RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.96 13.4582 0.294989
2 to 25 15.64 23.6040 0.869399
3 to 26 15.87 11.0937 0.148351
4 to 27 15.78 13.9649 0.330417
5 to 28 15.94 20.8663 0.767672
6 to 29 15.95 9.6943 0.084062
7 to 30 15.97 11.0680 0.146993
8 to 31 16.07 11.5379 0.172722
9 to 32 15.62 23.2714 0.859379
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.327012
Tough bday spacings test for dh-ranFile-2018-07-08_19:31: 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 39 74 95 100 76 50 35 15 8 1
(O-E)^2/E 0.5 0.2 0.0 0.1 0.1 0.1 0.1 0.9 0.0 0.3 2.3
Birthday Spacings: Sum(O-E)^2/E= 4.463, p= 0.076
RESULTS OF GCD FOR dh-ranFile-2018-07-08_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.260695
p-value, dist. of gcd's: 0.472672
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.641 0.174 0.414 0.726 0.118 0.948 0.371 0.996
Bits 8 to 15---> 0.484 0.517 0.286 0.871 0.537 0.173 0.683 0.705
Bits 16 to 23---> 0.929 0.089 0.729 0.838 0.051 0.366 0.550 0.537
Bits 24 to 31---> 0.879 0.604 0.253 0.223 0.727 0.583 0.926 0.088
KS test for the above 32 p values: 0.121
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_19:31,
p-values for 5 runs: 0.8700, 0.5092, 0.2924, 0.6001, 0.5187
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5123 5134.0 0.024 0.025
r= 30 23281 23103.0 1.371 1.396
r= 31 11384 11551.5 2.429 3.825
chi-square = 3.825 with df = 3; p-value = 0.719
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 182 211.4 4.093 4.093
r= 30 5145 5134.0 0.024 4.117
r= 31 23077 23103.0 0.029 4.146
r= 32 11596 11551.5 0.171 4.318
chi-square = 4.318 with df = 3; p-value = 0.771
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_19:31
b-rank test for bits 1 to 8, p=0.40328
b-rank test for bits 2 to 9, p=0.77143
b-rank test for bits 3 to 10, p=0.86706
b-rank test for bits 4 to 11, p=0.82157
b-rank test for bits 5 to 12, p=0.27987
b-rank test for bits 6 to 13, p=0.93087
b-rank test for bits 7 to 14, p=0.39129
b-rank test for bits 8 to 15, p=0.02350
b-rank test for bits 9 to 16, p=0.03423
b-rank test for bits 10 to 17, p=0.45162
b-rank test for bits 11 to 18, p=0.39654
b-rank test for bits 12 to 19, p=0.44225
b-rank test for bits 13 to 20, p=0.16844
b-rank test for bits 14 to 21, p=0.25766
b-rank test for bits 15 to 22, p=0.05877
b-rank test for bits 16 to 23, p=0.09131
b-rank test for bits 17 to 24, p=0.58634
b-rank test for bits 18 to 25, p=0.93864
b-rank test for bits 19 to 26, p=0.53021
b-rank test for bits 20 to 27, p=0.09235
b-rank test for bits 21 to 28, p=0.59843
b-rank test for bits 22 to 29, p=0.87476
b-rank test for bits 23 to 30, p=0.35193
b-rank test for bits 24 to 31, p=0.99410
b-rank test for bits 25 to 32, p=0.16761
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 = 0.636525
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_19:31
(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 141884 -0.06 0.476404
2 142216 0.72 0.763164
3 142249 0.79 0.786292
4 142403 1.15 0.875634
5 141879 -0.07 0.471753
6 141865 -0.10 0.458753
7 141459 -1.05 0.146360
8 141688 -0.52 0.302534
9 141978 0.16 0.563734
10 140813 -2.56 0.005211
11 142886 2.28 0.988754
12 142031 0.28 0.611900
13 142139 0.54 0.704232
14 142511 1.41 0.920104
15 141173 -1.72 0.042680
16 142148 0.56 0.711455
17 142071 0.38 0.647186
18 142415 1.18 0.881292
19 141661 -0.58 0.280886
20 142282 0.87 0.808048
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_19:31
Bits used No. missing words z-score p-value
23 to 32 142350 1.5196 0.935688
22 to 31 141676 -0.8046 0.210529
21 to 30 142464 1.9127 0.972104
20 to 29 141780 -0.4460 0.327811
19 to 28 142252 1.1816 0.881322
18 to 27 142682 2.6644 0.996143
17 to 26 142089 0.6196 0.732224
16 to 25 142318 1.4092 0.920613
15 to 24 141433 -1.6425 0.050241
14 to 23 141710 -0.6873 0.245933
13 to 22 141836 -0.2529 0.400187
12 to 21 141981 0.2471 0.597599
11 to 20 142492 2.0092 0.977742
10 to 19 142379 1.6196 0.947336
9 to 18 141833 -0.2632 0.396196
8 to 17 141870 -0.1356 0.446061
7 to 16 142483 1.9782 0.976045
6 to 15 141838 -0.2460 0.402855
5 to 14 141804 -0.3632 0.358225
4 to 13 142040 0.4506 0.673856
3 to 12 142179 0.9299 0.823788
2 to 11 142376 1.6092 0.946214
1 to 10 142431 1.7989 0.963980
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_19:31
Bits used No. missing words z-score p-value
28 to 32 141945 0.1209 0.548121
27 to 31 142488 1.9616 0.975095
26 to 30 142182 0.9243 0.822336
25 to 29 141763 -0.4960 0.309935
24 to 28 142074 0.5582 0.711647
23 to 27 142598 2.3345 0.990215
22 to 26 142034 0.4226 0.663710
21 to 25 142760 2.8836 0.998034
20 to 24 141741 -0.5706 0.284132
19 to 23 142302 1.3311 0.908419
18 to 22 141948 0.1311 0.552146
17 to 21 141983 0.2497 0.598602
16 to 20 141679 -0.7808 0.217466
15 to 19 142565 2.2226 0.986879
14 to 18 142088 0.6057 0.727630
13 to 17 141918 0.0294 0.511723
12 to 16 141310 -2.0316 0.021096
11 to 15 141513 -1.3435 0.089556
10 to 14 142220 1.0531 0.853857
9 to 13 141462 -1.5164 0.064713
8 to 12 141681 -0.7740 0.219465
7 to 11 141817 -0.3130 0.377147
6 to 10 141791 -0.4011 0.344166
5 to 9 142246 1.1413 0.873118
4 to 8 141797 -0.3808 0.351683
3 to 7 141261 -2.1977 0.013984
2 to 6 141774 -0.4587 0.323208
1 to 5 142277 1.2463 0.893680
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_19:31
Bits used No. missing words z-score p-value
31 to 32 141677 -0.6853 0.246565
30 to 31 142235 0.9607 0.831643
29 to 30 141838 -0.2104 0.416673
28 to 29 142110 0.5919 0.723057
27 to 28 142216 0.9046 0.817170
26 to 27 143071 3.4268 0.999695
25 to 26 142264 1.0462 0.852271
24 to 25 141487 -1.2458 0.106417
23 to 24 141835 -0.2193 0.413223
22 to 23 141821 -0.2606 0.397216
21 to 22 142564 1.9312 0.973270
20 to 21 141988 0.2321 0.591756
19 to 20 141862 -0.1396 0.444482
18 to 19 141754 -0.4582 0.323404
17 to 18 142102 0.5683 0.715101
16 to 17 142264 1.0462 0.852271
15 to 16 142229 0.9430 0.827154
14 to 15 141786 -0.3638 0.358002
13 to 14 142117 0.6126 0.729928
12 to 13 141657 -0.7443 0.228337
11 to 12 142102 0.5683 0.715101
10 to 11 141638 -0.8004 0.211744
9 to 10 142310 1.1819 0.881381
8 to 9 141393 -1.5231 0.063867
7 to 8 142108 0.5860 0.721078
6 to 7 142436 1.5536 0.939860
5 to 6 142362 1.3353 0.909113
4 to 5 141775 -0.3963 0.345959
3 to 4 141980 0.2085 0.582568
2 to 3 141515 -1.1632 0.122371
1 to 2 141902 -0.0216 0.491375
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2466.65 -0.472 0.318608
Test results for specific bytes for dh-ranFile-2018-07-08_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2347.40 -2.158 0.015463
2 to 9 2475.11 -0.352 0.362400
3 to 10 2517.39 0.246 0.597149
4 to 11 2538.35 0.542 0.706211
5 to 12 2549.64 0.702 0.758643
6 to 13 2435.30 -0.915 0.180085
7 to 14 2439.64 -0.854 0.196640
8 to 15 2446.33 -0.759 0.223937
9 to 16 2553.22 0.753 0.774163
10 to 17 2456.61 -0.614 0.269715
11 to 18 2461.07 -0.550 0.290990
12 to 19 2438.83 -0.865 0.193511
13 to 20 2492.33 -0.108 0.456815
14 to 21 2464.76 -0.498 0.309126
15 to 22 2436.43 -0.899 0.184327
16 to 23 2459.07 -0.579 0.281335
17 to 24 2383.84 -1.643 0.050217
18 to 25 2611.57 1.578 0.942702
19 to 26 2474.25 -0.364 0.357846
20 to 27 2395.56 -1.477 0.069843
21 to 28 2433.47 -0.941 0.173384
22 to 29 2430.39 -0.984 0.162449
23 to 30 2371.16 -1.822 0.034226
24 to 31 2572.55 1.026 0.847542
25 to 32 2536.94 0.522 0.699305
CDPARK for dh-ranFile-2018-07-08_19:31: 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
3491 -1.4612 0.071982
3496 -1.2329 0.108811
3485 -1.7352 0.041356
3475 -2.1918 0.014198
3516 -0.3196 0.374623
3547 1.0959 0.863437
3508 -0.6849 0.246694
3475 -2.1918 0.014198
3505 -0.8219 0.205562
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3501.20 sample std.=20.75
p-value of the KSTEST for those 10 p-values: 0.001578
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_19:31
0.0301,0.0496,0.3700,0.5301,0.8425,0.0635,0.3294,0.1044,0.1314,0.8025,
The KS test for those 10 p-values: 0.050922
The 3DSPHERES test for dh-ranFile-2018-07-08_19:31
sample no r^3 equiv. uni.
1 20.340 0.492369
2 26.843 0.591291
3 3.508 0.110368
4 32.798 0.664877
5 68.619 0.898459
6 64.635 0.884039
7 17.752 0.446636
8 3.078 0.097515
9 118.922 0.981014
10 15.316 0.399828
11 4.681 0.144463
12 20.782 0.499791
13 8.758 0.253171
14 166.482 0.996110
15 8.124 0.237237
16 18.405 0.458554
17 46.196 0.785594
18 53.502 0.831932
19 16.512 0.423289
20 21.444 0.510718
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.689039
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 1.5 0.6 0.9 -0.8
0.7 -0.1 -0.1 -0.1 0.4 1.6
0.4 0.7 -0.6 -1.1 1.7 -0.3
-1.1 -0.7 0.6 -0.1 1.6 -1.0
-0.3 -0.6 -0.7 0.8 -1.1 -0.9
-1.0 0.1 -1.8 0.4 -0.8 -0.7
-0.5 -0.7 3.4 -0.1 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:41.148550
z-score=-0.092901, p-value=0.491785
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_19:31
Test no p-value
1 0.612361
2 0.159022
3 0.046378
4 0.018561
5 0.022308
6 0.003805
7 0.443444
8 0.013124
9 0.370780
10 0.116539
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000054
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_19:31:
(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 66483 0.51 66637 0.01
3 25000.00 25201 1.62 24928 0.21
4 6666.67 6627 0.24 6786 2.14
5 1388.89 1393 0.01 1389 0.00
6 238.10 249 0.50 222 1.09
7 34.72 43 1.97 33 0.09
8 4.96 3 0.77 4 0.19
p=0.53279 p=0.28490
Number of rngs required: 687975, p-value: 0.311
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_19:31
No. of wins: Observed Expected
98641 98585.9
z-score= 0.247, pvalue=0.59740
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66859 66666.7 0.555 0.555
2 37440 37654.3 1.220 1.775
3 27161 26954.7 1.578 3.353
4 19332 19313.5 0.018 3.371
5 13779 13851.4 0.379 3.750
6 9966 9943.5 0.051 3.800
7 7150 7145.0 0.003 3.804
8 5075 5139.1 0.799 4.603
9 3720 3699.9 0.110 4.712
10 2700 2666.3 0.426 5.138
11 1885 1923.3 0.764 5.902
12 1352 1388.7 0.972 6.874
13 1030 1003.7 0.688 7.562
14 749 726.1 0.720 8.282
15 495 525.8 1.808 10.090
16 348 381.2 2.883 12.974
17 268 276.5 0.264 13.237
18 172 200.8 4.139 17.376
19 140 146.0 0.245 17.621
20 89 106.2 2.790 20.411
21 290 287.1 0.029 20.440
Chisq= 20.44 for 20 degrees of freedom, p= 0.56930
SUMMARY of craptest
p-value for no. of wins: 0.597401
p-value for throws/game: 0.569302
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_19:31
No. of wins: Observed Expected
97956 98585.9
z-score=-2.817, pvalue=0.00242
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66957 66666.7 1.264 1.264
2 37323 37654.3 2.915 4.180
3 27117 26954.7 0.977 5.157
4 19048 19313.5 3.649 8.805
5 13759 13851.4 0.617 9.422
6 10080 9943.5 1.873 11.295
7 7120 7145.0 0.088 11.382
8 5150 5139.1 0.023 11.405
9 3763 3699.9 1.077 12.483
10 2704 2666.3 0.533 13.016
11 1987 1923.3 2.108 15.124
12 1384 1388.7 0.016 15.140
13 1005 1003.7 0.002 15.142
14 701 726.1 0.870 16.012
15 518 525.8 0.117 16.129
16 382 381.2 0.002 16.131
17 280 276.5 0.043 16.174
18 203 200.8 0.023 16.197
19 147 146.0 0.007 16.204
20 89 106.2 2.790 18.995
21 283 287.1 0.059 19.054
Chisq= 19.05 for 20 degrees of freedom, p= 0.48166
SUMMARY of craptest
p-value for no. of wins: 0.002423
p-value for throws/game: 0.481658
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0016,0.0024,0.0038,0.0052,0.0131,0.0140,0.0142,0.0142,0.0155,
0.0186,0.0211,0.0223,0.0235,0.0301,0.0342,0.0342,0.0414,0.0427,0.0464,
0.0496,0.0502,0.0502,0.0509,0.0515,0.0588,0.0635,0.0639,0.0647,0.0698,
0.0720,0.0759,0.0841,0.0880,0.0890,0.0896,0.0913,0.0923,0.0975,0.1044,
0.1064,0.1088,0.1104,0.1165,0.1184,0.1205,0.1224,0.1314,0.1445,0.1464,
0.1470,0.1484,0.1590,0.1624,0.1676,0.1684,0.1727,0.1727,0.1734,0.1743,
0.1801,0.1843,0.1935,0.1966,0.2056,0.2105,0.2117,0.2175,0.2195,0.2231,
0.2239,0.2283,0.2372,0.2459,0.2466,0.2467,0.2531,0.2532,0.2577,0.2607,
0.2697,0.2799,0.2809,0.2813,0.2841,0.2849,0.2863,0.2910,0.2924,0.2950,
0.3025,0.3091,0.3099,0.3109,0.3186,0.3232,0.3234,0.3270,0.3278,0.3294,
0.3304,0.3406,0.3442,0.3460,0.3517,0.3519,0.3578,0.3580,0.3582,0.3624,
0.3662,0.3700,0.3706,0.3708,0.3746,0.3771,0.3913,0.3962,0.3965,0.3972,
0.3998,0.4002,0.4029,0.4033,0.4132,0.4138,0.4167,0.4233,0.4423,0.4434,
0.4445,0.4461,0.4466,0.4516,0.4568,0.4586,0.4588,0.4718,0.4727,0.4764,
0.4817,0.4842,0.4914,0.4918,0.4924,0.4998,0.5092,0.5107,0.5117,0.5167,
0.5187,0.5301,0.5302,0.5328,0.5366,0.5370,0.5481,0.5499,0.5521,0.5637,
0.5693,0.5826,0.5831,0.5863,0.5913,0.5918,0.5971,0.5974,0.5976,0.5984,
0.5986,0.6001,0.6041,0.6119,0.6124,0.6365,0.6414,0.6472,0.6637,0.6649,
0.6739,0.6830,0.6890,0.6993,0.7042,0.7054,0.7062,0.7115,0.7116,0.7151,
0.7151,0.7191,0.7211,0.7231,0.7261,0.7268,0.7276,0.7285,0.7299,0.7322,
0.7586,0.7632,0.7677,0.7708,0.7714,0.7742,0.7856,0.7863,0.8025,0.8080,
0.8172,0.8216,0.8223,0.8238,0.8272,0.8316,0.8319,0.8377,0.8425,0.8475,
0.8523,0.8523,0.8539,0.8594,0.8634,0.8671,0.8694,0.8700,0.8713,0.8731,
0.8748,0.8756,0.8792,0.8813,0.8813,0.8814,0.8840,0.8937,0.8985,0.9084,
0.9091,0.9201,0.9206,0.9264,0.9289,0.9309,0.9357,0.9386,0.9399,0.9427,
0.9462,0.9473,0.9485,0.9640,0.9721,0.9733,0.9751,0.9760,0.9777,0.9810,
0.9869,0.9888,0.9902,0.9941,0.9960,0.9961,0.9961,0.9980,0.9997,
Overall p-value after applying KStest on 269 p-values = 0.074592
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.