RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.72 31.0021 0.980039
2 to 25 15.94 18.2918 0.629340
3 to 26 15.50 24.7502 0.899558
4 to 27 15.81 39.6679 0.998559
5 to 28 15.65 23.6788 0.871573
6 to 29 15.46 30.5534 0.977381
7 to 30 15.42 26.5397 0.934827
8 to 31 15.33 33.9538 0.991488
9 to 32 15.72 13.4554 0.294795
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000016
Tough bday spacings test for dh-ranFile-2018-07-11_18:31: 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 30 74 108 86 93 42 24 18 7 7
(O-E)^2/E 0.4 1.2 0.0 1.1 1.4 2.8 2.0 1.1 0.7 0.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 12.755, p= 0.762
RESULTS OF GCD FOR dh-ranFile-2018-07-11_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.696922
p-value, dist. of gcd's: 0.410708
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.829 0.280 0.611 0.068 0.738 0.958 0.137 0.340
Bits 8 to 15---> 0.672 0.637 0.390 0.613 0.913 0.025 0.896 0.448
Bits 16 to 23---> 0.298 0.660 0.068 0.073 0.913 0.691 0.788 0.661
Bits 24 to 31---> 0.576 0.754 0.767 0.518 0.699 0.212 0.341 0.200
KS test for the above 32 p values: 0.215
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_18:31,
p-values for 5 runs: 0.1270, 0.4730, 0.0089, 0.8951, 0.2443
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 221 211.4 0.434 0.434
r= 29 5220 5134.0 1.440 1.875
r= 30 23028 23103.0 0.244 2.118
r= 31 11531 11551.5 0.036 2.155
chi-square = 2.155 with df = 3; p-value = 0.459
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5148 5134.0 0.038 0.066
r= 31 22979 23103.0 0.666 0.732
r= 32 11664 11551.5 1.095 1.827
chi-square = 1.827 with df = 3; p-value = 0.391
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_18:31
b-rank test for bits 1 to 8, p=0.73677
b-rank test for bits 2 to 9, p=0.25682
b-rank test for bits 3 to 10, p=0.94587
b-rank test for bits 4 to 11, p=0.78559
b-rank test for bits 5 to 12, p=0.49304
b-rank test for bits 6 to 13, p=0.98625
b-rank test for bits 7 to 14, p=0.69602
b-rank test for bits 8 to 15, p=0.66540
b-rank test for bits 9 to 16, p=0.51276
b-rank test for bits 10 to 17, p=0.76227
b-rank test for bits 11 to 18, p=0.66251
b-rank test for bits 12 to 19, p=0.18277
b-rank test for bits 13 to 20, p=0.36535
b-rank test for bits 14 to 21, p=0.98597
b-rank test for bits 15 to 22, p=0.48681
b-rank test for bits 16 to 23, p=0.60475
b-rank test for bits 17 to 24, p=0.70215
b-rank test for bits 18 to 25, p=0.40986
b-rank test for bits 19 to 26, p=0.07335
b-rank test for bits 20 to 27, p=0.18422
b-rank test for bits 21 to 28, p=0.05528
b-rank test for bits 22 to 29, p=0.87597
b-rank test for bits 23 to 30, p=0.58036
b-rank test for bits 24 to 31, p=0.09122
b-rank test for bits 25 to 32, p=0.34747
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 = 0.781927
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_18:31
(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 142032 0.29 0.612795
2 142155 0.57 0.717015
3 141712 -0.46 0.322381
4 142121 0.49 0.689543
5 141262 -1.51 0.065209
6 141236 -1.57 0.057836
7 142510 1.40 0.919756
8 142279 0.86 0.806128
9 141326 -1.36 0.086454
10 142164 0.60 0.724086
11 141928 0.04 0.517397
12 141672 -0.55 0.289615
13 141921 0.03 0.510876
14 140854 -2.47 0.006837
15 142299 0.91 0.818706
16 141971 0.14 0.557285
17 142271 0.85 0.800951
18 141546 -0.85 0.197968
19 141878 -0.07 0.470823
20 141482 -1.00 0.159034
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_18:31
Bits used No. missing words z-score p-value
23 to 32 142121 0.7299 0.767273
22 to 31 141438 -1.6253 0.052052
21 to 30 142319 1.4127 0.921121
20 to 29 142285 1.2954 0.902411
19 to 28 141921 0.0402 0.516050
18 to 27 141830 -0.2736 0.392215
17 to 26 141963 0.1851 0.573413
16 to 25 141831 -0.2701 0.393540
15 to 24 141550 -1.2391 0.107660
14 to 23 142033 0.4264 0.665109
13 to 22 142280 1.2782 0.899406
12 to 21 142625 2.4678 0.993203
11 to 20 142674 2.6368 0.995815
10 to 19 142425 1.7782 0.962312
9 to 18 141991 0.2816 0.610883
8 to 17 141678 -0.7977 0.212525
7 to 16 142174 0.9127 0.819288
6 to 15 141687 -0.7667 0.221643
5 to 14 141842 -0.2322 0.408202
4 to 13 142296 1.3333 0.908791
3 to 12 141877 -0.1115 0.455617
2 to 11 141873 -0.1253 0.450153
1 to 10 141937 0.0954 0.538007
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_18:31
Bits used No. missing words z-score p-value
28 to 32 141509 -1.3571 0.087383
27 to 31 142260 1.1887 0.882723
26 to 30 142112 0.6870 0.753964
25 to 29 141823 -0.2926 0.384897
24 to 28 141535 -1.2689 0.102236
23 to 27 142103 0.6565 0.744252
22 to 26 141816 -0.3164 0.375860
21 to 25 141654 -0.8655 0.193375
20 to 24 141703 -0.6994 0.242144
19 to 23 141793 -0.3943 0.346665
18 to 22 142564 2.2192 0.986764
17 to 21 142172 0.8904 0.813376
16 to 20 142015 0.3582 0.639905
15 to 19 141732 -0.6011 0.273881
14 to 18 141947 0.1277 0.550805
13 to 17 142098 0.6396 0.738770
12 to 16 142034 0.4226 0.663710
11 to 15 142196 0.9718 0.834416
10 to 14 142434 1.7785 0.962343
9 to 13 142161 0.8531 0.803203
8 to 12 142132 0.7548 0.774820
7 to 11 141937 0.0938 0.537365
6 to 10 141292 -2.0926 0.018190
5 to 9 141765 -0.4893 0.312331
4 to 8 141970 0.2057 0.581472
3 to 7 141387 -1.7706 0.038313
2 to 6 141530 -1.2859 0.099245
1 to 5 141252 -2.2282 0.012932
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_18:31
Bits used No. missing words z-score p-value
31 to 32 141820 -0.2635 0.396079
30 to 31 142366 1.3471 0.911027
29 to 30 142022 0.3324 0.630191
28 to 29 142158 0.7335 0.768385
27 to 28 141495 -1.2222 0.110814
26 to 27 141839 -0.2075 0.417824
25 to 26 142137 0.6716 0.749079
24 to 25 141885 -0.0718 0.471393
23 to 24 142267 1.0551 0.854304
22 to 23 142075 0.4887 0.687474
21 to 22 141204 -2.0806 0.018734
20 to 21 141758 -0.4464 0.327654
19 to 20 142162 0.7453 0.771967
18 to 19 142335 1.2557 0.895381
17 to 18 141625 -0.8387 0.200810
16 to 17 142174 0.7807 0.782522
15 to 16 142009 0.2940 0.615626
14 to 15 142510 1.7719 0.961793
13 to 14 141250 -1.9449 0.025892
12 to 13 141959 0.1465 0.558244
11 to 12 141541 -1.0865 0.138625
10 to 11 142717 2.3825 0.991402
9 to 10 142061 0.4474 0.672708
8 to 9 142134 0.6627 0.746253
7 to 8 142031 0.3589 0.640168
6 to 7 141318 -1.7443 0.040550
5 to 6 141934 0.0728 0.529007
4 to 5 141711 -0.5850 0.279259
3 to 4 141243 -1.9656 0.024674
2 to 3 141800 -0.3225 0.373534
1 to 2 141968 0.1731 0.568701
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2425.18 -1.058 0.145004
Test results for specific bytes for dh-ranFile-2018-07-11_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2575.28 1.065 0.856484
2 to 9 2532.56 0.460 0.677402
3 to 10 2564.65 0.914 0.819725
4 to 11 2473.74 -0.371 0.355200
5 to 12 2383.77 -1.644 0.050113
6 to 13 2412.32 -1.240 0.107480
7 to 14 2549.05 0.694 0.756067
8 to 15 2509.45 0.134 0.553136
9 to 16 2471.79 -0.399 0.344972
10 to 17 2458.70 -0.584 0.279591
11 to 18 2508.35 0.118 0.547006
12 to 19 2366.77 -1.884 0.029771
13 to 20 2561.16 0.865 0.806468
14 to 21 2455.53 -0.629 0.264725
15 to 22 2586.42 1.222 0.889171
16 to 23 2500.24 0.003 0.501364
17 to 24 2527.36 0.387 0.650590
18 to 25 2488.74 -0.159 0.436764
19 to 26 2506.14 0.087 0.534604
20 to 27 2430.02 -0.990 0.161181
21 to 28 2449.71 -0.711 0.238461
22 to 29 2450.81 -0.696 0.243330
23 to 30 2480.12 -0.281 0.389283
24 to 31 2545.72 0.647 0.741062
25 to 32 2570.71 1.000 0.841341
CDPARK for dh-ranFile-2018-07-11_18:31: 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
3517 -0.2740 0.392053
3494 -1.3242 0.092718
3505 -0.8219 0.205562
3518 -0.2283 0.409702
3532 0.4110 0.659449
3525 0.0913 0.536383
3517 -0.2740 0.392053
3543 0.9132 0.819442
3513 -0.4566 0.323972
3522 -0.0457 0.481790
Square side=100, avg. no. parked=3518.60 sample std.=12.86
p-value of the KSTEST for those 10 p-values: 0.416290
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_18:31
0.9158,0.9043,0.7127,0.7992,0.7845,0.6051,0.0087,0.9887,0.5430,0.1699,
The KS test for those 10 p-values: 0.117628
The 3DSPHERES test for dh-ranFile-2018-07-11_18:31
sample no r^3 equiv. uni.
1 14.836 0.390142
2 117.784 0.980280
3 4.592 0.141941
4 0.550 0.018157
5 19.813 0.483373
6 34.069 0.678784
7 74.768 0.917277
8 34.451 0.682841
9 23.284 0.539820
10 37.024 0.708909
11 3.279 0.103543
12 2.032 0.065490
13 39.152 0.728842
14 53.079 0.829550
15 5.100 0.156322
16 18.103 0.453065
17 31.818 0.653755
18 5.428 0.165506
19 26.077 0.580724
20 94.148 0.956642
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.897058
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.1 -0.6 0.0 2.8 1.0
2.4 0.9 -1.1 0.6 -0.8 -2.5
0.5 -0.7 1.1 -1.9 0.3 0.9
-1.2 0.2 1.3 -1.1 1.7 -1.5
-0.1 1.1 -0.6 1.8 2.6 -0.9
1.3 0.2 -0.7 -0.9 0.6 -0.3
0.5 -0.7 -0.8 -1.3 -1.3 -1.0
3.7
Chi-square with 42 degrees of freedom:78.699275
z-score=4.004219, p-value=0.999484
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_18:31
Test no p-value
1 0.944792
2 0.389840
3 0.548206
4 0.402420
5 0.065465
6 0.335703
7 0.960748
8 0.092699
9 0.364584
10 0.070865
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.333399
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_18:31:
(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 66789 0.22 66405 1.03
3 25000.00 25014 0.01 25272 2.96
4 6666.67 6515 3.45 6685 0.05
5 1388.89 1420 0.70 1392 0.01
6 238.10 219 1.53 211 3.08
7 34.72 36 0.05 31 0.40
8 4.96 6 0.22 3 0.77
p=0.59628 p=0.78308
Number of rngs required: 688077, p-value: 0.354
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_18:31
No. of wins: Observed Expected
98518 98585.9
z-score=-0.304, pvalue=0.38075
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66518 66666.7 0.332 0.332
2 37863 37654.3 1.156 1.488
3 26818 26954.7 0.694 2.182
4 19394 19313.5 0.336 2.517
5 13808 13851.4 0.136 2.654
6 10176 9943.5 5.434 8.088
7 7162 7145.0 0.040 8.128
8 5163 5139.1 0.111 8.240
9 3600 3699.9 2.696 10.935
10 2629 2666.3 0.522 11.457
11 1929 1923.3 0.017 11.474
12 1420 1388.7 0.704 12.177
13 976 1003.7 0.765 12.942
14 661 726.1 5.844 18.786
15 539 525.8 0.330 19.116
16 361 381.2 1.065 20.181
17 270 276.5 0.155 20.336
18 184 200.8 1.410 21.746
19 128 146.0 2.216 23.962
20 92 106.2 1.902 25.864
21 309 287.1 1.668 27.532
Chisq= 27.53 for 20 degrees of freedom, p= 0.87906
SUMMARY of craptest
p-value for no. of wins: 0.380753
p-value for throws/game: 0.879061
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_18:31
No. of wins: Observed Expected
98443 98585.9
z-score=-0.639, pvalue=0.26143
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66798 66666.7 0.259 0.259
2 37563 37654.3 0.221 0.480
3 26845 26954.7 0.447 0.927
4 19312 19313.5 0.000 0.927
5 14021 13851.4 2.076 3.003
6 9861 9943.5 0.685 3.688
7 7115 7145.0 0.126 3.815
8 5232 5139.1 1.680 5.495
9 3687 3699.9 0.045 5.540
10 2668 2666.3 0.001 5.541
11 1961 1923.3 0.738 6.279
12 1375 1388.7 0.136 6.415
13 989 1003.7 0.216 6.630
14 721 726.1 0.036 6.667
15 505 525.8 0.826 7.492
16 377 381.2 0.045 7.537
17 267 276.5 0.329 7.867
18 206 200.8 0.133 8.000
19 137 146.0 0.553 8.553
20 103 106.2 0.097 8.650
21 257 287.1 3.159 11.808
Chisq= 11.81 for 20 degrees of freedom, p= 0.07749
SUMMARY of craptest
p-value for no. of wins: 0.261429
p-value for throws/game: 0.077487
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0068,0.0087,0.0089,0.0129,0.0182,0.0182,0.0187,0.0247,0.0250,
0.0259,0.0298,0.0383,0.0406,0.0501,0.0521,0.0553,0.0578,0.0652,0.0655,
0.0655,0.0678,0.0683,0.0709,0.0732,0.0734,0.0775,0.0865,0.0874,0.0912,
0.0927,0.0927,0.0992,0.1022,0.1035,0.1075,0.1077,0.1108,0.1176,0.1270,
0.1367,0.1386,0.1419,0.1450,0.1563,0.1590,0.1612,0.1655,0.1699,0.1828,
0.1842,0.1934,0.1980,0.1998,0.2008,0.2056,0.2119,0.2125,0.2153,0.2216,
0.2385,0.2421,0.2433,0.2443,0.2568,0.2614,0.2647,0.2739,0.2793,0.2796,
0.2799,0.2896,0.2948,0.2976,0.3123,0.3224,0.3240,0.3277,0.3334,0.3357,
0.3404,0.3408,0.3450,0.3467,0.3475,0.3537,0.3552,0.3646,0.3653,0.3735,
0.3759,0.3808,0.3849,0.3893,0.3898,0.3898,0.3901,0.3909,0.3921,0.3921,
0.3922,0.3935,0.3961,0.4024,0.4082,0.4097,0.4099,0.4107,0.4163,0.4178,
0.4368,0.4485,0.4502,0.4531,0.4556,0.4591,0.4708,0.4714,0.4730,0.4818,
0.4834,0.4868,0.4930,0.5014,0.5109,0.5128,0.5160,0.5174,0.5185,0.5290,
0.5346,0.5364,0.5374,0.5380,0.5398,0.5430,0.5470,0.5482,0.5508,0.5531,
0.5573,0.5582,0.5687,0.5734,0.5764,0.5804,0.5807,0.5815,0.5963,0.6047,
0.6051,0.6106,0.6109,0.6127,0.6128,0.6156,0.6293,0.6302,0.6369,0.6399,
0.6402,0.6506,0.6538,0.6594,0.6596,0.6606,0.6625,0.6637,0.6651,0.6654,
0.6717,0.6727,0.6774,0.6788,0.6828,0.6875,0.6895,0.6908,0.6960,0.6969,
0.6989,0.7022,0.7089,0.7127,0.7170,0.7241,0.7288,0.7368,0.7378,0.7388,
0.7411,0.7443,0.7463,0.7491,0.7538,0.7540,0.7561,0.7623,0.7623,0.7673,
0.7674,0.7684,0.7720,0.7748,0.7819,0.7825,0.7831,0.7845,0.7856,0.7877,
0.7992,0.8010,0.8032,0.8061,0.8065,0.8134,0.8187,0.8193,0.8194,0.8197,
0.8288,0.8296,0.8344,0.8413,0.8543,0.8565,0.8716,0.8760,0.8791,0.8827,
0.8892,0.8951,0.8954,0.8961,0.8971,0.8994,0.8996,0.9024,0.9043,0.9088,
0.9110,0.9132,0.9134,0.9158,0.9173,0.9198,0.9211,0.9348,0.9448,0.9459,
0.9566,0.9579,0.9607,0.9618,0.9623,0.9623,0.9774,0.9800,0.9803,0.9860,
0.9862,0.9868,0.9887,0.9914,0.9915,0.9932,0.9958,0.9986,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.234940
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.