RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.63 23.5791 0.868671
2 to 25 15.67 21.6615 0.801910
3 to 26 15.65 27.6307 0.950557
4 to 27 15.71 22.3449 0.828183
5 to 28 15.34 30.2884 0.975661
6 to 29 15.44 25.8381 0.922538
7 to 30 15.85 12.2718 0.216596
8 to 31 15.66 12.4793 0.229715
9 to 32 15.54 20.2831 0.739992
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.013635
Tough bday spacings test for dh-ranFile-2018-07-03_14:31: 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 36 75 97 108 77 59 20 13 6 3
(O-E)^2/E 1.1 0.0 0.0 0.0 1.1 0.0 0.9 3.2 0.2 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.949, p= 0.270
RESULTS OF GCD FOR dh-ranFile-2018-07-03_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.554546
p-value, dist. of gcd's: 0.408071
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.617 0.794 0.824 0.294 0.122 0.501 0.104 0.664
Bits 8 to 15---> 0.387 0.890 0.713 0.635 0.320 0.969 0.445 0.866
Bits 16 to 23---> 0.007 0.215 0.676 0.962 0.962 0.245 0.729 0.117
Bits 24 to 31---> 0.221 0.315 0.886 0.315 0.144 0.274 0.975 0.973
KS test for the above 32 p values: 0.602
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_14:31,
p-values for 5 runs: 0.6762, 0.6786, 0.4638, 0.2824, 0.1127
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5109 5134.0 0.122 0.153
r= 30 22992 23103.0 0.534 0.687
r= 31 11685 11551.5 1.542 2.229
chi-square = 2.229 with df = 3; p-value = 0.474
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 224 211.4 0.749 0.749
r= 30 5184 5134.0 0.487 1.236
r= 31 23103 23103.0 0.000 1.236
r= 32 11489 11551.5 0.338 1.574
chi-square = 1.574 with df = 3; p-value = 0.335
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_14:31
b-rank test for bits 1 to 8, p=0.67910
b-rank test for bits 2 to 9, p=0.84562
b-rank test for bits 3 to 10, p=0.39499
b-rank test for bits 4 to 11, p=0.04703
b-rank test for bits 5 to 12, p=0.39000
b-rank test for bits 6 to 13, p=0.48492
b-rank test for bits 7 to 14, p=0.44090
b-rank test for bits 8 to 15, p=0.45940
b-rank test for bits 9 to 16, p=0.13610
b-rank test for bits 10 to 17, p=0.17612
b-rank test for bits 11 to 18, p=0.95587
b-rank test for bits 12 to 19, p=0.84599
b-rank test for bits 13 to 20, p=0.92951
b-rank test for bits 14 to 21, p=0.15044
b-rank test for bits 15 to 22, p=0.55690
b-rank test for bits 16 to 23, p=0.21891
b-rank test for bits 17 to 24, p=0.26321
b-rank test for bits 18 to 25, p=0.49883
b-rank test for bits 19 to 26, p=0.35683
b-rank test for bits 20 to 27, p=0.42542
b-rank test for bits 21 to 28, p=0.96582
b-rank test for bits 22 to 29, p=0.22148
b-rank test for bits 23 to 30, p=0.84008
b-rank test for bits 24 to 31, p=0.66430
b-rank test for bits 25 to 32, p=0.40302
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 = 0.798520
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_14:31
(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 142467 1.30 0.903707
2 142126 0.51 0.693655
3 141705 -0.48 0.316536
4 142374 1.09 0.861189
5 141961 0.12 0.548045
6 141529 -0.89 0.187103
7 141998 0.21 0.582063
8 141900 -0.02 0.491304
9 142455 1.27 0.898833
10 141473 -1.02 0.153992
11 141815 -0.22 0.412781
12 142271 0.85 0.800951
13 142259 0.82 0.793032
14 142242 0.78 0.781499
15 142229 0.75 0.772436
16 141434 -1.11 0.133374
17 141888 -0.05 0.480126
18 142365 1.06 0.856483
19 142028 0.28 0.609212
20 141885 -0.06 0.477334
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_14:31
Bits used No. missing words z-score p-value
23 to 32 141499 -1.4149 0.078544
22 to 31 141662 -0.8529 0.196868
21 to 30 142115 0.7092 0.760902
20 to 29 142626 2.4713 0.993268
19 to 28 141997 0.3023 0.618792
18 to 27 141963 0.1851 0.573413
17 to 26 141814 -0.3287 0.371182
16 to 25 142221 1.0747 0.858751
15 to 24 141782 -0.4391 0.330306
14 to 23 142490 2.0023 0.977374
13 to 22 141793 -0.4011 0.344159
12 to 21 141936 0.0920 0.536637
11 to 20 141871 -0.1322 0.447424
10 to 19 142331 1.4540 0.927032
9 to 18 141803 -0.3667 0.356938
8 to 17 141990 0.2782 0.609560
7 to 16 141803 -0.3667 0.356938
6 to 15 141461 -1.5460 0.061056
5 to 14 142054 0.4989 0.691062
4 to 13 141917 0.0264 0.510550
3 to 12 141619 -1.0011 0.158380
2 to 11 141741 -0.5804 0.280806
1 to 10 142059 0.5161 0.697109
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_14:31
Bits used No. missing words z-score p-value
28 to 32 141852 -0.1943 0.422955
27 to 31 142178 0.9107 0.818785
26 to 30 142401 1.6667 0.952211
25 to 29 141648 -0.8859 0.187845
24 to 28 142284 1.2701 0.897970
23 to 27 141931 0.0735 0.529279
22 to 26 141496 -1.4011 0.080589
21 to 25 142073 0.5548 0.710489
20 to 24 141872 -0.1265 0.449651
19 to 23 142435 1.7819 0.962620
18 to 22 141107 -2.7198 0.003266
17 to 21 141957 0.1616 0.564187
16 to 20 142071 0.5480 0.708166
15 to 19 142037 0.4328 0.667413
14 to 18 141926 0.0565 0.522532
13 to 17 142101 0.6497 0.742066
12 to 16 142203 0.9955 0.840251
11 to 15 141441 -1.5876 0.056193
10 to 14 141859 -0.1706 0.432265
9 to 13 141774 -0.4587 0.323208
8 to 12 141898 -0.0384 0.484682
7 to 11 141681 -0.7740 0.219465
6 to 10 141792 -0.3977 0.345415
5 to 9 141893 -0.0554 0.477928
4 to 8 141484 -1.4418 0.074680
3 to 7 142133 0.7582 0.775835
2 to 6 141235 -2.2859 0.011131
1 to 5 142090 0.6124 0.729877
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_14:31
Bits used No. missing words z-score p-value
31 to 32 141983 0.2173 0.586019
30 to 31 141485 -1.2517 0.105338
29 to 30 142032 0.3619 0.641271
28 to 29 142436 1.5536 0.939860
27 to 28 142256 1.0226 0.846758
26 to 27 141882 -0.0806 0.467872
25 to 26 142323 1.2203 0.888818
24 to 25 142135 0.6657 0.747196
23 to 24 141726 -0.5408 0.294324
22 to 23 142399 1.4445 0.925694
21 to 22 141712 -0.5821 0.280252
20 to 21 141646 -0.7768 0.218643
19 to 20 141548 -1.0659 0.143241
18 to 19 142488 1.7070 0.956088
17 to 18 142155 0.7247 0.765679
16 to 17 142511 1.7748 0.962038
15 to 16 142102 0.5683 0.715101
14 to 15 141961 0.1524 0.560572
13 to 14 141839 -0.2075 0.417824
12 to 13 141926 0.0492 0.519610
11 to 12 141569 -1.0039 0.157708
10 to 11 141783 -0.3727 0.354703
9 to 10 142064 0.4563 0.675896
8 to 9 142181 0.8014 0.788546
7 to 8 142129 0.6480 0.741506
6 to 7 142413 1.4858 0.931328
5 to 6 142214 0.8987 0.815602
4 to 5 142411 1.4799 0.930544
3 to 4 142098 0.5565 0.711082
2 to 3 142160 0.7394 0.770180
1 to 2 141348 -1.6558 0.048877
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2477.77 -0.314 0.376593
Test results for specific bytes for dh-ranFile-2018-07-03_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2540.35 0.571 0.715853
2 to 9 2464.03 -0.509 0.305482
3 to 10 2482.26 -0.251 0.400974
4 to 11 2432.75 -0.951 0.170776
5 to 12 2571.40 1.010 0.843688
6 to 13 2441.05 -0.834 0.202218
7 to 14 2557.66 0.815 0.792600
8 to 15 2466.65 -0.472 0.318576
9 to 16 2504.73 0.067 0.526650
10 to 17 2501.78 0.025 0.510014
11 to 18 2518.11 0.256 0.601061
12 to 19 2417.35 -1.169 0.121240
13 to 20 2337.42 -2.299 0.010744
14 to 21 2397.95 -1.443 0.074478
15 to 22 2544.03 0.623 0.733237
16 to 23 2563.31 0.895 0.814678
17 to 24 2451.43 -0.687 0.246089
18 to 25 2358.39 -2.003 0.022609
19 to 26 2582.64 1.169 0.878728
20 to 27 2487.69 -0.174 0.430920
21 to 28 2404.34 -1.353 0.088049
22 to 29 2481.69 -0.259 0.397830
23 to 30 2530.83 0.436 0.668605
24 to 31 2511.59 0.164 0.565072
25 to 32 2431.00 -0.976 0.164591
CDPARK for dh-ranFile-2018-07-03_14:31: 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
3492 -1.4155 0.078457
3522 -0.0457 0.481790
3536 0.5936 0.723613
3536 0.5936 0.723613
3538 0.6849 0.753306
3516 -0.3196 0.374623
3509 -0.6393 0.261324
3539 0.7306 0.767486
3548 1.1416 0.873180
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3525.40 sample std.=16.18
p-value of the KSTEST for those 10 p-values: 0.723553
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_14:31
0.0571,0.7982,0.3923,0.2997,0.5275,0.6751,0.6720,0.8438,0.6446,0.6275,
The KS test for those 10 p-values: 0.524382
The 3DSPHERES test for dh-ranFile-2018-07-03_14:31
sample no r^3 equiv. uni.
1 16.829 0.429347
2 50.310 0.813065
3 81.304 0.933472
4 17.577 0.443397
5 12.684 0.344797
6 59.072 0.860411
7 4.739 0.146134
8 20.995 0.503334
9 0.818 0.026893
10 118.348 0.980647
11 127.737 0.985848
12 27.981 0.606510
13 57.475 0.852779
14 6.941 0.206561
15 41.700 0.750923
16 67.975 0.896255
17 33.355 0.671041
18 28.790 0.616981
19 42.248 0.755437
20 50.064 0.811525
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.063962
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
3.4 -1.2 -0.4 -1.0 -0.6 -0.4
1.0 0.8 0.6 0.9 0.2 -1.1
-1.2 -1.1 -0.2 1.1 -1.4 -0.0
1.6 -0.4 -0.7 1.4 -1.1 -0.6
1.1 0.7 1.0 -0.8 0.2 0.9
-0.1 -0.5 0.0 1.5 0.2 1.1
0.3 -0.4 1.3 -0.1 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:41.309576
z-score=-0.075331, p-value=0.498872
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_14:31
Test no p-value
1 0.845431
2 0.011151
3 0.012323
4 0.182461
5 0.087769
6 0.004489
7 0.530347
8 0.020480
9 0.177278
10 0.008425
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000008
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_14:31:
(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 66905 0.85 66559 0.17
3 25000.00 24673 4.28 24948 0.11
4 6666.67 6672 0.00 6777 1.83
5 1388.89 1452 2.87 1419 0.65
6 238.10 253 0.93 253 0.93
7 34.72 39 0.53 39 0.53
8 4.96 5 0.00 4 0.19
p=0.85079 p=0.37825
Number of rngs required: 687916, p-value: 0.287
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_14:31
No. of wins: Observed Expected
98664 98585.9
z-score= 0.349, pvalue=0.63664
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66798 66666.7 0.259 0.259
2 37356 37654.3 2.363 2.622
3 27211 26954.7 2.436 5.059
4 19385 19313.5 0.265 5.324
5 14005 13851.4 1.703 7.026
6 9661 9943.5 8.028 15.055
7 7097 7145.0 0.323 15.378
8 5156 5139.1 0.056 15.433
9 3697 3699.9 0.002 15.436
10 2644 2666.3 0.186 15.622
11 1908 1923.3 0.122 15.744
12 1362 1388.7 0.515 16.259
13 1014 1003.7 0.105 16.365
14 756 726.1 1.228 17.592
15 538 525.8 0.281 17.874
16 387 381.2 0.090 17.964
17 254 276.5 1.837 19.801
18 209 200.8 0.332 20.133
19 149 146.0 0.062 20.195
20 111 106.2 0.216 20.411
21 302 287.1 0.772 21.183
Chisq= 21.18 for 20 degrees of freedom, p= 0.61355
SUMMARY of craptest
p-value for no. of wins: 0.636641
p-value for throws/game: 0.613546
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_14:31
No. of wins: Observed Expected
98563 98585.9
z-score=-0.102, pvalue=0.45928
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66580 66666.7 0.113 0.113
2 37712 37654.3 0.088 0.201
3 27364 26954.7 6.214 6.415
4 19128 19313.5 1.781 8.196
5 13764 13851.4 0.552 8.748
6 9875 9943.5 0.472 9.220
7 7282 7145.0 2.626 11.846
8 5119 5139.1 0.078 11.925
9 3595 3699.9 2.972 14.897
10 2647 2666.3 0.140 15.036
11 1925 1923.3 0.001 15.038
12 1389 1388.7 0.000 15.038
13 1030 1003.7 0.688 15.726
14 721 726.1 0.036 15.763
15 507 525.8 0.675 16.437
16 361 381.2 1.065 17.503
17 299 276.5 1.824 19.327
18 174 200.8 3.584 22.911
19 127 146.0 2.469 25.380
20 108 106.2 0.030 25.410
21 293 287.1 0.121 25.531
Chisq= 25.53 for 20 degrees of freedom, p= 0.81812
SUMMARY of craptest
p-value for no. of wins: 0.459284
p-value for throws/game: 0.818124
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0033,0.0045,0.0068,0.0084,0.0107,0.0111,0.0112,0.0123,0.0136,
0.0205,0.0226,0.0269,0.0470,0.0489,0.0562,0.0571,0.0611,0.0640,0.0745,
0.0747,0.0785,0.0785,0.0806,0.0878,0.0880,0.1039,0.1053,0.1127,0.1174,
0.1212,0.1217,0.1334,0.1361,0.1432,0.1442,0.1461,0.1504,0.1540,0.1577,
0.1584,0.1646,0.1708,0.1761,0.1773,0.1825,0.1871,0.1878,0.1969,0.2022,
0.2066,0.2145,0.2166,0.2186,0.2189,0.2195,0.2211,0.2215,0.2297,0.2454,
0.2461,0.2613,0.2632,0.2697,0.2738,0.2803,0.2808,0.2824,0.2872,0.2938,
0.2943,0.2997,0.3055,0.3147,0.3150,0.3165,0.3186,0.3197,0.3232,0.3303,
0.3347,0.3442,0.3448,0.3454,0.3547,0.3568,0.3569,0.3569,0.3712,0.3746,
0.3766,0.3782,0.3871,0.3900,0.3923,0.3950,0.3978,0.4010,0.4030,0.4081,
0.4097,0.4128,0.4178,0.4230,0.4254,0.4293,0.4309,0.4323,0.4409,0.4434,
0.4453,0.4474,0.4497,0.4593,0.4594,0.4638,0.4679,0.4738,0.4773,0.4779,
0.4801,0.4818,0.4847,0.4849,0.4913,0.4988,0.4989,0.5010,0.5033,0.5100,
0.5106,0.5196,0.5225,0.5244,0.5267,0.5275,0.5293,0.5303,0.5366,0.5480,
0.5545,0.5569,0.5606,0.5642,0.5651,0.5734,0.5821,0.5860,0.6011,0.6019,
0.6065,0.6092,0.6096,0.6135,0.6170,0.6173,0.6188,0.6275,0.6354,0.6366,
0.6413,0.6446,0.6643,0.6643,0.6674,0.6686,0.6710,0.6720,0.6751,0.6759,
0.6762,0.6763,0.6786,0.6791,0.6911,0.6937,0.6971,0.7082,0.7105,0.7111,
0.7129,0.7151,0.7159,0.7236,0.7236,0.7236,0.7295,0.7299,0.7332,0.7400,
0.7415,0.7421,0.7472,0.7509,0.7533,0.7554,0.7609,0.7657,0.7675,0.7702,
0.7724,0.7758,0.7815,0.7885,0.7926,0.7930,0.7944,0.7982,0.7985,0.8010,
0.8019,0.8115,0.8131,0.8147,0.8156,0.8181,0.8188,0.8235,0.8282,0.8401,
0.8403,0.8437,0.8438,0.8454,0.8456,0.8460,0.8468,0.8508,0.8528,0.8565,
0.8588,0.8604,0.8612,0.8659,0.8687,0.8732,0.8787,0.8858,0.8888,0.8897,
0.8963,0.8980,0.8988,0.9037,0.9225,0.9257,0.9270,0.9295,0.9305,0.9313,
0.9335,0.9399,0.9506,0.9522,0.9559,0.9561,0.9618,0.9620,0.9622,0.9626,
0.9658,0.9690,0.9732,0.9748,0.9757,0.9774,0.9806,0.9858,0.9933,
Overall p-value after applying KStest on 269 p-values = 0.272344
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.