RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.66 22.5689 0.836181
2 to 25 15.90 14.4148 0.362446
3 to 26 15.51 30.4482 0.976712
4 to 27 15.38 24.8331 0.901491
5 to 28 15.54 24.7773 0.900193
6 to 29 15.89 16.4024 0.504495
7 to 30 15.61 14.5066 0.369023
8 to 31 15.53 16.3545 0.501141
9 to 32 15.67 15.7932 0.461462
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.149003
Tough bday spacings test for dh-ranFile-2018-06-27_00:31: 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 9 41 83 107 86 73 43 37 15 4 2
(O-E)^2/E 0.0 0.5 1.3 0.9 1.4 0.3 1.6 1.8 0.0 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 9.872, p= 0.548
RESULTS OF GCD FOR dh-ranFile-2018-06-27_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.445830
p-value, dist. of gcd's: 0.295574
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.042 0.921 0.197 0.094 0.735 0.120 0.272 0.580
Bits 8 to 15---> 0.827 0.666 0.778 0.584 0.448 0.936 0.098 0.205
Bits 16 to 23---> 0.884 0.570 0.580 0.139 0.549 0.476 0.453 0.951
Bits 24 to 31---> 0.675 0.551 0.435 0.996 0.597 0.753 0.396 0.636
KS test for the above 32 p values: 0.336
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_00:31,
p-values for 5 runs: 0.3415, 0.6283, 0.6562, 0.6500, 0.2966
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5283 5134.0 4.324 4.379
r= 30 22951 23103.0 1.001 5.380
r= 31 11558 11551.5 0.004 5.383
chi-square = 5.383 with df = 3; p-value = 0.854
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5067 5134.0 0.875 0.935
r= 31 23107 23103.0 0.001 0.936
r= 32 11611 11551.5 0.306 1.242
chi-square = 1.242 with df = 3; p-value = 0.257
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_00:31
b-rank test for bits 1 to 8, p=0.11917
b-rank test for bits 2 to 9, p=0.70544
b-rank test for bits 3 to 10, p=0.54600
b-rank test for bits 4 to 11, p=0.43446
b-rank test for bits 5 to 12, p=0.09693
b-rank test for bits 6 to 13, p=0.56975
b-rank test for bits 7 to 14, p=0.75309
b-rank test for bits 8 to 15, p=0.41744
b-rank test for bits 9 to 16, p=0.44609
b-rank test for bits 10 to 17, p=0.07875
b-rank test for bits 11 to 18, p=0.03022
b-rank test for bits 12 to 19, p=0.96475
b-rank test for bits 13 to 20, p=0.64847
b-rank test for bits 14 to 21, p=0.49250
b-rank test for bits 15 to 22, p=0.84814
b-rank test for bits 16 to 23, p=0.16192
b-rank test for bits 17 to 24, p=0.41566
b-rank test for bits 18 to 25, p=0.09439
b-rank test for bits 19 to 26, p=0.05045
b-rank test for bits 20 to 27, p=0.01771
b-rank test for bits 21 to 28, p=0.64968
b-rank test for bits 22 to 29, p=0.29567
b-rank test for bits 23 to 30, p=0.43523
b-rank test for bits 24 to 31, p=0.97294
b-rank test for bits 25 to 32, p=0.37014
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 = 0.248702
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_00:31
(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 141567 -0.80 0.211903
2 141600 -0.72 0.234922
3 141792 -0.27 0.391990
4 141402 -1.19 0.117939
5 141996 0.20 0.580237
6 142029 0.28 0.610109
7 141684 -0.53 0.299280
8 141748 -0.38 0.353109
9 142201 0.68 0.752214
10 141835 -0.17 0.431063
11 141657 -0.59 0.277744
12 141664 -0.57 0.283254
13 141340 -1.33 0.091725
14 142243 0.78 0.782188
15 141349 -1.31 0.095236
16 142080 0.40 0.654966
17 142122 0.50 0.690368
18 141689 -0.51 0.303350
19 142310 0.94 0.825401
20 141563 -0.81 0.209205
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_00:31
Bits used No. missing words z-score p-value
23 to 32 142349 1.5161 0.935253
22 to 31 141592 -1.0942 0.136925
21 to 30 142001 0.3161 0.624038
20 to 29 142151 0.8333 0.797675
19 to 28 141999 0.3092 0.621418
18 to 27 142058 0.5127 0.695904
17 to 26 141765 -0.4977 0.309351
16 to 25 142093 0.6333 0.736746
15 to 24 141790 -0.4115 0.340359
14 to 23 141983 0.2540 0.600266
13 to 22 142324 1.4299 0.923627
12 to 21 142151 0.8333 0.797675
11 to 20 142080 0.5885 0.721907
10 to 19 141529 -1.3115 0.094847
9 to 18 141856 -0.1839 0.427047
8 to 17 141744 -0.5701 0.284304
7 to 16 141604 -1.0529 0.146202
6 to 15 141772 -0.4736 0.317910
5 to 14 142145 0.8127 0.791792
4 to 13 141539 -1.2770 0.100801
3 to 12 141546 -1.2529 0.105128
2 to 11 142391 1.6609 0.951636
1 to 10 141888 -0.0736 0.470684
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_00:31
Bits used No. missing words z-score p-value
28 to 32 141964 0.1853 0.573512
27 to 31 141963 0.1819 0.572182
26 to 30 141780 -0.4384 0.330546
25 to 29 142088 0.6057 0.727630
24 to 28 141969 0.2023 0.580148
23 to 27 141696 -0.7232 0.234793
22 to 26 141503 -1.3774 0.084196
21 to 25 141804 -0.3571 0.360527
20 to 24 142241 1.1243 0.869558
19 to 23 141940 0.1040 0.541402
18 to 22 141605 -1.0316 0.151123
17 to 21 142157 0.8396 0.799422
16 to 20 142002 0.3141 0.623291
15 to 19 142208 1.0124 0.844336
14 to 18 141871 -0.1299 0.448310
13 to 17 142004 0.3209 0.625863
12 to 16 142096 0.6328 0.736561
11 to 15 142532 2.1107 0.982603
10 to 14 142165 0.8667 0.806941
9 to 13 141408 -1.6994 0.044620
8 to 12 141731 -0.6045 0.272753
7 to 11 141966 0.1921 0.576169
6 to 10 142327 1.4158 0.921587
5 to 9 141992 0.2802 0.610352
4 to 8 142023 0.3853 0.650001
3 to 7 141410 -1.6926 0.045262
2 to 6 141721 -0.6384 0.261605
1 to 5 142310 1.3582 0.912800
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_00:31
Bits used No. missing words z-score p-value
31 to 32 141913 0.0108 0.504319
30 to 31 141856 -0.1573 0.437498
29 to 30 142618 2.0905 0.981712
28 to 29 141859 -0.1485 0.440988
27 to 28 141704 -0.6057 0.272359
26 to 27 141929 0.0580 0.523135
25 to 26 142217 0.9076 0.817950
24 to 25 141695 -0.6322 0.263614
23 to 24 141802 -0.3166 0.375771
22 to 23 141799 -0.3255 0.372418
21 to 22 142395 1.4327 0.924022
20 to 21 142313 1.1908 0.883127
19 to 20 142289 1.1200 0.868637
18 to 19 141767 -0.4199 0.337297
17 to 18 142084 0.5153 0.696811
16 to 17 141566 -1.0128 0.155584
15 to 16 141833 -0.2252 0.410927
14 to 15 141570 -1.0010 0.158420
13 to 14 141752 -0.4641 0.321288
12 to 13 141618 -0.8594 0.195065
11 to 12 141961 0.1524 0.560572
10 to 11 141813 -0.2842 0.388144
9 to 10 142312 1.1878 0.882547
8 to 9 141475 -1.2812 0.100060
7 to 8 141720 -0.5585 0.288253
6 to 7 141547 -1.0688 0.142575
5 to 6 141759 -0.4435 0.328720
4 to 5 141362 -1.6145 0.053205
3 to 4 141380 -1.5614 0.059209
2 to 3 141150 -2.2399 0.012548
1 to 2 141485 -1.2517 0.105338
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2461.49 -0.545 0.293022
Test results for specific bytes for dh-ranFile-2018-06-27_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2393.22 -1.510 0.065511
2 to 9 2433.71 -0.938 0.174241
3 to 10 2521.93 0.310 0.621784
4 to 11 2577.01 1.089 0.861945
5 to 12 2509.08 0.128 0.551098
6 to 13 2384.23 -1.637 0.050796
7 to 14 2397.68 -1.447 0.073953
8 to 15 2517.97 0.254 0.600308
9 to 16 2544.53 0.630 0.735558
10 to 17 2513.77 0.195 0.577207
11 to 18 2406.87 -1.317 0.093903
12 to 19 2477.99 -0.311 0.377776
13 to 20 2451.54 -0.685 0.246589
14 to 21 2399.87 -1.416 0.078370
15 to 22 2528.48 0.403 0.656421
16 to 23 2516.90 0.239 0.594474
17 to 24 2540.58 0.574 0.716999
18 to 25 2492.10 -0.112 0.455511
19 to 26 2483.42 -0.235 0.407296
20 to 27 2460.69 -0.556 0.289106
21 to 28 2642.07 2.009 0.977739
22 to 29 2472.21 -0.393 0.347154
23 to 30 2458.55 -0.586 0.278895
24 to 31 2477.29 -0.321 0.374024
25 to 32 2583.48 1.181 0.881108
CDPARK for dh-ranFile-2018-06-27_00:31: 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
3525 0.0913 0.536383
3505 -0.8219 0.205562
3491 -1.4612 0.071982
3526 0.1370 0.554479
3546 1.0502 0.853193
3517 -0.2740 0.392053
3526 0.1370 0.554479
3517 -0.2740 0.392053
3525 0.0913 0.536383
3464 -2.6941 0.003529
Square side=100, avg. no. parked=3514.20 sample std.=21.64
p-value of the KSTEST for those 10 p-values: 0.322969
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_00:31
0.0528,0.8323,0.8705,0.5772,0.2792,0.3596,0.5326,0.6904,0.5228,0.8123,
The KS test for those 10 p-values: 0.765786
The 3DSPHERES test for dh-ranFile-2018-06-27_00:31
sample no r^3 equiv. uni.
1 8.691 0.251501
2 1.865 0.060272
3 68.174 0.896943
4 0.693 0.022848
5 27.607 0.601568
6 82.375 0.935806
7 15.963 0.412635
8 46.331 0.786555
9 53.555 0.832233
10 49.047 0.805031
11 12.494 0.340627
12 13.265 0.357358
13 67.531 0.894711
14 62.763 0.876572
15 21.211 0.506890
16 3.728 0.116861
17 65.079 0.885744
18 36.867 0.707388
19 36.068 0.699485
20 38.329 0.721302
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.223344
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.7 0.1 0.2 -0.8 -1.3
-0.9 -0.4 -1.4 -0.3 -0.1 -0.2
0.6 -1.6 -0.3 0.4 -0.1 -0.2
1.3 2.0 1.3 -1.8 -1.3 1.6
0.0 -0.8 0.9 -0.4 0.0 -0.8
-1.0 1.2 1.4 0.4 -0.1 0.1
-1.2 -0.7 -1.6 -0.7 0.9 -1.0
1.8
Chi-square with 42 degrees of freedom:44.403970
z-score=0.262295, p-value=0.629275
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_00:31
Test no p-value
1 0.055370
2 0.717753
3 0.258317
4 0.153081
5 0.059014
6 0.105557
7 0.652518
8 0.547306
9 0.894742
10 0.245558
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.204994
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_00:31:
(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 66661 0.00 66691 0.01
3 25000.00 25050 0.10 25015 0.01
4 6666.67 6645 0.07 6670 0.00
5 1388.89 1364 0.45 1343 1.52
6 238.10 248 0.41 240 0.02
7 34.72 26 2.19 36 0.05
8 4.96 5 0.00 4 0.19
p=0.21915 p=0.06155
Number of rngs required: 688118, p-value: 0.371
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_00:31
No. of wins: Observed Expected
99088 98585.9
z-score= 2.246, pvalue=0.98764
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66658 66666.7 0.001 0.001
2 37782 37654.3 0.433 0.434
3 27029 26954.7 0.205 0.639
4 19123 19313.5 1.878 2.517
5 13841 13851.4 0.008 2.525
6 10099 9943.5 2.430 4.955
7 7026 7145.0 1.983 6.938
8 5074 5139.1 0.824 7.762
9 3725 3699.9 0.171 7.933
10 2706 2666.3 0.591 8.524
11 1946 1923.3 0.267 8.791
12 1291 1388.7 6.879 15.670
13 1031 1003.7 0.742 16.412
14 732 726.1 0.047 16.459
15 534 525.8 0.127 16.586
16 396 381.2 0.579 17.164
17 290 276.5 0.655 17.820
18 178 200.8 2.595 20.415
19 163 146.0 1.983 22.398
20 111 106.2 0.216 22.614
21 265 287.1 1.703 24.317
Chisq= 24.32 for 20 degrees of freedom, p= 0.77118
SUMMARY of craptest
p-value for no. of wins: 0.987644
p-value for throws/game: 0.771180
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_00:31
No. of wins: Observed Expected
98620 98585.9
z-score= 0.153, pvalue=0.56068
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66409 66666.7 0.996 0.996
2 37683 37654.3 0.022 1.018
3 26834 26954.7 0.541 1.558
4 19581 19313.5 3.706 5.265
5 13725 13851.4 1.154 6.418
6 9880 9943.5 0.406 6.824
7 7188 7145.0 0.258 7.083
8 5233 5139.1 1.717 8.800
9 3743 3699.9 0.503 9.303
10 2772 2666.3 4.190 13.493
11 1911 1923.3 0.079 13.572
12 1386 1388.7 0.005 13.577
13 990 1003.7 0.187 13.765
14 772 726.1 2.896 16.661
15 472 525.8 5.512 22.173
16 395 381.2 0.503 22.676
17 278 276.5 0.008 22.684
18 206 200.8 0.133 22.817
19 128 146.0 2.216 25.032
20 111 106.2 0.216 25.248
21 303 287.1 0.879 26.127
Chisq= 26.13 for 20 degrees of freedom, p= 0.83834
SUMMARY of craptest
p-value for no. of wins: 0.560683
p-value for throws/game: 0.838342
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0035,0.0125,0.0177,0.0228,0.0302,0.0420,0.0446,0.0453,0.0504,0.0508,
0.0528,0.0532,0.0554,0.0590,0.0592,0.0603,0.0615,0.0655,0.0720,0.0740,
0.0784,0.0788,0.0842,0.0917,0.0939,0.0941,0.0944,0.0948,0.0952,0.0969,
0.0982,0.1001,0.1008,0.1051,0.1053,0.1056,0.1169,0.1179,0.1192,0.1205,
0.1369,0.1394,0.1426,0.1462,0.1490,0.1511,0.1531,0.1556,0.1584,0.1619,
0.1742,0.1951,0.1971,0.2049,0.2050,0.2056,0.2092,0.2119,0.2191,0.2233,
0.2348,0.2349,0.2456,0.2466,0.2487,0.2515,0.2571,0.2583,0.2616,0.2636,
0.2717,0.2724,0.2728,0.2777,0.2789,0.2792,0.2833,0.2843,0.2883,0.2891,
0.2930,0.2956,0.2957,0.2966,0.2993,0.3034,0.3094,0.3179,0.3213,0.3230,
0.3287,0.3305,0.3361,0.3373,0.3404,0.3406,0.3415,0.3472,0.3531,0.3574,
0.3596,0.3605,0.3624,0.3690,0.3701,0.3714,0.3724,0.3740,0.3758,0.3778,
0.3881,0.3920,0.3921,0.3921,0.3963,0.4073,0.4109,0.4126,0.4157,0.4174,
0.4270,0.4311,0.4345,0.4348,0.4352,0.4375,0.4410,0.4458,0.4461,0.4480,
0.4483,0.4530,0.4555,0.4615,0.4707,0.4759,0.4925,0.5011,0.5043,0.5045,
0.5069,0.5228,0.5231,0.5326,0.5364,0.5364,0.5414,0.5460,0.5473,0.5482,
0.5493,0.5508,0.5511,0.5545,0.5545,0.5606,0.5607,0.5697,0.5698,0.5722,
0.5735,0.5762,0.5772,0.5772,0.5795,0.5795,0.5801,0.5802,0.5840,0.5945,
0.5975,0.6003,0.6003,0.6016,0.6101,0.6104,0.6214,0.6218,0.6233,0.6240,
0.6259,0.6283,0.6293,0.6357,0.6485,0.6497,0.6500,0.6500,0.6525,0.6550,
0.6562,0.6564,0.6655,0.6745,0.6904,0.6904,0.6959,0.6968,0.6995,0.7054,
0.7074,0.7170,0.7178,0.7213,0.7219,0.7276,0.7348,0.7356,0.7366,0.7367,
0.7522,0.7531,0.7533,0.7658,0.7712,0.7777,0.7822,0.7866,0.7918,0.7977,
0.7977,0.7994,0.8050,0.8069,0.8123,0.8180,0.8254,0.8270,0.8322,0.8323,
0.8362,0.8383,0.8443,0.8481,0.8532,0.8542,0.8619,0.8686,0.8696,0.8705,
0.8766,0.8811,0.8825,0.8831,0.8840,0.8857,0.8947,0.8947,0.8969,0.9002,
0.9015,0.9128,0.9206,0.9216,0.9236,0.9240,0.9353,0.9356,0.9358,0.9505,
0.9516,0.9648,0.9729,0.9767,0.9777,0.9817,0.9826,0.9876,0.9957,
Overall p-value after applying KStest on 269 p-values = 0.400274
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.