RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.78 17.2807 0.564489
2 to 25 15.67 27.3826 0.947310
3 to 26 15.47 21.5934 0.799134
4 to 27 15.82 20.9127 0.769780
5 to 28 15.99 17.6399 0.588106
6 to 29 15.68 11.5435 0.173042
7 to 30 16.00 11.7543 0.185220
8 to 31 16.02 15.3641 0.430725
9 to 32 15.90 15.5671 0.445294
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.885207
Tough bday spacings test for dh-ranFile-2018-06-19_08:31: 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 8 45 57 103 93 87 49 31 18 6 3
(O-E)^2/E 0.1 1.9 3.6 0.3 0.2 1.0 0.2 0.1 0.7 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 8.409, p= 0.411
RESULTS OF GCD FOR dh-ranFile-2018-06-19_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.019963
p-value, dist. of gcd's: 0.375420
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.286 0.306 0.981 0.308 0.549 0.576 0.629 0.042
Bits 8 to 15---> 0.649 0.352 0.957 0.504 0.811 0.311 0.094 0.966
Bits 16 to 23---> 0.191 0.360 0.403 0.269 0.420 0.370 0.703 0.885
Bits 24 to 31---> 0.900 0.281 0.200 0.033 0.565 0.171 0.387 0.145
KS test for the above 32 p values: 0.571
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_08:31,
p-values for 5 runs: 0.5863, 0.0743, 0.6369, 0.5114, 0.1632
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5077 5134.0 0.633 1.639
r= 30 23062 23103.0 0.073 1.712
r= 31 11635 11551.5 0.603 2.315
chi-square = 2.315 with df = 3; p-value = 0.490
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5085 5134.0 0.468 0.615
r= 31 22985 23103.0 0.603 1.218
r= 32 11713 11551.5 2.257 3.476
chi-square = 3.476 with df = 3; p-value = 0.676
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_08:31
b-rank test for bits 1 to 8, p=0.47478
b-rank test for bits 2 to 9, p=0.00573
b-rank test for bits 3 to 10, p=0.44674
b-rank test for bits 4 to 11, p=0.94977
b-rank test for bits 5 to 12, p=0.43485
b-rank test for bits 6 to 13, p=0.02044
b-rank test for bits 7 to 14, p=0.29828
b-rank test for bits 8 to 15, p=0.12833
b-rank test for bits 9 to 16, p=0.59578
b-rank test for bits 10 to 17, p=0.60174
b-rank test for bits 11 to 18, p=0.14489
b-rank test for bits 12 to 19, p=0.45565
b-rank test for bits 13 to 20, p=0.12125
b-rank test for bits 14 to 21, p=0.18311
b-rank test for bits 15 to 22, p=0.19336
b-rank test for bits 16 to 23, p=0.44104
b-rank test for bits 17 to 24, p=0.16393
b-rank test for bits 18 to 25, p=0.07770
b-rank test for bits 19 to 26, p=0.44327
b-rank test for bits 20 to 27, p=0.43499
b-rank test for bits 21 to 28, p=0.24887
b-rank test for bits 22 to 29, p=0.17109
b-rank test for bits 23 to 30, p=0.35817
b-rank test for bits 24 to 31, p=0.47946
b-rank test for bits 25 to 32, p=0.10651
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 = 0.002020
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_08:31
(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 142016 0.25 0.598408
2 141284 -1.46 0.072001
3 141246 -1.55 0.060590
4 141918 0.02 0.508081
5 141694 -0.50 0.307444
6 142050 0.33 0.628797
7 141686 -0.52 0.300905
8 142461 1.29 0.901292
9 142035 0.29 0.615476
10 141546 -0.85 0.197968
11 141561 -0.81 0.207864
12 142613 1.64 0.949921
13 141932 0.05 0.521121
14 142652 1.74 0.958648
15 142441 1.24 0.892922
16 142367 1.07 0.857538
17 141454 -1.06 0.143697
18 141649 -0.61 0.271512
19 141224 -1.60 0.054662
20 142412 1.17 0.879895
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_08:31
Bits used No. missing words z-score p-value
23 to 32 141569 -1.1736 0.120287
22 to 31 141982 0.2506 0.598933
21 to 30 142006 0.3333 0.630563
20 to 29 141603 -1.0563 0.145413
19 to 28 141681 -0.7873 0.215540
18 to 27 142129 0.7575 0.775620
17 to 26 142017 0.3713 0.644784
16 to 25 142695 2.7092 0.996628
15 to 24 142295 1.3299 0.908224
14 to 23 141756 -0.5287 0.298498
13 to 22 141763 -0.5046 0.306925
12 to 21 141708 -0.6942 0.243765
11 to 20 141640 -0.9287 0.176516
10 to 19 141775 -0.4632 0.321608
9 to 18 141788 -0.4184 0.337835
8 to 17 142217 1.0609 0.855639
7 to 16 141978 0.2368 0.593591
6 to 15 141502 -1.4046 0.080072
5 to 14 141589 -1.1046 0.134669
4 to 13 141748 -0.5563 0.288999
3 to 12 141892 -0.0598 0.476174
2 to 11 142186 0.9540 0.829967
1 to 10 142155 0.8471 0.801541
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_08:31
Bits used No. missing words z-score p-value
28 to 32 141653 -0.8689 0.192447
27 to 31 142553 2.1819 0.985443
26 to 30 142052 0.4836 0.685675
25 to 29 142187 0.9413 0.826713
24 to 28 141281 -2.1299 0.016589
23 to 27 142858 3.2158 0.999350
22 to 26 141767 -0.4825 0.314734
21 to 25 141651 -0.8757 0.190598
20 to 24 142072 0.5514 0.709328
19 to 23 141516 -1.3333 0.091213
18 to 22 141629 -0.9503 0.170987
17 to 21 141710 -0.6757 0.249617
16 to 20 141841 -0.2316 0.408414
15 to 19 142295 1.3074 0.904454
14 to 18 141823 -0.2926 0.384897
13 to 17 142209 1.0158 0.845145
12 to 16 141826 -0.2825 0.388790
11 to 15 141843 -0.2248 0.411049
10 to 14 142122 0.7209 0.764519
9 to 13 141648 -0.8859 0.187845
8 to 12 141581 -1.1130 0.132858
7 to 11 141432 -1.6181 0.052824
6 to 10 141284 -2.1198 0.017013
5 to 9 141721 -0.6384 0.261605
4 to 8 141414 -1.6791 0.046568
3 to 7 141864 -0.1537 0.438939
2 to 6 141879 -0.1028 0.459056
1 to 5 141842 -0.2282 0.409731
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_08:31
Bits used No. missing words z-score p-value
31 to 32 141542 -1.0836 0.139278
30 to 31 141554 -1.0482 0.147280
29 to 30 141227 -2.0128 0.022069
28 to 29 141769 -0.4140 0.339454
27 to 28 142056 0.4327 0.667367
26 to 27 141944 0.1023 0.540729
25 to 26 141397 -1.5113 0.065356
24 to 25 141687 -0.6558 0.255963
23 to 24 142182 0.8043 0.789399
22 to 23 142328 1.2350 0.891588
21 to 22 142878 2.8574 0.997865
20 to 21 141543 -1.0806 0.139933
19 to 20 141650 -0.7650 0.222140
18 to 19 141536 -1.1013 0.135390
17 to 18 142202 0.8633 0.806023
16 to 17 142191 0.8309 0.796981
15 to 16 142129 0.6480 0.741506
14 to 15 142150 0.7099 0.761130
13 to 14 142100 0.5624 0.713095
12 to 13 142032 0.3619 0.641271
11 to 12 141901 -0.0246 0.490198
10 to 11 142370 1.3589 0.912912
9 to 10 142205 0.8722 0.808446
8 to 9 142048 0.4091 0.658751
7 to 8 141806 -0.3048 0.380256
6 to 7 141725 -0.5437 0.293308
5 to 6 141570 -1.0010 0.158420
4 to 5 141899 -0.0305 0.487845
3 to 4 142310 1.1819 0.881381
2 to 3 141462 -1.3196 0.093491
1 to 2 141502 -1.2016 0.114766
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2572.75 1.029 0.848232
Test results for specific bytes for dh-ranFile-2018-06-19_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2621.44 1.717 0.957043
2 to 9 2518.47 0.261 0.603045
3 to 10 2470.60 -0.416 0.338792
4 to 11 2533.84 0.479 0.683874
5 to 12 2451.91 -0.680 0.248225
6 to 13 2500.36 0.005 0.502040
7 to 14 2512.25 0.173 0.568753
8 to 15 2672.49 2.439 0.992645
9 to 16 2539.51 0.559 0.711853
10 to 17 2477.75 -0.315 0.376503
11 to 18 2576.92 1.088 0.861649
12 to 19 2416.88 -1.175 0.119906
13 to 20 2459.34 -0.575 0.282657
14 to 21 2439.53 -0.855 0.196220
15 to 22 2348.34 -2.145 0.015986
16 to 23 2582.79 1.171 0.879161
17 to 24 2509.51 0.134 0.553477
18 to 25 2539.88 0.564 0.713642
19 to 26 2545.71 0.646 0.741006
20 to 27 2580.06 1.132 0.871235
21 to 28 2494.39 -0.079 0.468401
22 to 29 2613.31 1.602 0.945464
23 to 30 2482.27 -0.251 0.401026
24 to 31 2577.04 1.090 0.862044
25 to 32 2450.15 -0.705 0.240402
CDPARK for dh-ranFile-2018-06-19_08:31: 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
3501 -1.0046 0.157553
3554 1.4155 0.921543
3508 -0.6849 0.246694
3523 0.0000 0.500000
3536 0.5936 0.723613
3551 1.2785 0.899470
3514 -0.4110 0.340551
3516 -0.3196 0.374623
3560 1.6895 0.954438
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3528.20 sample std.=19.67
p-value of the KSTEST for those 10 p-values: 0.681159
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_08:31
0.2830,0.5998,0.0406,0.1447,0.3612,0.2310,0.6585,0.7230,0.5367,0.7816,
The KS test for those 10 p-values: 0.746338
The 3DSPHERES test for dh-ranFile-2018-06-19_08:31
sample no r^3 equiv. uni.
1 0.348 0.011527
2 2.259 0.072534
3 16.852 0.429783
4 3.756 0.117678
5 2.590 0.082721
6 19.414 0.476449
7 41.858 0.752230
8 62.232 0.874370
9 29.848 0.630250
10 0.891 0.029279
11 58.621 0.858301
12 0.188 0.006251
13 3.951 0.123408
14 10.170 0.287515
15 101.270 0.965805
16 16.216 0.417567
17 86.288 0.943655
18 1.317 0.042942
19 9.996 0.283366
20 1.959 0.063209
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.012498
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -1.1 0.2 -1.0 0.7
-0.2 0.6 0.7 0.6 0.3 -0.6
0.1 0.5 0.8 0.9 -0.6 0.2
0.7 -1.5 0.6 -0.8 -0.1 -0.9
-0.6 -0.1 0.8 -0.4 -1.4 -1.5
0.7 -0.7 0.5 1.7 -0.9 1.0
-0.2 -0.7 0.1 1.0 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:25.475915
z-score=-1.802926, p-value=0.020702
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_08:31
Test no p-value
1 0.029292
2 0.762437
3 0.526681
4 0.553356
5 0.002207
6 0.041594
7 0.177065
8 0.474427
9 0.760344
10 0.036510
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.024631
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_08:31:
(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 66970 1.38 66812 0.32
3 25000.00 24798 1.63 24834 1.10
4 6666.67 6567 1.49 6648 0.05
5 1388.89 1390 0.00 1433 1.40
6 238.10 230 0.28 233 0.11
7 34.72 39 0.53 35 0.00
8 4.96 5 0.00 4 0.19
p=0.49485 p=0.21269
Number of rngs required: 687983, p-value: 0.314
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_08:31
No. of wins: Observed Expected
98580 98585.9
z-score=-0.026, pvalue=0.48955
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66539 66666.7 0.244 0.244
2 37999 37654.3 3.155 3.400
3 26983 26954.7 0.030 3.429
4 19461 19313.5 1.127 4.556
5 13699 13851.4 1.677 6.234
6 9976 9943.5 0.106 6.339
7 6963 7145.0 4.637 10.977
8 5074 5139.1 0.824 11.801
9 3656 3699.9 0.520 12.321
10 2706 2666.3 0.591 12.912
11 1930 1923.3 0.023 12.935
12 1383 1388.7 0.024 12.959
13 994 1003.7 0.094 13.053
14 702 726.1 0.803 13.855
15 522 525.8 0.028 13.883
16 385 381.2 0.039 13.922
17 269 276.5 0.206 14.128
18 210 200.8 0.419 14.547
19 139 146.0 0.334 14.881
20 114 106.2 0.571 15.451
21 296 287.1 0.275 15.726
Chisq= 15.73 for 20 degrees of freedom, p= 0.26654
SUMMARY of craptest
p-value for no. of wins: 0.489548
p-value for throws/game: 0.266545
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_08:31
No. of wins: Observed Expected
98615 98585.9
z-score= 0.130, pvalue=0.55185
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66694 66666.7 0.011 0.011
2 37105 37654.3 8.014 8.025
3 27298 26954.7 4.371 12.396
4 19287 19313.5 0.036 12.433
5 14115 13851.4 5.016 17.448
6 10036 9943.5 0.860 18.308
7 7093 7145.0 0.379 18.687
8 5068 5139.1 0.983 19.670
9 3767 3699.9 1.218 20.888
10 2538 2666.3 6.173 27.061
11 1991 1923.3 2.381 29.442
12 1400 1388.7 0.091 29.534
13 988 1003.7 0.246 29.780
14 704 726.1 0.675 30.455
15 551 525.8 1.204 31.659
16 373 381.2 0.174 31.833
17 257 276.5 1.381 33.214
18 204 200.8 0.050 33.264
19 161 146.0 1.544 34.808
20 94 106.2 1.405 36.213
21 276 287.1 0.430 36.644
Chisq= 36.64 for 20 degrees of freedom, p= 0.98709
SUMMARY of craptest
p-value for no. of wins: 0.551850
p-value for throws/game: 0.987092
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0020,0.0022,0.0057,0.0063,0.0115,0.0125,0.0160,0.0166,0.0170,0.0200,
0.0204,0.0207,0.0221,0.0246,0.0293,0.0293,0.0331,0.0365,0.0406,0.0416,
0.0418,0.0429,0.0466,0.0528,0.0547,0.0606,0.0632,0.0654,0.0720,0.0725,
0.0743,0.0777,0.0801,0.0827,0.0912,0.0935,0.0945,0.1065,0.1148,0.1177,
0.1199,0.1203,0.1213,0.1234,0.1283,0.1329,0.1347,0.1354,0.1393,0.1399,
0.1437,0.1447,0.1448,0.1449,0.1454,0.1473,0.1576,0.1584,0.1632,0.1639,
0.1710,0.1711,0.1711,0.1730,0.1765,0.1771,0.1831,0.1852,0.1878,0.1906,
0.1912,0.1924,0.1934,0.1962,0.1980,0.1996,0.2079,0.2127,0.2155,0.2221,
0.2310,0.2404,0.2438,0.2467,0.2482,0.2489,0.2496,0.2560,0.2616,0.2665,
0.2690,0.2715,0.2811,0.2827,0.2830,0.2834,0.2865,0.2875,0.2890,0.2933,
0.2983,0.2985,0.3009,0.3064,0.3069,0.3074,0.3076,0.3110,0.3142,0.3147,
0.3216,0.3378,0.3388,0.3395,0.3406,0.3522,0.3582,0.3600,0.3612,0.3702,
0.3746,0.3754,0.3765,0.3803,0.3849,0.3869,0.3888,0.4010,0.4027,0.4084,
0.4097,0.4110,0.4110,0.4176,0.4202,0.4275,0.4298,0.4307,0.4348,0.4350,
0.4389,0.4410,0.4433,0.4453,0.4467,0.4557,0.4591,0.4684,0.4744,0.4748,
0.4762,0.4764,0.4795,0.4878,0.4895,0.4902,0.4903,0.4949,0.5000,0.5020,
0.5035,0.5081,0.5114,0.5211,0.5267,0.5367,0.5407,0.5490,0.5519,0.5534,
0.5535,0.5645,0.5654,0.5688,0.5712,0.5755,0.5863,0.5881,0.5936,0.5958,
0.5984,0.5989,0.5998,0.6017,0.6030,0.6155,0.6288,0.6292,0.6303,0.6306,
0.6369,0.6413,0.6448,0.6495,0.6585,0.6588,0.6674,0.6761,0.6812,0.6839,
0.6857,0.7032,0.7093,0.7119,0.7131,0.7136,0.7230,0.7236,0.7410,0.7415,
0.7463,0.7522,0.7603,0.7611,0.7624,0.7645,0.7698,0.7756,0.7816,0.7894,
0.7970,0.7991,0.8015,0.8060,0.8084,0.8107,0.8267,0.8300,0.8451,0.8482,
0.8556,0.8575,0.8583,0.8616,0.8620,0.8712,0.8744,0.8792,0.8799,0.8814,
0.8852,0.8854,0.8916,0.8929,0.8995,0.9002,0.9013,0.9045,0.9082,0.9129,
0.9215,0.9437,0.9455,0.9473,0.9498,0.9499,0.9544,0.9570,0.9573,0.9586,
0.9658,0.9660,0.9810,0.9854,0.9871,0.9926,0.9966,0.9979,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.003431
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.