RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_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 15.88 22.7192 0.841384
2 to 25 16.07 19.2433 0.685251
3 to 26 15.76 12.8331 0.252714
4 to 27 15.90 18.5095 0.642596
5 to 28 15.79 15.8948 0.468698
6 to 29 16.08 29.1697 0.967007
7 to 30 15.93 20.0178 0.726682
8 to 31 15.79 17.7379 0.594448
9 to 32 15.70 18.4450 0.638697
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.164126
Tough bday spacings test for dh-ranFile-2018-06-25_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 9 34 80 108 91 66 49 34 15 12 2
(O-E)^2/E 0.0 0.2 0.6 1.1 0.5 1.9 0.2 0.6 0.0 4.4 1.0
Birthday Spacings: Sum(O-E)^2/E= 10.464, p= 0.599
RESULTS OF GCD FOR dh-ranFile-2018-06-25_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.637585
p-value, dist. of gcd's: 0.068852
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.244 0.855 0.630 0.419 0.176 0.468 0.909 0.647
Bits 8 to 15---> 0.225 0.326 0.561 0.253 0.041 0.406 0.276 0.228
Bits 16 to 23---> 0.959 0.926 0.407 0.343 0.853 0.385 0.659 0.398
Bits 24 to 31---> 0.340 0.776 0.282 0.671 0.781 0.589 0.403 0.548
KS test for the above 32 p values: 0.589
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_14:31,
p-values for 5 runs: 0.8382, 0.4844, 0.2427, 0.5735, 0.8841
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5048 5134.0 1.441 1.496
r= 30 23211 23103.0 0.504 2.001
r= 31 11533 11551.5 0.030 2.030
chi-square = 2.030 with df = 3; p-value = 0.434
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 235 211.4 2.630 2.630
r= 30 5181 5134.0 0.430 3.060
r= 31 22994 23103.0 0.515 3.575
r= 32 11590 11551.5 0.128 3.703
chi-square = 3.703 with df = 3; p-value = 0.705
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_14:31
b-rank test for bits 1 to 8, p=0.11746
b-rank test for bits 2 to 9, p=0.33143
b-rank test for bits 3 to 10, p=0.02847
b-rank test for bits 4 to 11, p=0.34825
b-rank test for bits 5 to 12, p=0.30138
b-rank test for bits 6 to 13, p=0.08808
b-rank test for bits 7 to 14, p=0.64996
b-rank test for bits 8 to 15, p=0.71248
b-rank test for bits 9 to 16, p=0.01348
b-rank test for bits 10 to 17, p=0.46297
b-rank test for bits 11 to 18, p=0.38263
b-rank test for bits 12 to 19, p=0.31868
b-rank test for bits 13 to 20, p=0.27644
b-rank test for bits 14 to 21, p=0.53847
b-rank test for bits 15 to 22, p=0.72702
b-rank test for bits 16 to 23, p=0.26165
b-rank test for bits 17 to 24, p=0.26902
b-rank test for bits 18 to 25, p=0.23691
b-rank test for bits 19 to 26, p=0.74190
b-rank test for bits 20 to 27, p=0.16222
b-rank test for bits 21 to 28, p=0.94238
b-rank test for bits 22 to 29, p=0.96092
b-rank test for bits 23 to 30, p=0.00911
b-rank test for bits 24 to 31, p=0.03293
b-rank test for bits 25 to 32, p=0.55451
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 = 0.044007
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_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 141696 -0.50 0.309089
2 142251 0.80 0.787650
3 141613 -0.69 0.244356
4 142147 0.56 0.710657
5 142205 0.69 0.755160
6 141280 -1.47 0.070727
7 141246 -1.55 0.060590
8 141556 -0.83 0.204533
9 142163 0.59 0.723305
10 140849 -2.48 0.006617
11 142308 0.93 0.824195
12 142468 1.31 0.904105
13 141681 -0.53 0.296850
14 141415 -1.15 0.124050
15 142169 0.61 0.727977
16 141311 -1.40 0.081061
17 143332 3.32 0.999556
18 141964 0.13 0.550820
19 142176 0.62 0.733378
20 142157 0.58 0.718594
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_14:31
Bits used No. missing words z-score p-value
23 to 32 142063 0.5299 0.701908
22 to 31 141797 -0.3873 0.349251
21 to 30 141692 -0.7494 0.226804
20 to 29 141625 -0.9804 0.163432
19 to 28 141467 -1.5253 0.063595
18 to 27 141577 -1.1460 0.125905
17 to 26 142084 0.6023 0.726516
16 to 25 141732 -0.6115 0.270440
15 to 24 142086 0.6092 0.728806
14 to 23 142067 0.5437 0.706673
13 to 22 142095 0.6402 0.738992
12 to 21 142099 0.6540 0.743455
11 to 20 141936 0.0920 0.536637
10 to 19 142059 0.5161 0.697109
9 to 18 141989 0.2747 0.608236
8 to 17 142261 1.2127 0.887369
7 to 16 142030 0.4161 0.661333
6 to 15 142073 0.5644 0.713752
5 to 14 141881 -0.0977 0.461089
4 to 13 141707 -0.6977 0.242686
3 to 12 141820 -0.3080 0.379028
2 to 11 142175 0.9161 0.820194
1 to 10 141993 0.2885 0.613525
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_14:31
Bits used No. missing words z-score p-value
28 to 32 141377 -1.8045 0.035576
27 to 31 141813 -0.3265 0.372007
26 to 30 141851 -0.1977 0.421629
25 to 29 141543 -1.2418 0.107156
24 to 28 141788 -0.4113 0.340431
23 to 27 141673 -0.8011 0.211532
22 to 26 141707 -0.6859 0.246399
21 to 25 141496 -1.4011 0.080589
20 to 24 141740 -0.5740 0.282984
19 to 23 141608 -1.0215 0.153519
18 to 22 141438 -1.5977 0.055052
17 to 21 141753 -0.5299 0.298080
16 to 20 142085 0.5955 0.724243
15 to 19 141853 -0.1909 0.424283
14 to 18 142069 0.5413 0.705834
13 to 17 142004 0.3209 0.625863
12 to 16 141941 0.1074 0.542747
11 to 15 141396 -1.7401 0.040921
10 to 14 142072 0.5514 0.709328
9 to 13 142178 0.9107 0.818785
8 to 12 142049 0.4735 0.682057
7 to 11 141898 -0.0384 0.484682
6 to 10 142616 2.3955 0.991701
5 to 9 142336 1.4463 0.925959
4 to 8 142017 0.3650 0.642438
3 to 7 142396 1.6497 0.950501
2 to 6 141781 -0.4350 0.331775
1 to 5 142230 1.0870 0.861485
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_14:31
Bits used No. missing words z-score p-value
31 to 32 142061 0.4474 0.672708
30 to 31 141622 -0.8476 0.198336
29 to 30 141754 -0.4582 0.323404
28 to 29 142561 1.9223 0.972718
27 to 28 141533 -1.1101 0.133474
26 to 27 142017 0.3176 0.624610
25 to 26 141463 -1.3166 0.093985
24 to 25 142087 0.5241 0.699896
23 to 24 141800 -0.3225 0.373534
22 to 23 141623 -0.8446 0.199158
21 to 22 142134 0.6627 0.746253
20 to 21 142119 0.6185 0.731876
19 to 20 141436 -1.3963 0.081319
18 to 19 141273 -1.8771 0.030254
17 to 18 141687 -0.6558 0.255963
16 to 17 141680 -0.6765 0.249365
15 to 16 141687 -0.6558 0.255963
14 to 15 142129 0.6480 0.741506
13 to 14 141977 0.1996 0.579110
12 to 13 141915 0.0167 0.506672
11 to 12 142706 2.3501 0.990615
10 to 11 142187 0.8191 0.793631
9 to 10 141795 -0.3373 0.367962
8 to 9 141305 -1.7827 0.037319
7 to 8 142220 0.9164 0.820280
6 to 7 141824 -0.2517 0.400632
5 to 6 142014 0.3088 0.621248
4 to 5 142571 1.9518 0.974521
3 to 4 142566 1.9371 0.973632
2 to 3 142112 0.5978 0.725029
1 to 2 142165 0.7542 0.774632
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2487.68 -0.174 0.430824
Test results for specific bytes for dh-ranFile-2018-06-25_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2374.36 -1.777 0.037804
2 to 9 2598.25 1.390 0.917660
3 to 10 2463.42 -0.517 0.302477
4 to 11 2538.94 0.551 0.709080
5 to 12 2521.29 0.301 0.618348
6 to 13 2613.59 1.606 0.945901
7 to 14 2442.23 -0.817 0.206974
8 to 15 2497.17 -0.040 0.484043
9 to 16 2342.28 -2.231 0.012856
10 to 17 2468.98 -0.439 0.330446
11 to 18 2445.94 -0.764 0.222285
12 to 19 2530.86 0.436 0.668753
13 to 20 2441.31 -0.830 0.203272
14 to 21 2412.21 -1.242 0.107205
15 to 22 2423.98 -1.075 0.141163
16 to 23 2412.55 -1.237 0.108095
17 to 24 2490.54 -0.134 0.446812
18 to 25 2435.20 -0.916 0.179723
19 to 26 2477.08 -0.324 0.372922
20 to 27 2519.29 0.273 0.607516
21 to 28 2439.85 -0.851 0.197469
22 to 29 2416.48 -1.181 0.118780
23 to 30 2445.40 -0.772 0.220012
24 to 31 2515.40 0.218 0.586206
25 to 32 2505.15 0.073 0.529014
CDPARK for dh-ranFile-2018-06-25_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
3490 -1.5068 0.065925
3511 -0.5479 0.291865
3529 0.2740 0.607947
3521 -0.0913 0.463617
3559 1.6438 0.949895
3506 -0.7763 0.218799
3515 -0.3653 0.357445
3524 0.0457 0.518210
3526 0.1370 0.554479
3533 0.4566 0.676028
Square side=100, avg. no. parked=3521.40 sample std.=17.34
p-value of the KSTEST for those 10 p-values: 0.837643
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_14:31
0.1874,0.7995,0.4432,0.6357,0.5680,0.7351,0.2246,0.5087,0.4729,0.3217,
The KS test for those 10 p-values: 0.559846
The 3DSPHERES test for dh-ranFile-2018-06-25_14:31
sample no r^3 equiv. uni.
1 11.234 0.312352
2 2.156 0.069359
3 20.282 0.491389
4 16.378 0.420707
5 18.698 0.463806
6 24.505 0.558178
7 14.404 0.381293
8 60.179 0.865469
9 11.418 0.316552
10 29.565 0.626749
11 36.353 0.702329
12 2.157 0.069389
13 22.615 0.529446
14 14.213 0.377354
15 52.340 0.825295
16 38.046 0.718658
17 11.863 0.326622
18 3.358 0.105906
19 21.941 0.518745
20 22.967 0.534927
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.326709
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.2 -0.4 -0.3 -0.9 -1.3
0.7 -1.6 -0.2 -0.2 -0.7 -1.1
-0.2 1.6 1.2 0.5 0.8 0.4
0.4 -0.7 -0.9 -1.0 -0.4 -0.4
0.4 1.2 -1.0 1.5 0.2 -1.7
0.8 0.8 0.0 -0.6 -1.2 -0.7
-1.6 0.8 -0.8 1.0 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:33.925303
z-score=-0.881022, p-value=0.191945
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_14:31
Test no p-value
1 0.017786
2 0.144399
3 0.011470
4 0.086766
5 0.900943
6 0.350241
7 0.939233
8 0.018407
9 0.150193
10 0.448756
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.007426
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_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 66535 0.26 66557 0.18
3 25000.00 25187 1.40 25191 1.46
4 6666.67 6670 0.00 6621 0.31
5 1388.89 1330 2.50 1368 0.31
6 238.10 244 0.15 217 1.87
7 34.72 29 0.94 44 2.48
8 4.96 4 0.19 1 3.16
p=0.51029 p=0.86567
Number of rngs required: 687378, p-value: 0.117
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_14:31
No. of wins: Observed Expected
98223 98585.9
z-score=-1.623, pvalue=0.05230
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66404 66666.7 1.035 1.035
2 37888 37654.3 1.450 2.485
3 26990 26954.7 0.046 2.531
4 19473 19313.5 1.318 3.849
5 13717 13851.4 1.304 5.154
6 10181 9943.5 5.671 10.824
7 7010 7145.0 2.552 13.376
8 5136 5139.1 0.002 13.378
9 3710 3699.9 0.028 13.405
10 2703 2666.3 0.505 13.911
11 1888 1923.3 0.649 14.560
12 1338 1388.7 1.854 16.414
13 987 1003.7 0.278 16.692
14 714 726.1 0.203 16.895
15 499 525.8 1.370 18.264
16 357 381.2 1.530 19.795
17 283 276.5 0.151 19.946
18 181 200.8 1.958 21.904
19 132 146.0 1.340 23.243
20 132 106.2 6.260 29.503
21 277 287.1 0.356 29.859
Chisq= 29.86 for 20 degrees of freedom, p= 0.92783
SUMMARY of craptest
p-value for no. of wins: 0.052304
p-value for throws/game: 0.927829
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_14:31
No. of wins: Observed Expected
98617 98585.9
z-score= 0.139, pvalue=0.55539
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66730 66666.7 0.060 0.060
2 37536 37654.3 0.372 0.432
3 26737 26954.7 1.759 2.191
4 19517 19313.5 2.145 4.336
5 13863 13851.4 0.010 4.345
6 9990 9943.5 0.217 4.562
7 7073 7145.0 0.726 5.289
8 5166 5139.1 0.141 5.430
9 3749 3699.9 0.653 6.082
10 2687 2666.3 0.161 6.243
11 1920 1923.3 0.006 6.249
12 1412 1388.7 0.390 6.638
13 969 1003.7 1.201 7.839
14 709 726.1 0.405 8.244
15 534 525.8 0.127 8.370
16 356 381.2 1.660 10.030
17 292 276.5 0.864 10.894
18 199 200.8 0.017 10.911
19 143 146.0 0.061 10.972
20 101 106.2 0.256 11.228
21 317 287.1 3.111 14.339
Chisq= 14.34 for 20 degrees of freedom, p= 0.18709
SUMMARY of craptest
p-value for no. of wins: 0.555387
p-value for throws/game: 0.187092
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0066,0.0074,0.0091,0.0115,0.0129,0.0135,0.0178,0.0184,0.0285,0.0303,
0.0329,0.0356,0.0373,0.0378,0.0409,0.0414,0.0440,0.0523,0.0551,0.0606,
0.0636,0.0659,0.0689,0.0694,0.0694,0.0707,0.0806,0.0811,0.0813,0.0868,
0.0881,0.0940,0.1059,0.1072,0.1072,0.1081,0.1168,0.1175,0.1188,0.1241,
0.1259,0.1335,0.1412,0.1444,0.1502,0.1535,0.1622,0.1634,0.1641,0.1764,
0.1797,0.1871,0.1874,0.1919,0.1975,0.1983,0.1992,0.2033,0.2045,0.2070,
0.2115,0.2188,0.2200,0.2223,0.2246,0.2251,0.2268,0.2275,0.2369,0.2427,
0.2427,0.2438,0.2444,0.2464,0.2494,0.2527,0.2527,0.2560,0.2560,0.2617,
0.2690,0.2704,0.2763,0.2764,0.2818,0.2830,0.2919,0.2969,0.2981,0.3014,
0.3025,0.3091,0.3124,0.3166,0.3187,0.3217,0.3234,0.3259,0.3266,0.3267,
0.3304,0.3314,0.3318,0.3401,0.3404,0.3434,0.3483,0.3493,0.3502,0.3574,
0.3680,0.3720,0.3729,0.3735,0.3774,0.3790,0.3813,0.3826,0.3849,0.3980,
0.4006,0.4029,0.4062,0.4074,0.4191,0.4207,0.4216,0.4243,0.4308,0.4339,
0.4432,0.4468,0.4488,0.4611,0.4630,0.4636,0.4638,0.4685,0.4687,0.4729,
0.4840,0.4844,0.4847,0.4914,0.5067,0.5087,0.5103,0.5182,0.5187,0.5290,
0.5294,0.5349,0.5366,0.5385,0.5427,0.5480,0.5508,0.5545,0.5545,0.5554,
0.5582,0.5598,0.5605,0.5680,0.5735,0.5791,0.5862,0.5886,0.5892,0.5944,
0.5993,0.6075,0.6079,0.6082,0.6135,0.6183,0.6212,0.6246,0.6259,0.6267,
0.6301,0.6357,0.6376,0.6387,0.6424,0.6426,0.6465,0.6500,0.6586,0.6613,
0.6688,0.6712,0.6727,0.6760,0.6821,0.6853,0.6971,0.6999,0.7019,0.7023,
0.7047,0.7058,0.7067,0.7091,0.7093,0.7107,0.7125,0.7138,0.7186,0.7187,
0.7233,0.7242,0.7250,0.7265,0.7267,0.7270,0.7280,0.7288,0.7319,0.7334,
0.7351,0.7390,0.7415,0.7419,0.7435,0.7463,0.7552,0.7746,0.7764,0.7806,
0.7877,0.7936,0.7995,0.8188,0.8202,0.8203,0.8242,0.8253,0.8376,0.8382,
0.8414,0.8528,0.8548,0.8615,0.8655,0.8657,0.8841,0.8874,0.9009,0.9041,
0.9087,0.9177,0.9260,0.9262,0.9278,0.9392,0.9424,0.9459,0.9499,0.9505,
0.9585,0.9609,0.9670,0.9727,0.9736,0.9745,0.9906,0.9917,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.059535
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.