RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.85 9.1798 0.065549
2 to 25 15.63 9.6312 0.081642
3 to 26 15.84 11.3866 0.164226
4 to 27 15.70 29.4482 0.969390
5 to 28 15.80 21.4208 0.791968
6 to 29 15.73 21.4676 0.793929
7 to 30 15.87 13.6120 0.305650
8 to 31 15.62 19.0679 0.675351
9 to 32 15.67 20.6534 0.757821
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.682414
Tough bday spacings test for dh-ranFile-2018-06-17_09:31: 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 4 36 66 93 95 85 55 32 18 9 7
(O-E)^2/E 2.9 0.0 0.7 0.2 0.1 0.6 0.2 0.2 0.7 0.9 2.1
Birthday Spacings: Sum(O-E)^2/E= 8.492, p= 0.419
RESULTS OF GCD FOR dh-ranFile-2018-06-17_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.614139
p-value, dist. of gcd's: 0.847666
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.757 0.317 0.650 0.223 0.541 0.516 0.264 0.698
Bits 8 to 15---> 0.319 0.421 0.104 0.025 0.306 0.213 0.533 0.804
Bits 16 to 23---> 0.609 0.104 0.337 0.279 0.710 0.425 0.647 0.605
Bits 24 to 31---> 0.419 0.411 0.138 0.868 0.814 0.621 0.060 0.650
KS test for the above 32 p values: 0.740
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_09:31,
p-values for 5 runs: 0.6418, 0.2397, 0.1529, 0.4773, 0.9797
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 225 211.4 0.873 0.873
r= 29 5084 5134.0 0.487 1.360
r= 30 23139 23103.0 0.056 1.416
r= 31 11552 11551.5 0.000 1.416
chi-square = 1.416 with df = 3; p-value = 0.298
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 221 211.4 0.434 0.434
r= 30 4988 5134.0 4.153 4.587
r= 31 23176 23103.0 0.230 4.817
r= 32 11615 11551.5 0.349 5.166
chi-square = 5.166 with df = 3; p-value = 0.840
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_09:31
b-rank test for bits 1 to 8, p=0.95359
b-rank test for bits 2 to 9, p=0.79745
b-rank test for bits 3 to 10, p=0.14146
b-rank test for bits 4 to 11, p=0.59554
b-rank test for bits 5 to 12, p=0.93821
b-rank test for bits 6 to 13, p=0.34972
b-rank test for bits 7 to 14, p=0.40138
b-rank test for bits 8 to 15, p=0.88083
b-rank test for bits 9 to 16, p=0.28416
b-rank test for bits 10 to 17, p=0.59273
b-rank test for bits 11 to 18, p=0.12668
b-rank test for bits 12 to 19, p=0.96491
b-rank test for bits 13 to 20, p=0.99614
b-rank test for bits 14 to 21, p=0.42854
b-rank test for bits 15 to 22, p=0.40333
b-rank test for bits 16 to 23, p=0.52764
b-rank test for bits 17 to 24, p=0.11477
b-rank test for bits 18 to 25, p=0.72408
b-rank test for bits 19 to 26, p=0.33224
b-rank test for bits 20 to 27, p=0.49076
b-rank test for bits 21 to 28, p=0.00005
b-rank test for bits 22 to 29, p=0.52637
b-rank test for bits 23 to 30, p=0.31236
b-rank test for bits 24 to 31, p=0.05935
b-rank test for bits 25 to 32, p=0.08251
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 = 0.564531
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_09:31
(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 142123 0.50 0.691191
2 142333 0.99 0.838884
3 142100 0.45 0.672017
4 141782 -0.30 0.383042
5 141530 -0.89 0.187732
6 142071 0.38 0.647186
7 142179 0.63 0.735676
8 141559 -0.82 0.206528
9 141563 -0.81 0.209205
10 141975 0.15 0.560972
11 141222 -1.61 0.054147
12 142426 1.21 0.886317
13 141792 -0.27 0.391990
14 141995 0.20 0.579324
15 141365 -1.27 0.101722
16 142418 1.19 0.882678
17 141327 -1.36 0.086823
18 141477 -1.01 0.156220
19 142835 2.16 0.984721
20 141972 0.15 0.558207
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_09:31
Bits used No. missing words z-score p-value
23 to 32 141972 0.2161 0.585547
22 to 31 142001 0.3161 0.624038
21 to 30 142052 0.4920 0.688628
20 to 29 142222 1.0782 0.859522
19 to 28 142096 0.6437 0.740112
18 to 27 141896 -0.0460 0.481669
17 to 26 141573 -1.1598 0.123074
16 to 25 141583 -1.1253 0.130236
15 to 24 142569 2.2747 0.988539
14 to 23 142348 1.5127 0.934816
13 to 22 142162 0.8713 0.808198
12 to 21 142141 0.7989 0.787815
11 to 20 142086 0.6092 0.728806
10 to 19 142082 0.5954 0.724217
9 to 18 141497 -1.4218 0.077538
8 to 17 142122 0.7333 0.768326
7 to 16 141405 -1.7391 0.041011
6 to 15 141630 -0.9632 0.167722
5 to 14 141893 -0.0563 0.477547
4 to 13 142044 0.4644 0.678812
3 to 12 141825 -0.2908 0.385605
2 to 11 142014 0.3609 0.640925
1 to 10 141865 -0.1529 0.439254
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_09:31
Bits used No. missing words z-score p-value
28 to 32 141641 -0.9096 0.181519
27 to 31 141693 -0.7333 0.231681
26 to 30 141339 -1.9333 0.026598
25 to 29 142039 0.4396 0.669872
24 to 28 141467 -1.4994 0.066882
23 to 27 141610 -1.0147 0.155130
22 to 26 141851 -0.1977 0.421629
21 to 25 141333 -1.9537 0.025371
20 to 24 142356 1.5141 0.935004
19 to 23 141683 -0.7672 0.221475
18 to 22 141742 -0.5672 0.285282
17 to 21 141571 -1.1469 0.125715
16 to 20 142328 1.4192 0.922083
15 to 19 141921 0.0396 0.515778
14 to 18 142395 1.6463 0.950153
13 to 17 142293 1.3006 0.903298
12 to 16 142013 0.3514 0.637365
11 to 15 141674 -0.7977 0.212514
10 to 14 142175 0.9006 0.816093
9 to 13 141983 0.2497 0.598602
8 to 12 142199 0.9819 0.836933
7 to 11 142460 1.8667 0.969027
6 to 10 141989 0.2701 0.606446
5 to 9 141709 -0.6791 0.248542
4 to 8 142128 0.7413 0.770730
3 to 7 142269 1.2192 0.888620
2 to 6 142162 0.8565 0.804142
1 to 5 142098 0.6396 0.738770
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_09:31
Bits used No. missing words z-score p-value
31 to 32 142445 1.5801 0.942963
30 to 31 141408 -1.4788 0.069590
29 to 30 142379 1.3855 0.917044
28 to 29 141919 0.0285 0.511378
27 to 28 141950 0.1200 0.547747
26 to 27 141872 -0.1101 0.456158
25 to 26 142088 0.5271 0.700921
24 to 25 141736 -0.5113 0.304571
23 to 24 142513 1.7807 0.962522
22 to 23 141781 -0.3786 0.352509
21 to 22 141931 0.0639 0.525484
20 to 21 141685 -0.6617 0.254069
19 to 20 142086 0.5212 0.698869
18 to 19 141926 0.0492 0.519610
17 to 18 141852 -0.1691 0.432853
16 to 17 141457 -1.3343 0.091052
15 to 16 142091 0.5359 0.703986
14 to 15 141887 -0.0659 0.473741
13 to 14 141846 -0.1868 0.425903
12 to 13 141417 -1.4523 0.073209
11 to 12 141875 -0.1013 0.459669
10 to 11 141589 -0.9449 0.172348
9 to 10 141883 -0.0777 0.469045
8 to 9 141784 -0.3697 0.355801
7 to 8 141646 -0.7768 0.218643
6 to 7 142533 1.8397 0.967096
5 to 6 141365 -1.6057 0.054171
4 to 5 142464 1.6362 0.949101
3 to 4 141551 -1.0570 0.145251
2 to 3 142175 0.7837 0.783388
1 to 2 142073 0.4828 0.685382
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2526.85 0.380 0.647922
Test results for specific bytes for dh-ranFile-2018-06-17_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2526.88 0.380 0.648058
2 to 9 2641.38 1.999 0.977219
3 to 10 2544.31 0.627 0.734541
4 to 11 2444.29 -0.788 0.215396
5 to 12 2429.06 -1.003 0.157856
6 to 13 2456.46 -0.616 0.269036
7 to 14 2418.06 -1.159 0.123258
8 to 15 2290.65 -2.961 0.001535
9 to 16 2524.55 0.347 0.635795
10 to 17 2545.44 0.643 0.739764
11 to 18 2392.61 -1.519 0.064423
12 to 19 2573.25 1.036 0.849891
13 to 20 2626.66 1.791 0.963370
14 to 21 2491.23 -0.124 0.450631
15 to 22 2386.63 -1.603 0.054436
16 to 23 2547.89 0.677 0.750869
17 to 24 2482.88 -0.242 0.404340
18 to 25 2460.42 -0.560 0.287839
19 to 26 2585.43 1.208 0.886505
20 to 27 2423.93 -1.076 0.140994
21 to 28 2480.74 -0.272 0.392663
22 to 29 2577.46 1.095 0.863333
23 to 30 2562.67 0.886 0.812288
24 to 31 2508.38 0.119 0.547179
25 to 32 2402.16 -1.384 0.083240
CDPARK for dh-ranFile-2018-06-17_09:31: 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
3520 -0.1370 0.445521
3512 -0.5023 0.307734
3512 -0.5023 0.307734
3526 0.1370 0.554479
3519 -0.1826 0.427537
3546 1.0502 0.853193
3532 0.4110 0.659449
3512 -0.5023 0.307734
3513 -0.4566 0.323972
3515 -0.3653 0.357445
Square side=100, avg. no. parked=3520.70 sample std.=10.57
p-value of the KSTEST for those 10 p-values: 0.213453
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_09:31
0.4212,0.9649,0.6829,0.0582,0.3360,0.6881,0.4706,0.3289,0.3167,0.1411,
The KS test for those 10 p-values: 0.724506
The 3DSPHERES test for dh-ranFile-2018-06-17_09:31
sample no r^3 equiv. uni.
1 2.514 0.080380
2 23.146 0.537689
3 19.502 0.477993
4 42.798 0.759877
5 14.066 0.374292
6 17.911 0.449549
7 5.085 0.155924
8 22.119 0.521595
9 1.616 0.052454
10 8.124 0.237219
11 10.583 0.297268
12 19.170 0.472188
13 34.217 0.680358
14 46.503 0.787776
15 1.254 0.040933
16 34.217 0.680359
17 9.247 0.265258
18 69.474 0.901314
19 8.602 0.249284
20 84.174 0.939543
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.762672
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 -2.0 -0.4 -0.6 -0.2
-0.7 0.2 0.2 1.8 -1.0 -1.7
0.4 1.2 0.1 0.8 0.2 0.0
0.3 -0.5 1.1 -1.5 -1.0 0.0
-0.2 0.4 -0.7 -0.2 0.8 0.6
-0.6 0.0 -0.5 -0.1 -0.8 1.3
0.0 1.5 -1.2 -1.3 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:31.797869
z-score=-1.113144, p-value=0.126252
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_09:31
Test no p-value
1 0.695990
2 0.348994
3 0.274159
4 0.003627
5 0.183878
6 0.115674
7 0.080908
8 0.333192
9 0.790916
10 0.251463
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.047586
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_09:31:
(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 66518 0.33 66715 0.04
3 25000.00 25117 0.55 24872 0.66
4 6666.67 6669 0.00 6666 0.00
5 1388.89 1436 1.60 1453 2.96
6 238.10 214 2.44 257 1.50
7 34.72 42 1.53 32 0.21
8 4.96 3 0.77 4 0.19
p=0.69878 p=0.52453
Number of rngs required: 687841, p-value: 0.258
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_09:31
No. of wins: Observed Expected
98298 98585.9
z-score=-1.287, pvalue=0.09897
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66098 66666.7 4.851 4.851
2 37885 37654.3 1.413 6.264
3 26957 26954.7 0.000 6.264
4 19460 19313.5 1.112 7.376
5 13793 13851.4 0.246 7.622
6 9995 9943.5 0.266 7.889
7 7231 7145.0 1.035 8.923
8 5133 5139.1 0.007 8.930
9 3876 3699.9 8.385 17.315
10 2586 2666.3 2.418 19.734
11 1933 1923.3 0.049 19.782
12 1382 1388.7 0.033 19.815
13 1012 1003.7 0.068 19.883
14 735 726.1 0.108 19.991
15 519 525.8 0.089 20.080
16 405 381.2 1.492 21.573
17 256 276.5 1.526 23.098
18 199 200.8 0.017 23.115
19 138 146.0 0.437 23.551
20 94 106.2 1.405 24.956
21 313 287.1 2.334 27.290
Chisq= 27.29 for 20 degrees of freedom, p= 0.87270
SUMMARY of craptest
p-value for no. of wins: 0.098965
p-value for throws/game: 0.872703
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_09:31
No. of wins: Observed Expected
98208 98585.9
z-score=-1.690, pvalue=0.04551
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66409 66666.7 0.996 0.996
2 37531 37654.3 0.404 1.400
3 27135 26954.7 1.206 2.605
4 19453 19313.5 1.008 3.614
5 13984 13851.4 1.269 4.883
6 10043 9943.5 0.995 5.877
7 7082 7145.0 0.556 6.433
8 5165 5139.1 0.131 6.564
9 3632 3699.9 1.245 7.809
10 2660 2666.3 0.015 7.824
11 1885 1923.3 0.764 8.588
12 1428 1388.7 1.110 9.697
13 1013 1003.7 0.086 9.783
14 641 726.1 9.983 19.766
15 529 525.8 0.019 19.785
16 429 381.2 6.007 25.792
17 265 276.5 0.482 26.274
18 198 200.8 0.040 26.314
19 131 146.0 1.538 27.852
20 113 106.2 0.433 28.285
21 274 287.1 0.599 28.884
Chisq= 28.88 for 20 degrees of freedom, p= 0.90993
SUMMARY of craptest
p-value for no. of wins: 0.045514
p-value for throws/game: 0.909931
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0015,0.0036,0.0247,0.0254,0.0266,0.0409,0.0410,0.0455,0.0476,
0.0525,0.0541,0.0542,0.0544,0.0582,0.0594,0.0604,0.0644,0.0655,0.0669,
0.0696,0.0732,0.0775,0.0804,0.0809,0.0816,0.0825,0.0832,0.0868,0.0911,
0.0990,0.1017,0.1039,0.1042,0.1148,0.1157,0.1231,0.1233,0.1257,0.1263,
0.1267,0.1302,0.1384,0.1410,0.1411,0.1415,0.1453,0.1529,0.1551,0.1559,
0.1562,0.1579,0.1642,0.1677,0.1723,0.1815,0.1839,0.1877,0.2065,0.2092,
0.2125,0.2130,0.2135,0.2154,0.2186,0.2215,0.2233,0.2317,0.2372,0.2397,
0.2485,0.2493,0.2515,0.2541,0.2583,0.2641,0.2653,0.2690,0.2742,0.2792,
0.2842,0.2853,0.2878,0.2973,0.2981,0.3046,0.3057,0.3058,0.3077,0.3077,
0.3077,0.3124,0.3166,0.3167,0.3186,0.3240,0.3289,0.3322,0.3332,0.3360,
0.3373,0.3490,0.3497,0.3525,0.3558,0.3574,0.3743,0.3830,0.3856,0.3920,
0.3927,0.4014,0.4033,0.4043,0.4110,0.4187,0.4191,0.4212,0.4215,0.4216,
0.4254,0.4259,0.4275,0.4285,0.4329,0.4393,0.4455,0.4495,0.4506,0.4562,
0.4597,0.4690,0.4706,0.4722,0.4737,0.4773,0.4775,0.4780,0.4817,0.4908,
0.5114,0.5158,0.5159,0.5196,0.5216,0.5245,0.5255,0.5264,0.5276,0.5334,
0.5377,0.5409,0.5472,0.5477,0.5545,0.5582,0.5610,0.5645,0.5793,0.5855,
0.5927,0.5955,0.5986,0.6049,0.6064,0.6095,0.6141,0.6207,0.6240,0.6358,
0.6374,0.6409,0.6418,0.6471,0.6472,0.6479,0.6481,0.6497,0.6505,0.6594,
0.6699,0.6720,0.6754,0.6788,0.6804,0.6804,0.6824,0.6829,0.6854,0.6881,
0.6886,0.6912,0.6960,0.6978,0.6988,0.6989,0.7009,0.7040,0.7095,0.7241,
0.7242,0.7245,0.7288,0.7345,0.7357,0.7388,0.7398,0.7399,0.7401,0.7509,
0.7573,0.7578,0.7599,0.7627,0.7683,0.7707,0.7834,0.7878,0.7878,0.7909,
0.7920,0.7939,0.7974,0.8041,0.8043,0.8082,0.8123,0.8140,0.8161,0.8369,
0.8389,0.8400,0.8477,0.8499,0.8532,0.8595,0.8633,0.8679,0.8727,0.8808,
0.8827,0.8863,0.8865,0.8886,0.9013,0.9033,0.9099,0.9170,0.9221,0.9348,
0.9350,0.9382,0.9395,0.9430,0.9491,0.9502,0.9536,0.9625,0.9634,0.9649,
0.9649,0.9671,0.9690,0.9694,0.9772,0.9797,0.9847,0.9885,0.9961,
Overall p-value after applying KStest on 269 p-values = 0.588842
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.