RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.20 10.6126 0.124022
2 to 25 16.03 14.7939 0.389678
3 to 26 15.74 11.1171 0.149588
4 to 27 15.64 24.6337 0.896787
5 to 28 15.74 19.3939 0.693605
6 to 29 15.78 18.5774 0.646681
7 to 30 15.77 12.0843 0.204994
8 to 31 15.99 15.2777 0.424513
9 to 32 15.76 11.8755 0.192385
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.554055
Tough bday spacings test for dh-ranFile-2018-06-26_13:31: 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 30 76 105 107 77 50 28 13 6 0
(O-E)^2/E 0.1 1.2 0.1 0.5 0.9 0.0 0.1 0.1 0.2 0.1 4.1
Birthday Spacings: Sum(O-E)^2/E= 7.454, p= 0.318
RESULTS OF GCD FOR dh-ranFile-2018-06-26_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.032812
p-value, dist. of gcd's: 0.997538
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.386 0.712 0.581 0.953 0.609 0.552 0.717 0.827
Bits 8 to 15---> 0.137 0.496 0.678 0.070 0.186 0.848 0.802 0.208
Bits 16 to 23---> 0.569 0.820 0.332 0.441 0.272 0.924 0.809 0.913
Bits 24 to 31---> 0.267 0.410 0.977 0.415 0.254 0.447 0.178 0.380
KS test for the above 32 p values: 0.318
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_13:31,
p-values for 5 runs: 0.2783, 0.3577, 0.1302, 0.6675, 0.4696
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 5017 5134.0 2.667 3.086
r= 30 23211 23103.0 0.504 3.591
r= 31 11570 11551.5 0.030 3.620
chi-square = 3.620 with df = 3; p-value = 0.695
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 5220 5134.0 1.440 1.701
r= 31 23124 23103.0 0.019 1.720
r= 32 11452 11551.5 0.857 2.577
chi-square = 2.577 with df = 3; p-value = 0.538
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_13:31
b-rank test for bits 1 to 8, p=0.17513
b-rank test for bits 2 to 9, p=0.47589
b-rank test for bits 3 to 10, p=0.69313
b-rank test for bits 4 to 11, p=0.46330
b-rank test for bits 5 to 12, p=0.03742
b-rank test for bits 6 to 13, p=0.59755
b-rank test for bits 7 to 14, p=0.01905
b-rank test for bits 8 to 15, p=0.99666
b-rank test for bits 9 to 16, p=0.86399
b-rank test for bits 10 to 17, p=0.49498
b-rank test for bits 11 to 18, p=0.10874
b-rank test for bits 12 to 19, p=0.82766
b-rank test for bits 13 to 20, p=0.66072
b-rank test for bits 14 to 21, p=0.93853
b-rank test for bits 15 to 22, p=0.94754
b-rank test for bits 16 to 23, p=0.37668
b-rank test for bits 17 to 24, p=0.34434
b-rank test for bits 18 to 25, p=0.67575
b-rank test for bits 19 to 26, p=0.37147
b-rank test for bits 20 to 27, p=0.00876
b-rank test for bits 21 to 28, p=0.07335
b-rank test for bits 22 to 29, p=0.70726
b-rank test for bits 23 to 30, p=0.81481
b-rank test for bits 24 to 31, p=0.71573
b-rank test for bits 25 to 32, p=0.94577
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 = 0.486777
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_13:31
(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 141188 -1.69 0.045960
2 142315 0.95 0.828391
3 141451 -1.07 0.142115
4 141760 -0.35 0.363582
5 142602 1.62 0.947210
6 142482 1.34 0.909554
7 141634 -0.64 0.260017
8 142458 1.28 0.900068
9 141712 -0.46 0.322381
10 141861 -0.11 0.455047
11 141456 -1.06 0.144758
12 142051 0.33 0.629680
13 141106 -1.88 0.030263
14 141755 -0.36 0.359205
15 141819 -0.21 0.416424
16 142431 1.22 0.888550
17 140177 -4.05 0.000026
18 141924 0.03 0.513671
19 142550 1.50 0.932789
20 142325 0.97 0.834274
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_13:31
Bits used No. missing words z-score p-value
23 to 32 142003 0.3230 0.626652
22 to 31 142109 0.6885 0.754436
21 to 30 142276 1.2644 0.896953
20 to 29 142396 1.6782 0.953343
19 to 28 141734 -0.6046 0.272727
18 to 27 141940 0.1058 0.542113
17 to 26 141946 0.1264 0.550312
16 to 25 142102 0.6644 0.746776
15 to 24 142134 0.7747 0.780749
14 to 23 141903 -0.0218 0.491293
13 to 22 141935 0.0885 0.535267
12 to 21 141459 -1.5529 0.060228
11 to 20 141510 -1.3770 0.084256
10 to 19 142353 1.5299 0.936979
9 to 18 142265 1.2264 0.889985
8 to 17 141857 -0.1804 0.428400
7 to 16 141506 -1.3908 0.082144
6 to 15 142111 0.6954 0.756602
5 to 14 141897 -0.0425 0.483043
4 to 13 142208 1.0299 0.848471
3 to 12 142362 1.5609 0.940730
2 to 11 142252 1.1816 0.881322
1 to 10 142103 0.6678 0.747878
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_13:31
Bits used No. missing words z-score p-value
28 to 32 141708 -0.6825 0.247470
27 to 31 141679 -0.7808 0.217466
26 to 30 141819 -0.3062 0.379725
25 to 29 142140 0.7819 0.782873
24 to 28 141966 0.1921 0.576169
23 to 27 141453 -1.5469 0.060946
22 to 26 142011 0.3446 0.634819
21 to 25 142299 1.3209 0.906735
20 to 24 141970 0.2057 0.581472
19 to 23 141612 -1.0079 0.156752
18 to 22 141654 -0.8655 0.193375
17 to 21 141621 -0.9774 0.164188
16 to 20 142012 0.3480 0.636093
15 to 19 142082 0.5853 0.720834
14 to 18 141877 -0.1096 0.456366
13 to 17 141844 -0.2215 0.412368
12 to 16 142034 0.4226 0.663710
11 to 15 141483 -1.4452 0.074203
10 to 14 141778 -0.4452 0.328093
9 to 13 142063 0.5209 0.698787
8 to 12 142123 0.7243 0.765561
7 to 11 141876 -0.1130 0.455022
6 to 10 141806 -0.3503 0.363068
5 to 9 141850 -0.2011 0.420303
4 to 8 142289 1.2870 0.900956
3 to 7 141512 -1.3469 0.089009
2 to 6 141728 -0.6147 0.269384
1 to 5 141841 -0.2316 0.408414
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_13:31
Bits used No. missing words z-score p-value
31 to 32 142092 0.5388 0.705005
30 to 31 141570 -1.0010 0.158420
29 to 30 142098 0.5565 0.711082
28 to 29 141800 -0.3225 0.373534
27 to 28 141935 0.0757 0.530180
26 to 27 142048 0.4091 0.658751
25 to 26 142329 1.2380 0.892135
24 to 25 141889 -0.0600 0.476090
23 to 24 141645 -0.7797 0.217774
22 to 23 141970 0.1790 0.571018
21 to 22 141943 0.0993 0.539559
20 to 21 141990 0.2380 0.594046
19 to 20 141437 -1.3933 0.081764
18 to 19 141978 0.2026 0.580263
17 to 18 141281 -1.8535 0.031907
16 to 17 141253 -1.9361 0.026429
15 to 16 141704 -0.6057 0.272359
14 to 15 142173 0.7778 0.781653
13 to 14 141967 0.1701 0.567541
12 to 13 142379 1.3855 0.917044
11 to 12 141702 -0.6116 0.270404
10 to 11 141887 -0.0659 0.473741
9 to 10 141846 -0.1868 0.425903
8 to 9 142381 1.3914 0.917941
7 to 8 142313 1.1908 0.883127
6 to 7 141630 -0.8240 0.204975
5 to 6 142401 1.4504 0.926520
4 to 5 141887 -0.0659 0.473741
3 to 4 141600 -0.9125 0.180759
2 to 3 141942 0.0964 0.538387
1 to 2 142073 0.4828 0.685382
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2591.67 1.296 0.902578
Test results for specific bytes for dh-ranFile-2018-06-26_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2387.78 -1.587 0.056247
2 to 9 2557.39 0.812 0.791511
3 to 10 2449.76 -0.710 0.238715
4 to 11 2349.85 -2.124 0.016856
5 to 12 2448.52 -0.728 0.233310
6 to 13 2377.30 -1.735 0.041347
7 to 14 2515.64 0.221 0.587506
8 to 15 2482.37 -0.249 0.401548
9 to 16 2581.09 1.147 0.874260
10 to 17 2460.51 -0.559 0.288241
11 to 18 2552.81 0.747 0.772441
12 to 19 2504.41 0.062 0.524869
13 to 20 2453.53 -0.657 0.255549
14 to 21 2478.37 -0.306 0.379816
15 to 22 2644.58 2.045 0.979558
16 to 23 2497.19 -0.040 0.484140
17 to 24 2465.82 -0.483 0.314415
18 to 25 2516.51 0.233 0.592293
19 to 26 2457.22 -0.605 0.272602
20 to 27 2486.82 -0.186 0.426093
21 to 28 2480.94 -0.270 0.393745
22 to 29 2485.40 -0.206 0.418214
23 to 30 2567.30 0.952 0.829391
24 to 31 2499.55 -0.006 0.497480
25 to 32 2511.59 0.164 0.565119
CDPARK for dh-ranFile-2018-06-26_13:31: 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
3539 0.7306 0.767486
3521 -0.0913 0.463617
3533 0.4566 0.676028
3541 0.8219 0.794438
3546 1.0502 0.853193
3520 -0.1370 0.445521
3485 -1.7352 0.041356
3483 -1.8265 0.033889
3530 0.3196 0.625377
3511 -0.5479 0.291865
Square side=100, avg. no. parked=3520.90 sample std.=21.01
p-value of the KSTEST for those 10 p-values: 0.789752
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_13:31
0.7695,0.8009,0.1769,0.2665,0.9782,0.3130,0.0175,0.9873,0.3807,0.7062,
The KS test for those 10 p-values: 0.517862
The 3DSPHERES test for dh-ranFile-2018-06-26_13:31
sample no r^3 equiv. uni.
1 12.510 0.340973
2 9.528 0.272095
3 4.660 0.143880
4 54.657 0.838283
5 23.318 0.540343
6 6.845 0.204003
7 4.267 0.132595
8 12.798 0.347277
9 4.297 0.133462
10 69.532 0.901503
11 19.351 0.475352
12 64.895 0.885040
13 55.293 0.841672
14 6.614 0.197847
15 51.471 0.820164
16 9.324 0.267132
17 3.644 0.114385
18 12.335 0.337132
19 8.949 0.257928
20 53.010 0.829156
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.265393
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -2.0 -0.4 0.0 0.5 -0.8
-1.3 0.7 1.7 -0.9 0.4 -1.1
0.8 -0.2 0.7 0.5 -1.0 -0.9
0.6 -1.0 -0.1 0.3 1.0 1.8
-1.0 -0.3 -0.0 -0.0 -0.3 0.4
0.8 -1.5 -1.2 0.2 1.0 -0.5
-0.2 -0.1 0.5 0.4 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:29.445005
z-score=-1.369862, p-value=0.071902
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_13:31
Test no p-value
1 0.524272
2 0.033416
3 0.247383
4 0.633760
5 0.721181
6 0.197156
7 0.954663
8 0.309328
9 0.316386
10 0.404630
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.756635
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_13:31:
(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 66666 0.00 66701 0.02
3 25000.00 24980 0.02 25019 0.01
4 6666.67 6705 0.22 6616 0.39
5 1388.89 1368 0.31 1400 0.09
6 238.10 248 0.41 221 1.23
7 34.72 24 3.31 38 0.31
8 4.96 8 1.86 4 0.19
p=0.59184 p=0.10254
Number of rngs required: 688939, p-value: 0.732
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_13:31
No. of wins: Observed Expected
98042 98585.9
z-score=-2.432, pvalue=0.00750
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66387 66666.7 1.173 1.173
2 37651 37654.3 0.000 1.173
3 27026 26954.7 0.188 1.362
4 19488 19313.5 1.577 2.939
5 13927 13851.4 0.412 3.352
6 9873 9943.5 0.500 3.852
7 7069 7145.0 0.809 4.661
8 5187 5139.1 0.447 5.108
9 3686 3699.9 0.052 5.160
10 2610 2666.3 1.189 6.349
11 1925 1923.3 0.001 6.350
12 1445 1388.7 2.279 8.629
13 1030 1003.7 0.688 9.318
14 709 726.1 0.405 9.722
15 565 525.8 2.917 12.639
16 355 381.2 1.794 14.433
17 317 276.5 5.920 20.353
18 201 200.8 0.000 20.353
19 161 146.0 1.544 21.898
20 111 106.2 0.216 22.113
21 277 287.1 0.356 22.470
Chisq= 22.47 for 20 degrees of freedom, p= 0.68442
SUMMARY of craptest
p-value for no. of wins: 0.007498
p-value for throws/game: 0.684416
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_13:31
No. of wins: Observed Expected
98436 98585.9
z-score=-0.670, pvalue=0.25135
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66299 66666.7 2.028 2.028
2 37451 37654.3 1.098 3.126
3 27241 26954.7 3.040 6.166
4 19452 19313.5 0.994 7.160
5 14027 13851.4 2.226 9.385
6 9880 9943.5 0.406 9.791
7 7125 7145.0 0.056 9.847
8 5261 5139.1 2.893 12.740
9 3689 3699.9 0.032 12.772
10 2646 2666.3 0.155 12.927
11 1923 1923.3 0.000 12.927
12 1391 1388.7 0.004 12.930
13 990 1003.7 0.187 13.118
14 659 726.1 6.208 19.326
15 560 525.8 2.220 21.545
16 406 381.2 1.620 23.165
17 278 276.5 0.008 23.173
18 179 200.8 2.373 25.546
19 155 146.0 0.557 26.103
20 105 106.2 0.014 26.117
21 283 287.1 0.059 26.176
Chisq= 26.18 for 20 degrees of freedom, p= 0.83991
SUMMARY of craptest
p-value for no. of wins: 0.251348
p-value for throws/game: 0.839913
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0075,0.0088,0.0169,0.0175,0.0190,0.0264,0.0303,0.0319,0.0328,
0.0334,0.0339,0.0374,0.0413,0.0414,0.0460,0.0562,0.0602,0.0609,0.0703,
0.0719,0.0734,0.0742,0.0818,0.0821,0.0843,0.0890,0.1025,0.1087,0.1144,
0.1240,0.1302,0.1326,0.1335,0.1366,0.1421,0.1439,0.1448,0.1496,0.1568,
0.1584,0.1642,0.1751,0.1769,0.1776,0.1808,0.1864,0.1924,0.1934,0.1972,
0.1978,0.2040,0.2050,0.2050,0.2075,0.2175,0.2178,0.2333,0.2387,0.2474,
0.2475,0.2513,0.2543,0.2555,0.2579,0.2600,0.2654,0.2665,0.2669,0.2671,
0.2694,0.2704,0.2717,0.2721,0.2724,0.2726,0.2727,0.2783,0.2882,0.2919,
0.3093,0.3130,0.3144,0.3164,0.3180,0.3181,0.3224,0.3281,0.3324,0.3371,
0.3410,0.3443,0.3473,0.3577,0.3592,0.3631,0.3636,0.3715,0.3735,0.3767,
0.3797,0.3797,0.3798,0.3807,0.3860,0.3897,0.3937,0.4015,0.4046,0.4084,
0.4104,0.4124,0.4151,0.4164,0.4182,0.4203,0.4245,0.4259,0.4261,0.4284,
0.4410,0.4455,0.4472,0.4550,0.4550,0.4564,0.4633,0.4636,0.4696,0.4737,
0.4737,0.4754,0.4759,0.4761,0.4830,0.4841,0.4868,0.4913,0.4950,0.4959,
0.4975,0.5137,0.5179,0.5243,0.5249,0.5302,0.5353,0.5384,0.5385,0.5396,
0.5403,0.5421,0.5503,0.5521,0.5541,0.5651,0.5675,0.5691,0.5710,0.5762,
0.5803,0.5812,0.5815,0.5875,0.5918,0.5923,0.5940,0.5975,0.6093,0.6254,
0.6267,0.6297,0.6338,0.6348,0.6361,0.6467,0.6588,0.6607,0.6637,0.6675,
0.6757,0.6760,0.6777,0.6844,0.6854,0.6931,0.6936,0.6945,0.6988,0.7050,
0.7062,0.7073,0.7111,0.7125,0.7157,0.7169,0.7208,0.7212,0.7318,0.7468,
0.7479,0.7544,0.7566,0.7566,0.7656,0.7675,0.7695,0.7724,0.7807,0.7817,
0.7829,0.7898,0.7915,0.7944,0.8009,0.8018,0.8090,0.8148,0.8201,0.8202,
0.8266,0.8277,0.8284,0.8292,0.8294,0.8343,0.8383,0.8399,0.8417,0.8477,
0.8485,0.8532,0.8640,0.8743,0.8813,0.8831,0.8850,0.8886,0.8900,0.8921,
0.8968,0.8970,0.9001,0.9010,0.9015,0.9026,0.9067,0.9096,0.9135,0.9170,
0.9179,0.9241,0.9265,0.9328,0.9370,0.9385,0.9407,0.9458,0.9472,0.9475,
0.9530,0.9533,0.9547,0.9772,0.9782,0.9796,0.9873,0.9967,0.9975,
Overall p-value after applying KStest on 269 p-values = 0.976860
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.