RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_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 15.62 20.1903 0.735387
2 to 25 15.85 22.2146 0.823394
3 to 26 16.10 22.9363 0.848663
4 to 27 16.00 5.1319 0.002627
5 to 28 15.90 23.3968 0.863226
6 to 29 15.56 22.3620 0.828806
7 to 30 15.54 22.0487 0.817147
8 to 31 15.86 15.0072 0.405036
9 to 32 15.82 12.4391 0.227149
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.111666
Tough bday spacings test for dh-ranFile-2018-06-15_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 10 43 75 87 92 82 48 31 18 7 7
(O-E)^2/E 0.1 1.1 0.0 1.2 0.3 0.2 0.3 0.1 0.7 0.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 6.079, p= 0.191
RESULTS OF GCD FOR dh-ranFile-2018-06-15_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.494056
p-value, dist. of gcd's: 0.679759
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.725 0.570 0.161 0.465 0.759 0.436 0.156 0.232
Bits 8 to 15---> 0.654 0.837 0.239 0.964 0.276 0.690 0.775 0.082
Bits 16 to 23---> 0.002 0.521 0.139 0.609 0.446 0.669 0.948 0.280
Bits 24 to 31---> 0.866 0.418 0.853 0.994 0.702 0.857 0.776 0.254
KS test for the above 32 p values: 0.307
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_19:31,
p-values for 5 runs: 0.2486, 0.7945, 0.3985, 0.3357, 0.8265
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 232 211.4 2.004 2.004
r= 29 5138 5134.0 0.003 2.007
r= 30 22947 23103.0 1.054 3.061
r= 31 11683 11551.5 1.496 4.557
chi-square = 4.557 with df = 3; p-value = 0.793
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5083 5134.0 0.507 0.538
r= 31 23240 23103.0 0.812 1.350
r= 32 11463 11551.5 0.678 2.029
chi-square = 2.029 with df = 3; p-value = 0.434
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_19:31
b-rank test for bits 1 to 8, p=0.85064
b-rank test for bits 2 to 9, p=0.79727
b-rank test for bits 3 to 10, p=0.86048
b-rank test for bits 4 to 11, p=0.86470
b-rank test for bits 5 to 12, p=0.27973
b-rank test for bits 6 to 13, p=0.51036
b-rank test for bits 7 to 14, p=0.90429
b-rank test for bits 8 to 15, p=0.82662
b-rank test for bits 9 to 16, p=0.36328
b-rank test for bits 10 to 17, p=0.67513
b-rank test for bits 11 to 18, p=0.10848
b-rank test for bits 12 to 19, p=0.39123
b-rank test for bits 13 to 20, p=0.20479
b-rank test for bits 14 to 21, p=0.29869
b-rank test for bits 15 to 22, p=0.78598
b-rank test for bits 16 to 23, p=0.33003
b-rank test for bits 17 to 24, p=0.62738
b-rank test for bits 18 to 25, p=0.14111
b-rank test for bits 19 to 26, p=0.13900
b-rank test for bits 20 to 27, p=0.11143
b-rank test for bits 21 to 28, p=0.12792
b-rank test for bits 22 to 29, p=0.41119
b-rank test for bits 23 to 30, p=0.26792
b-rank test for bits 24 to 31, p=0.86826
b-rank test for bits 25 to 32, p=0.66587
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 = 0.687991
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_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 142125 0.50 0.692835
2 142307 0.93 0.823591
3 141221 -1.61 0.053890
4 141978 0.16 0.563734
5 141701 -0.49 0.313217
6 141905 -0.01 0.495964
7 141994 0.20 0.578410
8 140648 -2.95 0.001604
9 142404 1.16 0.876113
10 142438 1.24 0.891624
11 141692 -0.51 0.305804
12 141074 -1.95 0.025487
13 142543 1.48 0.930635
14 141988 0.18 0.572918
15 142464 1.30 0.902505
16 142493 1.36 0.913671
17 141199 -1.66 0.048492
18 141871 -0.09 0.464320
19 141216 -1.62 0.052624
20 142301 0.92 0.819935
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_19:31
Bits used No. missing words z-score p-value
23 to 32 141730 -0.6184 0.268163
22 to 31 141707 -0.6977 0.242686
21 to 30 141264 -2.2253 0.013031
20 to 29 141916 0.0230 0.509175
19 to 28 141255 -2.2563 0.012026
18 to 27 141801 -0.3736 0.354369
17 to 26 141781 -0.4425 0.329058
16 to 25 141950 0.1402 0.555765
15 to 24 142068 0.5471 0.707858
14 to 23 141883 -0.0908 0.463829
13 to 22 141808 -0.3494 0.363389
12 to 21 141817 -0.3184 0.375099
11 to 20 141619 -1.0011 0.158380
10 to 19 141961 0.1782 0.570706
9 to 18 142184 0.9471 0.828216
8 to 17 141995 0.2954 0.616161
7 to 16 142232 1.1127 0.867072
6 to 15 141991 0.2816 0.610883
5 to 14 141954 0.1540 0.561209
4 to 13 142142 0.8023 0.788813
3 to 12 141518 -1.3494 0.088602
2 to 11 141325 -2.0149 0.021956
1 to 10 142015 0.3644 0.642213
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_19:31
Bits used No. missing words z-score p-value
28 to 32 141910 0.0023 0.500906
27 to 31 141583 -1.1062 0.134319
26 to 30 141672 -0.8045 0.210552
25 to 29 141608 -1.0215 0.153519
24 to 28 141656 -0.8587 0.195240
23 to 27 142198 0.9785 0.836097
22 to 26 142162 0.8565 0.804142
21 to 25 142344 1.4735 0.929686
20 to 24 142026 0.3955 0.653760
19 to 23 142382 1.6023 0.945452
18 to 22 141277 -2.1435 0.016037
17 to 21 141884 -0.0859 0.465787
16 to 20 141695 -0.7265 0.233753
15 to 19 142104 0.6599 0.745341
14 to 18 141302 -2.0587 0.019759
13 to 17 141755 -0.5232 0.300434
12 to 16 141599 -1.0520 0.146408
11 to 15 142221 1.0565 0.854632
10 to 14 141510 -1.3537 0.087922
9 to 13 141745 -0.5571 0.288746
8 to 12 142137 0.7718 0.779873
7 to 11 141662 -0.8384 0.200901
6 to 10 141713 -0.6655 0.252857
5 to 9 141758 -0.5130 0.303982
4 to 8 142004 0.3209 0.625863
3 to 7 141768 -0.4791 0.315939
2 to 6 141741 -0.5706 0.284132
1 to 5 141721 -0.6384 0.261605
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_19:31
Bits used No. missing words z-score p-value
31 to 32 142710 2.3619 0.990908
30 to 31 141654 -0.7532 0.225669
29 to 30 141796 -0.3343 0.369074
28 to 29 141800 -0.3225 0.373534
27 to 28 141742 -0.4936 0.310795
26 to 27 142157 0.7306 0.767485
25 to 26 141878 -0.0924 0.463183
24 to 25 141689 -0.6499 0.257865
23 to 24 142216 0.9046 0.817170
22 to 23 141866 -0.1278 0.449147
21 to 22 142517 1.7925 0.963477
20 to 21 142057 0.4356 0.668438
19 to 20 141799 -0.3255 0.372418
18 to 19 142304 1.1642 0.877832
17 to 18 142347 1.2911 0.901659
16 to 17 141743 -0.4906 0.311837
15 to 16 141407 -1.4818 0.069197
14 to 15 142233 0.9548 0.830155
13 to 14 141770 -0.4110 0.340535
12 to 13 141201 -2.0895 0.018333
11 to 12 141353 -1.6411 0.050389
10 to 11 141592 -0.9361 0.174617
9 to 10 141555 -1.0452 0.147960
8 to 9 141603 -0.9036 0.183096
7 to 8 142039 0.3825 0.648958
6 to 7 142139 0.6775 0.750953
5 to 6 142203 0.8663 0.806833
4 to 5 142090 0.5329 0.702966
3 to 4 141856 -0.1573 0.437498
2 to 3 141942 0.0964 0.538387
1 to 2 142229 0.9430 0.827154
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2463.89 -0.511 0.304794
Test results for specific bytes for dh-ranFile-2018-06-15_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2585.54 1.210 0.886811
2 to 9 2554.09 0.765 0.777865
3 to 10 2474.48 -0.361 0.359108
4 to 11 2476.54 -0.332 0.370041
5 to 12 2462.61 -0.529 0.298488
6 to 13 2494.66 -0.075 0.469927
7 to 14 2586.12 1.218 0.888362
8 to 15 2508.05 0.114 0.545310
9 to 16 2561.02 0.863 0.805909
10 to 17 2438.79 -0.866 0.193334
11 to 18 2379.66 -1.702 0.044394
12 to 19 2497.79 -0.031 0.487548
13 to 20 2295.19 -2.896 0.001887
14 to 21 2489.17 -0.153 0.439140
15 to 22 2626.35 1.787 0.963015
16 to 23 2454.05 -0.650 0.257890
17 to 24 2380.65 -1.688 0.045712
18 to 25 2438.22 -0.874 0.191140
19 to 26 2467.51 -0.459 0.322954
20 to 27 2483.66 -0.231 0.408600
21 to 28 2591.98 1.301 0.903332
22 to 29 2418.64 -1.151 0.124933
23 to 30 2525.61 0.362 0.641385
24 to 31 2523.78 0.336 0.631680
25 to 32 2551.19 0.724 0.765464
CDPARK for dh-ranFile-2018-06-15_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
3507 -0.7306 0.232514
3535 0.5479 0.708135
3524 0.0457 0.518210
3516 -0.3196 0.374623
3512 -0.5023 0.307734
3528 0.2283 0.590298
3497 -1.1872 0.117571
3508 -0.6849 0.246694
3546 1.0502 0.853193
3535 0.5479 0.708135
Square side=100, avg. no. parked=3520.80 sample std.=14.57
p-value of the KSTEST for those 10 p-values: 0.807944
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_19:31
0.5658,0.7710,0.5977,0.7543,0.5243,0.8499,0.1847,0.2652,0.8022,0.2739,
The KS test for those 10 p-values: 0.579195
The 3DSPHERES test for dh-ranFile-2018-06-15_19:31
sample no r^3 equiv. uni.
1 37.067 0.709334
2 42.818 0.760038
3 10.306 0.290747
4 3.672 0.115209
5 5.176 0.158472
6 12.206 0.334278
7 25.209 0.568424
8 81.048 0.932902
9 22.559 0.528565
10 59.208 0.861045
11 57.361 0.852222
12 9.618 0.274288
13 10.162 0.287318
14 24.961 0.564832
15 0.334 0.011068
16 2.010 0.064803
17 12.555 0.341974
18 32.637 0.663075
19 11.275 0.313286
20 4.520 0.139864
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.614742
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.7 0.1 0.5 2.7 -1.3
-0.5 0.6 -0.3 0.3 -0.6 -0.0
0.6 -1.0 -1.4 0.6 0.7 0.2
1.0 0.8 -0.5 -0.3 1.4 0.3
-0.8 -0.7 -1.2 -1.5 -0.6 -0.4
-0.6 1.8 1.0 -0.5 1.3 -0.7
-0.9 -0.4 1.7 0.4 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:40.227747
z-score=-0.193369, p-value=0.451022
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_19:31
Test no p-value
1 0.180446
2 0.003946
3 0.112671
4 0.891509
5 0.280918
6 0.156339
7 0.477262
8 0.016751
9 0.026543
10 0.039393
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000504
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_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 66489 0.47 66756 0.12
3 25000.00 25191 1.46 25063 0.16
4 6666.67 6581 1.10 6542 2.33
5 1388.89 1434 1.47 1368 0.31
6 238.10 249 0.50 219 1.53
7 34.72 49 5.87 46 3.66
8 4.96 6 0.22 5 0.00
p=0.91435 p=0.77059
Number of rngs required: 688247, p-value: 0.429
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_19:31
No. of wins: Observed Expected
98902 98585.9
z-score= 1.414, pvalue=0.92131
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66469 66666.7 0.586 0.586
2 37799 37654.3 0.556 1.142
3 27138 26954.7 1.246 2.388
4 19444 19313.5 0.882 3.270
5 13802 13851.4 0.176 3.447
6 10044 9943.5 1.015 4.462
7 7091 7145.0 0.409 4.870
8 4884 5139.1 12.660 17.530
9 3752 3699.9 0.735 18.265
10 2625 2666.3 0.640 18.905
11 1865 1923.3 1.769 20.674
12 1376 1388.7 0.117 20.790
13 950 1003.7 2.875 23.665
14 699 726.1 1.014 24.679
15 605 525.8 11.918 36.598
16 408 381.2 1.891 38.489
17 288 276.5 0.475 38.964
18 220 200.8 1.830 40.794
19 142 146.0 0.109 40.902
20 119 106.2 1.539 42.441
21 280 287.1 0.176 42.618
Chisq= 42.62 for 20 degrees of freedom, p= 0.99770
SUMMARY of craptest
p-value for no. of wins: 0.921314
p-value for throws/game: 0.997704
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_19:31
No. of wins: Observed Expected
98693 98585.9
z-score= 0.479, pvalue=0.68410
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67057 66666.7 2.285 2.285
2 37598 37654.3 0.084 2.370
3 27077 26954.7 0.555 2.924
4 19311 19313.5 0.000 2.925
5 13726 13851.4 1.136 4.060
6 9940 9943.5 0.001 4.061
7 7089 7145.0 0.439 4.501
8 5034 5139.1 2.148 6.649
9 3657 3699.9 0.497 7.146
10 2622 2666.3 0.736 7.882
11 1887 1923.3 0.686 8.568
12 1377 1388.7 0.099 8.667
13 982 1003.7 0.470 9.137
14 753 726.1 0.994 10.130
15 490 525.8 2.442 12.573
16 380 381.2 0.003 12.576
17 285 276.5 0.259 12.835
18 182 200.8 1.765 14.600
19 146 146.0 0.000 14.600
20 117 106.2 1.095 15.695
21 290 287.1 0.029 15.724
Chisq= 15.72 for 20 degrees of freedom, p= 0.26644
SUMMARY of craptest
p-value for no. of wins: 0.684101
p-value for throws/game: 0.266437
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0016,0.0019,0.0023,0.0026,0.0039,0.0111,0.0120,0.0130,0.0160,
0.0168,0.0183,0.0198,0.0220,0.0255,0.0265,0.0394,0.0444,0.0457,0.0485,
0.0504,0.0526,0.0539,0.0648,0.0692,0.0821,0.0879,0.0886,0.1085,0.1114,
0.1117,0.1127,0.1152,0.1176,0.1249,0.1279,0.1343,0.1390,0.1390,0.1399,
0.1411,0.1464,0.1480,0.1535,0.1563,0.1564,0.1584,0.1585,0.1606,0.1746,
0.1804,0.1831,0.1847,0.1911,0.1914,0.1933,0.1952,0.2009,0.2048,0.2106,
0.2257,0.2271,0.2321,0.2325,0.2338,0.2388,0.2427,0.2467,0.2486,0.2529,
0.2542,0.2579,0.2579,0.2616,0.2652,0.2664,0.2679,0.2682,0.2739,0.2743,
0.2755,0.2797,0.2805,0.2809,0.2841,0.2873,0.2887,0.2907,0.2985,0.2987,
0.3004,0.3040,0.3048,0.3058,0.3074,0.3077,0.3108,0.3118,0.3132,0.3133,
0.3159,0.3230,0.3291,0.3300,0.3343,0.3357,0.3405,0.3420,0.3544,0.3591,
0.3633,0.3634,0.3691,0.3700,0.3724,0.3735,0.3746,0.3751,0.3912,0.3985,
0.4050,0.4086,0.4112,0.4185,0.4288,0.4335,0.4365,0.4375,0.4391,0.4463,
0.4491,0.4510,0.4632,0.4638,0.4643,0.4645,0.4658,0.4699,0.4773,0.4875,
0.4941,0.4960,0.5009,0.5092,0.5104,0.5182,0.5210,0.5243,0.5286,0.5384,
0.5453,0.5558,0.5612,0.5637,0.5648,0.5658,0.5684,0.5697,0.5707,0.5729,
0.5784,0.5792,0.5903,0.5977,0.6092,0.6109,0.6147,0.6162,0.6259,0.6274,
0.6317,0.6414,0.6422,0.6490,0.6538,0.6538,0.6631,0.6659,0.6684,0.6686,
0.6751,0.6798,0.6841,0.6880,0.6904,0.6928,0.7023,0.7030,0.7079,0.7081,
0.7081,0.7093,0.7246,0.7354,0.7453,0.7510,0.7543,0.7586,0.7600,0.7655,
0.7675,0.7706,0.7710,0.7752,0.7760,0.7779,0.7799,0.7860,0.7888,0.7928,
0.7945,0.7973,0.8022,0.8041,0.8059,0.8068,0.8079,0.8171,0.8172,0.8199,
0.8234,0.8236,0.8265,0.8266,0.8272,0.8282,0.8288,0.8302,0.8361,0.8375,
0.8487,0.8499,0.8506,0.8522,0.8531,0.8532,0.8546,0.8571,0.8605,0.8610,
0.8632,0.8647,0.8660,0.8671,0.8683,0.8761,0.8778,0.8868,0.8884,0.8915,
0.8916,0.9017,0.9025,0.9033,0.9043,0.9137,0.9144,0.9213,0.9297,0.9306,
0.9329,0.9455,0.9481,0.9630,0.9635,0.9642,0.9909,0.9935,0.9977,
Overall p-value after applying KStest on 269 p-values = 0.171539
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.