RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 15.9606 0.473367
2 to 25 15.67 17.5970 0.585322
3 to 26 15.55 28.1613 0.956912
4 to 27 15.82 11.2182 0.155001
5 to 28 15.79 25.3897 0.913680
6 to 29 15.77 11.1584 0.151788
7 to 30 15.53 22.9566 0.849330
8 to 31 15.92 23.4841 0.865857
9 to 32 15.68 37.4858 0.997110
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.061745
Tough bday spacings test for dh-ranFile-2018-06-28_13:31: 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 6 38 67 111 108 72 52 23 5 9 9
(O-E)^2/E 1.1 0.1 0.5 1.8 1.1 0.5 0.0 1.5 6.6 0.9 6.0
Birthday Spacings: Sum(O-E)^2/E= 20.014, p= 0.971
RESULTS OF GCD FOR dh-ranFile-2018-06-28_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.613731
p-value, dist. of gcd's: 0.649947
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.943 0.433 0.976 0.336 0.162 0.597 0.294 0.397
Bits 8 to 15---> 0.900 0.882 0.498 0.903 0.451 0.329 0.234 0.493
Bits 16 to 23---> 0.864 0.850 0.523 0.616 0.451 0.559 0.673 0.090
Bits 24 to 31---> 0.570 0.858 0.773 0.489 0.647 0.187 0.599 0.671
KS test for the above 32 p values: 0.827
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_13:31,
p-values for 5 runs: 0.8332, 0.4688, 0.1453, 0.5675, 0.7401
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5142 5134.0 0.012 0.742
r= 30 23239 23103.0 0.800 1.542
r= 31 11420 11551.5 1.498 3.039
chi-square = 3.039 with df = 3; p-value = 0.614
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5178 5134.0 0.377 0.582
r= 31 23109 23103.0 0.002 0.583
r= 32 11495 11551.5 0.277 0.860
chi-square = 0.860 with df = 3; p-value = 0.165
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_13:31
b-rank test for bits 1 to 8, p=0.88588
b-rank test for bits 2 to 9, p=0.48433
b-rank test for bits 3 to 10, p=0.62261
b-rank test for bits 4 to 11, p=0.48606
b-rank test for bits 5 to 12, p=0.32724
b-rank test for bits 6 to 13, p=0.59205
b-rank test for bits 7 to 14, p=0.36519
b-rank test for bits 8 to 15, p=0.28127
b-rank test for bits 9 to 16, p=0.75867
b-rank test for bits 10 to 17, p=0.11073
b-rank test for bits 11 to 18, p=0.92017
b-rank test for bits 12 to 19, p=0.99129
b-rank test for bits 13 to 20, p=0.39276
b-rank test for bits 14 to 21, p=0.27888
b-rank test for bits 15 to 22, p=0.15298
b-rank test for bits 16 to 23, p=0.53226
b-rank test for bits 17 to 24, p=0.02895
b-rank test for bits 18 to 25, p=0.33273
b-rank test for bits 19 to 26, p=0.35448
b-rank test for bits 20 to 27, p=0.26992
b-rank test for bits 21 to 28, p=0.46266
b-rank test for bits 22 to 29, p=0.53647
b-rank test for bits 23 to 30, p=0.22178
b-rank test for bits 24 to 31, p=0.73024
b-rank test for bits 25 to 32, p=0.39593
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 = 0.394394
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_13:31
(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 141040 -2.03 0.021120
2 142033 0.29 0.613690
3 142549 1.49 0.932485
4 141692 -0.51 0.305804
5 141848 -0.14 0.443029
6 141325 -1.37 0.086086
7 142391 1.13 0.869790
8 142239 0.77 0.779426
9 141591 -0.74 0.228510
10 141297 -1.43 0.076261
11 142146 0.55 0.709857
12 142201 0.68 0.752214
13 142515 1.42 0.921483
14 141983 0.17 0.568331
15 142851 2.20 0.986102
16 141971 0.14 0.557285
17 141551 -0.84 0.201235
18 141453 -1.07 0.143169
19 142054 0.34 0.632324
20 142308 0.93 0.824195
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_13:31
Bits used No. missing words z-score p-value
23 to 32 141583 -1.1253 0.130236
22 to 31 142055 0.5023 0.692275
21 to 30 142215 1.0540 0.854066
20 to 29 142082 0.5954 0.724217
19 to 28 142436 1.8161 0.965323
18 to 27 142127 0.7506 0.773549
17 to 26 142187 0.9575 0.830838
16 to 25 141853 -0.1942 0.422994
15 to 24 142351 1.5230 0.936121
14 to 23 141840 -0.2391 0.405526
13 to 22 142219 1.0678 0.857201
12 to 21 141861 -0.1667 0.433821
11 to 20 142110 0.6920 0.755521
10 to 19 141424 -1.6736 0.047109
9 to 18 141710 -0.6873 0.245933
8 to 17 141682 -0.7839 0.216550
7 to 16 142085 0.6058 0.727663
6 to 15 142231 1.1092 0.866330
5 to 14 142189 0.9644 0.832572
4 to 13 141887 -0.0770 0.469312
3 to 12 141972 0.2161 0.585547
2 to 11 141330 -1.9977 0.022875
1 to 10 141799 -0.3804 0.351806
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_13:31
Bits used No. missing words z-score p-value
28 to 32 141499 -1.3909 0.082120
27 to 31 141578 -1.1232 0.130686
26 to 30 141771 -0.4689 0.319565
25 to 29 141910 0.0023 0.500906
24 to 28 142107 0.6701 0.748593
23 to 27 142089 0.6091 0.728755
22 to 26 142393 1.6396 0.949452
21 to 25 142306 1.3446 0.910630
20 to 24 141972 0.2124 0.584118
19 to 23 142355 1.5107 0.934573
18 to 22 141867 -0.1435 0.442951
17 to 21 142115 0.6972 0.757157
16 to 20 142664 2.5582 0.994739
15 to 19 142265 1.2057 0.886026
14 to 18 141585 -1.0994 0.135792
13 to 17 142169 0.8802 0.810635
12 to 16 141755 -0.5232 0.300434
11 to 15 141519 -1.3232 0.092892
10 to 14 141135 -2.6248 0.004334
9 to 13 142765 2.9006 0.998138
8 to 12 141624 -0.9672 0.166717
7 to 11 141689 -0.7469 0.227568
6 to 10 142339 1.4565 0.927374
5 to 9 141729 -0.6113 0.270504
4 to 8 141610 -1.0147 0.155130
3 to 7 142172 0.8904 0.813376
2 to 6 141650 -0.8791 0.189678
1 to 5 141600 -1.0486 0.147187
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_13:31
Bits used No. missing words z-score p-value
31 to 32 141879 -0.0895 0.464355
30 to 31 141809 -0.2960 0.383631
29 to 30 141856 -0.1573 0.437498
28 to 29 141148 -2.2458 0.012358
27 to 28 142133 0.6598 0.745307
26 to 27 142107 0.5831 0.720086
25 to 26 142238 0.9695 0.833859
24 to 25 141275 -1.8712 0.030660
23 to 24 141546 -1.0718 0.141912
22 to 23 141917 0.0226 0.509025
21 to 22 142023 0.3353 0.631304
20 to 21 141672 -0.7001 0.241936
19 to 20 141944 0.1023 0.540729
18 to 19 141680 -0.6765 0.249365
17 to 18 142907 2.9430 0.998375
16 to 17 141196 -2.1042 0.017680
15 to 16 141895 -0.0423 0.483141
14 to 15 141572 -0.9951 0.159850
13 to 14 141922 0.0374 0.514907
12 to 13 142373 1.3678 0.914306
11 to 12 142322 1.2173 0.888258
10 to 11 142196 0.8456 0.801122
9 to 10 142705 2.3471 0.990540
8 to 9 141063 -2.4965 0.006270
7 to 8 142427 1.5271 0.936626
6 to 7 141992 0.2439 0.596332
5 to 6 141611 -0.8800 0.189422
4 to 5 141904 -0.0157 0.493728
3 to 4 141551 -1.0570 0.145251
2 to 3 142926 2.9990 0.998646
1 to 2 142101 0.5654 0.714099
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2430.35 -0.985 0.162314
Test results for specific bytes for dh-ranFile-2018-06-28_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2433.50 -0.940 0.173494
2 to 9 2412.53 -1.237 0.108049
3 to 10 2511.22 0.159 0.563037
4 to 11 2492.26 -0.109 0.456422
5 to 12 2564.37 0.910 0.818673
6 to 13 2401.76 -1.389 0.082377
7 to 14 2367.13 -1.879 0.030116
8 to 15 2535.72 0.505 0.693269
9 to 16 2380.19 -1.694 0.045094
10 to 17 2596.94 1.371 0.914804
11 to 18 2483.05 -0.240 0.405297
12 to 19 2563.85 0.903 0.816732
13 to 20 2555.18 0.780 0.782403
14 to 21 2610.11 1.557 0.940293
15 to 22 2578.77 1.114 0.867362
16 to 23 2469.95 -0.425 0.335446
17 to 24 2544.93 0.635 0.737433
18 to 25 2463.13 -0.521 0.301019
19 to 26 2395.39 -1.479 0.069520
20 to 27 2502.91 0.041 0.516393
21 to 28 2524.14 0.341 0.633585
22 to 29 2436.21 -0.902 0.183510
23 to 30 2447.25 -0.746 0.227815
24 to 31 2497.23 -0.039 0.484382
25 to 32 2444.63 -0.783 0.216785
CDPARK for dh-ranFile-2018-06-28_13:31: 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
3529 0.2740 0.607947
3557 1.5525 0.939730
3517 -0.2740 0.392053
3512 -0.5023 0.307734
3527 0.1826 0.572463
3479 -2.0091 0.022262
3514 -0.4110 0.340551
3535 0.5479 0.708135
3480 -1.9635 0.024796
3545 1.0046 0.842447
Square side=100, avg. no. parked=3519.50 sample std.=23.95
p-value of the KSTEST for those 10 p-values: 0.787310
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_13:31
0.0970,0.6095,0.6622,0.4212,0.3366,0.6694,0.1044,0.1159,0.0185,0.9395,
The KS test for those 10 p-values: 0.345594
The 3DSPHERES test for dh-ranFile-2018-06-28_13:31
sample no r^3 equiv. uni.
1 20.000 0.486584
2 9.924 0.281646
3 10.960 0.306025
4 44.101 0.770086
5 28.798 0.617080
6 50.293 0.812961
7 128.404 0.986159
8 2.301 0.073827
9 4.946 0.152002
10 61.092 0.869501
11 53.543 0.832162
12 6.800 0.202805
13 44.001 0.769311
14 52.139 0.824124
15 11.469 0.317713
16 6.408 0.192334
17 24.178 0.553332
18 3.061 0.096995
19 37.457 0.713085
20 88.274 0.947265
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.731403
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -2.0 -0.8 1.1 -1.0 0.5
1.8 -0.2 -0.5 -0.3 -1.3 0.5
-0.6 0.9 -0.7 -0.5 -0.1 -0.2
1.5 -1.1 -0.7 1.1 1.8 -0.7
0.2 0.0 0.9 -0.7 -0.5 -1.2
0.9 0.4 -0.6 1.2 0.2 -0.8
1.0 -1.3 -1.6 0.4 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:39.386334
z-score=-0.285174, p-value=0.413671
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_13:31
Test no p-value
1 0.397664
2 0.724808
3 0.056814
4 0.001559
5 0.514077
6 0.998504
7 0.943906
8 0.421464
9 0.422715
10 0.043692
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.195141
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_13:31:
(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 66531 0.28 66408 1.00
3 25000.00 25145 0.84 25099 0.39
4 6666.67 6643 0.08 6829 3.95
5 1388.89 1401 0.11 1380 0.06
6 238.10 234 0.07 242 0.06
7 34.72 36 0.05 34 0.01
8 4.96 9 3.29 7 0.84
p=0.41915 p=0.61203
Number of rngs required: 688358, p-value: 0.479
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_13:31
No. of wins: Observed Expected
98809 98585.9
z-score= 0.998, pvalue=0.84086
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66666 66666.7 0.000 0.000
2 37715 37654.3 0.098 0.098
3 26839 26954.7 0.497 0.595
4 19491 19313.5 1.632 2.227
5 13968 13851.4 0.981 3.208
6 9894 9943.5 0.247 3.455
7 7105 7145.0 0.224 3.679
8 5168 5139.1 0.163 3.842
9 3540 3699.9 6.907 10.749
10 2638 2666.3 0.300 11.050
11 1924 1923.3 0.000 11.050
12 1373 1388.7 0.178 11.228
13 964 1003.7 1.571 12.800
14 749 726.1 0.720 13.519
15 531 525.8 0.051 13.570
16 416 381.2 3.186 16.756
17 291 276.5 0.756 17.513
18 213 200.8 0.737 18.250
19 151 146.0 0.172 18.422
20 107 106.2 0.006 18.428
21 257 287.1 3.159 21.587
Chisq= 21.59 for 20 degrees of freedom, p= 0.63665
SUMMARY of craptest
p-value for no. of wins: 0.840865
p-value for throws/game: 0.636647
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_13:31
No. of wins: Observed Expected
98470 98585.9
z-score=-0.518, pvalue=0.30216
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66710 66666.7 0.028 0.028
2 37616 37654.3 0.039 0.067
3 26818 26954.7 0.694 0.761
4 19458 19313.5 1.082 1.842
5 13938 13851.4 0.541 2.384
6 9832 9943.5 1.251 3.635
7 7183 7145.0 0.202 3.837
8 5200 5139.1 0.722 4.559
9 3627 3699.9 1.435 5.994
10 2705 2666.3 0.562 6.556
11 1877 1923.3 1.116 7.672
12 1350 1388.7 1.081 8.753
13 999 1003.7 0.022 8.775
14 787 726.1 5.101 13.875
15 525 525.8 0.001 13.877
16 358 381.2 1.406 15.283
17 280 276.5 0.043 15.326
18 185 200.8 1.248 16.574
19 170 146.0 3.951 20.525
20 101 106.2 0.256 20.781
21 281 287.1 0.130 20.911
Chisq= 20.91 for 20 degrees of freedom, p= 0.59761
SUMMARY of craptest
p-value for no. of wins: 0.302164
p-value for throws/game: 0.597611
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0043,0.0063,0.0124,0.0177,0.0185,0.0211,0.0223,0.0229,0.0248,
0.0290,0.0301,0.0307,0.0437,0.0451,0.0471,0.0568,0.0617,0.0695,0.0738,
0.0763,0.0821,0.0824,0.0861,0.0900,0.0929,0.0970,0.0970,0.1044,0.1080,
0.1107,0.1159,0.1302,0.1307,0.1358,0.1419,0.1432,0.1453,0.1453,0.1472,
0.1518,0.1520,0.1530,0.1550,0.1551,0.1599,0.1617,0.1623,0.1649,0.1667,
0.1735,0.1835,0.1870,0.1894,0.1897,0.1923,0.1951,0.2012,0.2028,0.2166,
0.2168,0.2218,0.2276,0.2278,0.2285,0.2335,0.2419,0.2459,0.2494,0.2699,
0.2705,0.2789,0.2813,0.2816,0.2943,0.3004,0.3010,0.3022,0.3058,0.3060,
0.3077,0.3177,0.3196,0.3272,0.3287,0.3327,0.3354,0.3359,0.3366,0.3406,
0.3456,0.3518,0.3545,0.3652,0.3836,0.3921,0.3928,0.3944,0.3959,0.3966,
0.3977,0.4053,0.4055,0.4137,0.4191,0.4212,0.4215,0.4227,0.4230,0.4328,
0.4338,0.4375,0.4430,0.4430,0.4511,0.4513,0.4564,0.4627,0.4644,0.4688,
0.4693,0.4734,0.4794,0.4831,0.4843,0.4844,0.4861,0.4866,0.4894,0.4935,
0.4937,0.4980,0.5009,0.5090,0.5141,0.5149,0.5164,0.5229,0.5323,0.5365,
0.5407,0.5533,0.5573,0.5594,0.5630,0.5675,0.5683,0.5697,0.5725,0.5841,
0.5853,0.5855,0.5920,0.5963,0.5973,0.5976,0.5988,0.6079,0.6095,0.6120,
0.6137,0.6137,0.6144,0.6163,0.6171,0.6226,0.6313,0.6323,0.6336,0.6366,
0.6468,0.6499,0.6622,0.6694,0.6711,0.6729,0.6923,0.6933,0.7081,0.7099,
0.7131,0.7141,0.7201,0.7242,0.7248,0.7277,0.7288,0.7302,0.7314,0.7374,
0.7401,0.7453,0.7486,0.7522,0.7555,0.7572,0.7587,0.7693,0.7701,0.7730,
0.7735,0.7794,0.7824,0.7873,0.8011,0.8106,0.8130,0.8134,0.8167,0.8187,
0.8241,0.8242,0.8271,0.8308,0.8322,0.8326,0.8332,0.8339,0.8409,0.8424,
0.8493,0.8503,0.8541,0.8572,0.8578,0.8639,0.8659,0.8663,0.8674,0.8695,
0.8698,0.8815,0.8859,0.8860,0.8883,0.9004,0.9035,0.9106,0.9137,0.9143,
0.9148,0.9202,0.9215,0.9274,0.9325,0.9346,0.9361,0.9366,0.9395,0.9397,
0.9403,0.9427,0.9439,0.9473,0.9495,0.9569,0.9653,0.9709,0.9755,0.9861,
0.9862,0.9905,0.9913,0.9947,0.9971,0.9981,0.9984,0.9985,0.9986,
Overall p-value after applying KStest on 269 p-values = 0.401034
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.