RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.68 25.7410 0.920690
2 to 25 15.82 23.9984 0.880521
3 to 26 15.72 29.4617 0.969501
4 to 27 16.01 14.2325 0.349422
5 to 28 16.10 18.7625 0.657664
6 to 29 16.02 16.3635 0.501770
7 to 30 15.91 19.7350 0.711995
8 to 31 16.15 24.7682 0.899981
9 to 32 15.71 16.4266 0.506182
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.043614
Tough bday spacings test for dh-ranFile-2018-07-05_12:31: 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 33 76 101 106 69 53 26 10 12 7
(O-E)^2/E 0.5 0.4 0.1 0.1 0.7 1.1 0.0 0.5 1.6 4.4 2.1
Birthday Spacings: Sum(O-E)^2/E= 11.458, p= 0.677
RESULTS OF GCD FOR dh-ranFile-2018-07-05_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.128652
p-value, dist. of gcd's: 0.646116
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.556 0.439 0.611 0.154 0.955 0.890 0.586 0.049
Bits 8 to 15---> 0.611 0.989 0.928 0.174 0.592 0.108 0.057 0.330
Bits 16 to 23---> 0.014 0.305 0.996 0.539 0.084 0.728 0.336 0.717
Bits 24 to 31---> 0.417 0.279 0.099 0.419 0.965 0.238 0.365 0.513
KS test for the above 32 p values: 0.456
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_12:31,
p-values for 5 runs: 0.5630, 0.8101, 0.7702, 0.3344, 0.9472
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5120 5134.0 0.038 0.568
r= 30 23170 23103.0 0.194 0.762
r= 31 11488 11551.5 0.349 1.111
chi-square = 1.111 with df = 3; p-value = 0.226
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5092 5134.0 0.344 0.404
r= 31 23215 23103.0 0.542 0.947
r= 32 11478 11551.5 0.468 1.415
chi-square = 1.415 with df = 3; p-value = 0.298
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_12:31
b-rank test for bits 1 to 8, p=0.67997
b-rank test for bits 2 to 9, p=0.07472
b-rank test for bits 3 to 10, p=0.70572
b-rank test for bits 4 to 11, p=0.44766
b-rank test for bits 5 to 12, p=0.90705
b-rank test for bits 6 to 13, p=0.15288
b-rank test for bits 7 to 14, p=0.90759
b-rank test for bits 8 to 15, p=0.51152
b-rank test for bits 9 to 16, p=0.70666
b-rank test for bits 10 to 17, p=0.81964
b-rank test for bits 11 to 18, p=0.14860
b-rank test for bits 12 to 19, p=0.63031
b-rank test for bits 13 to 20, p=0.51443
b-rank test for bits 14 to 21, p=0.14361
b-rank test for bits 15 to 22, p=0.73902
b-rank test for bits 16 to 23, p=0.75000
b-rank test for bits 17 to 24, p=0.35566
b-rank test for bits 18 to 25, p=0.92916
b-rank test for bits 19 to 26, p=0.85716
b-rank test for bits 20 to 27, p=0.93431
b-rank test for bits 21 to 28, p=0.09272
b-rank test for bits 22 to 29, p=0.02505
b-rank test for bits 23 to 30, p=0.88598
b-rank test for bits 24 to 31, p=0.59512
b-rank test for bits 25 to 32, p=0.12153
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 = 0.411872
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_12:31
(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 141908 -0.00 0.498760
2 142067 0.37 0.643708
3 141861 -0.11 0.455047
4 141448 -1.08 0.140545
5 141983 0.17 0.568331
6 141853 -0.13 0.447646
7 142226 0.74 0.770315
8 141861 -0.11 0.455047
9 142240 0.77 0.780119
10 141947 0.09 0.535067
11 142097 0.44 0.669481
12 141572 -0.79 0.215303
13 141154 -1.76 0.038800
14 141693 -0.51 0.306624
15 141737 -0.40 0.343607
16 142307 0.93 0.823591
17 141780 -0.30 0.381260
18 141818 -0.21 0.415512
19 140946 -2.25 0.012200
20 143347 3.36 0.999609
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_12:31
Bits used No. missing words z-score p-value
23 to 32 142379 1.6196 0.947336
22 to 31 141918 0.0299 0.511925
21 to 30 141834 -0.2598 0.397525
20 to 29 141907 -0.0080 0.496795
19 to 28 142137 0.7851 0.783793
18 to 27 141609 -1.0356 0.150190
17 to 26 142144 0.8092 0.790802
16 to 25 141401 -1.7529 0.039813
15 to 24 141765 -0.4977 0.309351
14 to 23 141849 -0.2080 0.417601
13 to 22 141697 -0.7322 0.232032
12 to 21 141882 -0.0942 0.462459
11 to 20 141535 -1.2908 0.098388
10 to 19 141897 -0.0425 0.483043
9 to 18 141968 0.2023 0.580163
8 to 17 142265 1.2264 0.889985
7 to 16 141782 -0.4391 0.330306
6 to 15 141858 -0.1770 0.429754
5 to 14 141915 0.0196 0.507800
4 to 13 141676 -0.8046 0.210529
3 to 12 141723 -0.6425 0.260269
2 to 11 141679 -0.7942 0.213528
1 to 10 142802 3.0782 0.998959
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_12:31
Bits used No. missing words z-score p-value
28 to 32 141880 -0.0994 0.460401
27 to 31 142111 0.6836 0.752895
26 to 30 142077 0.5684 0.715109
25 to 29 141819 -0.3062 0.379725
24 to 28 141862 -0.1604 0.436267
23 to 27 141614 -1.0011 0.158385
22 to 26 141736 -0.5876 0.278414
21 to 25 142266 1.2091 0.886678
20 to 24 142172 0.8904 0.813376
19 to 23 141990 0.2735 0.607749
18 to 22 142033 0.4192 0.662473
17 to 21 141613 -1.0045 0.157567
16 to 20 142192 0.9582 0.831020
15 to 19 141703 -0.6994 0.242144
14 to 18 141957 0.1616 0.564187
13 to 17 142232 1.0938 0.862978
12 to 16 142034 0.4226 0.663710
11 to 15 142165 0.8667 0.806941
10 to 14 141966 0.1921 0.576169
9 to 13 141500 -1.3876 0.082636
8 to 12 141683 -0.7672 0.221475
7 to 11 141585 -1.0994 0.135792
6 to 10 142018 0.3684 0.643702
5 to 9 141519 -1.3232 0.092892
4 to 8 141919 0.0328 0.513075
3 to 7 141618 -0.9876 0.161684
2 to 6 142044 0.4565 0.675988
1 to 5 142156 0.8362 0.798470
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_12:31
Bits used No. missing words z-score p-value
31 to 32 142259 1.0315 0.848841
30 to 31 142128 0.6450 0.740551
29 to 30 142636 2.1436 0.983966
28 to 29 141871 -0.1131 0.454988
27 to 28 142018 0.3206 0.625728
26 to 27 141000 -2.6824 0.003655
25 to 26 142311 1.1849 0.881965
24 to 25 141694 -0.6352 0.262652
23 to 24 142092 0.5388 0.705005
22 to 23 141774 -0.3992 0.344872
21 to 22 142230 0.9459 0.827908
20 to 21 142017 0.3176 0.624610
19 to 20 141643 -0.7856 0.216041
18 to 19 141540 -1.0895 0.137974
17 to 18 142122 0.6273 0.734784
16 to 17 141710 -0.5880 0.278268
15 to 16 142396 1.4356 0.924443
14 to 15 141737 -0.5083 0.305605
13 to 14 141831 -0.2311 0.408633
12 to 13 141984 0.2203 0.587168
11 to 12 142076 0.4917 0.688517
10 to 11 142428 1.5300 0.936992
9 to 10 141891 -0.0541 0.478439
8 to 9 142186 0.8161 0.792789
7 to 8 141632 -0.8181 0.206655
6 to 7 141173 -2.1721 0.014925
5 to 6 142472 1.6598 0.951522
4 to 5 141162 -2.2045 0.013744
3 to 4 141715 -0.5732 0.283240
2 to 3 142288 1.1170 0.868007
1 to 2 141918 0.0256 0.510202
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2458.78 -0.583 0.279954
Test results for specific bytes for dh-ranFile-2018-07-05_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2635.79 1.920 0.972594
2 to 9 2520.68 0.292 0.615030
3 to 10 2441.05 -0.834 0.202245
4 to 11 2490.52 -0.134 0.446666
5 to 12 2537.64 0.532 0.702745
6 to 13 2459.83 -0.568 0.284965
7 to 14 2562.58 0.885 0.811914
8 to 15 2382.77 -1.658 0.048665
9 to 16 2392.88 -1.515 0.064890
10 to 17 2419.74 -1.135 0.128174
11 to 18 2472.54 -0.388 0.348885
12 to 19 2522.65 0.320 0.625613
13 to 20 2614.29 1.616 0.946981
14 to 21 2491.66 -0.118 0.453070
15 to 22 2467.90 -0.454 0.324912
16 to 23 2533.56 0.475 0.682451
17 to 24 2442.16 -0.818 0.206665
18 to 25 2377.71 -1.729 0.041863
19 to 26 2560.93 0.862 0.805571
20 to 27 2533.30 0.471 0.681163
21 to 28 2681.26 2.563 0.994818
22 to 29 2448.85 -0.723 0.234725
23 to 30 2536.68 0.519 0.698020
24 to 31 2377.00 -1.740 0.040973
25 to 32 2485.09 -0.211 0.416516
CDPARK for dh-ranFile-2018-07-05_12:31: 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
3477 -2.1005 0.017844
3542 0.8676 0.807188
3555 1.4612 0.928018
3536 0.5936 0.723613
3534 0.5023 0.692266
3515 -0.3653 0.357445
3516 -0.3196 0.374623
3492 -1.4155 0.078457
3524 0.0457 0.518210
3520 -0.1370 0.445521
Square side=100, avg. no. parked=3521.10 sample std.=22.00
p-value of the KSTEST for those 10 p-values: 0.961521
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_12:31
0.3484,0.5771,0.2661,0.4725,0.6007,0.6757,0.6411,0.4980,0.5099,0.2884,
The KS test for those 10 p-values: 0.194819
The 3DSPHERES test for dh-ranFile-2018-07-05_12:31
sample no r^3 equiv. uni.
1 27.678 0.602515
2 7.532 0.222025
3 11.431 0.316849
4 19.868 0.484327
5 8.055 0.235470
6 39.364 0.730759
7 67.879 0.895925
8 18.564 0.461417
9 37.541 0.713883
10 55.393 0.842203
11 79.459 0.929252
12 4.557 0.140927
13 60.567 0.867198
14 67.604 0.894967
15 20.835 0.500672
16 27.219 0.596382
17 98.131 0.962033
18 8.180 0.238646
19 40.297 0.738997
20 13.234 0.356697
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.293600
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 0.1 -0.7 2.2 -1.7
0.5 -1.1 0.6 -0.6 -0.8 -1.3
0.3 0.1 -1.2 -0.2 0.2 0.7
0.1 -1.9 2.2 0.2 1.4 0.9
0.5 0.1 0.4 -0.7 -0.3 -0.4
0.2 -0.8 -0.3 -0.5 0.3 -0.3
-0.2 0.5 -0.4 -1.8 -0.6 1.0
0.8
Chi-square with 42 degrees of freedom:34.418231
z-score=-0.827239, p-value=0.209244
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_12:31
Test no p-value
1 0.057510
2 0.209842
3 0.094465
4 0.444951
5 0.001533
6 0.105129
7 0.574493
8 0.031247
9 0.406570
10 0.822262
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.009664
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_12:31:
(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 66981 1.48 66898 0.80
3 25000.00 24828 1.18 24901 0.39
4 6666.67 6575 1.26 6508 3.78
5 1388.89 1325 2.94 1397 0.05
6 238.10 248 0.41 252 0.81
7 34.72 37 0.15 34 0.01
8 4.96 5 0.00 9 3.29
p=0.71684 p=0.83393
Number of rngs required: 687927, p-value: 0.292
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_12:31
No. of wins: Observed Expected
98389 98585.9
z-score=-0.880, pvalue=0.18930
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66625 66666.7 0.026 0.026
2 37756 37654.3 0.275 0.301
3 26873 26954.7 0.248 0.548
4 19176 19313.5 0.978 1.527
5 13793 13851.4 0.246 1.773
6 9953 9943.5 0.009 1.782
7 7159 7145.0 0.027 1.810
8 5100 5139.1 0.297 2.107
9 3740 3699.9 0.435 2.542
10 2696 2666.3 0.331 2.873
11 1916 1923.3 0.028 2.901
12 1457 1388.7 3.355 6.256
13 1016 1003.7 0.150 6.406
14 744 726.1 0.439 6.846
15 534 525.8 0.127 6.972
16 407 381.2 1.753 8.725
17 276 276.5 0.001 8.726
18 204 200.8 0.050 8.776
19 153 146.0 0.337 9.114
20 114 106.2 0.571 9.684
21 308 287.1 1.519 11.204
Chisq= 11.20 for 20 degrees of freedom, p= 0.05923
SUMMARY of craptest
p-value for no. of wins: 0.189303
p-value for throws/game: 0.059227
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_12:31
No. of wins: Observed Expected
98799 98585.9
z-score= 0.953, pvalue=0.82978
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66816 66666.7 0.335 0.335
2 37512 37654.3 0.538 0.872
3 26986 26954.7 0.036 0.909
4 19200 19313.5 0.667 1.575
5 13902 13851.4 0.185 1.760
6 9952 9943.5 0.007 1.767
7 7226 7145.0 0.918 2.685
8 5079 5139.1 0.702 3.387
9 3777 3699.9 1.608 4.995
10 2763 2666.3 3.507 8.502
11 1861 1923.3 2.020 10.522
12 1379 1388.7 0.068 10.591
13 992 1003.7 0.137 10.727
14 731 726.1 0.033 10.760
15 486 525.8 3.018 13.778
16 352 381.2 2.229 16.007
17 284 276.5 0.201 16.208
18 186 200.8 1.095 17.304
19 157 146.0 0.831 18.135
20 97 106.2 0.800 18.934
21 262 287.1 2.197 21.131
Chisq= 21.13 for 20 degrees of freedom, p= 0.61054
SUMMARY of craptest
p-value for no. of wins: 0.829779
p-value for throws/game: 0.610542
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0015,0.0037,0.0097,0.0122,0.0136,0.0137,0.0149,0.0178,0.0250,0.0312,
0.0388,0.0398,0.0410,0.0419,0.0436,0.0487,0.0490,0.0573,0.0575,0.0592,
0.0649,0.0747,0.0785,0.0826,0.0837,0.0927,0.0929,0.0945,0.0984,0.0986,
0.1051,0.1084,0.1215,0.1282,0.1287,0.1358,0.1380,0.1405,0.1409,0.1436,
0.1486,0.1502,0.1529,0.1539,0.1576,0.1584,0.1617,0.1740,0.1893,0.1948,
0.2022,0.2067,0.2067,0.2092,0.2098,0.2105,0.2135,0.2153,0.2160,0.2215,
0.2220,0.2256,0.2320,0.2347,0.2355,0.2384,0.2386,0.2421,0.2603,0.2627,
0.2661,0.2783,0.2784,0.2789,0.2800,0.2832,0.2850,0.2884,0.2916,0.2936,
0.2980,0.3047,0.3056,0.3066,0.3094,0.3168,0.3249,0.3295,0.3303,0.3344,
0.3365,0.3436,0.3449,0.3484,0.3489,0.3494,0.3557,0.3567,0.3574,0.3648,
0.3746,0.3797,0.3813,0.3975,0.4066,0.4086,0.4119,0.4155,0.4165,0.4174,
0.4176,0.4191,0.4298,0.4363,0.4389,0.4450,0.4455,0.4467,0.4476,0.4477,
0.4531,0.4550,0.4550,0.4550,0.4563,0.4604,0.4614,0.4625,0.4725,0.4784,
0.4830,0.4843,0.4968,0.4980,0.4988,0.5007,0.5018,0.5062,0.5078,0.5099,
0.5102,0.5115,0.5119,0.5131,0.5131,0.5144,0.5182,0.5351,0.5387,0.5562,
0.5630,0.5642,0.5683,0.5745,0.5762,0.5771,0.5802,0.5862,0.5872,0.5917,
0.5951,0.5964,0.6007,0.6025,0.6077,0.6105,0.6108,0.6113,0.6150,0.6246,
0.6256,0.6257,0.6303,0.6411,0.6437,0.6437,0.6461,0.6577,0.6625,0.6637,
0.6695,0.6757,0.6760,0.6770,0.6800,0.6812,0.6825,0.6885,0.6923,0.6980,
0.7027,0.7050,0.7057,0.7067,0.7120,0.7139,0.7151,0.7168,0.7170,0.7236,
0.7280,0.7308,0.7348,0.7390,0.7390,0.7406,0.7500,0.7529,0.7702,0.7703,
0.7801,0.7838,0.7908,0.7928,0.7985,0.8056,0.8069,0.8072,0.8101,0.8119,
0.8134,0.8196,0.8223,0.8236,0.8279,0.8298,0.8310,0.8339,0.8422,0.8488,
0.8572,0.8630,0.8672,0.8680,0.8805,0.8820,0.8860,0.8867,0.8899,0.8900,
0.8950,0.8959,0.9000,0.9070,0.9076,0.9207,0.9244,0.9279,0.9280,0.9292,
0.9293,0.9343,0.9370,0.9470,0.9472,0.9473,0.9515,0.9554,0.9615,0.9620,
0.9652,0.9695,0.9726,0.9840,0.9891,0.9948,0.9959,0.9990,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.997724
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.