RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.69 23.5656 0.868274
2 to 25 15.83 25.1424 0.908433
3 to 26 15.84 8.5948 0.047877
4 to 27 15.58 35.0133 0.993804
5 to 28 15.91 10.2195 0.105847
6 to 29 15.61 23.3435 0.861602
7 to 30 16.03 17.6576 0.589259
8 to 31 15.74 15.4872 0.439567
9 to 32 15.55 22.1891 0.822444
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.141359
Tough bday spacings test for dh-ranFile-2018-06-30_20:31: 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 27 76 107 87 78 56 37 15 5 4
(O-E)^2/E 0.1 2.5 0.1 0.9 1.2 0.0 0.3 1.8 0.0 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.283, p= 0.301
RESULTS OF GCD FOR dh-ranFile-2018-06-30_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.909210
p-value, dist. of gcd's: 0.456493
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.443 0.326 0.124 0.415 0.122 0.223 0.897 0.739
Bits 8 to 15---> 0.048 0.874 0.601 0.805 0.109 0.727 0.334 0.957
Bits 16 to 23---> 0.945 0.865 0.552 0.446 0.766 0.088 0.653 0.584
Bits 24 to 31---> 0.589 0.546 0.532 0.171 0.602 0.833 0.161 0.134
KS test for the above 32 p values: 0.054
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_20:31,
p-values for 5 runs: 0.4764, 0.1509, 0.3401, 0.5547, 0.7834
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 225 211.4 0.873 0.873
r= 29 5202 5134.0 0.900 1.773
r= 30 23074 23103.0 0.037 1.809
r= 31 11499 11551.5 0.239 2.048
chi-square = 2.048 with df = 3; p-value = 0.438
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5187 5134.0 0.547 0.882
r= 31 23170 23103.0 0.194 1.076
r= 32 11440 11551.5 1.077 2.153
chi-square = 2.153 with df = 3; p-value = 0.459
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_20:31
b-rank test for bits 1 to 8, p=0.32289
b-rank test for bits 2 to 9, p=0.28122
b-rank test for bits 3 to 10, p=0.24368
b-rank test for bits 4 to 11, p=0.40750
b-rank test for bits 5 to 12, p=0.76565
b-rank test for bits 6 to 13, p=0.12382
b-rank test for bits 7 to 14, p=0.17086
b-rank test for bits 8 to 15, p=0.39318
b-rank test for bits 9 to 16, p=0.26033
b-rank test for bits 10 to 17, p=0.03585
b-rank test for bits 11 to 18, p=0.30416
b-rank test for bits 12 to 19, p=0.47074
b-rank test for bits 13 to 20, p=0.44242
b-rank test for bits 14 to 21, p=0.25359
b-rank test for bits 15 to 22, p=0.58664
b-rank test for bits 16 to 23, p=0.15121
b-rank test for bits 17 to 24, p=0.29793
b-rank test for bits 18 to 25, p=0.44840
b-rank test for bits 19 to 26, p=0.22404
b-rank test for bits 20 to 27, p=0.50120
b-rank test for bits 21 to 28, p=0.45017
b-rank test for bits 22 to 29, p=0.94467
b-rank test for bits 23 to 30, p=0.42149
b-rank test for bits 24 to 31, p=0.59502
b-rank test for bits 25 to 32, p=0.40454
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 = 0.016383
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_20:31
(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 141538 -0.87 0.192808
2 142038 0.30 0.618152
3 141991 0.19 0.575666
4 142483 1.34 0.909934
5 142582 1.57 0.941985
6 141671 -0.56 0.288816
7 142321 0.96 0.831936
8 141545 -0.85 0.197319
9 141886 -0.05 0.478265
10 142053 0.34 0.631443
11 142489 1.35 0.912191
12 142205 0.69 0.755160
13 142752 1.97 0.975515
14 142313 0.94 0.827199
15 142143 0.55 0.707453
16 141851 -0.14 0.445798
17 141355 -1.30 0.097632
18 142215 0.71 0.762443
19 141500 -0.96 0.169441
20 141662 -0.58 0.281675
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_20:31
Bits used No. missing words z-score p-value
23 to 32 142092 0.6299 0.735619
22 to 31 142102 0.6644 0.746776
21 to 30 142194 0.9816 0.836857
20 to 29 142324 1.4299 0.923627
19 to 28 141816 -0.3218 0.373792
18 to 27 142294 1.3264 0.907654
17 to 26 141943 0.1161 0.546215
16 to 25 141737 -0.5942 0.276175
15 to 24 142301 1.3506 0.911586
14 to 23 142410 1.7264 0.957867
13 to 22 141979 0.2402 0.594928
12 to 21 141812 -0.3356 0.368579
11 to 20 142049 0.4816 0.684962
10 to 19 141392 -1.7839 0.037220
9 to 18 141553 -1.2287 0.109588
8 to 17 141960 0.1747 0.569352
7 to 16 142242 1.1471 0.874338
6 to 15 141902 -0.0253 0.489918
5 to 14 141817 -0.3184 0.375099
4 to 13 142061 0.5230 0.699513
3 to 12 141672 -0.8184 0.206570
2 to 11 141730 -0.6184 0.268163
1 to 10 142201 1.0058 0.842734
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_20:31
Bits used No. missing words z-score p-value
28 to 32 142101 0.6497 0.742066
27 to 31 141713 -0.6655 0.252857
26 to 30 141686 -0.7571 0.224510
25 to 29 142012 0.3480 0.636093
24 to 28 141644 -0.8994 0.184214
23 to 27 142206 1.0057 0.842711
22 to 26 141720 -0.6418 0.260503
21 to 25 141810 -0.3367 0.368167
20 to 24 141705 -0.6926 0.244267
19 to 23 142374 1.5752 0.942389
18 to 22 142117 0.7040 0.759273
17 to 21 141886 -0.0791 0.468483
16 to 20 141540 -1.2520 0.105291
15 to 19 141950 0.1379 0.554826
14 to 18 141772 -0.4655 0.320778
13 to 17 141413 -1.6825 0.046238
12 to 16 141820 -0.3028 0.381016
11 to 15 142157 0.8396 0.799422
10 to 14 141952 0.1446 0.557504
9 to 13 141811 -0.3333 0.369446
8 to 12 142163 0.8599 0.805077
7 to 11 142281 1.2599 0.896147
6 to 10 142342 1.4667 0.928768
5 to 9 141784 -0.4248 0.335474
4 to 8 141372 -1.8215 0.034269
3 to 7 142084 0.5921 0.723109
2 to 6 141639 -0.9164 0.179736
1 to 5 141938 0.0972 0.538711
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_20:31
Bits used No. missing words z-score p-value
31 to 32 142094 0.5447 0.707037
30 to 31 141840 -0.2045 0.418976
29 to 30 142010 0.2970 0.616752
28 to 29 141624 -0.8417 0.199983
27 to 28 142043 0.3943 0.653323
26 to 27 141905 -0.0128 0.494905
25 to 26 141667 -0.7148 0.237355
24 to 25 142216 0.9046 0.817170
23 to 24 141733 -0.5201 0.301480
22 to 23 141736 -0.5113 0.304571
21 to 22 141900 -0.0275 0.489022
20 to 21 142156 0.7276 0.766583
19 to 20 142299 1.1495 0.874819
18 to 19 141964 0.1613 0.564059
17 to 18 141747 -0.4788 0.316023
16 to 17 141645 -0.7797 0.217774
15 to 16 141408 -1.4788 0.069590
14 to 15 142732 2.4268 0.992383
13 to 14 141342 -1.6735 0.047111
12 to 13 141523 -1.1396 0.127223
11 to 12 142702 2.3383 0.990313
10 to 11 141008 -2.6588 0.003921
9 to 10 141659 -0.7384 0.230125
8 to 9 141997 0.2586 0.602033
7 to 8 141716 -0.5703 0.284239
6 to 7 142186 0.8161 0.792789
5 to 6 142569 1.9459 0.974168
4 to 5 141949 0.1170 0.546578
3 to 4 142119 0.6185 0.731876
2 to 3 141992 0.2439 0.596332
1 to 2 141785 -0.3668 0.356901
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2591.99 1.301 0.903369
Test results for specific bytes for dh-ranFile-2018-06-30_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2576.59 1.083 0.860626
2 to 9 2546.94 0.664 0.746610
3 to 10 2469.64 -0.429 0.333827
4 to 11 2606.12 1.501 0.933295
5 to 12 2584.09 1.189 0.882808
6 to 13 2385.61 -1.618 0.052868
7 to 14 2482.73 -0.244 0.403551
8 to 15 2458.27 -0.590 0.277546
9 to 16 2472.29 -0.392 0.347581
10 to 17 2532.83 0.464 0.678765
11 to 18 2594.67 1.339 0.909685
12 to 19 2519.88 0.281 0.610685
13 to 20 2481.78 -0.258 0.398316
14 to 21 2487.75 -0.173 0.431248
15 to 22 2532.47 0.459 0.676961
16 to 23 2508.93 0.126 0.550250
17 to 24 2447.34 -0.745 0.228199
18 to 25 2473.90 -0.369 0.356031
19 to 26 2435.14 -0.917 0.179508
20 to 27 2406.61 -1.321 0.093298
21 to 28 2401.06 -1.399 0.080873
22 to 29 2506.21 0.088 0.535004
23 to 30 2667.11 2.363 0.990942
24 to 31 2433.64 -0.938 0.173994
25 to 32 2417.37 -1.169 0.121301
CDPARK for dh-ranFile-2018-06-30_20:31: 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
3518 -0.2283 0.409702
3537 0.6393 0.738676
3472 -2.3288 0.009936
3513 -0.4566 0.323972
3507 -0.7306 0.232514
3511 -0.5479 0.291865
3528 0.2283 0.590298
3520 -0.1370 0.445521
3510 -0.5936 0.276387
3529 0.2740 0.607947
Square side=100, avg. no. parked=3514.50 sample std.=16.85
p-value of the KSTEST for those 10 p-values: 0.250940
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_20:31
0.1138,0.0903,0.8340,0.9077,0.2330,0.5173,0.0080,0.9948,0.5400,0.2016,
The KS test for those 10 p-values: 0.370605
The 3DSPHERES test for dh-ranFile-2018-06-30_20:31
sample no r^3 equiv. uni.
1 118.299 0.980616
2 9.225 0.264714
3 151.978 0.993692
4 35.247 0.691148
5 30.934 0.643398
6 13.261 0.357265
7 1.442 0.046930
8 19.007 0.469300
9 73.604 0.914005
10 10.882 0.304231
11 44.049 0.769683
12 38.239 0.720471
13 2.427 0.077720
14 92.819 0.954678
15 9.510 0.271670
16 36.490 0.703689
17 4.036 0.125880
18 64.481 0.883444
19 8.670 0.250975
20 4.361 0.135281
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.560200
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 0.1 0.6 0.3 -0.1
1.0 -1.5 0.5 1.2 0.8 -0.0
0.1 -0.8 -0.9 -0.6 -0.7 0.9
-0.1 1.9 0.6 -1.1 -1.4 0.5
-0.6 0.1 1.7 0.5 -1.0 -0.8
-1.6 0.4 0.9 1.6 0.5 2.0
-0.5 -2.0 1.3 -0.1 2.4 1.0
2.7
Chi-square with 42 degrees of freedom:55.378679
z-score=1.459734, p-value=0.919162
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_20:31
Test no p-value
1 0.521985
2 0.054328
3 0.346129
4 0.359330
5 0.251219
6 0.972210
7 0.025224
8 0.680856
9 0.049344
10 0.055485
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.046699
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_20:31:
(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 66452 0.69 66566 0.15
3 25000.00 25239 2.28 25087 0.30
4 6666.67 6686 0.06 6689 0.07
5 1388.89 1337 1.94 1394 0.02
6 238.10 240 0.02 219 1.53
7 34.72 38 0.31 42 1.53
8 4.96 7 0.84 2 1.77
p=0.59175 p=0.50303
Number of rngs required: 687810, p-value: 0.247
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_20:31
No. of wins: Observed Expected
98659 98585.9
z-score= 0.327, pvalue=0.62822
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66548 66666.7 0.211 0.211
2 37391 37654.3 1.841 2.053
3 26878 26954.7 0.218 2.271
4 19544 19313.5 2.752 5.023
5 13854 13851.4 0.000 5.023
6 10061 9943.5 1.387 6.411
7 7233 7145.0 1.083 7.494
8 5123 5139.1 0.050 7.544
9 3621 3699.9 1.681 9.225
10 2699 2666.3 0.401 9.626
11 1944 1923.3 0.222 9.849
12 1388 1388.7 0.000 9.849
13 1028 1003.7 0.588 10.437
14 696 726.1 1.251 11.688
15 534 525.8 0.127 11.814
16 408 381.2 1.891 13.706
17 291 276.5 0.756 14.462
18 196 200.8 0.116 14.578
19 157 146.0 0.831 15.409
20 121 106.2 2.058 17.467
21 285 287.1 0.016 17.483
Chisq= 17.48 for 20 degrees of freedom, p= 0.37857
SUMMARY of craptest
p-value for no. of wins: 0.628216
p-value for throws/game: 0.378568
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_20:31
No. of wins: Observed Expected
98812 98585.9
z-score= 1.011, pvalue=0.84410
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67000 66666.7 1.667 1.667
2 37733 37654.3 0.164 1.831
3 27161 26954.7 1.578 3.410
4 19326 19313.5 0.008 3.418
5 13597 13851.4 4.673 8.091
6 10043 9943.5 0.995 9.086
7 6957 7145.0 4.948 14.034
8 5024 5139.1 2.577 16.610
9 3614 3699.9 1.993 18.603
10 2587 2666.3 2.358 20.961
11 1883 1923.3 0.846 21.807
12 1352 1388.7 0.972 22.779
13 1068 1003.7 4.117 26.896
14 729 726.1 0.011 26.907
15 495 525.8 1.808 28.716
16 373 381.2 0.174 28.890
17 271 276.5 0.111 29.001
18 202 200.8 0.007 29.008
19 180 146.0 7.926 36.934
20 92 106.2 1.902 38.836
21 313 287.1 2.334 41.170
Chisq= 41.17 for 20 degrees of freedom, p= 0.99646
SUMMARY of craptest
p-value for no. of wins: 0.844096
p-value for throws/game: 0.996458
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0039,0.0080,0.0099,0.0164,0.0252,0.0343,0.0359,0.0372,0.0462,0.0467,
0.0469,0.0471,0.0477,0.0479,0.0493,0.0529,0.0543,0.0543,0.0555,0.0696,
0.0777,0.0809,0.0882,0.0903,0.0933,0.0976,0.1053,0.1058,0.1092,0.1096,
0.1138,0.1213,0.1224,0.1236,0.1238,0.1259,0.1272,0.1339,0.1353,0.1414,
0.1509,0.1512,0.1606,0.1694,0.1709,0.1712,0.1740,0.1795,0.1797,0.1842,
0.1928,0.1973,0.2000,0.2016,0.2066,0.2178,0.2231,0.2240,0.2245,0.2282,
0.2301,0.2325,0.2330,0.2374,0.2437,0.2443,0.2468,0.2509,0.2510,0.2512,
0.2529,0.2536,0.2603,0.2605,0.2647,0.2682,0.2717,0.2762,0.2764,0.2775,
0.2812,0.2817,0.2842,0.2888,0.2919,0.2979,0.3015,0.3015,0.3042,0.3042,
0.3046,0.3160,0.3208,0.3229,0.3240,0.3255,0.3338,0.3338,0.3355,0.3401,
0.3461,0.3476,0.3560,0.3569,0.3573,0.3593,0.3682,0.3686,0.3694,0.3706,
0.3738,0.3751,0.3786,0.3810,0.3932,0.3983,0.4036,0.4045,0.4075,0.4097,
0.4148,0.4190,0.4215,0.4312,0.4375,0.4396,0.4424,0.4433,0.4455,0.4455,
0.4458,0.4484,0.4502,0.4565,0.4587,0.4685,0.4693,0.4707,0.4764,0.4783,
0.4890,0.4899,0.4949,0.5012,0.5030,0.5173,0.5220,0.5321,0.5350,0.5387,
0.5400,0.5456,0.5462,0.5466,0.5502,0.5524,0.5547,0.5548,0.5575,0.5602,
0.5641,0.5694,0.5757,0.5841,0.5866,0.5891,0.5893,0.5903,0.5918,0.5949,
0.5950,0.5963,0.6011,0.6020,0.6022,0.6079,0.6107,0.6168,0.6182,0.6282,
0.6314,0.6361,0.6434,0.6532,0.6533,0.6770,0.6788,0.6809,0.6850,0.6911,
0.6995,0.7037,0.7070,0.7075,0.7205,0.7231,0.7267,0.7319,0.7356,0.7387,
0.7391,0.7421,0.7466,0.7468,0.7552,0.7593,0.7624,0.7656,0.7660,0.7666,
0.7697,0.7834,0.7928,0.7994,0.8051,0.8052,0.8172,0.8224,0.8272,0.8319,
0.8334,0.8340,0.8369,0.8427,0.8427,0.8441,0.8606,0.8616,0.8651,0.8683,
0.8738,0.8743,0.8748,0.8828,0.8834,0.8961,0.8966,0.9034,0.9077,0.9077,
0.9084,0.9092,0.9097,0.9099,0.9116,0.9122,0.9140,0.9192,0.9236,0.9288,
0.9333,0.9420,0.9424,0.9447,0.9452,0.9547,0.9575,0.9579,0.9722,0.9742,
0.9755,0.9806,0.9903,0.9909,0.9924,0.9937,0.9938,0.9948,0.9965,
Overall p-value after applying KStest on 269 p-values = 0.616247
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.