RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_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 15.71 22.9873 0.850337
2 to 25 15.53 27.2335 0.945269
3 to 26 15.64 18.4214 0.637267
4 to 27 15.94 28.0072 0.955146
5 to 28 15.96 15.0258 0.406376
6 to 29 16.12 16.1130 0.484159
7 to 30 15.78 17.4319 0.574506
8 to 31 15.73 18.9011 0.665763
9 to 32 15.72 25.3849 0.913581
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.037833
Tough bday spacings test for dh-ranFile-2018-06-17_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 7 39 84 115 89 78 54 16 6 9 3
(O-E)^2/E 0.5 0.2 1.6 3.1 0.8 0.0 0.1 6.4 5.3 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 18.959, p= 0.959
RESULTS OF GCD FOR dh-ranFile-2018-06-17_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.074403
p-value, dist. of gcd's: 0.820401
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.023 0.036 0.311 0.717 0.895 0.319 0.096 0.870
Bits 8 to 15---> 0.299 0.482 0.425 0.838 0.278 0.310 0.948 0.208
Bits 16 to 23---> 0.227 0.574 0.847 0.655 0.876 0.246 0.311 0.269
Bits 24 to 31---> 0.602 0.585 0.149 0.106 0.411 0.916 0.358 0.461
KS test for the above 32 p values: 0.477
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_13:31,
p-values for 5 runs: 0.0154, 0.6751, 0.7839, 0.6347, 0.7797
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 213 211.4 0.012 0.012
r= 29 5151 5134.0 0.056 0.068
r= 30 22932 23103.0 1.266 1.334
r= 31 11704 11551.5 2.013 3.347
chi-square = 3.347 with df = 3; p-value = 0.659
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 199 211.4 0.729 0.729
r= 30 5068 5134.0 0.849 1.578
r= 31 23200 23103.0 0.407 1.985
r= 32 11533 11551.5 0.030 2.015
chi-square = 2.015 with df = 3; p-value = 0.431
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_13:31
b-rank test for bits 1 to 8, p=0.04195
b-rank test for bits 2 to 9, p=0.60672
b-rank test for bits 3 to 10, p=0.72461
b-rank test for bits 4 to 11, p=0.28415
b-rank test for bits 5 to 12, p=0.38302
b-rank test for bits 6 to 13, p=0.57466
b-rank test for bits 7 to 14, p=0.68143
b-rank test for bits 8 to 15, p=0.27069
b-rank test for bits 9 to 16, p=0.67214
b-rank test for bits 10 to 17, p=0.69804
b-rank test for bits 11 to 18, p=0.79675
b-rank test for bits 12 to 19, p=0.15716
b-rank test for bits 13 to 20, p=0.13670
b-rank test for bits 14 to 21, p=0.08788
b-rank test for bits 15 to 22, p=0.66223
b-rank test for bits 16 to 23, p=0.67265
b-rank test for bits 17 to 24, p=0.08237
b-rank test for bits 18 to 25, p=0.29692
b-rank test for bits 19 to 26, p=0.13318
b-rank test for bits 20 to 27, p=0.24227
b-rank test for bits 21 to 28, p=0.33697
b-rank test for bits 22 to 29, p=0.90068
b-rank test for bits 23 to 30, p=0.99802
b-rank test for bits 24 to 31, p=0.86701
b-rank test for bits 25 to 32, p=0.69247
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 = 0.744515
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_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 142343 1.01 0.844529
2 142353 1.04 0.850042
3 142186 0.65 0.740998
4 141876 -0.08 0.468964
5 142331 0.99 0.837740
6 141081 -1.94 0.026474
7 141971 0.14 0.557285
8 141281 -1.47 0.071044
9 141332 -1.35 0.088684
10 142354 1.04 0.850586
11 141922 0.03 0.511808
12 141253 -1.53 0.062579
13 142523 1.43 0.924187
14 142764 2.00 0.977082
15 142531 1.45 0.926819
16 141615 -0.69 0.245825
17 142120 0.49 0.688718
18 142360 1.05 0.853822
19 141676 -0.55 0.292821
20 142255 0.81 0.790351
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_13:31
Bits used No. missing words z-score p-value
23 to 32 142145 0.8127 0.791792
22 to 31 142141 0.7989 0.787815
21 to 30 142226 1.0920 0.862576
20 to 29 142129 0.7575 0.775620
19 to 28 141722 -0.6460 0.259151
18 to 27 141695 -0.7391 0.229933
17 to 26 142033 0.4264 0.665109
16 to 25 141875 -0.1184 0.452884
15 to 24 141899 -0.0356 0.485792
14 to 23 141879 -0.1046 0.458352
13 to 22 141925 0.0540 0.521546
12 to 21 141986 0.2644 0.604256
11 to 20 141827 -0.2839 0.388245
10 to 19 141939 0.1023 0.540745
9 to 18 141875 -0.1184 0.452884
8 to 17 142187 0.9575 0.830838
7 to 16 141804 -0.3632 0.358225
6 to 15 142350 1.5196 0.935688
5 to 14 142026 0.4023 0.656272
4 to 13 142197 0.9920 0.839393
3 to 12 142201 1.0058 0.842734
2 to 11 141844 -0.2253 0.410882
1 to 10 142067 0.5437 0.706673
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_13:31
Bits used No. missing words z-score p-value
28 to 32 141861 -0.1638 0.434932
27 to 31 141898 -0.0384 0.484682
26 to 30 141811 -0.3333 0.369446
25 to 29 141971 0.2091 0.582796
24 to 28 142347 1.4836 0.931046
23 to 27 142167 0.8735 0.808793
22 to 26 141490 -1.4215 0.077592
21 to 25 142323 1.4023 0.919583
20 to 24 142419 1.7277 0.957979
19 to 23 141670 -0.8113 0.208600
18 to 22 141339 -1.9333 0.026598
17 to 21 141303 -2.0554 0.019922
16 to 20 141752 -0.5333 0.296905
15 to 19 141975 0.2226 0.588081
14 to 18 141911 0.0057 0.502258
13 to 17 141822 -0.2960 0.383602
12 to 16 142143 0.7921 0.785849
11 to 15 141897 -0.0418 0.483330
10 to 14 142043 0.4531 0.674768
9 to 13 142079 0.5752 0.717406
8 to 12 142357 1.5175 0.935433
7 to 11 142024 0.3887 0.651255
6 to 10 141987 0.2633 0.603836
5 to 9 141930 0.0701 0.527930
4 to 8 142007 0.3311 0.629710
3 to 7 141924 0.0497 0.519831
2 to 6 141821 -0.2994 0.382308
1 to 5 141592 -1.0757 0.141032
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_13:31
Bits used No. missing words z-score p-value
31 to 32 142057 0.4356 0.668438
30 to 31 142405 1.4622 0.928150
29 to 30 142072 0.4799 0.684334
28 to 29 142316 1.1996 0.884856
27 to 28 142369 1.3560 0.912444
26 to 27 141622 -0.8476 0.198336
25 to 26 141593 -0.9331 0.175377
24 to 25 141561 -1.0275 0.152087
23 to 24 142281 1.0964 0.863542
22 to 23 141980 0.2085 0.582568
21 to 22 141904 -0.0157 0.493728
20 to 21 142045 0.4002 0.655498
19 to 20 141545 -1.0747 0.141250
18 to 19 141287 -1.8358 0.033195
17 to 18 142233 0.9548 0.830155
16 to 17 141738 -0.5054 0.306640
15 to 16 141831 -0.2311 0.408633
14 to 15 141686 -0.6588 0.255015
13 to 14 142263 1.0433 0.851589
12 to 13 141204 -2.0806 0.018734
11 to 12 142541 1.8633 0.968792
10 to 11 142156 0.7276 0.766583
9 to 10 142471 1.6568 0.951224
8 to 9 142144 0.6922 0.755607
7 to 8 141776 -0.3933 0.347048
6 to 7 141954 0.1318 0.552417
5 to 6 141776 -0.3933 0.347048
4 to 5 142006 0.2852 0.612240
3 to 4 142325 1.2262 0.889932
2 to 3 142323 1.2203 0.888818
1 to 2 141523 -1.1396 0.127223
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2520.18 0.285 0.612352
Test results for specific bytes for dh-ranFile-2018-06-17_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2703.92 2.884 0.998036
2 to 9 2446.27 -0.760 0.223679
3 to 10 2497.75 -0.032 0.487315
4 to 11 2507.31 0.103 0.541143
5 to 12 2643.28 2.026 0.978629
6 to 13 2390.31 -1.551 0.060418
7 to 14 2516.14 0.228 0.590288
8 to 15 2481.56 -0.261 0.397152
9 to 16 2379.84 -1.699 0.044631
10 to 17 2624.87 1.766 0.961296
11 to 18 2583.07 1.175 0.879960
12 to 19 2458.54 -0.586 0.278804
13 to 20 2656.00 2.206 0.986314
14 to 21 2540.21 0.569 0.715217
15 to 22 2468.39 -0.447 0.327442
16 to 23 2554.81 0.775 0.780851
17 to 24 2494.24 -0.081 0.467549
18 to 25 2507.74 0.110 0.543604
19 to 26 2498.77 -0.017 0.493045
20 to 27 2400.66 -1.405 0.080021
21 to 28 2493.38 -0.094 0.462725
22 to 29 2446.71 -0.754 0.225528
23 to 30 2537.31 0.528 0.701110
24 to 31 2448.73 -0.725 0.234199
25 to 32 2434.00 -0.933 0.175300
CDPARK for dh-ranFile-2018-06-17_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
3489 -1.5525 0.060270
3500 -1.0502 0.146807
3541 0.8219 0.794438
3533 0.4566 0.676028
3483 -1.8265 0.033889
3551 1.2785 0.899470
3523 0.0000 0.500000
3536 0.5936 0.723613
3544 0.9589 0.831196
3508 -0.6849 0.246694
Square side=100, avg. no. parked=3520.80 sample std.=22.98
p-value of the KSTEST for those 10 p-values: 0.782558
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_13:31
0.2517,0.5826,0.6918,0.6040,0.6642,0.2840,0.7453,0.1955,0.3446,0.5059,
The KS test for those 10 p-values: 0.469295
The 3DSPHERES test for dh-ranFile-2018-06-17_13:31
sample no r^3 equiv. uni.
1 1.677 0.054376
2 97.862 0.961691
3 0.949 0.031122
4 18.419 0.458804
5 48.775 0.803250
6 12.357 0.337607
7 21.457 0.510920
8 6.951 0.206817
9 33.082 0.668040
10 7.682 0.225898
11 217.556 0.999291
12 76.508 0.921939
13 61.440 0.871006
14 11.471 0.317745
15 21.751 0.515688
16 5.635 0.171239
17 14.859 0.390604
18 2.123 0.068315
19 15.912 0.411640
20 18.561 0.461353
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.661627
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 0.1 0.0 -1.4 -0.7
1.0 0.0 -1.3 0.0 0.6 0.5
-1.3 0.2 -0.7 0.0 0.6 -2.2
0.0 1.1 0.7 -0.1 1.2 -0.7
1.2 -0.5 0.8 0.8 -0.0 -0.5
0.5 1.0 -1.6 0.4 -1.0 -1.0
0.5 2.1 0.1 -0.1 -1.3 -1.0
0.8
Chi-square with 42 degrees of freedom:34.628460
z-score=-0.804301, p-value=0.216840
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_13:31
Test no p-value
1 0.610970
2 0.312449
3 0.683353
4 0.537374
5 0.001855
6 0.005539
7 0.549174
8 0.000295
9 0.062904
10 0.058584
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000818
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_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 66598 0.07 66418 0.93
3 25000.00 25027 0.03 25004 0.00
4 6666.67 6681 0.03 6839 4.45
5 1388.89 1416 0.53 1449 2.60
6 238.10 237 0.01 248 0.41
7 34.72 35 0.00 36 0.05
8 4.96 5 0.00 5 0.00
p=0.00483 p=0.79265
Number of rngs required: 689907, p-value: 0.961
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_13:31
No. of wins: Observed Expected
98189 98585.9
z-score=-1.775, pvalue=0.03795
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66659 66666.7 0.001 0.001
2 37712 37654.3 0.088 0.089
3 27022 26954.7 0.168 0.257
4 19468 19313.5 1.237 1.494
5 13778 13851.4 0.389 1.883
6 9970 9943.5 0.070 1.953
7 7090 7145.0 0.424 2.377
8 5164 5139.1 0.121 2.498
9 3606 3699.9 2.381 4.879
10 2599 2666.3 1.699 6.578
11 1960 1923.3 0.699 7.277
12 1334 1388.7 2.158 9.435
13 1032 1003.7 0.797 10.232
14 730 726.1 0.021 10.252
15 526 525.8 0.000 10.252
16 350 381.2 2.546 12.798
17 285 276.5 0.259 13.057
18 165 200.8 6.392 19.449
19 148 146.0 0.028 19.477
20 114 106.2 0.571 20.048
21 288 287.1 0.003 20.051
Chisq= 20.05 for 20 degrees of freedom, p= 0.54523
SUMMARY of craptest
p-value for no. of wins: 0.037950
p-value for throws/game: 0.545230
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_13:31
No. of wins: Observed Expected
98551 98585.9
z-score=-0.156, pvalue=0.43805
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66675 66666.7 0.001 0.001
2 37618 37654.3 0.035 0.036
3 26740 26954.7 1.711 1.747
4 19254 19313.5 0.183 1.930
5 13887 13851.4 0.091 2.021
6 10050 9943.5 1.140 3.161
7 7156 7145.0 0.017 3.178
8 5329 5139.1 7.019 10.197
9 3693 3699.9 0.013 10.210
10 2674 2666.3 0.022 10.232
11 1927 1923.3 0.007 10.239
12 1375 1388.7 0.136 10.375
13 975 1003.7 0.822 11.197
14 745 726.1 0.490 11.686
15 524 525.8 0.006 11.693
16 352 381.2 2.229 13.922
17 284 276.5 0.201 14.123
18 188 200.8 0.820 14.943
19 160 146.0 1.346 16.289
20 105 106.2 0.014 16.303
21 289 287.1 0.012 16.315
Chisq= 16.31 for 20 degrees of freedom, p= 0.30310
SUMMARY of craptest
p-value for no. of wins: 0.438053
p-value for throws/game: 0.303100
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0008,0.0019,0.0048,0.0055,0.0154,0.0187,0.0199,0.0225,0.0265,
0.0266,0.0311,0.0332,0.0339,0.0355,0.0378,0.0380,0.0419,0.0446,0.0544,
0.0586,0.0603,0.0604,0.0626,0.0629,0.0683,0.0710,0.0744,0.0776,0.0800,
0.0824,0.0879,0.0887,0.0956,0.1061,0.1272,0.1332,0.1367,0.1410,0.1413,
0.1468,0.1495,0.1521,0.1572,0.1712,0.1753,0.1754,0.1955,0.1983,0.2068,
0.2083,0.2086,0.2168,0.2237,0.2255,0.2259,0.2272,0.2299,0.2342,0.2423,
0.2458,0.2459,0.2467,0.2517,0.2550,0.2592,0.2695,0.2707,0.2782,0.2788,
0.2840,0.2841,0.2928,0.2969,0.2969,0.2990,0.3031,0.3066,0.3097,0.3109,
0.3112,0.3124,0.3177,0.3191,0.3274,0.3370,0.3376,0.3446,0.3470,0.3470,
0.3577,0.3582,0.3694,0.3823,0.3830,0.3836,0.3882,0.3906,0.3972,0.4064,
0.4086,0.4106,0.4109,0.4116,0.4246,0.4306,0.4349,0.4381,0.4529,0.4529,
0.4584,0.4588,0.4612,0.4614,0.4627,0.4675,0.4690,0.4693,0.4768,0.4823,
0.4833,0.4842,0.4847,0.4858,0.4873,0.4930,0.4937,0.5000,0.5023,0.5059,
0.5109,0.5118,0.5157,0.5198,0.5215,0.5279,0.5374,0.5407,0.5411,0.5436,
0.5452,0.5492,0.5524,0.5573,0.5735,0.5745,0.5747,0.5826,0.5826,0.5828,
0.5847,0.5881,0.5903,0.6020,0.6038,0.6040,0.6043,0.6067,0.6110,0.6122,
0.6124,0.6297,0.6347,0.6373,0.6513,0.6545,0.6555,0.6563,0.6589,0.6616,
0.6622,0.6642,0.6651,0.6658,0.6680,0.6684,0.6721,0.6726,0.6748,0.6751,
0.6760,0.6814,0.6834,0.6843,0.6887,0.6918,0.6925,0.6980,0.7011,0.7067,
0.7152,0.7166,0.7174,0.7236,0.7246,0.7410,0.7445,0.7453,0.7556,0.7666,
0.7756,0.7797,0.7809,0.7826,0.7839,0.7858,0.7878,0.7904,0.7918,0.7926,
0.7944,0.7967,0.8033,0.8088,0.8204,0.8302,0.8308,0.8312,0.8377,0.8383,
0.8394,0.8427,0.8445,0.8466,0.8500,0.8503,0.8506,0.8516,0.8538,0.8626,
0.8635,0.8670,0.8705,0.8710,0.8764,0.8800,0.8849,0.8888,0.8899,0.8950,
0.8995,0.9007,0.9124,0.9136,0.9163,0.9196,0.9219,0.9242,0.9268,0.9282,
0.9310,0.9354,0.9357,0.9453,0.9480,0.9512,0.9551,0.9580,0.9592,0.9613,
0.9613,0.9617,0.9688,0.9771,0.9786,0.9863,0.9980,0.9980,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.460973
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.