145.0 1.515 4.858
8 5079 5139.1 0.702 5.560
9 3745 3699.9 0.551 6.111
10 2621 2666.3 0.770 6.880
11 1971 1923.3 1.182 8.062
12 1381 1388.7 0.043 8.105
13 1026 1003.7 0.495 8.600
14 715 726.1 0.171 8.770
15 519 525.8 0.089 8.859
16 389 381.2 0.162 9.021
17 278 276.5 0.008 9.029
18 245 200.8 9.715 18.743
19 142 146.0 0.109 18.852
20 83 106.2 5.074 23.926
21 277 287.1 0.356 24.282
Chisq= 24.28 for 20 degrees of freedom, p= 0.76973
SUMMARY of craptest
p-value for no. of wins: 0.928899
p-value for throws/game: 0.769730
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0062,0.0082,0.0086,0.0087,0.0089,0.0137,0.0137,0.0169,0.0219,
0.0252,0.0285,0.0414,0.0448,0.0493,0.0538,0.0546,0.0640,0.0667,0.0682,
0.0745,0.0801,0.0899,0.0912,0.0955,0.1005,0.1219,0.1226,0.1250,0.1256,
0.1266,0.1271,0.1275,0.1278,0.1322,0.1332,0.1360,0.1369,0.1415,0.1421,
0.1426,0.1478,0.1530,0.1562,0.1634,0.1660,0.1912,0.1969,0.2031,0.2048,
0.2092,0.2116,0.2177,0.2206,0.2225,0.2248,0.2249,0.2261,0.2351,0.2352,
0.2353,0.2407,0.2498,0.2518,0.2570,0.2669,0.2676,0.2762,0.2764,0.2849,
0.2852,0.2861,0.2876,0.2888,0.2923,0.2956,0.2981,0.3012,0.3159,0.3160,
0.3277,0.3305,0.3306,0.3342,0.3488,0.3520,0.3521,0.3547,0.3560,0.3652,
0.3707,0.3786,0.3803,0.3820,0.3838,0.3838,0.3921,0.3949,0.3989,0.4075,
0.4097,0.4163,0.4200,0.4219,0.4239,0.4257,0.4296,0.4370,0.4414,0.4565,
0.4576,0.4583,0.4585,0.4592,0.4606,0.4651,0.4715,0.4718,0.4755,0.4826,
0.4833,0.4861,0.4935,0.4954,0.5015,0.5040,0.5061,0.5106,0.5114,0.5116,
0.5117,0.5138,0.5153,0.5208,0.5214,0.5281,0.5304,0.5311,0.5360,0.5460,
0.5495,0.5519,0.5531,0.5545,0.5547,0.5638,0.5682,0.5750,0.5821,0.5860,
0.5863,0.5921,0.5942,0.6016,0.6018,0.6035,0.6105,0.6109,0.6140,0.6147,
0.6159,0.6165,0.6220,0.6254,0.6297,0.6302,0.6358,0.6395,0.6426,0.6426,
0.6445,0.6475,0.6493,0.6584,0.6646,0.6653,0.6732,0.6763,0.6788,0.6800,
0.6822,0.6874,0.6926,0.6961,0.6964,0.7070,0.7089,0.7096,0.7151,0.7193,
0.7224,0.7230,0.7240,0.7248,0.7281,0.7338,0.7338,0.7348,0.7373,0.7380,
0.7383,0.7386,0.7437,0.7445,0.7512,0.7519,0.7552,0.7580,0.7603,0.7645,
0.7675,0.7697,0.7725,0.7799,0.7870,0.7878,0.7913,0.8019,0.8097,0.8132,
0.8182,0.8241,0.8309,0.8317,0.8378,0.8424,0.8424,0.8445,0.8505,0.8550,
0.8645,0.8647,0.8744,0.8753,0.8758,0.8759,0.8772,0.8793,0.8937,0.8975,
0.8984,0.9050,0.9148,0.9175,0.9232,0.9240,0.9258,0.9280,0.9283,0.9289,
0.9310,0.9321,0.9373,0.9430,0.9442,0.9463,0.9488,0.9545,0.9546,0.9590,
0.9593,0.9676,0.9693,0.9742,0.9743,0.9748,0.9849,0.9939,0.9942,
Overall p-value after applying KStest on 269 p-values = 0.653377
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.