RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.89 16.5054 0.511669
2 to 25 15.78 18.3436 0.632519
3 to 26 15.91 20.5468 0.752779
4 to 27 15.83 28.3900 0.959417
5 to 28 15.58 23.8689 0.876958
6 to 29 15.58 16.0584 0.480302
7 to 30 15.88 14.3002 0.354253
8 to 31 15.70 15.2328 0.421279
9 to 32 15.69 13.9783 0.331359
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.438403
Tough bday spacings test for dh-ranFile-2018-06-27_21:31: 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 10 34 69 104 108 62 62 30 10 7 4
(O-E)^2/E 0.1 0.2 0.2 0.4 1.1 3.3 1.9 0.0 1.6 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.859, p= 0.454
RESULTS OF GCD FOR dh-ranFile-2018-06-27_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.355435
p-value, dist. of gcd's: 0.623806
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.056 0.676 0.239 0.966 0.939 0.669 0.109 0.496
Bits 8 to 15---> 0.136 0.649 0.258 0.047 0.859 0.544 0.262 0.974
Bits 16 to 23---> 0.480 0.350 0.693 0.129 0.519 0.989 0.611 0.144
Bits 24 to 31---> 0.051 0.124 0.722 0.263 0.048 0.786 0.586 0.925
KS test for the above 32 p values: 0.460
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_21:31,
p-values for 5 runs: 0.7727, 0.6909, 0.9535, 0.1805, 0.4055
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 184 211.4 3.556 3.556
r= 29 5153 5134.0 0.070 3.626
r= 30 23213 23103.0 0.523 4.149
r= 31 11450 11551.5 0.892 5.042
chi-square = 5.042 with df = 3; p-value = 0.831
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 185 211.4 3.301 3.301
r= 30 5148 5134.0 0.038 3.339
r= 31 23102 23103.0 0.000 3.339
r= 32 11565 11551.5 0.016 3.355
chi-square = 3.355 with df = 3; p-value = 0.660
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_21:31
b-rank test for bits 1 to 8, p=0.44674
b-rank test for bits 2 to 9, p=0.42017
b-rank test for bits 3 to 10, p=0.49896
b-rank test for bits 4 to 11, p=0.77976
b-rank test for bits 5 to 12, p=0.22402
b-rank test for bits 6 to 13, p=0.96359
b-rank test for bits 7 to 14, p=0.21298
b-rank test for bits 8 to 15, p=0.83871
b-rank test for bits 9 to 16, p=0.96585
b-rank test for bits 10 to 17, p=0.84593
b-rank test for bits 11 to 18, p=0.22386
b-rank test for bits 12 to 19, p=0.34203
b-rank test for bits 13 to 20, p=0.42385
b-rank test for bits 14 to 21, p=0.23216
b-rank test for bits 15 to 22, p=0.26936
b-rank test for bits 16 to 23, p=0.76787
b-rank test for bits 17 to 24, p=0.12491
b-rank test for bits 18 to 25, p=0.03600
b-rank test for bits 19 to 26, p=0.63108
b-rank test for bits 20 to 27, p=0.11118
b-rank test for bits 21 to 28, p=0.34342
b-rank test for bits 22 to 29, p=0.30461
b-rank test for bits 23 to 30, p=0.72740
b-rank test for bits 24 to 31, p=0.20545
b-rank test for bits 25 to 32, p=0.13255
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 = 0.396344
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_21:31
(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 141916 0.02 0.506217
2 142413 1.18 0.880362
3 141353 -1.30 0.096829
4 141753 -0.37 0.357460
5 141802 -0.25 0.400996
6 142034 0.29 0.614583
7 142144 0.55 0.708255
8 141883 -0.06 0.475473
9 141561 -0.81 0.207864
10 141974 0.15 0.560051
11 142028 0.28 0.609212
12 141505 -0.94 0.172407
13 141546 -0.85 0.197968
14 141958 0.11 0.545268
15 141782 -0.30 0.383042
16 142343 1.01 0.844529
17 141411 -1.16 0.122147
18 141901 -0.02 0.492236
19 141789 -0.28 0.389300
20 141583 -0.76 0.222895
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_21:31
Bits used No. missing words z-score p-value
23 to 32 141872 -0.1287 0.448788
22 to 31 141657 -0.8701 0.192122
21 to 30 142471 1.9368 0.973615
20 to 29 142253 1.1851 0.882005
19 to 28 141619 -1.0011 0.158380
18 to 27 142130 0.7609 0.776651
17 to 26 141660 -0.8598 0.194961
16 to 25 142130 0.7609 0.776651
15 to 24 142050 0.4851 0.686186
14 to 23 141258 -2.2460 0.012353
13 to 22 142125 0.7437 0.771468
12 to 21 141972 0.2161 0.585547
11 to 20 141857 -0.1804 0.428400
10 to 19 142462 1.9058 0.971659
9 to 18 141410 -1.7218 0.042550
8 to 17 141833 -0.2632 0.396196
7 to 16 141554 -1.2253 0.110236
6 to 15 141580 -1.1356 0.128058
5 to 14 141738 -0.5908 0.277330
4 to 13 141305 -2.0839 0.018585
3 to 12 141608 -1.0391 0.149386
2 to 11 141749 -0.5529 0.290179
1 to 10 141954 0.1540 0.561209
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_21:31
Bits used No. missing words z-score p-value
28 to 32 141587 -1.0926 0.137275
27 to 31 141751 -0.5367 0.295733
26 to 30 141779 -0.4418 0.329318
25 to 29 141778 -0.4452 0.328093
24 to 28 141850 -0.2011 0.420303
23 to 27 142266 1.2091 0.886678
22 to 26 141457 -1.5333 0.062598
21 to 25 142159 0.8463 0.801318
20 to 24 142008 0.3345 0.630989
19 to 23 141918 0.0294 0.511723
18 to 22 141658 -0.8520 0.197116
17 to 21 142179 0.9141 0.819677
16 to 20 142035 0.4260 0.664946
15 to 19 141763 -0.4960 0.309935
14 to 18 141840 -0.2350 0.407098
13 to 17 142235 1.1040 0.865196
12 to 16 141885 -0.0825 0.467135
11 to 15 142185 0.9345 0.824970
10 to 14 141808 -0.3435 0.365614
9 to 13 142255 1.1718 0.879354
8 to 12 141909 -0.0011 0.499554
7 to 11 141482 -1.4486 0.073728
6 to 10 141889 -0.0689 0.472529
5 to 9 141828 -0.2757 0.391391
4 to 8 141857 -0.1774 0.429601
3 to 7 141885 -0.0825 0.467135
2 to 6 141454 -1.5435 0.061356
1 to 5 141622 -0.9740 0.165028
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_21:31
Bits used No. missing words z-score p-value
31 to 32 141986 0.2262 0.589464
30 to 31 142405 1.4622 0.928150
29 to 30 142140 0.6804 0.751888
28 to 29 142101 0.5654 0.714099
27 to 28 141712 -0.5821 0.280252
26 to 27 141963 0.1583 0.562897
25 to 26 142025 0.3412 0.633527
24 to 25 142009 0.2940 0.615626
23 to 24 141799 -0.3255 0.372418
22 to 23 141888 -0.0629 0.474915
21 to 22 141808 -0.2989 0.382505
20 to 21 141983 0.2173 0.586019
19 to 20 141891 -0.0541 0.478439
18 to 19 142014 0.3088 0.621248
17 to 18 142596 2.0256 0.978596
16 to 17 142114 0.6037 0.726994
15 to 16 140985 -2.7266 0.003199
14 to 15 141568 -1.0069 0.156998
13 to 14 142422 1.5123 0.934771
12 to 13 141803 -0.3137 0.376891
11 to 12 141680 -0.6765 0.249365
10 to 11 141731 -0.5260 0.299428
9 to 10 142520 1.8014 0.964179
8 to 9 142265 1.0492 0.852951
7 to 8 141669 -0.7089 0.239182
6 to 7 142026 0.3442 0.634637
5 to 6 141701 -0.6145 0.269428
4 to 5 141752 -0.4641 0.321288
3 to 4 141840 -0.2045 0.418976
2 to 3 141924 0.0433 0.517259
1 to 2 141375 -1.5762 0.057490
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2529.89 0.423 0.663737
Test results for specific bytes for dh-ranFile-2018-06-27_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2562.00 0.877 0.809696
2 to 9 2486.98 -0.184 0.426936
3 to 10 2486.19 -0.195 0.422599
4 to 11 2354.39 -2.059 0.019733
5 to 12 2583.43 1.180 0.880968
6 to 13 2404.48 -1.351 0.088376
7 to 14 2637.23 1.941 0.973851
8 to 15 2444.40 -0.786 0.215828
9 to 16 2501.31 0.018 0.507363
10 to 17 2507.19 0.102 0.540511
11 to 18 2621.73 1.722 0.957421
12 to 19 2562.13 0.879 0.810186
13 to 20 2480.39 -0.277 0.390780
14 to 21 2480.49 -0.276 0.391319
15 to 22 2766.51 3.769 0.999918
16 to 23 2620.39 1.703 0.955675
17 to 24 2488.47 -0.163 0.435215
18 to 25 2554.79 0.775 0.780797
19 to 26 2447.63 -0.741 0.229442
20 to 27 2635.05 1.910 0.971926
21 to 28 2404.87 -1.345 0.089260
22 to 29 2580.25 1.135 0.871800
23 to 30 2495.76 -0.060 0.476114
24 to 31 2427.35 -1.027 0.152115
25 to 32 2420.62 -1.123 0.130805
CDPARK for dh-ranFile-2018-06-27_21:31: 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
3513 -0.4566 0.323972
3505 -0.8219 0.205562
3486 -1.6895 0.045562
3531 0.3653 0.642555
3496 -1.2329 0.108811
3528 0.2283 0.590298
3546 1.0502 0.853193
3516 -0.3196 0.374623
3507 -0.7306 0.232514
3512 -0.5023 0.307734
Square side=100, avg. no. parked=3514.00 sample std.=16.60
p-value of the KSTEST for those 10 p-values: 0.262399
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_21:31
0.9674,0.6098,0.9789,0.4028,0.4125,0.3240,0.4896,0.0199,0.4718,0.7699,
The KS test for those 10 p-values: 0.575497
The 3DSPHERES test for dh-ranFile-2018-06-27_21:31
sample no r^3 equiv. uni.
1 12.402 0.338600
2 14.552 0.384353
3 12.678 0.344656
4 4.107 0.127928
5 12.573 0.342370
6 57.758 0.854164
7 2.269 0.072838
8 11.987 0.329390
9 3.779 0.118349
10 37.228 0.710885
11 30.494 0.638131
12 24.047 0.551370
13 6.428 0.192862
14 6.456 0.193608
15 1.411 0.045932
16 9.702 0.276326
17 13.729 0.367218
18 65.007 0.885468
19 55.593 0.843247
20 17.234 0.436993
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.181495
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 0.3 -0.4 1.9 -0.5
0.4 -0.1 -0.3 -1.4 0.3 0.7
-1.1 -0.6 -0.1 0.1 -0.4 0.2
-0.6 2.8 -1.0 0.5 -0.1 1.0
-0.6 1.5 -0.6 0.6 -1.3 -0.4
-0.4 -1.3 0.1 -1.7 -1.3 1.9
0.3 -0.4 0.1 0.4 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:36.201361
z-score=-0.632683, p-value=0.277359
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_21:31
Test no p-value
1 0.474204
2 0.006974
3 0.291392
4 0.122630
5 0.892866
6 0.530329
7 0.454880
8 0.116360
9 0.548405
10 0.589242
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.381967
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_21:31:
(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 66676 0.00 66768 0.15
3 25000.00 25056 0.13 25031 0.04
4 6666.67 6577 1.21 6480 5.23
5 1388.89 1372 0.21 1419 0.65
6 238.10 260 2.02 250 0.60
7 34.72 49 5.87 44 2.48
8 4.96 9 3.29 7 0.84
p=0.95225 p=0.87479
Number of rngs required: 688321, p-value: 0.462
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_21:31
No. of wins: Observed Expected
98950 98585.9
z-score= 1.629, pvalue=0.94831
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66814 66666.7 0.326 0.326
2 37672 37654.3 0.008 0.334
3 26929 26954.7 0.025 0.358
4 19367 19313.5 0.148 0.507
5 13915 13851.4 0.292 0.799
6 9893 9943.5 0.257 1.056
7 7108 7145.0 0.192 1.248
8 5091 5139.1 0.450 1.697
9 3641 3699.9 0.937 2.634
10 2649 2666.3 0.112 2.746
11 1876 1923.3 1.165 3.911
12 1394 1388.7 0.020 3.931
13 998 1003.7 0.033 3.963
14 717 726.1 0.115 4.078
15 490 525.8 2.442 6.520
16 398 381.2 0.745 7.265
17 298 276.5 1.665 8.931
18 209 200.8 0.332 9.263
19 141 146.0 0.170 9.433
20 104 106.2 0.046 9.479
21 296 287.1 0.275 9.754
Chisq= 9.75 for 20 degrees of freedom, p= 0.02759
SUMMARY of craptest
p-value for no. of wins: 0.948307
p-value for throws/game: 0.027590
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_21:31
No. of wins: Observed Expected
98774 98585.9
z-score= 0.841, pvalue=0.79996
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66961 66666.7 1.299 1.299
2 37585 37654.3 0.128 1.427
3 27197 26954.7 2.177 3.605
4 19200 19313.5 0.667 4.271
5 13788 13851.4 0.290 4.562
6 9848 9943.5 0.918 5.480
7 7195 7145.0 0.350 5.829
8 5063 5139.1 1.126 6.955
9 3622 3699.9 1.639 8.594
10 2631 2666.3 0.467 9.061
11 1888 1923.3 0.649 9.710
12 1377 1388.7 0.099 9.809
13 1002 1003.7 0.003 9.812
14 732 726.1 0.047 9.860
15 535 525.8 0.160 10.019
16 378 381.2 0.026 10.045
17 271 276.5 0.111 10.156
18 182 200.8 1.765 11.922
19 161 146.0 1.544 13.466
20 106 106.2 0.000 13.467
21 278 287.1 0.289 13.756
Chisq= 13.76 for 20 degrees of freedom, p= 0.15735
SUMMARY of craptest
p-value for no. of wins: 0.799960
p-value for throws/game: 0.157351
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0032,0.0070,0.0124,0.0186,0.0197,0.0199,0.0276,0.0360,0.0426,0.0456,
0.0459,0.0472,0.0484,0.0509,0.0565,0.0575,0.0614,0.0626,0.0728,0.0737,
0.0884,0.0893,0.0968,0.1087,0.1088,0.1102,0.1112,0.1164,0.1183,0.1221,
0.1226,0.1241,0.1249,0.1279,0.1281,0.1289,0.1308,0.1326,0.1362,0.1373,
0.1440,0.1494,0.1521,0.1570,0.1574,0.1584,0.1650,0.1724,0.1805,0.1815,
0.1921,0.1929,0.1936,0.1950,0.1971,0.1980,0.2055,0.2056,0.2079,0.2130,
0.2158,0.2229,0.2239,0.2240,0.2294,0.2322,0.2325,0.2392,0.2392,0.2494,
0.2580,0.2624,0.2625,0.2631,0.2694,0.2694,0.2763,0.2773,0.2774,0.2803,
0.2902,0.2914,0.2957,0.2994,0.3046,0.3077,0.3099,0.3213,0.3240,0.3240,
0.3281,0.3293,0.3294,0.3314,0.3386,0.3420,0.3424,0.3434,0.3447,0.3500,
0.3543,0.3554,0.3575,0.3656,0.3672,0.3724,0.3746,0.3769,0.3820,0.3825,
0.3830,0.3844,0.3893,0.3908,0.3913,0.3914,0.3962,0.3963,0.4010,0.4028,
0.4055,0.4071,0.4125,0.4190,0.4202,0.4203,0.4213,0.4226,0.4238,0.4269,
0.4284,0.4296,0.4352,0.4370,0.4384,0.4467,0.4488,0.4545,0.4549,0.4600,
0.4624,0.4671,0.4671,0.4718,0.4725,0.4742,0.4749,0.4755,0.4761,0.4784,
0.4803,0.4803,0.4896,0.4922,0.4960,0.4990,0.4996,0.5062,0.5074,0.5117,
0.5117,0.5173,0.5193,0.5303,0.5405,0.5439,0.5453,0.5484,0.5514,0.5601,
0.5612,0.5629,0.5755,0.5855,0.5858,0.5860,0.5892,0.5895,0.5903,0.6092,
0.6098,0.6110,0.6146,0.6156,0.6212,0.6238,0.6310,0.6311,0.6325,0.6335,
0.6346,0.6381,0.6426,0.6489,0.6599,0.6637,0.6649,0.6686,0.6764,0.6862,
0.6909,0.6931,0.7083,0.7109,0.7141,0.7220,0.7270,0.7274,0.7519,0.7528,
0.7679,0.7699,0.7715,0.7727,0.7767,0.7767,0.7798,0.7808,0.7856,0.8000,
0.8013,0.8097,0.8102,0.8197,0.8250,0.8312,0.8387,0.8432,0.8445,0.8459,
0.8530,0.8532,0.8542,0.8587,0.8652,0.8718,0.8748,0.8770,0.8794,0.8804,
0.8810,0.8820,0.8855,0.8867,0.8929,0.9255,0.9282,0.9348,0.9393,0.9483,
0.9522,0.9535,0.9557,0.9574,0.9594,0.9636,0.9642,0.9658,0.9660,0.9674,
0.9717,0.9719,0.9736,0.9739,0.9742,0.9786,0.9789,0.9893,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.107314
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.