RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.94 13.5305 0.299987
2 to 25 15.91 14.7381 0.385660
3 to 26 15.90 11.3883 0.164320
4 to 27 16.02 15.1623 0.416207
5 to 28 15.59 17.5171 0.580102
6 to 29 16.15 17.6652 0.589747
7 to 30 15.68 20.6236 0.756421
8 to 31 15.87 29.2907 0.968062
9 to 32 15.74 15.0791 0.410218
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.746802
Tough bday spacings test for dh-ranFile-2018-07-06_19:31: 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 11 38 65 87 99 71 58 31 25 13 2
(O-E)^2/E 0.4 0.1 0.9 1.2 0.0 0.7 0.7 0.1 6.9 6.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 17.997, p= 0.945
RESULTS OF GCD FOR dh-ranFile-2018-07-06_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.501826
p-value, dist. of gcd's: 0.635047
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.876 0.477 0.656 0.848 0.604 0.983 0.547 0.210
Bits 8 to 15---> 0.781 0.355 0.253 0.989 0.106 0.885 0.504 0.886
Bits 16 to 23---> 0.612 0.178 0.410 0.832 0.483 0.530 0.319 0.397
Bits 24 to 31---> 0.207 0.311 0.456 0.082 0.834 0.458 0.503 0.676
KS test for the above 32 p values: 0.504
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_19:31,
p-values for 5 runs: 0.9766, 0.8462, 0.0921, 0.6895, 0.3711
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5043 5134.0 1.613 1.641
r= 30 23270 23103.0 1.206 2.847
r= 31 11478 11551.5 0.468 3.315
chi-square = 3.315 with df = 3; p-value = 0.655
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 237 211.4 3.095 3.095
r= 30 5093 5134.0 0.328 3.423
r= 31 22931 23103.0 1.281 4.704
r= 32 11739 11551.5 3.043 7.747
chi-square = 7.747 with df = 3; p-value = 0.948
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_19:31
b-rank test for bits 1 to 8, p=0.05860
b-rank test for bits 2 to 9, p=0.77533
b-rank test for bits 3 to 10, p=0.77395
b-rank test for bits 4 to 11, p=0.99565
b-rank test for bits 5 to 12, p=0.65858
b-rank test for bits 6 to 13, p=0.10708
b-rank test for bits 7 to 14, p=0.96771
b-rank test for bits 8 to 15, p=0.70962
b-rank test for bits 9 to 16, p=0.94622
b-rank test for bits 10 to 17, p=0.65502
b-rank test for bits 11 to 18, p=0.80484
b-rank test for bits 12 to 19, p=0.17068
b-rank test for bits 13 to 20, p=0.67541
b-rank test for bits 14 to 21, p=0.82953
b-rank test for bits 15 to 22, p=0.97512
b-rank test for bits 16 to 23, p=0.50450
b-rank test for bits 17 to 24, p=0.82069
b-rank test for bits 18 to 25, p=0.36021
b-rank test for bits 19 to 26, p=0.03342
b-rank test for bits 20 to 27, p=0.33354
b-rank test for bits 21 to 28, p=0.06707
b-rank test for bits 22 to 29, p=0.49375
b-rank test for bits 23 to 30, p=0.78387
b-rank test for bits 24 to 31, p=0.69534
b-rank test for bits 25 to 32, p=0.99171
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 = 0.039029
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_19:31
(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 142284 0.88 0.809321
2 142499 1.38 0.915857
3 140598 -3.06 0.001093
4 142030 0.28 0.611005
5 141286 -1.46 0.072644
6 142278 0.86 0.805485
7 141776 -0.31 0.377703
8 141897 -0.03 0.488509
9 141787 -0.29 0.387509
10 142451 1.27 0.897169
11 141926 0.04 0.515534
12 141207 -1.64 0.050403
13 142482 1.34 0.909554
14 142061 0.35 0.638469
15 141596 -0.73 0.232060
16 141445 -1.08 0.138987
17 141232 -1.58 0.056762
18 141468 -1.03 0.151236
19 141696 -0.50 0.309089
20 142019 0.26 0.601117
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_19:31
Bits used No. missing words z-score p-value
23 to 32 142004 0.3264 0.627957
22 to 31 141469 -1.5184 0.064459
21 to 30 141593 -1.0908 0.137682
20 to 29 141880 -0.1011 0.459721
19 to 28 141811 -0.3391 0.367279
18 to 27 141978 0.2368 0.593591
17 to 26 141935 0.0885 0.535267
16 to 25 142127 0.7506 0.773549
15 to 24 142008 0.3402 0.633163
14 to 23 141804 -0.3632 0.358225
13 to 22 141938 0.0989 0.539376
12 to 21 142273 1.2540 0.895085
11 to 20 142172 0.9058 0.817468
10 to 19 141796 -0.3908 0.347975
9 to 18 141628 -0.9701 0.165998
8 to 17 141925 0.0540 0.521546
7 to 16 141753 -0.5391 0.294920
6 to 15 141665 -0.8425 0.199749
5 to 14 141448 -1.5908 0.055828
4 to 13 141649 -0.8977 0.184676
3 to 12 141568 -1.1770 0.119598
2 to 11 141597 -1.0770 0.140740
1 to 10 142119 0.7230 0.765160
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_19:31
Bits used No. missing words z-score p-value
28 to 32 141681 -0.7740 0.219465
27 to 31 142144 0.7955 0.786836
26 to 30 141553 -1.2079 0.113543
25 to 29 141652 -0.8723 0.191521
24 to 28 142161 0.8531 0.803203
23 to 27 142008 0.3345 0.630989
22 to 26 141573 -1.1401 0.127122
21 to 25 141809 -0.3401 0.366890
20 to 24 142264 1.2023 0.885371
19 to 23 141526 -1.2994 0.096899
18 to 22 141929 0.0667 0.526581
17 to 21 142247 1.1446 0.873822
16 to 20 141697 -0.7198 0.235836
15 to 19 142155 0.8328 0.797516
14 to 18 142374 1.5752 0.942389
13 to 17 142650 2.5107 0.993976
12 to 16 141823 -0.2926 0.384897
11 to 15 142501 2.0057 0.977554
10 to 14 142016 0.3616 0.641172
9 to 13 141976 0.2260 0.589399
8 to 12 141249 -2.2384 0.012597
7 to 11 141471 -1.4859 0.068658
6 to 10 141525 -1.3028 0.096319
5 to 9 142164 0.8633 0.806011
4 to 8 141966 0.1921 0.576169
3 to 7 141944 0.1175 0.546778
2 to 6 142128 0.7413 0.770730
1 to 5 141807 -0.3469 0.364340
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_19:31
Bits used No. missing words z-score p-value
31 to 32 141556 -1.0423 0.148643
30 to 31 141686 -0.6588 0.255015
29 to 30 141221 -2.0305 0.021154
28 to 29 141527 -1.1278 0.129699
27 to 28 141101 -2.3845 0.008552
26 to 27 142607 2.0580 0.980206
25 to 26 142475 1.6686 0.952406
24 to 25 142419 1.5035 0.933639
23 to 24 142320 1.2114 0.887132
22 to 23 142039 0.3825 0.648958
21 to 22 141808 -0.2989 0.382505
20 to 21 142177 0.7896 0.785116
19 to 20 142118 0.6155 0.730903
18 to 19 141696 -0.6293 0.264579
17 to 18 142182 0.8043 0.789399
16 to 17 141547 -1.0688 0.142575
15 to 16 142160 0.7394 0.770180
14 to 15 142012 0.3029 0.619002
13 to 14 141780 -0.3815 0.351415
12 to 13 141664 -0.7237 0.234629
11 to 12 141672 -0.7001 0.241936
10 to 11 141519 -1.1514 0.124781
9 to 10 141830 -0.2340 0.407488
8 to 9 142042 0.3914 0.652233
7 to 8 142539 1.8574 0.968375
6 to 7 141821 -0.2606 0.397216
5 to 6 141926 0.0492 0.519610
4 to 5 141836 -0.2163 0.414372
3 to 4 142146 0.6981 0.757456
2 to 3 141933 0.0698 0.527833
1 to 2 141415 -1.4582 0.072393
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2527.71 0.392 0.652450
Test results for specific bytes for dh-ranFile-2018-07-06_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2443.10 -0.805 0.210484
2 to 9 2525.41 0.359 0.640338
3 to 10 2464.54 -0.501 0.308034
4 to 11 2482.85 -0.242 0.404203
5 to 12 2491.75 -0.117 0.453538
6 to 13 2457.03 -0.608 0.271694
7 to 14 2463.08 -0.522 0.300768
8 to 15 2506.06 0.086 0.534126
9 to 16 2534.60 0.489 0.687680
10 to 17 2588.46 1.251 0.894539
11 to 18 2500.62 0.009 0.503476
12 to 19 2475.12 -0.352 0.362492
13 to 20 2376.89 -1.741 0.040839
14 to 21 2510.09 0.143 0.556757
15 to 22 2484.73 -0.216 0.414504
16 to 23 2462.56 -0.529 0.298242
17 to 24 2561.29 0.867 0.806950
18 to 25 2482.28 -0.251 0.401051
19 to 26 2540.81 0.577 0.718085
20 to 27 2536.39 0.515 0.696582
21 to 28 2484.77 -0.215 0.414753
22 to 29 2505.23 0.074 0.529486
23 to 30 2540.20 0.568 0.715140
24 to 31 2513.42 0.190 0.575262
25 to 32 2383.45 -1.648 0.049655
CDPARK for dh-ranFile-2018-07-06_19:31: 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
3543 0.9132 0.819442
3535 0.5479 0.708135
3527 0.1826 0.572463
3535 0.5479 0.708135
3530 0.3196 0.625377
3487 -1.6438 0.050105
3525 0.0913 0.536383
3538 0.6849 0.753306
3554 1.4155 0.921543
3546 1.0502 0.853193
Square side=100, avg. no. parked=3532.00 sample std.=17.20
p-value of the KSTEST for those 10 p-values: 0.096342
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_19:31
0.8003,0.1290,0.4711,0.7136,0.2271,0.9040,0.5037,0.9006,0.8906,0.4558,
The KS test for those 10 p-values: 0.421129
The 3DSPHERES test for dh-ranFile-2018-07-06_19:31
sample no r^3 equiv. uni.
1 8.105 0.236735
2 158.472 0.994920
3 21.662 0.514253
4 45.720 0.782165
5 91.748 0.953031
6 9.926 0.281709
7 16.822 0.429212
8 14.951 0.392481
9 27.535 0.600614
10 66.162 0.889795
11 3.634 0.114084
12 8.357 0.243142
13 38.362 0.721613
14 21.714 0.515093
15 26.500 0.586592
16 39.604 0.732901
17 10.909 0.304855
18 3.306 0.104338
19 62.071 0.873692
20 18.928 0.467904
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.829384
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 0.3 -0.1 2.5 -0.8
-0.4 0.3 0.4 0.5 0.6 1.1
0.7 -0.9 -1.5 -1.1 0.0 0.3
-0.2 1.5 0.4 -1.4 0.4 1.9
-0.2 -0.4 -1.2 -1.6 0.5 -0.8
0.8 1.0 -1.5 1.2 -0.2 -1.4
-1.6 0.2 1.3 -0.7 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:42.627427
z-score=0.068458, p-value=0.556006
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_19:31
Test no p-value
1 0.272509
2 0.129026
3 0.858431
4 0.278112
5 0.293811
6 0.003282
7 0.292992
8 0.601856
9 0.638215
10 0.270945
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.141883
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_19:31:
(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 66694 0.01 66666 0.00
3 25000.00 24944 0.13 25008 0.00
4 6666.67 6753 1.12 6745 0.92
5 1388.89 1325 2.94 1332 2.33
6 238.10 239 0.00 209 3.56
7 34.72 41 1.14 32 0.21
8 4.96 3 0.77 7 0.84
p=0.58873 p=0.75151
Number of rngs required: 688524, p-value: 0.555
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_19:31
No. of wins: Observed Expected
98921 98585.9
z-score= 1.499, pvalue=0.93306
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66622 66666.7 0.030 0.030
2 37705 37654.3 0.068 0.098
3 27045 26954.7 0.302 0.400
4 19242 19313.5 0.264 0.665
5 13694 13851.4 1.789 2.454
6 10149 9943.5 4.245 6.699
7 7170 7145.0 0.087 6.786
8 5053 5139.1 1.442 8.228
9 3674 3699.9 0.181 8.409
10 2685 2666.3 0.131 8.540
11 1976 1923.3 1.442 9.982
12 1371 1388.7 0.227 10.209
13 1007 1003.7 0.011 10.220
14 737 726.1 0.162 10.382
15 519 525.8 0.089 10.471
16 380 381.2 0.003 10.475
17 267 276.5 0.329 10.804
18 206 200.8 0.133 10.937
19 143 146.0 0.061 10.998
20 89 106.2 2.790 13.788
21 266 287.1 1.553 15.341
Chisq= 15.34 for 20 degrees of freedom, p= 0.24340
SUMMARY of craptest
p-value for no. of wins: 0.933056
p-value for throws/game: 0.243404
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_19:31
No. of wins: Observed Expected
98357 98585.9
z-score=-1.024, pvalue=0.15301
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66534 66666.7 0.264 0.264
2 37618 37654.3 0.035 0.299
3 26962 26954.7 0.002 0.301
4 19234 19313.5 0.327 0.628
5 13987 13851.4 1.327 1.955
6 9966 9943.5 0.051 2.006
7 7142 7145.0 0.001 2.007
8 5208 5139.1 0.924 2.932
9 3701 3699.9 0.000 2.932
10 2708 2666.3 0.652 3.584
11 1918 1923.3 0.015 3.599
12 1370 1388.7 0.253 3.852
13 1007 1003.7 0.011 3.863
14 737 726.1 0.162 4.025
15 514 525.8 0.266 4.291
16 383 381.2 0.009 4.300
17 273 276.5 0.045 4.346
18 208 200.8 0.256 4.602
19 159 146.0 1.160 5.762
20 100 106.2 0.364 6.126
21 271 287.1 0.904 7.030
Chisq= 7.03 for 20 degrees of freedom, p= 0.00341
SUMMARY of craptest
p-value for no. of wins: 0.153015
p-value for throws/game: 0.003415
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0033,0.0034,0.0086,0.0126,0.0212,0.0334,0.0390,0.0408,0.0497,
0.0501,0.0504,0.0558,0.0568,0.0586,0.0645,0.0671,0.0687,0.0724,0.0726,
0.0822,0.0921,0.0963,0.0963,0.0969,0.1043,0.1060,0.1071,0.1135,0.1141,
0.1196,0.1248,0.1271,0.1290,0.1290,0.1297,0.1377,0.1390,0.1407,0.1419,
0.1426,0.1486,0.1512,0.1530,0.1643,0.1660,0.1707,0.1777,0.1847,0.1915,
0.1997,0.2071,0.2103,0.2105,0.2195,0.2271,0.2321,0.2346,0.2358,0.2367,
0.2419,0.2431,0.2434,0.2527,0.2550,0.2646,0.2709,0.2717,0.2725,0.2781,
0.2817,0.2930,0.2938,0.2949,0.2982,0.3000,0.3008,0.3049,0.3080,0.3091,
0.3113,0.3189,0.3335,0.3480,0.3514,0.3553,0.3582,0.3602,0.3625,0.3643,
0.3669,0.3673,0.3711,0.3777,0.3825,0.3849,0.3857,0.3875,0.3925,0.3970,
0.3972,0.4011,0.4042,0.4075,0.4101,0.4102,0.4144,0.4145,0.4148,0.4162,
0.4211,0.4292,0.4535,0.4558,0.4561,0.4578,0.4597,0.4679,0.4711,0.4767,
0.4826,0.4885,0.4937,0.5018,0.5032,0.5035,0.5037,0.5041,0.5041,0.5045,
0.5143,0.5151,0.5155,0.5196,0.5215,0.5266,0.5278,0.5295,0.5299,0.5341,
0.5353,0.5364,0.5394,0.5468,0.5468,0.5554,0.5560,0.5568,0.5725,0.5753,
0.5762,0.5801,0.5866,0.5887,0.5894,0.5897,0.5936,0.6006,0.6011,0.6019,
0.6036,0.6110,0.6120,0.6190,0.6254,0.6280,0.6310,0.6332,0.6350,0.6382,
0.6385,0.6403,0.6412,0.6490,0.6522,0.6525,0.6545,0.6550,0.6555,0.6586,
0.6754,0.6761,0.6877,0.6895,0.6953,0.6966,0.7081,0.7081,0.7096,0.7136,
0.7151,0.7181,0.7216,0.7309,0.7329,0.7468,0.7515,0.7533,0.7564,0.7575,
0.7652,0.7702,0.7707,0.7735,0.7740,0.7753,0.7814,0.7822,0.7839,0.7851,
0.7868,0.7894,0.7975,0.8003,0.8032,0.8048,0.8055,0.8060,0.8069,0.8093,
0.8175,0.8194,0.8207,0.8294,0.8295,0.8319,0.8342,0.8462,0.8484,0.8532,
0.8584,0.8737,0.8738,0.8761,0.8848,0.8854,0.8860,0.8871,0.8898,0.8906,
0.8945,0.8951,0.8972,0.9006,0.9040,0.9096,0.9159,0.9215,0.9331,0.9336,
0.9424,0.9450,0.9462,0.9485,0.9524,0.9530,0.9677,0.9681,0.9684,0.9751,
0.9766,0.9776,0.9802,0.9826,0.9887,0.9917,0.9940,0.9949,0.9956,
Overall p-value after applying KStest on 269 p-values = 0.851209
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.