RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.01 30.6254 0.977828
2 to 25 15.56 15.9889 0.475378
3 to 26 15.83 18.7640 0.657757
4 to 27 15.68 19.3127 0.689120
5 to 28 15.90 19.2359 0.684836
6 to 29 15.89 14.3609 0.358589
7 to 30 15.59 22.1402 0.820614
8 to 31 15.78 14.9652 0.402013
9 to 32 15.83 15.9228 0.470684
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.258296
Tough bday spacings test for dh-ranFile-2018-07-03_17:31: 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 2 34 83 89 103 79 58 19 21 8 4
(O-E)^2/E 5.6 0.2 1.3 0.8 0.3 0.0 0.7 3.9 2.5 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 15.516, p= 0.886
RESULTS OF GCD FOR dh-ranFile-2018-07-03_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.716035
p-value, dist. of gcd's: 0.059078
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.856 0.559 0.021 0.012 0.974 0.629 0.306 0.553
Bits 8 to 15---> 0.910 0.351 0.473 0.088 0.052 0.707 0.134 0.496
Bits 16 to 23---> 0.978 0.899 0.084 0.447 0.501 0.545 0.781 0.854
Bits 24 to 31---> 0.722 0.290 0.815 0.125 0.983 0.359 0.828 0.515
KS test for the above 32 p values: 0.328
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_17:31,
p-values for 5 runs: 0.9131, 0.3163, 0.3842, 0.3202, 0.5025
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5147 5134.0 0.033 0.034
r= 30 23148 23103.0 0.087 0.122
r= 31 11493 11551.5 0.297 0.418
chi-square = 0.418 with df = 3; p-value = 0.064
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 222 211.4 0.530 0.530
r= 30 5095 5134.0 0.296 0.826
r= 31 23227 23103.0 0.665 1.491
r= 32 11456 11551.5 0.790 2.281
chi-square = 2.281 with df = 3; p-value = 0.484
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_17:31
b-rank test for bits 1 to 8, p=0.98488
b-rank test for bits 2 to 9, p=0.19537
b-rank test for bits 3 to 10, p=0.25327
b-rank test for bits 4 to 11, p=0.14784
b-rank test for bits 5 to 12, p=0.97389
b-rank test for bits 6 to 13, p=0.54632
b-rank test for bits 7 to 14, p=0.39252
b-rank test for bits 8 to 15, p=0.57766
b-rank test for bits 9 to 16, p=0.41146
b-rank test for bits 10 to 17, p=0.46113
b-rank test for bits 11 to 18, p=0.70248
b-rank test for bits 12 to 19, p=0.70951
b-rank test for bits 13 to 20, p=0.98516
b-rank test for bits 14 to 21, p=0.65713
b-rank test for bits 15 to 22, p=0.32809
b-rank test for bits 16 to 23, p=0.08326
b-rank test for bits 17 to 24, p=0.58951
b-rank test for bits 18 to 25, p=0.09675
b-rank test for bits 19 to 26, p=0.50576
b-rank test for bits 20 to 27, p=0.95081
b-rank test for bits 21 to 28, p=0.76124
b-rank test for bits 22 to 29, p=0.54559
b-rank test for bits 23 to 30, p=0.88347
b-rank test for bits 24 to 31, p=0.56931
b-rank test for bits 25 to 32, p=0.59190
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 = 0.356543
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_17:31
(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 141686 -0.52 0.300905
2 141631 -0.65 0.257748
3 141742 -0.39 0.347914
4 141720 -0.44 0.329114
5 141834 -0.18 0.430145
6 142466 1.30 0.903308
7 142950 2.43 0.992481
8 141779 -0.30 0.380370
9 141923 0.03 0.512740
10 141559 -0.82 0.206528
11 141760 -0.35 0.363582
12 141586 -0.76 0.224991
13 141764 -0.34 0.367095
14 143273 3.19 0.999279
15 141649 -0.61 0.271512
16 141198 -1.66 0.048258
17 141705 -0.48 0.316536
18 141233 -1.58 0.057029
19 142043 0.31 0.622599
20 142506 1.39 0.918355
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_17:31
Bits used No. missing words z-score p-value
23 to 32 141925 0.0540 0.521546
22 to 31 141365 -1.8770 0.030259
21 to 30 141970 0.2092 0.582857
20 to 29 142028 0.4092 0.658806
19 to 28 142262 1.2161 0.888027
18 to 27 141621 -0.9942 0.160053
17 to 26 142009 0.3437 0.634460
16 to 25 142461 1.9023 0.971435
15 to 24 142076 0.5747 0.717261
14 to 23 141773 -0.4701 0.319141
13 to 22 142012 0.3540 0.638344
12 to 21 141594 -1.0873 0.138442
11 to 20 141300 -2.1011 0.017814
10 to 19 142008 0.3402 0.633163
9 to 18 142613 2.4264 0.992376
8 to 17 142134 0.7747 0.780749
7 to 16 141799 -0.3804 0.351806
6 to 15 141490 -1.4460 0.074093
5 to 14 141717 -0.6632 0.253599
4 to 13 141487 -1.4563 0.072653
3 to 12 142329 1.4471 0.926071
2 to 11 142085 0.6058 0.727663
1 to 10 142031 0.4196 0.662594
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_17:31
Bits used No. missing words z-score p-value
28 to 32 142206 1.0057 0.842711
27 to 31 142154 0.8294 0.796558
26 to 30 142093 0.6226 0.733230
25 to 29 142296 1.3107 0.905028
24 to 28 141966 0.1921 0.576169
23 to 27 142498 1.9955 0.977005
22 to 26 141407 -1.7028 0.044301
21 to 25 141925 0.0531 0.521181
20 to 24 141677 -0.7876 0.215477
19 to 23 141415 -1.6757 0.046899
18 to 22 141563 -1.1740 0.120198
17 to 21 142075 0.5616 0.712803
16 to 20 142004 0.3209 0.625863
15 to 19 141883 -0.0893 0.464440
14 to 18 141789 -0.4079 0.341674
13 to 17 142293 1.3006 0.903298
12 to 16 141627 -0.9571 0.169271
11 to 15 141665 -0.8282 0.203768
10 to 14 142207 1.0091 0.843525
9 to 13 141870 -0.1333 0.446969
8 to 12 142415 1.7141 0.956748
7 to 11 141409 -1.6960 0.044940
6 to 10 142390 1.6294 0.948385
5 to 9 141745 -0.5571 0.288746
4 to 8 142318 1.3853 0.917023
3 to 7 142122 0.7209 0.764519
2 to 6 141817 -0.3130 0.377147
1 to 5 141864 -0.1537 0.438939
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_17:31
Bits used No. missing words z-score p-value
31 to 32 141715 -0.5732 0.283240
30 to 31 141954 0.1318 0.552417
29 to 30 141498 -1.2134 0.112496
28 to 29 141821 -0.2606 0.397216
27 to 28 142006 0.2852 0.612240
26 to 27 141923 0.0403 0.516083
25 to 26 141769 -0.4140 0.339454
24 to 25 141729 -0.5319 0.297381
23 to 24 141801 -0.3196 0.374652
22 to 23 142160 0.7394 0.770180
21 to 22 142085 0.5182 0.697841
20 to 21 141810 -0.2930 0.384758
19 to 20 141898 -0.0334 0.486669
18 to 19 141513 -1.1691 0.121179
17 to 18 142313 1.1908 0.883127
16 to 17 141686 -0.6588 0.255015
15 to 16 142512 1.7778 0.962281
14 to 15 141060 -2.5054 0.006116
13 to 14 142238 0.9695 0.833859
12 to 13 141376 -1.5732 0.057831
11 to 12 141988 0.2321 0.591756
10 to 11 141675 -0.6912 0.244708
9 to 10 142107 0.5831 0.720086
8 to 9 142083 0.5123 0.695780
7 to 8 142542 1.8663 0.968999
6 to 7 141525 -1.1337 0.128457
5 to 6 141899 -0.0305 0.487845
4 to 5 142411 1.4799 0.930544
3 to 4 142299 1.1495 0.874819
2 to 3 141803 -0.3137 0.376891
1 to 2 142216 0.9046 0.817170
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2562.57 0.885 0.811887
Test results for specific bytes for dh-ranFile-2018-07-03_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2572.93 1.031 0.848819
2 to 9 2493.76 -0.088 0.464818
3 to 10 2516.95 0.240 0.594735
4 to 11 2364.75 -1.913 0.027891
5 to 12 2485.57 -0.204 0.419144
6 to 13 2267.62 -3.286 0.000507
7 to 14 2463.56 -0.515 0.303177
8 to 15 2417.85 -1.162 0.122663
9 to 16 2609.92 1.554 0.939962
10 to 17 2515.36 0.217 0.585970
11 to 18 2446.27 -0.760 0.223687
12 to 19 2375.15 -1.766 0.038730
13 to 20 2417.60 -1.165 0.121958
14 to 21 2499.61 -0.006 0.497800
15 to 22 2561.03 0.863 0.805969
16 to 23 2464.55 -0.501 0.308043
17 to 24 2461.55 -0.544 0.293319
18 to 25 2519.45 0.275 0.608348
19 to 26 2458.81 -0.583 0.280092
20 to 27 2589.56 1.267 0.897351
21 to 28 2573.69 1.042 0.851313
22 to 29 2431.66 -0.966 0.166907
23 to 30 2474.74 -0.357 0.360485
24 to 31 2401.02 -1.400 0.080782
25 to 32 2419.48 -1.139 0.127405
CDPARK for dh-ranFile-2018-07-03_17:31: 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
3515 -0.3653 0.357445
3516 -0.3196 0.374623
3558 1.5982 0.944998
3481 -1.9178 0.027568
3482 -1.8721 0.030593
3508 -0.6849 0.246694
3492 -1.4155 0.078457
3533 0.4566 0.676028
3508 -0.6849 0.246694
3500 -1.0502 0.146807
Square side=100, avg. no. parked=3509.30 sample std.=22.24
p-value of the KSTEST for those 10 p-values: 0.045146
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_17:31
0.4913,0.4734,0.2224,0.3278,0.1021,0.2573,0.2203,0.7494,0.9756,0.0498,
The KS test for those 10 p-values: 0.329189
The 3DSPHERES test for dh-ranFile-2018-07-03_17:31
sample no r^3 equiv. uni.
1 78.921 0.927972
2 3.933 0.122875
3 40.151 0.737724
4 3.079 0.097538
5 14.285 0.378836
6 37.542 0.713892
7 9.098 0.261589
8 19.447 0.477036
9 15.881 0.411023
10 25.330 0.570161
11 52.245 0.824743
12 75.532 0.919358
13 29.237 0.622648
14 3.489 0.109783
15 24.444 0.557270
16 16.815 0.429068
17 21.179 0.506367
18 29.455 0.625372
19 1.458 0.047453
20 10.320 0.291072
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.929296
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 1.5 0.0 -0.7 0.2
1.2 0.7 3.0 0.4 -0.0 0.7
-1.2 0.2 -0.5 -1.3 0.1 -0.7
0.5 0.1 -0.8 1.4 -1.1 0.9
-0.9 1.1 -0.3 0.5 0.3 -0.7
0.6 -1.6 -1.0 0.7 0.3 0.4
0.5 0.2 -0.4 -0.7 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:33.879153
z-score=-0.886057, p-value=0.190363
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_17:31
Test no p-value
1 0.417194
2 0.806406
3 0.027033
4 0.206577
5 0.389108
6 0.083909
7 0.563723
8 0.140877
9 0.006348
10 0.451366
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.046793
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_17:31:
(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 66828 0.39 66700 0.02
3 25000.00 24945 0.12 24943 0.13
4 6666.67 6608 0.52 6677 0.02
5 1388.89 1366 0.38 1401 0.11
6 238.10 222 1.09 246 0.26
7 34.72 26 2.19 27 1.72
8 4.96 4 0.19 5 0.00
p=0.43926 p=0.10442
Number of rngs required: 688128, p-value: 0.376
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_17:31
No. of wins: Observed Expected
98461 98585.9
z-score=-0.558, pvalue=0.28827
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67012 66666.7 1.789 1.789
2 37262 37654.3 4.088 5.876
3 26858 26954.7 0.347 6.224
4 19273 19313.5 0.085 6.308
5 13838 13851.4 0.013 6.321
6 9950 9943.5 0.004 6.326
7 7127 7145.0 0.045 6.371
8 5257 5139.1 2.706 9.077
9 3618 3699.9 1.811 10.889
10 2732 2666.3 1.619 12.508
11 1912 1923.3 0.067 12.574
12 1437 1388.7 1.677 14.251
13 1006 1003.7 0.005 14.257
14 691 726.1 1.701 15.957
15 571 525.8 3.879 19.836
16 396 381.2 0.579 20.415
17 287 276.5 0.396 20.810
18 212 200.8 0.621 21.432
19 162 146.0 1.757 23.189
20 93 106.2 1.644 24.833
21 306 287.1 1.242 26.075
Chisq= 26.08 for 20 degrees of freedom, p= 0.83666
SUMMARY of craptest
p-value for no. of wins: 0.288272
p-value for throws/game: 0.836662
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_17:31
No. of wins: Observed Expected
98591 98585.9
z-score= 0.023, pvalue=0.50917
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66675 66666.7 0.001 0.001
2 37625 37654.3 0.023 0.024
3 27035 26954.7 0.239 0.263
4 19192 19313.5 0.764 1.027
5 13909 13851.4 0.239 1.266
6 9947 9943.5 0.001 1.267
7 7135 7145.0 0.014 1.281
8 5178 5139.1 0.295 1.576
9 3721 3699.9 0.121 1.697
10 2723 2666.3 1.206 2.903
11 1921 1923.3 0.003 2.906
12 1428 1388.7 1.110 4.016
13 964 1003.7 1.571 5.587
14 690 726.1 1.799 7.386
15 520 525.8 0.065 7.451
16 378 381.2 0.026 7.477
17 246 276.5 3.373 10.849
18 218 200.8 1.468 12.317
19 144 146.0 0.027 12.344
20 92 106.2 1.902 14.247
21 259 287.1 2.753 17.000
Chisq= 17.00 for 20 degrees of freedom, p= 0.34699
SUMMARY of craptest
p-value for no. of wins: 0.509173
p-value for throws/game: 0.346994
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0061,0.0063,0.0119,0.0178,0.0213,0.0270,0.0276,0.0279,0.0303,
0.0306,0.0387,0.0443,0.0449,0.0451,0.0468,0.0469,0.0475,0.0483,0.0498,
0.0520,0.0570,0.0578,0.0591,0.0636,0.0727,0.0741,0.0785,0.0808,0.0833,
0.0836,0.0839,0.0881,0.0967,0.0975,0.1021,0.1044,0.1098,0.1125,0.1202,
0.1212,0.1220,0.1227,0.1229,0.1249,0.1274,0.1285,0.1339,0.1384,0.1409,
0.1468,0.1478,0.1601,0.1669,0.1693,0.1904,0.1954,0.2038,0.2065,0.2066,
0.2155,0.2203,0.2224,0.2237,0.2250,0.2447,0.2467,0.2467,0.2533,0.2536,
0.2550,0.2573,0.2577,0.2583,0.2616,0.2715,0.2801,0.2832,0.2883,0.2887,
0.2897,0.2911,0.2933,0.2974,0.3009,0.3032,0.3064,0.3080,0.3163,0.3165,
0.3191,0.3202,0.3278,0.3281,0.3283,0.3291,0.3292,0.3395,0.3417,0.3470,
0.3479,0.3505,0.3518,0.3565,0.3574,0.3586,0.3592,0.3605,0.3636,0.3671,
0.3746,0.3747,0.3758,0.3769,0.3771,0.3788,0.3804,0.3842,0.3848,0.3891,
0.3925,0.3972,0.4020,0.4110,0.4115,0.4172,0.4191,0.4291,0.4301,0.4389,
0.4393,0.4467,0.4470,0.4514,0.4611,0.4644,0.4648,0.4707,0.4727,0.4734,
0.4754,0.4770,0.4838,0.4867,0.4878,0.4913,0.4965,0.4978,0.5010,0.5025,
0.5058,0.5064,0.5092,0.5127,0.5146,0.5161,0.5212,0.5215,0.5447,0.5456,
0.5463,0.5524,0.5528,0.5573,0.5594,0.5637,0.5693,0.5702,0.5762,0.5777,
0.5829,0.5860,0.5895,0.5918,0.5919,0.5947,0.6083,0.6122,0.6226,0.6226,
0.6254,0.6259,0.6287,0.6332,0.6345,0.6383,0.6571,0.6578,0.6588,0.6626,
0.6760,0.6848,0.6891,0.6958,0.6978,0.7025,0.7067,0.7095,0.7128,0.7139,
0.7160,0.7173,0.7201,0.7224,0.7277,0.7332,0.7377,0.7494,0.7612,0.7645,
0.7702,0.7807,0.7807,0.7966,0.8060,0.8064,0.8119,0.8149,0.8172,0.8206,
0.8247,0.8284,0.8339,0.8367,0.8427,0.8435,0.8488,0.8513,0.8539,0.8564,
0.8748,0.8831,0.8835,0.8857,0.8880,0.8974,0.8990,0.9033,0.9033,0.9050,
0.9095,0.9131,0.9170,0.9184,0.9194,0.9261,0.9280,0.9293,0.9305,0.9400,
0.9450,0.9484,0.9508,0.9567,0.9623,0.9690,0.9714,0.9739,0.9743,0.9756,
0.9770,0.9778,0.9783,0.9835,0.9849,0.9852,0.9924,0.9925,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.172837
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.