RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.96 21.2624 0.785229
2 to 25 15.62 17.6177 0.586668
3 to 26 15.66 12.8855 0.256181
4 to 27 15.96 13.7983 0.318674
5 to 28 15.45 16.3438 0.500392
6 to 29 15.94 12.3935 0.224252
7 to 30 15.31 24.3056 0.888632
8 to 31 15.70 33.5449 0.990393
9 to 32 15.73 25.7788 0.921414
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.364380
Tough bday spacings test for dh-ranFile-2018-06-27_23:31: 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 43 78 100 77 75 54 34 21 4 3
(O-E)^2/E 0.4 1.1 0.3 0.1 4.4 0.1 0.1 0.6 2.5 1.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.841, p= 0.630
RESULTS OF GCD FOR dh-ranFile-2018-06-27_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.054785
p-value, dist. of gcd's: 0.032036
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.095 0.267 0.371 0.473 0.518 0.165 0.443 0.354
Bits 8 to 15---> 0.878 0.831 0.840 0.983 0.195 0.435 0.436 0.894
Bits 16 to 23---> 0.624 0.392 0.989 0.625 0.434 0.150 0.207 0.301
Bits 24 to 31---> 0.312 0.202 0.415 0.881 0.022 0.390 0.619 0.910
KS test for the above 32 p values: 0.429
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_23:31,
p-values for 5 runs: 0.9621, 0.4231, 0.6128, 0.6825, 0.0117
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5189 5134.0 0.589 3.447
r= 30 23239 23103.0 0.800 4.247
r= 31 11336 11551.5 4.021 8.268
chi-square = 8.268 with df = 3; p-value = 0.959
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5192 5134.0 0.655 0.860
r= 31 23171 23103.0 0.200 1.060
r= 32 11419 11551.5 1.520 2.580
chi-square = 2.580 with df = 3; p-value = 0.539
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_23:31
b-rank test for bits 1 to 8, p=0.12134
b-rank test for bits 2 to 9, p=0.08414
b-rank test for bits 3 to 10, p=0.18954
b-rank test for bits 4 to 11, p=0.94604
b-rank test for bits 5 to 12, p=0.78694
b-rank test for bits 6 to 13, p=0.03926
b-rank test for bits 7 to 14, p=0.26527
b-rank test for bits 8 to 15, p=0.29662
b-rank test for bits 9 to 16, p=0.59614
b-rank test for bits 10 to 17, p=0.25741
b-rank test for bits 11 to 18, p=0.06092
b-rank test for bits 12 to 19, p=0.37180
b-rank test for bits 13 to 20, p=0.97726
b-rank test for bits 14 to 21, p=0.26379
b-rank test for bits 15 to 22, p=0.40754
b-rank test for bits 16 to 23, p=0.57733
b-rank test for bits 17 to 24, p=0.29113
b-rank test for bits 18 to 25, p=0.74027
b-rank test for bits 19 to 26, p=0.97630
b-rank test for bits 20 to 27, p=0.33236
b-rank test for bits 21 to 28, p=0.18605
b-rank test for bits 22 to 29, p=0.15916
b-rank test for bits 23 to 30, p=0.85879
b-rank test for bits 24 to 31, p=0.51898
b-rank test for bits 25 to 32, p=0.19906
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 = 0.167585
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_23:31
(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 142077 0.39 0.652379
2 142043 0.31 0.622599
3 141624 -0.67 0.252495
4 142228 0.74 0.771730
5 142188 0.65 0.742508
6 142531 1.45 0.926819
7 142188 0.65 0.742508
8 142027 0.27 0.608315
9 142679 1.80 0.963935
10 142274 0.85 0.802902
11 142215 0.71 0.762443
12 141872 -0.09 0.465249
13 141855 -0.13 0.449494
14 142263 0.83 0.795692
15 141040 -2.03 0.021120
16 141798 -0.26 0.397387
17 141102 -1.89 0.029628
18 141370 -1.26 0.103814
19 141617 -0.68 0.247299
20 141971 0.14 0.557285
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_23:31
Bits used No. missing words z-score p-value
23 to 32 142118 0.7196 0.764100
22 to 31 141878 -0.1080 0.456984
21 to 30 141835 -0.2563 0.398856
20 to 29 142105 0.6747 0.750075
19 to 28 142277 1.2678 0.897570
18 to 27 142766 2.9540 0.998432
17 to 26 142221 1.0747 0.858751
16 to 25 141793 -0.4011 0.344159
15 to 24 141828 -0.2804 0.389567
14 to 23 141406 -1.7356 0.041315
13 to 22 141667 -0.8356 0.201684
12 to 21 142080 0.5885 0.721907
11 to 20 141678 -0.7977 0.212525
10 to 19 141856 -0.1839 0.427047
9 to 18 142311 1.3851 0.916984
8 to 17 142267 1.2333 0.891276
7 to 16 142152 0.8368 0.798646
6 to 15 141906 -0.0115 0.495419
5 to 14 142035 0.4333 0.667618
4 to 13 141951 0.1437 0.557127
3 to 12 142107 0.6816 0.752261
2 to 11 141761 -0.5115 0.304507
1 to 10 142167 0.8885 0.812869
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_23:31
Bits used No. missing words z-score p-value
28 to 32 141838 -0.2418 0.404469
27 to 31 142224 1.0667 0.856941
26 to 30 142157 0.8396 0.799422
25 to 29 141207 -2.3808 0.008638
24 to 28 141800 -0.3706 0.355464
23 to 27 141653 -0.8689 0.192447
22 to 26 141838 -0.2418 0.404469
21 to 25 141850 -0.2011 0.420303
20 to 24 141946 0.1243 0.549463
19 to 23 141958 0.1650 0.565521
18 to 22 142275 1.2396 0.892431
17 to 21 141620 -0.9808 0.163351
16 to 20 142353 1.5040 0.933705
15 to 19 141973 0.2158 0.585440
14 to 18 141913 0.0124 0.504963
13 to 17 141918 0.0294 0.511723
12 to 16 141443 -1.5808 0.056964
11 to 15 141842 -0.2282 0.409731
10 to 14 142128 0.7413 0.770730
9 to 13 141882 -0.0926 0.463093
8 to 12 142365 1.5446 0.938784
7 to 11 142121 0.7175 0.763475
6 to 10 142161 0.8531 0.803203
5 to 9 142618 2.4023 0.991853
4 to 8 141996 0.2938 0.615543
3 to 7 141522 -1.3130 0.094594
2 to 6 141783 -0.4282 0.334239
1 to 5 141791 -0.4011 0.344166
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_23:31
Bits used No. missing words z-score p-value
31 to 32 141713 -0.5791 0.281246
30 to 31 141630 -0.8240 0.204975
29 to 30 141698 -0.6234 0.266513
28 to 29 141667 -0.7148 0.237355
27 to 28 141681 -0.6735 0.250302
26 to 27 141757 -0.4494 0.326589
25 to 26 141998 0.2616 0.603171
24 to 25 141920 0.0315 0.512555
23 to 24 141590 -0.9420 0.173102
22 to 23 141918 0.0256 0.510202
21 to 22 141752 -0.4641 0.321288
20 to 21 142128 0.6450 0.740551
19 to 20 141872 -0.1101 0.456158
18 to 19 142295 1.1377 0.872371
17 to 18 142673 2.2527 0.987861
16 to 17 142282 1.0993 0.864186
15 to 16 142321 1.2144 0.887696
14 to 15 141756 -0.4523 0.325526
13 to 14 142249 1.0020 0.841823
12 to 13 142062 0.4504 0.673772
11 to 12 141813 -0.2842 0.388144
10 to 11 142368 1.3530 0.911974
9 to 10 142191 0.8309 0.796981
8 to 9 142027 0.3471 0.635745
7 to 8 142690 2.3029 0.989357
6 to 7 142410 1.4769 0.930149
5 to 6 142583 1.9872 0.976551
4 to 5 142295 1.1377 0.872371
3 to 4 141895 -0.0423 0.483141
2 to 3 141834 -0.2222 0.412074
1 to 2 141481 -1.2635 0.103203
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2606.13 1.501 0.933305
Test results for specific bytes for dh-ranFile-2018-06-27_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2464.55 -0.501 0.308062
2 to 9 2436.66 -0.896 0.185202
3 to 10 2432.01 -0.961 0.168154
4 to 11 2667.56 2.370 0.991097
5 to 12 2695.40 2.763 0.997139
6 to 13 2534.71 0.491 0.688247
7 to 14 2511.10 0.157 0.562393
8 to 15 2456.25 -0.619 0.268045
9 to 16 2516.11 0.228 0.590084
10 to 17 2482.10 -0.253 0.400067
11 to 18 2544.17 0.625 0.733901
12 to 19 2480.26 -0.279 0.390034
13 to 20 2556.22 0.795 0.786701
14 to 21 2513.89 0.196 0.577874
15 to 22 2391.60 -1.533 0.062635
16 to 23 2469.30 -0.434 0.332078
17 to 24 2536.82 0.521 0.698739
18 to 25 2532.80 0.464 0.678614
19 to 26 2663.34 2.310 0.989556
20 to 27 2583.38 1.179 0.880848
21 to 28 2662.01 2.291 0.989022
22 to 29 2440.47 -0.842 0.199932
23 to 30 2446.81 -0.752 0.225970
24 to 31 2394.21 -1.496 0.067317
25 to 32 2654.90 2.191 0.985761
CDPARK for dh-ranFile-2018-06-27_23:31: 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
3506 -0.7763 0.218799
3528 0.2283 0.590298
3473 -2.2831 0.011212
3514 -0.4110 0.340551
3520 -0.1370 0.445521
3514 -0.4110 0.340551
3524 0.0457 0.518210
3529 0.2740 0.607947
3545 1.0046 0.842447
3530 0.3196 0.625377
Square side=100, avg. no. parked=3518.30 sample std.=18.26
p-value of the KSTEST for those 10 p-values: 0.568098
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_23:31
0.6620,0.2719,0.5458,0.6717,0.4560,0.5643,0.1096,0.4016,0.1365,0.7500,
The KS test for those 10 p-values: 0.595727
The 3DSPHERES test for dh-ranFile-2018-06-27_23:31
sample no r^3 equiv. uni.
1 4.123 0.128419
2 17.126 0.434958
3 0.428 0.014176
4 32.360 0.659955
5 41.056 0.745520
6 14.942 0.392293
7 15.234 0.398178
8 1.114 0.036453
9 1.960 0.063231
10 1.076 0.035231
11 12.742 0.346059
12 35.060 0.689223
13 15.686 0.407183
14 1.302 0.042487
15 2.239 0.071917
16 42.282 0.755708
17 6.451 0.193477
18 27.013 0.593604
19 39.777 0.734434
20 33.218 0.669535
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.032160
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 -0.4 -0.3 1.4 0.1
-0.3 0.1 -0.7 0.6 -1.4 0.4
-0.5 0.3 0.1 2.1 0.8 1.1
-1.9 -0.5 -1.9 0.3 -0.8 0.3
-1.1 0.3 1.0 0.3 0.5 0.4
0.9 1.2 -0.5 0.2 0.2 0.2
-0.5 -0.7 0.5 -0.7 1.6 -1.0
0.8
Chi-square with 42 degrees of freedom:31.509345
z-score=-1.144624, p-value=0.118536
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_23:31
Test no p-value
1 0.264385
2 0.556216
3 0.574457
4 0.216481
5 0.519653
6 0.548593
7 0.034876
8 0.259202
9 0.060166
10 0.111775
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.060153
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_23:31:
(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 66799 0.26 66699 0.02
3 25000.00 24924 0.23 24972 0.03
4 6666.67 6616 0.39 6665 0.00
5 1388.89 1379 0.07 1395 0.03
6 238.10 232 0.16 234 0.07
7 34.72 46 3.66 25 2.72
8 4.96 3 0.77 9 3.29
p=0.52391 p=0.59412
Number of rngs required: 687735, p-value: 0.220
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_23:31
No. of wins: Observed Expected
98730 98585.9
z-score= 0.645, pvalue=0.74043
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66844 66666.7 0.472 0.472
2 37767 37654.3 0.337 0.809
3 27038 26954.7 0.257 1.066
4 19150 19313.5 1.383 2.450
5 13778 13851.4 0.389 2.839
6 9892 9943.5 0.267 3.106
7 7182 7145.0 0.191 3.297
8 5198 5139.1 0.676 3.973
9 3617 3699.9 1.856 5.829
10 2645 2666.3 0.170 5.999
11 1932 1923.3 0.039 6.038
12 1349 1388.7 1.137 7.175
13 1000 1003.7 0.014 7.189
14 694 726.1 1.423 8.612
15 509 525.8 0.539 9.151
16 390 381.2 0.205 9.356
17 244 276.5 3.829 13.185
18 215 200.8 1.000 14.185
19 148 146.0 0.028 14.213
20 121 106.2 2.058 16.271
21 287 287.1 0.000 16.271
Chisq= 16.27 for 20 degrees of freedom, p= 0.30030
SUMMARY of craptest
p-value for no. of wins: 0.740434
p-value for throws/game: 0.300303
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_23:31
No. of wins: Observed Expected
98873 98585.9
z-score= 1.284, pvalue=0.90048
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66609 66666.7 0.050 0.050
2 37426 37654.3 1.384 1.434
3 26864 26954.7 0.305 1.740
4 19378 19313.5 0.216 1.955
5 13819 13851.4 0.076 2.031
6 10147 9943.5 4.163 6.194
7 7096 7145.0 0.336 6.531
8 5094 5139.1 0.395 6.926
9 3648 3699.9 0.727 7.653
10 2731 2666.3 1.570 9.223
11 2039 1923.3 6.957 16.180
12 1430 1388.7 1.226 17.406
13 995 1003.7 0.076 17.481
14 753 726.1 0.994 18.475
15 564 525.8 2.770 21.245
16 370 381.2 0.326 21.571
17 287 276.5 0.396 21.966
18 199 200.8 0.017 21.983
19 161 146.0 1.544 23.528
20 112 106.2 0.315 23.843
21 278 287.1 0.289 24.132
Chisq= 24.13 for 20 degrees of freedom, p= 0.76333
SUMMARY of craptest
p-value for no. of wins: 0.900475
p-value for throws/game: 0.763326
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0086,0.0112,0.0117,0.0142,0.0211,0.0218,0.0296,0.0320,0.0322,0.0349,
0.0352,0.0365,0.0393,0.0413,0.0425,0.0548,0.0570,0.0602,0.0602,0.0609,
0.0626,0.0632,0.0673,0.0719,0.0841,0.0946,0.0946,0.1032,0.1038,0.1096,
0.1118,0.1185,0.1213,0.1284,0.1365,0.1497,0.1592,0.1634,0.1654,0.1676,
0.1682,0.1731,0.1852,0.1861,0.1895,0.1924,0.1935,0.1947,0.1991,0.1999,
0.2017,0.2017,0.2050,0.2071,0.2125,0.2165,0.2188,0.2201,0.2243,0.2260,
0.2374,0.2473,0.2503,0.2525,0.2562,0.2574,0.2592,0.2638,0.2644,0.2653,
0.2665,0.2670,0.2680,0.2719,0.2812,0.2911,0.2966,0.3003,0.3014,0.3045,
0.3081,0.3119,0.3187,0.3213,0.3255,0.3266,0.3321,0.3324,0.3342,0.3406,
0.3406,0.3442,0.3442,0.3461,0.3540,0.3555,0.3644,0.3714,0.3718,0.3881,
0.3896,0.3900,0.3904,0.3923,0.3925,0.3974,0.3982,0.3989,0.4001,0.4016,
0.4045,0.4045,0.4072,0.4075,0.4097,0.4121,0.4146,0.4203,0.4231,0.4270,
0.4289,0.4342,0.4346,0.4350,0.4358,0.4434,0.4455,0.4495,0.4560,0.4562,
0.4570,0.4631,0.4652,0.4733,0.4831,0.4954,0.5004,0.5050,0.5102,0.5117,
0.5126,0.5182,0.5185,0.5190,0.5197,0.5239,0.5390,0.5458,0.5486,0.5495,
0.5562,0.5571,0.5573,0.5624,0.5643,0.5655,0.5681,0.5745,0.5773,0.5779,
0.5854,0.5867,0.5901,0.5903,0.5936,0.5941,0.5957,0.5961,0.6032,0.6079,
0.6083,0.6128,0.6155,0.6187,0.6226,0.6236,0.6253,0.6254,0.6300,0.6357,
0.6524,0.6600,0.6620,0.6676,0.6695,0.6717,0.6738,0.6786,0.6825,0.6882,
0.6892,0.6987,0.7219,0.7339,0.7344,0.7403,0.7404,0.7406,0.7425,0.7425,
0.7455,0.7500,0.7501,0.7523,0.7557,0.7624,0.7633,0.7635,0.7641,0.7707,
0.7717,0.7852,0.7867,0.7869,0.7957,0.7970,0.7986,0.7994,0.8029,0.8032,
0.8129,0.8307,0.8404,0.8418,0.8424,0.8569,0.8588,0.8588,0.8642,0.8724,
0.8724,0.8779,0.8808,0.8814,0.8877,0.8886,0.8913,0.8924,0.8939,0.8976,
0.9005,0.9102,0.9120,0.9170,0.9214,0.9268,0.9301,0.9333,0.9337,0.9388,
0.9460,0.9592,0.9621,0.9639,0.9763,0.9766,0.9773,0.9832,0.9858,0.9879,
0.9890,0.9894,0.9895,0.9896,0.9904,0.9911,0.9919,0.9971,0.9984,
Overall p-value after applying KStest on 269 p-values = 0.666214
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.