RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.72 26.9883 0.941760
2 to 25 15.96 23.6407 0.870468
3 to 26 15.61 18.6639 0.651841
4 to 27 15.57 18.4200 0.637182
5 to 28 15.81 16.3167 0.498497
6 to 29 15.79 30.1237 0.974533
7 to 30 15.52 19.9299 0.722168
8 to 31 15.66 17.3880 0.571609
9 to 32 15.57 18.3956 0.635696
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.027449
Tough bday spacings test for dh-ranFile-2018-06-29_10:31: 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 12 29 70 94 92 88 57 30 16 9 3
(O-E)^2/E 0.9 1.6 0.1 0.1 0.3 1.2 0.5 0.0 0.1 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.015, p= 0.186
RESULTS OF GCD FOR dh-ranFile-2018-06-29_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.576968
p-value, dist. of gcd's: 0.521188
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.592 0.077 0.800 0.541 0.976 0.984 0.858 0.990
Bits 8 to 15---> 0.142 0.603 0.557 0.072 0.016 0.638 0.004 0.107
Bits 16 to 23---> 0.407 0.588 0.406 0.241 0.332 0.785 0.430 0.289
Bits 24 to 31---> 0.217 0.596 0.220 0.789 0.231 0.222 0.068 0.751
KS test for the above 32 p values: 0.537
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_10:31,
p-values for 5 runs: 0.6501, 0.7153, 0.4370, 0.3436, 0.3335
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5108 5134.0 0.132 0.224
r= 30 23113 23103.0 0.004 0.228
r= 31 11572 11551.5 0.036 0.265
chi-square = 0.265 with df = 3; p-value = 0.033
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5112 5134.0 0.094 0.155
r= 31 23079 23103.0 0.025 0.180
r= 32 11594 11551.5 0.156 0.336
chi-square = 0.336 with df = 3; p-value = 0.047
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_10:31
b-rank test for bits 1 to 8, p=0.51925
b-rank test for bits 2 to 9, p=0.25674
b-rank test for bits 3 to 10, p=0.94402
b-rank test for bits 4 to 11, p=0.93362
b-rank test for bits 5 to 12, p=0.28315
b-rank test for bits 6 to 13, p=0.19406
b-rank test for bits 7 to 14, p=0.02949
b-rank test for bits 8 to 15, p=0.62987
b-rank test for bits 9 to 16, p=0.81954
b-rank test for bits 10 to 17, p=0.45264
b-rank test for bits 11 to 18, p=0.83412
b-rank test for bits 12 to 19, p=0.43424
b-rank test for bits 13 to 20, p=0.68428
b-rank test for bits 14 to 21, p=0.15920
b-rank test for bits 15 to 22, p=0.32014
b-rank test for bits 16 to 23, p=0.22739
b-rank test for bits 17 to 24, p=0.31786
b-rank test for bits 18 to 25, p=0.16545
b-rank test for bits 19 to 26, p=0.30101
b-rank test for bits 20 to 27, p=0.18462
b-rank test for bits 21 to 28, p=0.84792
b-rank test for bits 22 to 29, p=0.68691
b-rank test for bits 23 to 30, p=0.10275
b-rank test for bits 24 to 31, p=0.67948
b-rank test for bits 25 to 32, p=0.65275
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 = 0.770949
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_10:31
(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 141738 -0.40 0.344466
2 142281 0.87 0.807409
3 141821 -0.21 0.418248
4 142140 0.54 0.705039
5 142131 0.52 0.697743
6 142619 1.66 0.951352
7 142442 1.24 0.893353
8 141515 -0.92 0.178439
9 142370 1.08 0.859111
10 142049 0.33 0.627913
11 141843 -0.15 0.438420
12 141907 -0.01 0.497828
13 141481 -1.00 0.158469
14 141176 -1.71 0.043321
15 141566 -0.80 0.211227
16 141666 -0.57 0.284838
17 142646 1.72 0.957392
18 141937 0.06 0.525774
19 141613 -0.69 0.244356
20 141936 0.06 0.524843
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_10:31
Bits used No. missing words z-score p-value
23 to 32 142161 0.8678 0.807256
22 to 31 141672 -0.8184 0.206570
21 to 30 142150 0.8299 0.796701
20 to 29 142336 1.4713 0.929392
19 to 28 142257 1.1989 0.884709
18 to 27 141553 -1.2287 0.109588
17 to 26 141733 -0.6080 0.271582
16 to 25 141980 0.2437 0.596264
15 to 24 142025 0.3989 0.655003
14 to 23 142144 0.8092 0.790802
13 to 22 142251 1.1782 0.880636
12 to 21 141878 -0.1080 0.456984
11 to 20 141790 -0.4115 0.340359
10 to 19 141625 -0.9804 0.163432
9 to 18 141918 0.0299 0.511925
8 to 17 141674 -0.8115 0.208544
7 to 16 141782 -0.4391 0.330306
6 to 15 142014 0.3609 0.640925
5 to 14 142222 1.0782 0.859522
4 to 13 141920 0.0368 0.514675
3 to 12 141775 -0.4632 0.321608
2 to 11 141922 0.0437 0.517424
1 to 10 141712 -0.6804 0.248110
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_10:31
Bits used No. missing words z-score p-value
28 to 32 142208 1.0124 0.844336
27 to 31 141568 -1.1571 0.123626
26 to 30 141856 -0.1808 0.428270
25 to 29 142126 0.7345 0.768670
24 to 28 142007 0.3311 0.629710
23 to 27 141903 -0.0215 0.491440
22 to 26 142147 0.8057 0.789781
21 to 25 142054 0.4904 0.688077
20 to 24 141812 -0.3299 0.370726
19 to 23 141534 -1.2723 0.101632
18 to 22 141349 -1.8994 0.028754
17 to 21 142565 2.2226 0.986879
16 to 20 142398 1.6565 0.951191
15 to 19 141592 -1.0757 0.141032
14 to 18 142266 1.2091 0.886678
13 to 17 141902 -0.0248 0.490088
12 to 16 142139 0.7785 0.781875
11 to 15 142053 0.4870 0.686877
10 to 14 141805 -0.3537 0.361797
9 to 13 141723 -0.6316 0.263815
8 to 12 141626 -0.9604 0.168417
7 to 11 141999 0.3040 0.619423
6 to 10 141652 -0.8723 0.191521
5 to 9 141807 -0.3469 0.364340
4 to 8 141726 -0.6215 0.267149
3 to 7 141794 -0.3909 0.347917
2 to 6 141864 -0.1537 0.438939
1 to 5 142049 0.4735 0.682057
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_10:31
Bits used No. missing words z-score p-value
31 to 32 141790 -0.3520 0.362417
30 to 31 142526 1.8191 0.965551
29 to 30 141956 0.1377 0.554749
28 to 29 142179 0.7955 0.786835
27 to 28 142455 1.6096 0.946262
26 to 27 141498 -1.2134 0.112496
25 to 26 141727 -0.5378 0.295342
24 to 25 141974 0.1908 0.575646
23 to 24 141859 -0.1485 0.440988
22 to 23 141935 0.0757 0.530180
21 to 22 142900 2.9223 0.998263
20 to 21 142181 0.8014 0.788546
19 to 20 141891 -0.0541 0.478439
18 to 19 141374 -1.5791 0.057151
17 to 18 141961 0.1524 0.560572
16 to 17 141325 -1.7237 0.042382
15 to 16 141593 -0.9331 0.175377
14 to 15 142165 0.7542 0.774632
13 to 14 141777 -0.3904 0.348137
12 to 13 141671 -0.7030 0.241016
11 to 12 142105 0.5772 0.718097
10 to 11 142422 1.5123 0.934771
9 to 10 141754 -0.4582 0.323404
8 to 9 141705 -0.6027 0.273340
7 to 8 142162 0.7453 0.771967
6 to 7 141526 -1.1308 0.129077
5 to 6 141678 -0.6824 0.247496
4 to 5 142418 1.5005 0.933258
3 to 4 141843 -0.1957 0.422437
2 to 3 142145 0.6952 0.756532
1 to 2 142029 0.3530 0.637959
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2515.58 0.220 0.587176
Test results for specific bytes for dh-ranFile-2018-06-29_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2366.63 -1.886 0.029639
2 to 9 2378.84 -1.713 0.043318
3 to 10 2544.62 0.631 0.735989
4 to 11 2355.21 -2.048 0.020301
5 to 12 2421.89 -1.105 0.134644
6 to 13 2437.06 -0.890 0.186711
7 to 14 2562.13 0.879 0.810199
8 to 15 2492.52 -0.106 0.457873
9 to 16 2585.12 1.204 0.885656
10 to 17 2524.67 0.349 0.636390
11 to 18 2600.76 1.425 0.922922
12 to 19 2499.76 -0.003 0.498654
13 to 20 2546.52 0.658 0.744677
14 to 21 2366.30 -1.891 0.029323
15 to 22 2501.27 0.018 0.507146
16 to 23 2504.24 0.060 0.523895
17 to 24 2527.69 0.392 0.652320
18 to 25 2616.78 1.651 0.950679
19 to 26 2552.24 0.739 0.769988
20 to 27 2396.01 -1.471 0.070701
21 to 28 2503.63 0.051 0.520446
22 to 29 2355.85 -2.039 0.020743
23 to 30 2531.19 0.441 0.670406
24 to 31 2548.85 0.691 0.755160
25 to 32 2525.18 0.356 0.639091
CDPARK for dh-ranFile-2018-06-29_10:31: 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
3535 0.5479 0.708135
3527 0.1826 0.572463
3515 -0.3653 0.357445
3538 0.6849 0.753306
3522 -0.0457 0.481790
3520 -0.1370 0.445521
3517 -0.2740 0.392053
3528 0.2283 0.590298
3563 1.8265 0.966111
3495 -1.2785 0.100530
Square side=100, avg. no. parked=3526.00 sample std.=16.77
p-value of the KSTEST for those 10 p-values: 0.700102
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_10:31
0.3956,0.0690,0.6305,0.5165,0.2677,0.8930,0.3771,0.0079,0.2792,0.1844,
The KS test for those 10 p-values: 0.219031
The 3DSPHERES test for dh-ranFile-2018-06-29_10:31
sample no r^3 equiv. uni.
1 10.786 0.301992
2 197.907 0.998635
3 12.924 0.350012
4 16.092 0.415158
5 0.429 0.014202
6 36.393 0.702724
7 39.547 0.732393
8 52.849 0.828235
9 8.973 0.258522
10 22.594 0.529108
11 18.413 0.458688
12 8.536 0.247640
13 8.942 0.257757
14 18.023 0.451600
15 31.548 0.650623
16 8.868 0.255919
17 4.582 0.141637
18 23.565 0.544115
19 40.874 0.743969
20 3.275 0.103422
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.516750
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 1.5 -0.5 -0.4 -0.6
0.1 0.8 0.5 1.4 -0.6 0.2
-0.2 -0.5 -0.7 1.0 -1.0 1.2
-0.2 0.8 0.3 0.0 0.3 0.7
-2.2 -2.2 0.6 -0.2 0.9 -1.2
-0.0 -0.1 -0.5 -0.3 0.6 -0.8
0.7 -0.7 1.7 -1.8 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:34.812544
z-score=-0.784216, p-value=0.223593
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_10:31
Test no p-value
1 0.044409
2 0.145326
3 0.466953
4 0.900731
5 0.125032
6 0.130971
7 0.050190
8 0.610114
9 0.178263
10 0.539447
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.049156
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_10:31:
(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 66488 0.48 66309 1.92
3 25000.00 25109 0.48 25173 1.20
4 6666.67 6705 0.22 6808 3.00
5 1388.89 1439 1.81 1409 0.29
6 238.10 228 0.43 253 0.93
7 34.72 26 2.19 37 0.15
8 4.96 4 0.19 10 5.12
p=0.55245 p=0.95029
Number of rngs required: 689819, p-value: 0.951
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_10:31
No. of wins: Observed Expected
98374 98585.9
z-score=-0.948, pvalue=0.17168
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66833 66666.7 0.415 0.415
2 37611 37654.3 0.050 0.465
3 26636 26954.7 3.769 4.234
4 19158 19313.5 1.251 5.485
5 13966 13851.4 0.948 6.433
6 10106 9943.5 2.654 9.087
7 7186 7145.0 0.235 9.322
8 5116 5139.1 0.104 9.426
9 3716 3699.9 0.070 9.496
10 2596 2666.3 1.853 11.349
11 1956 1923.3 0.555 11.904
12 1403 1388.7 0.146 12.051
13 986 1003.7 0.313 12.364
14 675 726.1 3.602 15.965
15 561 525.8 2.352 18.317
16 427 381.2 5.515 23.832
17 302 276.5 2.344 26.176
18 189 200.8 0.697 26.873
19 173 146.0 4.999 31.873
20 123 106.2 2.652 34.525
21 281 287.1 0.130 34.655
Chisq= 34.66 for 20 degrees of freedom, p= 0.97798
SUMMARY of craptest
p-value for no. of wins: 0.171678
p-value for throws/game: 0.977980
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_10:31
No. of wins: Observed Expected
98512 98585.9
z-score=-0.330, pvalue=0.37057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66775 66666.7 0.176 0.176
2 37781 37654.3 0.426 0.602
3 26933 26954.7 0.018 0.620
4 19441 19313.5 0.842 1.462
5 13646 13851.4 3.046 4.508
6 9873 9943.5 0.500 5.009
7 7146 7145.0 0.000 5.009
8 5130 5139.1 0.016 5.025
9 3662 3699.9 0.388 5.413
10 2620 2666.3 0.804 6.216
11 1938 1923.3 0.112 6.328
12 1385 1388.7 0.010 6.338
13 964 1003.7 1.571 7.910
14 723 726.1 0.014 7.923
15 547 525.8 0.852 8.775
16 359 381.2 1.287 10.063
17 293 276.5 0.980 11.042
18 215 200.8 1.000 12.042
19 155 146.0 0.557 12.599
20 111 106.2 0.216 12.814
21 303 287.1 0.879 13.693
Chisq= 13.69 for 20 degrees of freedom, p= 0.15431
SUMMARY of craptest
p-value for no. of wins: 0.370572
p-value for throws/game: 0.154306
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0042,0.0079,0.0142,0.0155,0.0203,0.0207,0.0274,0.0288,0.0293,0.0295,
0.0296,0.0335,0.0424,0.0433,0.0433,0.0444,0.0469,0.0492,0.0502,0.0572,
0.0677,0.0690,0.0707,0.0715,0.0767,0.1005,0.1016,0.1027,0.1034,0.1072,
0.1096,0.1125,0.1236,0.1250,0.1291,0.1310,0.1346,0.1410,0.1416,0.1418,
0.1453,0.1543,0.1585,0.1592,0.1634,0.1654,0.1684,0.1717,0.1754,0.1783,
0.1784,0.1844,0.1846,0.1860,0.1867,0.1915,0.1941,0.2066,0.2085,0.2112,
0.2169,0.2190,0.2203,0.2219,0.2236,0.2274,0.2315,0.2410,0.2411,0.2444,
0.2475,0.2476,0.2481,0.2559,0.2567,0.2578,0.2585,0.2638,0.2671,0.2677,
0.2716,0.2733,0.2792,0.2831,0.2848,0.2891,0.2953,0.3010,0.3020,0.3179,
0.3201,0.3216,0.3234,0.3303,0.3324,0.3335,0.3404,0.3436,0.3445,0.3479,
0.3481,0.3500,0.3574,0.3618,0.3624,0.3643,0.3706,0.3707,0.3771,0.3921,
0.3956,0.4059,0.4075,0.4152,0.4182,0.4224,0.4283,0.4297,0.4342,0.4370,
0.4384,0.4389,0.4410,0.4455,0.4516,0.4526,0.4570,0.4579,0.4587,0.4670,
0.4784,0.4818,0.4901,0.4914,0.4978,0.4985,0.4987,0.5071,0.5119,0.5147,
0.5165,0.5167,0.5174,0.5192,0.5204,0.5212,0.5239,0.5248,0.5258,0.5291,
0.5302,0.5368,0.5394,0.5413,0.5441,0.5524,0.5547,0.5570,0.5606,0.5716,
0.5725,0.5756,0.5770,0.5872,0.5879,0.5903,0.5922,0.5963,0.5963,0.6031,
0.6101,0.6194,0.6279,0.6297,0.6299,0.6305,0.6357,0.6364,0.6372,0.6377,
0.6380,0.6391,0.6409,0.6501,0.6506,0.6518,0.6523,0.6528,0.6550,0.6704,
0.6795,0.6821,0.6843,0.6869,0.6869,0.6881,0.6977,0.7001,0.7027,0.7050,
0.7081,0.7153,0.7181,0.7222,0.7324,0.7360,0.7440,0.7447,0.7512,0.7533,
0.7552,0.7565,0.7687,0.7700,0.7709,0.7720,0.7746,0.7819,0.7848,0.7868,
0.7885,0.7889,0.7898,0.7908,0.7967,0.7997,0.8073,0.8074,0.8102,0.8195,
0.8282,0.8341,0.8443,0.8479,0.8580,0.8591,0.8595,0.8705,0.8806,0.8847,
0.8857,0.8867,0.8930,0.8934,0.9007,0.9229,0.9294,0.9333,0.9336,0.9348,
0.9418,0.9440,0.9463,0.9503,0.9507,0.9512,0.9514,0.9515,0.9574,0.9656,
0.9661,0.9745,0.9765,0.9780,0.9841,0.9869,0.9897,0.9983,0.9986,
Overall p-value after applying KStest on 269 p-values = 0.613832
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.