RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.82 15.3055 0.426514
2 to 25 15.59 18.0875 0.616659
3 to 26 15.52 19.5044 0.699638
4 to 27 15.62 19.4081 0.694381
5 to 28 15.85 13.2972 0.283925
6 to 29 15.58 19.2522 0.685752
7 to 30 15.82 13.8334 0.321145
8 to 31 15.72 9.7365 0.085705
9 to 32 16.02 24.5272 0.894196
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.851159
Tough bday spacings test for dh-ranFile-2018-07-08_17:31: 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 4 36 84 90 97 72 53 29 21 8 6
(O-E)^2/E 2.9 0.0 1.6 0.6 0.0 0.5 0.0 0.0 2.5 0.3 0.9
Birthday Spacings: Sum(O-E)^2/E= 9.339, p= 0.500
RESULTS OF GCD FOR dh-ranFile-2018-07-08_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.160522
p-value, dist. of gcd's: 0.654260
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.904 0.992 0.510 0.137 0.297 0.432 0.816 0.071
Bits 8 to 15---> 0.777 0.352 0.525 0.608 0.653 0.566 0.360 0.323
Bits 16 to 23---> 0.357 0.017 0.742 0.896 0.771 0.532 0.362 0.092
Bits 24 to 31---> 0.638 0.147 0.661 0.586 0.828 0.403 0.497 0.435
KS test for the above 32 p values: 0.275
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_17:31,
p-values for 5 runs: 0.2896, 0.1693, 0.2116, 0.0375, 0.2596
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5236 5134.0 2.026 2.221
r= 30 23145 23103.0 0.076 2.297
r= 31 11414 11551.5 1.637 3.934
chi-square = 3.934 with df = 3; p-value = 0.731
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 184 211.4 3.556 3.556
r= 30 5187 5134.0 0.547 4.103
r= 31 23255 23103.0 0.999 5.102
r= 32 11374 11551.5 2.728 7.830
chi-square = 7.830 with df = 3; p-value = 0.950
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_17:31
b-rank test for bits 1 to 8, p=0.15191
b-rank test for bits 2 to 9, p=0.67116
b-rank test for bits 3 to 10, p=0.77373
b-rank test for bits 4 to 11, p=0.40001
b-rank test for bits 5 to 12, p=0.47775
b-rank test for bits 6 to 13, p=0.38807
b-rank test for bits 7 to 14, p=0.87950
b-rank test for bits 8 to 15, p=0.22399
b-rank test for bits 9 to 16, p=0.24887
b-rank test for bits 10 to 17, p=0.81339
b-rank test for bits 11 to 18, p=0.54935
b-rank test for bits 12 to 19, p=0.35578
b-rank test for bits 13 to 20, p=0.34393
b-rank test for bits 14 to 21, p=0.93844
b-rank test for bits 15 to 22, p=0.47871
b-rank test for bits 16 to 23, p=0.87677
b-rank test for bits 17 to 24, p=0.01643
b-rank test for bits 18 to 25, p=0.28981
b-rank test for bits 19 to 26, p=0.00410
b-rank test for bits 20 to 27, p=0.19514
b-rank test for bits 21 to 28, p=0.15185
b-rank test for bits 22 to 29, p=0.28653
b-rank test for bits 23 to 30, p=0.55310
b-rank test for bits 24 to 31, p=0.62261
b-rank test for bits 25 to 32, p=0.81729
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 = 0.709345
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_17:31
(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 142061 0.35 0.638469
2 141427 -1.13 0.129884
3 141470 -1.03 0.152335
4 142018 0.25 0.600214
5 141519 -0.91 0.180888
6 141361 -1.28 0.100071
7 141683 -0.53 0.298469
8 142288 0.88 0.811852
9 140731 -2.75 0.002952
10 141661 -0.58 0.280886
11 141267 -1.50 0.066707
12 141505 -0.94 0.172407
13 142087 0.42 0.660972
14 141312 -1.40 0.081413
15 141673 -0.55 0.290415
16 143015 2.58 0.995108
17 141310 -1.40 0.080711
18 142220 0.73 0.766039
19 142508 1.40 0.919058
20 142238 0.77 0.778733
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_17:31
Bits used No. missing words z-score p-value
23 to 32 142420 1.7609 0.960875
22 to 31 141798 -0.3839 0.350528
21 to 30 142088 0.6161 0.731087
20 to 29 141579 -1.1391 0.127337
19 to 28 141879 -0.1046 0.458352
18 to 27 141883 -0.0908 0.463829
17 to 26 142080 0.5885 0.721907
16 to 25 141641 -0.9253 0.177411
15 to 24 141752 -0.5425 0.293731
14 to 23 141792 -0.4046 0.342891
13 to 22 141790 -0.4115 0.340359
12 to 21 141879 -0.1046 0.458352
11 to 20 141868 -0.1425 0.443336
10 to 19 141604 -1.0529 0.146202
9 to 18 141773 -0.4701 0.319141
8 to 17 141809 -0.3460 0.364684
7 to 16 142102 0.6644 0.746776
6 to 15 142111 0.6954 0.756602
5 to 14 141941 0.1092 0.543481
4 to 13 141999 0.3092 0.621418
3 to 12 141362 -1.8873 0.029557
2 to 11 142249 1.1713 0.879256
1 to 10 141768 -0.4873 0.313007
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_17:31
Bits used No. missing words z-score p-value
28 to 32 142105 0.6633 0.746427
27 to 31 142163 0.8599 0.805077
26 to 30 141863 -0.1571 0.437602
25 to 29 142004 0.3209 0.625863
24 to 28 141498 -1.3943 0.081608
23 to 27 142013 0.3514 0.637365
22 to 26 141733 -0.5977 0.275010
21 to 25 141587 -1.0926 0.137275
20 to 24 141875 -0.1164 0.453679
19 to 23 141969 0.2023 0.580148
18 to 22 141952 0.1446 0.557504
17 to 21 142089 0.6091 0.728755
16 to 20 142638 2.4701 0.993246
15 to 19 141751 -0.5367 0.295733
14 to 18 142137 0.7718 0.779873
13 to 17 141696 -0.7232 0.234793
12 to 16 142190 0.9514 0.829305
11 to 15 142237 1.1107 0.866661
10 to 14 141634 -0.9333 0.175327
9 to 13 141938 0.0972 0.538711
8 to 12 142605 2.3582 0.990818
7 to 11 142153 0.8260 0.795598
6 to 10 141675 -0.7943 0.213499
5 to 9 142033 0.4192 0.662473
4 to 8 142043 0.4531 0.674768
3 to 7 142103 0.6565 0.744252
2 to 6 142363 1.5379 0.937959
1 to 5 142816 3.0735 0.998942
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_17:31
Bits used No. missing words z-score p-value
31 to 32 141951 0.1229 0.548915
30 to 31 141381 -1.5585 0.059558
29 to 30 141473 -1.2871 0.099028
28 to 29 142112 0.5978 0.725029
27 to 28 141615 -0.8682 0.192634
26 to 27 140872 -3.0600 0.001107
25 to 26 141400 -1.5024 0.066491
24 to 25 141821 -0.2606 0.397216
23 to 24 141900 -0.0275 0.489022
22 to 23 142030 0.3560 0.639064
21 to 22 142348 1.2940 0.902169
20 to 21 141195 -2.1072 0.017552
19 to 20 142349 1.2970 0.902678
18 to 19 142513 1.7807 0.962522
17 to 18 141841 -0.2016 0.420129
16 to 17 141777 -0.3904 0.348137
15 to 16 142208 0.8810 0.810850
14 to 15 141706 -0.5998 0.274322
13 to 14 141391 -1.5290 0.063133
12 to 13 141857 -0.1544 0.438661
11 to 12 141713 -0.5791 0.281246
10 to 11 141566 -1.0128 0.155584
9 to 10 141780 -0.3815 0.351415
8 to 9 141652 -0.7591 0.223901
7 to 8 141654 -0.7532 0.225669
6 to 7 141968 0.1731 0.568701
5 to 6 142376 1.3766 0.915683
4 to 5 141863 -0.1367 0.445647
3 to 4 141508 -1.1839 0.118233
2 to 3 141622 -0.8476 0.198336
1 to 2 141874 -0.1042 0.458498
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2520.07 0.284 0.611746
Test results for specific bytes for dh-ranFile-2018-07-08_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2518.76 0.265 0.604596
2 to 9 2405.70 -1.334 0.091164
3 to 10 2441.47 -0.828 0.203913
4 to 11 2582.01 1.160 0.876938
5 to 12 2569.48 0.983 0.837092
6 to 13 2634.59 1.903 0.971507
7 to 14 2479.19 -0.294 0.384243
8 to 15 2526.57 0.376 0.646442
9 to 16 2520.74 0.293 0.615352
10 to 17 2484.62 -0.217 0.413923
11 to 18 2431.94 -0.962 0.167902
12 to 19 2412.42 -1.239 0.107753
13 to 20 2447.69 -0.740 0.229716
14 to 21 2461.15 -0.549 0.291365
15 to 22 2610.50 1.563 0.940942
16 to 23 2432.53 -0.954 0.170004
17 to 24 2553.24 0.753 0.774246
18 to 25 2553.62 0.758 0.775846
19 to 26 2509.31 0.132 0.552395
20 to 27 2585.08 1.203 0.885553
21 to 28 2487.02 -0.184 0.427161
22 to 29 2475.68 -0.344 0.365430
23 to 30 2445.20 -0.775 0.219191
24 to 31 2603.21 1.460 0.927798
25 to 32 2496.08 -0.055 0.477902
CDPARK for dh-ranFile-2018-07-08_17:31: 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
3568 2.0548 0.980051
3529 0.2740 0.607947
3559 1.6438 0.949895
3545 1.0046 0.842447
3502 -0.9589 0.168804
3506 -0.7763 0.218799
3555 1.4612 0.928018
3568 2.0548 0.980051
3527 0.1826 0.572463
3515 -0.3653 0.357445
Square side=100, avg. no. parked=3537.40 sample std.=23.72
p-value of the KSTEST for those 10 p-values: 0.046158
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_17:31
0.7920,0.8908,0.8381,0.3965,0.2670,0.1070,0.6984,0.5526,0.2995,0.3741,
The KS test for those 10 p-values: 0.945830
The 3DSPHERES test for dh-ranFile-2018-07-08_17:31
sample no r^3 equiv. uni.
1 31.114 0.645534
2 2.853 0.090732
3 7.285 0.215586
4 41.308 0.747646
5 40.742 0.742841
6 3.744 0.117313
7 43.538 0.765727
8 18.586 0.461797
9 16.588 0.424740
10 70.178 0.903601
11 8.821 0.254758
12 3.711 0.116343
13 46.972 0.791066
14 5.087 0.155964
15 8.764 0.253326
16 4.825 0.148555
17 5.644 0.171485
18 41.888 0.752481
19 0.872 0.028657
20 72.662 0.911263
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.305091
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -0.7 -0.6 -0.3 0.0 -0.4
-1.5 0.9 -0.2 0.7 -0.9 1.4
-0.6 0.7 0.4 -2.1 0.1 -0.3
-1.7 -0.3 -0.4 -0.5 0.4 -0.0
1.0 2.9 2.3 0.5 -0.4 -0.1
0.2 4.3 0.6 -1.4 0.8 -0.7
0.7 -2.0 -1.2 0.4 0.1 -1.0
0.8
Chi-square with 42 degrees of freedom:63.036464
z-score=2.295266, p-value=0.980578
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_17:31
Test no p-value
1 0.078925
2 0.178163
3 0.043024
4 0.570956
5 0.618375
6 0.348925
7 0.075442
8 0.832605
9 0.270003
10 0.053927
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.038047
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_17:31:
(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 66696 0.01 66638 0.01
3 25000.00 25111 0.49 25033 0.04
4 6666.67 6576 1.23 6633 0.17
5 1388.89 1365 0.41 1423 0.84
6 238.10 216 2.05 227 0.52
7 34.72 30 0.64 38 0.31
8 4.96 5 0.00 7 0.84
p=0.43580 p=0.15806
Number of rngs required: 688092, p-value: 0.360
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_17:31
No. of wins: Observed Expected
98457 98585.9
z-score=-0.576, pvalue=0.28220
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66306 66666.7 1.951 1.951
2 38194 37654.3 7.735 9.686
3 26665 26954.7 3.114 12.800
4 19369 19313.5 0.160 12.960
5 13799 13851.4 0.198 13.159
6 10049 9943.5 1.118 14.277
7 7119 7145.0 0.095 14.372
8 5125 5139.1 0.039 14.410
9 3724 3699.9 0.157 14.568
10 2605 2666.3 1.409 15.977
11 1929 1923.3 0.017 15.994
12 1436 1388.7 1.608 17.602
13 1011 1003.7 0.053 17.655
14 723 726.1 0.014 17.668
15 540 525.8 0.382 18.050
16 358 381.2 1.406 19.456
17 269 276.5 0.206 19.662
18 215 200.8 1.000 20.661
19 149 146.0 0.062 20.724
20 102 106.2 0.167 20.891
21 313 287.1 2.334 23.225
Chisq= 23.22 for 20 degrees of freedom, p= 0.72211
SUMMARY of craptest
p-value for no. of wins: 0.282196
p-value for throws/game: 0.722111
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_17:31
No. of wins: Observed Expected
98046 98585.9
z-score=-2.415, pvalue=0.00788
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66752 66666.7 0.109 0.109
2 37875 37654.3 1.293 1.403
3 26711 26954.7 2.204 3.606
4 19147 19313.5 1.435 5.041
5 14050 13851.4 2.847 7.888
6 9993 9943.5 0.246 8.134
7 7064 7145.0 0.919 9.053
8 5122 5139.1 0.057 9.110
9 3600 3699.9 2.696 11.805
10 2653 2666.3 0.066 11.871
11 1868 1923.3 1.592 13.463
12 1419 1388.7 0.659 14.122
13 1054 1003.7 2.519 16.642
14 724 726.1 0.006 16.648
15 552 525.8 1.302 17.950
16 369 381.2 0.387 18.337
17 301 276.5 2.164 20.501
18 215 200.8 1.000 21.501
19 150 146.0 0.110 21.611
20 97 106.2 0.800 22.411
21 284 287.1 0.034 22.444
Chisq= 22.44 for 20 degrees of freedom, p= 0.68311
SUMMARY of craptest
p-value for no. of wins: 0.007877
p-value for throws/game: 0.683107
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0030,0.0041,0.0079,0.0164,0.0174,0.0176,0.0287,0.0296,0.0375,
0.0380,0.0430,0.0462,0.0539,0.0596,0.0631,0.0665,0.0667,0.0708,0.0754,
0.0789,0.0807,0.0814,0.0816,0.0857,0.0907,0.0912,0.0915,0.0990,0.1001,
0.1070,0.1078,0.1163,0.1173,0.1182,0.1273,0.1299,0.1373,0.1373,0.1462,
0.1470,0.1486,0.1519,0.1519,0.1523,0.1556,0.1560,0.1581,0.1605,0.1679,
0.1688,0.1693,0.1700,0.1715,0.1724,0.1753,0.1774,0.1782,0.1809,0.1926,
0.1951,0.1983,0.2039,0.2116,0.2135,0.2156,0.2188,0.2192,0.2239,0.2240,
0.2257,0.2297,0.2348,0.2489,0.2533,0.2548,0.2596,0.2670,0.2700,0.2743,
0.2750,0.2752,0.2809,0.2812,0.2822,0.2839,0.2865,0.2896,0.2898,0.2904,
0.2914,0.2937,0.2957,0.2973,0.2985,0.2995,0.3051,0.3130,0.3191,0.3211,
0.3230,0.3404,0.3429,0.3439,0.3481,0.3489,0.3505,0.3514,0.3518,0.3558,
0.3574,0.3575,0.3601,0.3602,0.3621,0.3647,0.3654,0.3741,0.3842,0.3881,
0.3965,0.3972,0.4000,0.4034,0.4139,0.4201,0.4247,0.4265,0.4272,0.4320,
0.4350,0.4358,0.4376,0.4387,0.4433,0.4456,0.4537,0.4584,0.4584,0.4585,
0.4618,0.4638,0.4777,0.4779,0.4787,0.4890,0.4967,0.4998,0.5100,0.5250,
0.5316,0.5387,0.5435,0.5489,0.5494,0.5524,0.5526,0.5531,0.5575,0.5665,
0.5687,0.5710,0.5725,0.5801,0.5860,0.6002,0.6046,0.6078,0.6079,0.6117,
0.6154,0.6167,0.6184,0.6214,0.6226,0.6259,0.6374,0.6378,0.6385,0.6391,
0.6455,0.6464,0.6534,0.6543,0.6606,0.6610,0.6625,0.6712,0.6748,0.6831,
0.6858,0.6944,0.6984,0.6996,0.7093,0.7219,0.7221,0.7250,0.7288,0.7311,
0.7314,0.7420,0.7428,0.7443,0.7464,0.7468,0.7476,0.7525,0.7566,0.7657,
0.7660,0.7713,0.7737,0.7742,0.7758,0.7775,0.7787,0.7799,0.7911,0.7920,
0.7956,0.8051,0.8108,0.8119,0.8134,0.8159,0.8173,0.8283,0.8293,0.8326,
0.8371,0.8381,0.8424,0.8512,0.8667,0.8768,0.8769,0.8793,0.8795,0.8856,
0.8908,0.8942,0.8957,0.9022,0.9027,0.9036,0.9039,0.9113,0.9157,0.9191,
0.9278,0.9280,0.9380,0.9384,0.9409,0.9458,0.9499,0.9503,0.9609,0.9625,
0.9715,0.9801,0.9801,0.9806,0.9908,0.9916,0.9932,0.9951,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.284820
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.