RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-14_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 15.84 9.7414 0.085899
2 to 25 15.96 10.6579 0.126216
3 to 26 15.57 20.2789 0.739787
4 to 27 15.76 14.5384 0.371310
5 to 28 15.62 23.8003 0.875038
6 to 29 15.94 9.9876 0.095869
7 to 30 15.87 19.1275 0.678737
8 to 31 15.94 21.9603 0.813751
9 to 32 15.86 25.3311 0.912459
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.644362
Tough bday spacings test for dh-ranFile-2018-06-14_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 8 32 67 105 85 83 62 31 11 14 2
(O-E)^2/E 0.1 0.6 0.5 0.5 1.6 0.3 1.9 0.1 1.0 8.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 16.003, p= 0.900
RESULTS OF GCD FOR dh-ranFile-2018-06-14_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.289494
p-value, dist. of gcd's: 0.400768
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-14_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.534 0.734 0.421 0.076 0.042 0.886 0.557 0.361
Bits 8 to 15---> 0.613 0.034 0.413 0.096 0.042 0.752 0.044 0.833
Bits 16 to 23---> 0.776 0.773 0.119 0.603 0.861 0.232 0.042 0.137
Bits 24 to 31---> 0.641 0.276 0.345 0.390 0.149 0.860 0.795 0.885
KS test for the above 32 p values: 0.771
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-14_14:31,
p-values for 5 runs: 0.1214, 0.0865, 0.6499, 0.6260, 0.8355
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-14_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5075 5134.0 0.678 1.530
r= 30 23147 23103.0 0.084 1.613
r= 31 11580 11551.5 0.070 1.684
chi-square = 1.684 with df = 3; p-value = 0.359
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-14_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5074 5134.0 0.701 0.702
r= 31 23207 23103.0 0.468 1.170
r= 32 11508 11551.5 0.164 1.334
chi-square = 1.334 with df = 3; p-value = 0.279
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-14_14:31
b-rank test for bits 1 to 8, p=0.52241
b-rank test for bits 2 to 9, p=0.60761
b-rank test for bits 3 to 10, p=0.15979
b-rank test for bits 4 to 11, p=0.81090
b-rank test for bits 5 to 12, p=0.13916
b-rank test for bits 6 to 13, p=0.86933
b-rank test for bits 7 to 14, p=0.77510
b-rank test for bits 8 to 15, p=0.95715
b-rank test for bits 9 to 16, p=0.64004
b-rank test for bits 10 to 17, p=0.20362
b-rank test for bits 11 to 18, p=0.00245
b-rank test for bits 12 to 19, p=0.80879
b-rank test for bits 13 to 20, p=0.74912
b-rank test for bits 14 to 21, p=0.37708
b-rank test for bits 15 to 22, p=0.86294
b-rank test for bits 16 to 23, p=0.44087
b-rank test for bits 17 to 24, p=0.75429
b-rank test for bits 18 to 25, p=0.24215
b-rank test for bits 19 to 26, p=0.40026
b-rank test for bits 20 to 27, p=0.26243
b-rank test for bits 21 to 28, p=0.23010
b-rank test for bits 22 to 29, p=0.54067
b-rank test for bits 23 to 30, p=0.10756
b-rank test for bits 24 to 31, p=0.88417
b-rank test for bits 25 to 32, p=0.92565
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 = 0.812478
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-14_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 141849 -0.14 0.443952
2 141952 0.10 0.539707
3 141774 -0.32 0.375929
4 141383 -1.23 0.109397
5 141930 0.05 0.519259
6 142082 0.40 0.656686
7 142015 0.25 0.597504
8 142318 0.95 0.830170
9 141721 -0.44 0.329960
10 142152 0.57 0.714638
11 142312 0.94 0.826601
12 141821 -0.21 0.418248
13 142575 1.56 0.940063
14 142126 0.51 0.693655
15 141717 -0.45 0.326583
16 142187 0.65 0.741754
17 142270 0.84 0.800298
18 142411 1.17 0.879427
19 141762 -0.34 0.365337
20 141469 -1.03 0.151785
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-14_14:31
Bits used No. missing words z-score p-value
23 to 32 141631 -0.9598 0.168588
22 to 31 142024 0.3954 0.653731
21 to 30 142047 0.4747 0.682508
20 to 29 142123 0.7368 0.769376
19 to 28 141490 -1.4460 0.074093
18 to 27 141554 -1.2253 0.110236
17 to 26 141784 -0.4322 0.332808
16 to 25 141837 -0.2494 0.401520
15 to 24 141856 -0.1839 0.427047
14 to 23 141984 0.2575 0.601597
13 to 22 141880 -0.1011 0.459721
12 to 21 142075 0.5713 0.716094
11 to 20 142099 0.6540 0.743455
10 to 19 141888 -0.0736 0.470684
9 to 18 142038 0.4437 0.671367
8 to 17 142146 0.8161 0.792780
7 to 16 141970 0.2092 0.582857
6 to 15 142044 0.4644 0.678812
5 to 14 142312 1.3885 0.917510
4 to 13 142136 0.7816 0.782781
3 to 12 141419 -1.6908 0.045438
2 to 11 141267 -2.2149 0.013382
1 to 10 141387 -1.8011 0.035841
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-14_14:31
Bits used No. missing words z-score p-value
28 to 32 142053 0.4870 0.686877
27 to 31 142179 0.9141 0.819677
26 to 30 141623 -0.9706 0.165871
25 to 29 141764 -0.4926 0.311132
24 to 28 141662 -0.8384 0.200901
23 to 27 141292 -2.0926 0.018190
22 to 26 142002 0.3141 0.623291
21 to 25 141902 -0.0248 0.490088
20 to 24 141151 -2.5706 0.005076
19 to 23 141566 -1.1638 0.122246
18 to 22 141813 -0.3265 0.372007
17 to 21 142462 1.8735 0.969497
16 to 20 142074 0.5582 0.711647
15 to 19 141850 -0.2011 0.420303
14 to 18 142026 0.3955 0.653760
13 to 17 141368 -1.8350 0.033252
12 to 16 141847 -0.2113 0.416331
11 to 15 142146 0.8023 0.788802
10 to 14 141785 -0.4215 0.336711
9 to 13 142146 0.8023 0.788802
8 to 12 142080 0.5785 0.718551
7 to 11 142064 0.5243 0.699967
6 to 10 141788 -0.4113 0.340431
5 to 9 142153 0.8260 0.795598
4 to 8 141654 -0.8655 0.193375
3 to 7 141668 -0.8181 0.206659
2 to 6 141780 -0.4384 0.330546
1 to 5 141872 -0.1265 0.449651
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-14_14:31
Bits used No. missing words z-score p-value
31 to 32 141868 -0.1219 0.451482
30 to 31 142584 1.9902 0.976714
29 to 30 142303 1.1613 0.877234
28 to 29 141684 -0.6647 0.253124
27 to 28 142219 0.9135 0.819505
26 to 27 142333 1.2498 0.894307
25 to 26 142340 1.2704 0.898031
24 to 25 141613 -0.8741 0.191024
23 to 24 142050 0.4150 0.660913
22 to 23 141395 -1.5172 0.064608
21 to 22 142499 1.7394 0.959021
20 to 21 142221 0.9194 0.821052
19 to 20 141677 -0.6853 0.246565
18 to 19 142696 2.3206 0.989845
17 to 18 141733 -0.5201 0.301480
16 to 17 141786 -0.3638 0.358002
15 to 16 142173 0.7778 0.781653
14 to 15 141781 -0.3786 0.352509
13 to 14 141914 0.0138 0.505496
12 to 13 142207 0.8781 0.810051
11 to 12 141834 -0.2222 0.412074
10 to 11 141291 -1.8240 0.034077
9 to 10 141902 -0.0216 0.491375
8 to 9 142266 1.0521 0.853629
7 to 8 142102 0.5683 0.715101
6 to 7 142114 0.6037 0.726994
5 to 6 142105 0.5772 0.718097
4 to 5 142100 0.5624 0.713095
3 to 4 141294 -1.8151 0.034752
2 to 3 142293 1.1318 0.871134
1 to 2 141919 0.0285 0.511378
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-14_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2291.86 -2.943 0.001623
Test results for specific bytes for dh-ranFile-2018-06-14_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2442.80 -0.809 0.209286
2 to 9 2515.16 0.214 0.584859
3 to 10 2585.00 1.202 0.885338
4 to 11 2478.56 -0.303 0.380891
5 to 12 2572.79 1.029 0.848369
6 to 13 2422.94 -1.090 0.137893
7 to 14 2618.29 1.673 0.952818
8 to 15 2483.96 -0.227 0.410280
9 to 16 2544.80 0.634 0.736819
10 to 17 2561.69 0.872 0.808531
11 to 18 2443.83 -0.794 0.213502
12 to 19 2595.82 1.355 0.912316
13 to 20 2411.62 -1.250 0.105670
14 to 21 2444.68 -0.782 0.217006
15 to 22 2508.53 0.121 0.548030
16 to 23 2447.72 -0.739 0.229831
17 to 24 2605.87 1.497 0.932828
18 to 25 2393.51 -1.506 0.066026
19 to 26 2484.71 -0.216 0.414381
20 to 27 2609.08 1.543 0.938544
21 to 28 2497.57 -0.034 0.486283
22 to 29 2592.99 1.315 0.905751
23 to 30 2582.35 1.165 0.877900
24 to 31 2594.33 1.334 0.908899
25 to 32 2578.27 1.107 0.865831
CDPARK for dh-ranFile-2018-06-14_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
3542 0.8676 0.807188
3545 1.0046 0.842447
3501 -1.0046 0.157553
3530 0.3196 0.625377
3511 -0.5479 0.291865
3514 -0.4110 0.340551
3493 -1.3699 0.085365
3546 1.0502 0.853193
3530 0.3196 0.625377
3512 -0.5023 0.307734
Square side=100, avg. no. parked=3522.40 sample std.=17.88
p-value of the KSTEST for those 10 p-values: 0.933094
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-14_14:31
0.8309,0.9569,0.2223,0.3379,0.0713,0.0379,0.1462,0.0651,0.0242,0.3609,
The KS test for those 10 p-values: 0.018030
The 3DSPHERES test for dh-ranFile-2018-06-14_14:31
sample no r^3 equiv. uni.
1 1.366 0.044514
2 23.759 0.547054
3 52.877 0.828395
4 4.596 0.142029
5 6.219 0.187216
6 92.199 0.953731
7 21.431 0.510491
8 10.196 0.288147
9 30.289 0.635648
10 4.669 0.144128
11 0.179 0.005959
12 12.185 0.333792
13 53.312 0.830866
14 45.300 0.779089
15 8.896 0.256609
16 31.185 0.646370
17 2.996 0.095030
18 37.504 0.713532
19 41.623 0.750288
20 15.593 0.405348
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.796893
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-14_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.3 1.5 -0.4 -0.5 -0.9
-0.1 1.0 1.5 -0.3 -0.3 1.5
-1.4 -0.1 1.0 -0.7 -1.0 -0.1
2.2 -0.3 1.3 -0.6 -0.2 -1.0
0.2 -0.4 0.5 -1.2 -0.5 -1.9
-1.0 -0.5 -0.2 -1.1 0.5 1.3
-0.5 -0.4 1.7 -0.1 2.4 -1.0
-1.1
Chi-square with 42 degrees of freedom:46.529081
z-score=0.494163, p-value=0.708714
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-14_14:31
Test no p-value
1 0.419783
2 0.337420
3 0.080562
4 0.027547
5 0.327864
6 0.750980
7 0.682421
8 0.096475
9 0.381761
10 0.014017
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.045080
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-14_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 66352 1.49 66687 0.01
3 25000.00 25295 3.48 25009 0.00
4 6666.67 6699 0.16 6644 0.08
5 1388.89 1391 0.00 1368 0.31
6 238.10 228 0.43 255 1.20
7 34.72 30 0.64 31 0.40
8 4.96 4 0.19 5 0.00
p=0.61819 p=0.08029
Number of rngs required: 689100, p-value: 0.790
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-14_14:31
No. of wins: Observed Expected
98821 98585.9
z-score= 1.052, pvalue=0.85353
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67112 66666.7 2.975 2.975
2 37610 37654.3 0.052 3.027
3 27130 26954.7 1.140 4.167
4 19217 19313.5 0.482 4.648
5 13804 13851.4 0.162 4.811
6 9750 9943.5 3.767 8.578
7 7172 7145.0 0.102 8.680
8 4988 5139.1 4.441 13.121
9 3693 3699.9 0.013 13.134
10 2696 2666.3 0.331 13.464
11 1793 1923.3 8.831 22.296
12 1323 1388.7 3.112 25.408
13 1020 1003.7 0.264 25.672
14 733 726.1 0.065 25.737
15 544 525.8 0.627 26.364
16 390 381.2 0.205 26.570
17 268 276.5 0.264 26.833
18 203 200.8 0.023 26.857
19 145 146.0 0.007 26.864
20 113 106.2 0.433 27.297
21 296 287.1 0.275 27.572
Chisq= 27.57 for 20 degrees of freedom, p= 0.88007
SUMMARY of craptest
p-value for no. of wins: 0.853529
p-value for throws/game: 0.880074
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-14_14:31
No. of wins: Observed Expected
99004 98585.9
z-score= 1.870, pvalue=0.96927
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66884 66666.7 0.709 0.709
2 37666 37654.3 0.004 0.712
3 26724 26954.7 1.975 2.687
4 19504 19313.5 1.880 4.567
5 14025 13851.4 2.175 6.742
6 9644 9943.5 9.024 15.766
7 7101 7145.0 0.271 16.037
8 5222 5139.1 1.338 17.375
9 3748 3699.9 0.626 18.001
10 2552 2666.3 4.900 22.901
11 1948 1923.3 0.316 23.218
12 1387 1388.7 0.002 23.220
13 980 1003.7 0.560 23.780
14 730 726.1 0.021 23.801
15 516 525.8 0.184 23.985
16 375 381.2 0.099 24.084
17 273 276.5 0.045 24.129
18 200 200.8 0.003 24.133
19 150 146.0 0.110 24.243
20 109 106.2 0.073 24.316
21 262 287.1 2.197 26.513
Chisq= 26.51 for 20 degrees of freedom, p= 0.85046
SUMMARY of craptest
p-value for no. of wins: 0.969270
p-value for throws/game: 0.850462
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0024,0.0051,0.0060,0.0134,0.0140,0.0180,0.0182,0.0242,0.0275,
0.0333,0.0341,0.0342,0.0348,0.0358,0.0379,0.0422,0.0423,0.0425,0.0444,
0.0445,0.0451,0.0454,0.0646,0.0651,0.0660,0.0713,0.0741,0.0762,0.0803,
0.0806,0.0854,0.0859,0.0865,0.0950,0.0958,0.0959,0.0965,0.1057,0.1076,
0.1094,0.1102,0.1189,0.1214,0.1222,0.1262,0.1373,0.1379,0.1392,0.1420,
0.1441,0.1462,0.1493,0.1518,0.1576,0.1598,0.1659,0.1686,0.1872,0.1910,
0.1934,0.2009,0.2036,0.2067,0.2093,0.2135,0.2170,0.2223,0.2298,0.2301,
0.2320,0.2421,0.2466,0.2531,0.2566,0.2624,0.2760,0.2789,0.2881,0.2895,
0.2919,0.3015,0.3077,0.3111,0.3266,0.3279,0.3300,0.3305,0.3328,0.3338,
0.3367,0.3374,0.3379,0.3404,0.3406,0.3447,0.3525,0.3580,0.3594,0.3609,
0.3611,0.3653,0.3713,0.3720,0.3759,0.3771,0.3809,0.3818,0.3903,0.4003,
0.4008,0.4015,0.4053,0.4103,0.4121,0.4131,0.4144,0.4163,0.4182,0.4198,
0.4203,0.4208,0.4270,0.4409,0.4440,0.4497,0.4515,0.4597,0.4707,0.4863,
0.4901,0.4914,0.5055,0.5105,0.5114,0.5193,0.5224,0.5343,0.5397,0.5407,
0.5471,0.5480,0.5573,0.5829,0.5849,0.5975,0.6016,0.6027,0.6076,0.6131,
0.6182,0.6233,0.6254,0.6254,0.6260,0.6356,0.6400,0.6408,0.6444,0.6464,
0.6499,0.6537,0.6538,0.6567,0.6609,0.6714,0.6787,0.6788,0.6824,0.6825,
0.6869,0.6937,0.7000,0.7087,0.7116,0.7131,0.7135,0.7146,0.7151,0.7161,
0.7181,0.7186,0.7270,0.7344,0.7368,0.7398,0.7418,0.7435,0.7491,0.7503,
0.7510,0.7518,0.7543,0.7694,0.7709,0.7734,0.7751,0.7757,0.7791,0.7817,
0.7828,0.7888,0.7888,0.7898,0.7928,0.7950,0.7956,0.7969,0.8003,0.8072,
0.8085,0.8088,0.8101,0.8109,0.8125,0.8138,0.8195,0.8197,0.8211,0.8266,
0.8284,0.8302,0.8309,0.8309,0.8333,0.8355,0.8424,0.8484,0.8505,0.8532,
0.8535,0.8536,0.8600,0.8613,0.8629,0.8658,0.8693,0.8711,0.8750,0.8772,
0.8779,0.8794,0.8801,0.8842,0.8852,0.8853,0.8858,0.8943,0.8980,0.9004,
0.9058,0.9089,0.9123,0.9125,0.9175,0.9257,0.9328,0.9331,0.9385,0.9401,
0.9528,0.9537,0.9569,0.9571,0.9590,0.9693,0.9695,0.9767,0.9898,
Overall p-value after applying KStest on 269 p-values = 0.106666
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.