RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2019-10-11_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.63 22.8067 0.844350
2 to 25 15.64 13.4791 0.296433
3 to 26 15.76 14.3955 0.361067
4 to 27 15.78 27.6400 0.950675
5 to 28 15.86 19.4060 0.694268
6 to 29 15.44 32.1950 0.985770
7 to 30 15.58 18.9070 0.666105
8 to 31 15.70 17.7714 0.596604
9 to 32 15.75 17.7280 0.593806
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.130939
Tough bday spacings test for dh-ranFile-2019-10-11_08:31: 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 4 37 67 96 102 75 60 32 14 7 6
(O-E)^2/E 2.9 0.0 0.5 0.0 0.2 0.1 1.2 0.2 0.1 0.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 6.151, p= 0.198
RESULTS OF GCD FOR dh-ranFile-2019-10-11_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.921262
p-value, dist. of gcd's: 0.702724
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2019-10-11_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.884 0.343 0.325 0.177 0.758 0.124 0.769 0.171
Bits 8 to 15---> 0.758 0.078 0.522 0.025 0.954 0.818 0.424 0.711
Bits 16 to 23---> 0.716 0.942 0.505 0.529 0.421 0.604 0.329 0.509
Bits 24 to 31---> 0.911 0.700 0.239 0.025 0.034 0.500 0.434 0.419
KS test for the above 32 p values: 0.052
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2019-10-11_08:31,
p-values for 5 runs: 0.8998, 0.6556, 0.0734, 0.6177, 0.6973
Rank test for binary matrices (31x31) for dh-ranFile-2019-10-11_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5165 5134.0 0.187 0.447
r= 30 23103 23103.0 0.000 0.447
r= 31 11528 11551.5 0.048 0.495
chi-square = 0.495 with df = 3; p-value = 0.080
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2019-10-11_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5100 5134.0 0.225 0.253
r= 31 23055 23103.0 0.100 0.353
r= 32 11636 11551.5 0.618 0.971
chi-square = 0.971 with df = 3; p-value = 0.192
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2019-10-11_08:31
b-rank test for bits 1 to 8, p=0.66512
b-rank test for bits 2 to 9, p=0.80880
b-rank test for bits 3 to 10, p=0.46780
b-rank test for bits 4 to 11, p=0.11024
b-rank test for bits 5 to 12, p=0.00984
b-rank test for bits 6 to 13, p=0.89372
b-rank test for bits 7 to 14, p=0.63571
b-rank test for bits 8 to 15, p=0.32190
b-rank test for bits 9 to 16, p=0.58475
b-rank test for bits 10 to 17, p=0.81095
b-rank test for bits 11 to 18, p=0.68837
b-rank test for bits 12 to 19, p=0.90832
b-rank test for bits 13 to 20, p=0.75600
b-rank test for bits 14 to 21, p=0.54251
b-rank test for bits 15 to 22, p=0.48295
b-rank test for bits 16 to 23, p=0.58352
b-rank test for bits 17 to 24, p=0.17951
b-rank test for bits 18 to 25, p=0.61609
b-rank test for bits 19 to 26, p=0.11193
b-rank test for bits 20 to 27, p=0.26007
b-rank test for bits 21 to 28, p=0.21849
b-rank test for bits 22 to 29, p=0.19397
b-rank test for bits 23 to 30, p=0.82257
b-rank test for bits 24 to 31, p=0.41047
b-rank test for bits 25 to 32, p=0.86549
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 = 0.874627
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2019-10-11_08:31
(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 141504 -0.95 0.171811
2 141711 -0.46 0.321543
3 141449 -1.08 0.141067
4 141805 -0.24 0.403708
5 142512 1.41 0.920450
6 141455 -1.06 0.144227
7 141394 -1.20 0.114287
8 141556 -0.83 0.204533
9 142258 0.81 0.792364
10 141449 -1.08 0.141067
11 141983 0.17 0.568331
12 142334 0.99 0.839455
13 142593 1.60 0.944907
14 142634 1.69 0.954787
15 142276 0.86 0.804196
16 141973 0.15 0.559129
17 141618 -0.68 0.248038
18 141857 -0.12 0.451344
19 142033 0.29 0.613690
20 141714 -0.46 0.324059
----------------------------------------------------------------
OPSO test for dh-ranFile-2019-10-11_08:31
Bits used No. missing words z-score p-value
23 to 32 142481 1.9713 0.975654
22 to 31 141819 -0.3115 0.377717
21 to 30 142407 1.7161 0.956928
20 to 29 142092 0.6299 0.735619
19 to 28 142455 1.8816 0.970056
18 to 27 142323 1.4264 0.923131
17 to 26 142073 0.5644 0.713752
16 to 25 141673 -0.8149 0.207556
15 to 24 141969 0.2058 0.581510
14 to 23 141904 -0.0184 0.492668
13 to 22 141484 -1.4667 0.071235
12 to 21 141608 -1.0391 0.149386
11 to 20 142091 0.6264 0.734490
10 to 19 141685 -0.7736 0.219598
9 to 18 141930 0.0713 0.528411
8 to 17 142511 2.0747 0.980994
7 to 16 141648 -0.9011 0.183758
6 to 15 141640 -0.9287 0.176516
5 to 14 141779 -0.4494 0.326567
4 to 13 141890 -0.0667 0.473428
3 to 12 142456 1.8851 0.970290
2 to 11 142064 0.5333 0.703103
1 to 10 141695 -0.7391 0.229933
-----------------------------------------------------------------
OQSO test for dh-ranFile-2019-10-11_08:31
Bits used No. missing words z-score p-value
28 to 32 142134 0.7616 0.776849
27 to 31 141666 -0.8248 0.204729
26 to 30 142025 0.3921 0.652509
25 to 29 141730 -0.6079 0.271628
24 to 28 141978 0.2328 0.592034
23 to 27 141441 -1.5876 0.056193
22 to 26 141871 -0.1299 0.448310
21 to 25 142184 0.9311 0.824095
20 to 24 142312 1.3650 0.913871
19 to 23 142118 0.7074 0.760327
18 to 22 142182 0.9243 0.822336
17 to 21 141273 -2.1571 0.015501
16 to 20 142350 1.4938 0.932386
15 to 19 142045 0.4599 0.677205
14 to 18 141706 -0.6893 0.245332
13 to 17 142280 1.2565 0.895534
12 to 16 142337 1.4497 0.926433
11 to 15 142190 0.9514 0.829305
10 to 14 141572 -1.1435 0.126417
9 to 13 142490 1.9684 0.975487
8 to 12 141899 -0.0350 0.486033
7 to 11 142195 0.9684 0.833571
6 to 10 141974 0.2192 0.586761
5 to 9 142453 1.8429 0.967332
4 to 8 141734 -0.5943 0.276143
3 to 7 141999 0.3040 0.619423
2 to 6 142776 2.9379 0.998348
1 to 5 141823 -0.2926 0.384897
-----------------------------------------------------------------
DNA test for dh-ranFile-2019-10-11_08:31
Bits used No. missing words z-score p-value
31 to 32 142577 1.9695 0.975554
30 to 31 142239 0.9725 0.834594
29 to 30 142126 0.6391 0.738636
28 to 29 142265 1.0492 0.852951
27 to 28 141934 0.0728 0.529007
26 to 27 142017 0.3176 0.624610
25 to 26 141767 -0.4199 0.337297
24 to 25 142158 0.7335 0.768385
23 to 24 142329 1.2380 0.892135
22 to 23 141889 -0.0600 0.476090
21 to 22 141529 -1.1219 0.130949
20 to 21 141718 -0.5644 0.286243
19 to 20 141507 -1.1868 0.117650
18 to 19 142237 0.9666 0.833123
17 to 18 142096 0.5506 0.709063
16 to 17 141482 -1.2606 0.103734
15 to 16 141941 0.0934 0.537216
14 to 15 141553 -1.0511 0.146602
13 to 14 141849 -0.1780 0.429375
12 to 13 141829 -0.2370 0.406343
11 to 12 142174 0.7807 0.782522
10 to 11 142360 1.3294 0.908144
9 to 10 141722 -0.5526 0.290270
8 to 9 142329 1.2380 0.892135
7 to 8 142311 1.1849 0.881965
6 to 7 142225 0.9312 0.824120
5 to 6 141590 -0.9420 0.173102
4 to 5 141854 -0.1632 0.435174
3 to 4 142562 1.9253 0.972903
2 to 3 141804 -0.3107 0.378011
1 to 2 142617 2.0875 0.981580
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2019-10-11_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2485.47 -0.206 0.418582
Test results for specific bytes for dh-ranFile-2019-10-11_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2628.40 1.816 0.965302
2 to 9 2510.76 0.152 0.560496
3 to 10 2507.35 0.104 0.541410
4 to 11 2477.39 -0.320 0.374558
5 to 12 2517.36 0.246 0.596981
6 to 13 2524.27 0.343 0.634262
7 to 14 2431.59 -0.968 0.166647
8 to 15 2585.87 1.214 0.887706
9 to 16 2583.27 1.178 0.880529
10 to 17 2568.48 0.968 0.833601
11 to 18 2529.91 0.423 0.663868
12 to 19 2535.84 0.507 0.693875
13 to 20 2497.83 -0.031 0.487772
14 to 21 2424.44 -1.069 0.142640
15 to 22 2418.89 -1.147 0.125688
16 to 23 2446.90 -0.751 0.226338
17 to 24 2449.13 -0.719 0.235933
18 to 25 2456.83 -0.610 0.270773
19 to 26 2493.69 -0.089 0.464461
20 to 27 2483.17 -0.238 0.405942
21 to 28 2374.16 -1.780 0.037566
22 to 29 2541.39 0.585 0.720840
23 to 30 2440.15 -0.846 0.198668
24 to 31 2498.29 -0.024 0.490328
25 to 32 2395.03 -1.485 0.068833
CDPARK for dh-ranFile-2019-10-11_08:31: 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
3530 0.3196 0.625377
3511 -0.5479 0.291865
3528 0.2283 0.590298
3539 0.7306 0.767486
3520 -0.1370 0.445521
3530 0.3196 0.625377
3510 -0.5936 0.276387
3522 -0.0457 0.481790
3529 0.2740 0.607947
3524 0.0457 0.518210
Square side=100, avg. no. parked=3524.30 sample std.=8.50
p-value of the KSTEST for those 10 p-values: 0.210568
Results for the MINIMUM DISTANCE test for dh-ranFile-2019-10-11_08:31
0.2786,0.7726,0.0020,0.1424,0.2584,0.8167,0.9333,0.2737,0.8025,0.8762,
The KS test for those 10 p-values: 0.432639
The 3DSPHERES test for dh-ranFile-2019-10-11_08:31
sample no r^3 equiv. uni.
1 31.040 0.644654
2 26.031 0.580083
3 14.935 0.392146
4 143.322 0.991582
5 6.260 0.188338
6 19.334 0.475064
7 11.392 0.315950
8 16.589 0.424755
9 60.441 0.866638
10 19.846 0.483945
11 76.324 0.921460
12 3.449 0.108596
13 2.849 0.090607
14 10.389 0.292707
15 25.135 0.567354
16 45.277 0.778922
17 118.408 0.980686
18 32.168 0.657765
19 98.035 0.961911
20 45.829 0.782950
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.365005
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2019-10-11_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 1.1 2.1 2.0 -1.0
1.7 -1.4 0.4 0.0 1.1 -0.7
-1.7 0.6 -0.4 -0.6 0.4 0.2
-0.7 -1.0 1.3 0.9 1.0 0.2
1.5 -1.3 -0.3 -1.3 0.3 -0.4
1.2 -0.6 -0.5 0.7 -0.9 -3.0
0.7 -0.1 1.3 -1.8 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:52.756186
z-score=1.173596, p-value=0.876472
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2019-10-11_08:31
Test no p-value
1 0.543533
2 0.480613
3 0.003713
4 0.052849
5 0.141905
6 0.033555
7 0.333115
8 0.265246
9 0.299699
10 0.849430
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.032622
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2019-10-11_08:31:
(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 66937 1.10 66745 0.09
3 25000.00 24746 2.58 24894 0.45
4 6666.67 6641 0.10 6702 0.19
5 1388.89 1419 0.65 1379 0.07
6 238.10 217 1.87 241 0.04
7 34.72 36 0.05 32 0.21
8 4.96 3 0.77 6 0.22
p=0.69003 p=0.02649
Number of rngs required: 687739, p-value: 0.222
RESULTS OF CRAPS TEST for dh-ranFile-2019-10-11_08:31
No. of wins: Observed Expected
99249 98585.9
z-score= 2.966, pvalue=0.99849
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66899 66666.7 0.810 0.810
2 37471 37654.3 0.893 1.702
3 26909 26954.7 0.078 1.780
4 19327 19313.5 0.009 1.789
5 13825 13851.4 0.050 1.840
6 9942 9943.5 0.000 1.840
7 7172 7145.0 0.102 1.942
8 5194 5139.1 0.587 2.529
9 3737 3699.9 0.373 2.902
10 2601 2666.3 1.599 4.501
11 1887 1923.3 0.686 5.187
12 1387 1388.7 0.002 5.189
13 991 1003.7 0.161 5.350
14 746 726.1 0.543 5.893
15 519 525.8 0.089 5.982
16 405 381.2 1.492 7.474
17 259 276.5 1.112 8.587
18 188 200.8 0.820 9.407
19 145 146.0 0.007 9.413
20 123 106.2 2.652 12.066
21 273 287.1 0.694 12.759
Chisq= 12.76 for 20 degrees of freedom, p= 0.11253
SUMMARY of craptest
p-value for no. of wins: 0.998491
p-value for throws/game: 0.112533
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2019-10-11_08:31
No. of wins: Observed Expected
98641 98585.9
z-score= 0.247, pvalue=0.59740
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66553 66666.7 0.194 0.194
2 38094 37654.3 5.134 5.328
3 26835 26954.7 0.532 5.860
4 19271 19313.5 0.093 5.953
5 13750 13851.4 0.743 6.696
6 10008 9943.5 0.418 7.113
7 7058 7145.0 1.060 8.173
8 5156 5139.1 0.056 8.229
9 3646 3699.9 0.784 9.013
10 2597 2666.3 1.801 10.814
11 2047 1923.3 7.952 18.767
12 1387 1388.7 0.002 18.769
13 961 1003.7 1.818 20.587
14 723 726.1 0.014 20.600
15 508 525.8 0.605 21.205
16 414 381.2 2.831 24.036
17 282 276.5 0.108 24.144
18 199 200.8 0.017 24.161
19 148 146.0 0.028 24.189
20 86 106.2 3.847 28.036
21 277 287.1 0.356 28.392
Chisq= 28.39 for 20 degrees of freedom, p= 0.89957
SUMMARY of craptest
p-value for no. of wins: 0.597401
p-value for throws/game: 0.899565
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0020,0.0037,0.0098,0.0155,0.0248,0.0255,0.0265,0.0326,0.0336,0.0339,
0.0376,0.0517,0.0528,0.0562,0.0688,0.0712,0.0734,0.0784,0.0801,0.0906,
0.1037,0.1086,0.1102,0.1119,0.1125,0.1143,0.1177,0.1237,0.1257,0.1264,
0.1309,0.1309,0.1411,0.1411,0.1419,0.1424,0.1426,0.1442,0.1466,0.1494,
0.1666,0.1710,0.1718,0.1731,0.1765,0.1774,0.1795,0.1838,0.1883,0.1916,
0.1940,0.1976,0.1987,0.2045,0.2047,0.2076,0.2106,0.2185,0.2196,0.2215,
0.2263,0.2299,0.2359,0.2391,0.2453,0.2480,0.2584,0.2601,0.2652,0.2708,
0.2716,0.2737,0.2761,0.2764,0.2786,0.2862,0.2903,0.2919,0.2927,0.2964,
0.2997,0.3160,0.3215,0.3219,0.3241,0.3252,0.3266,0.3288,0.3331,0.3373,
0.3428,0.3611,0.3650,0.3746,0.3777,0.3780,0.3849,0.3921,0.4037,0.4059,
0.4063,0.4105,0.4186,0.4190,0.4207,0.4240,0.4248,0.4294,0.4326,0.4341,
0.4352,0.4455,0.4483,0.4513,0.4645,0.4678,0.4734,0.4751,0.4761,0.4806,
0.4818,0.4829,0.4839,0.4860,0.4878,0.4903,0.4927,0.4997,0.5048,0.5091,
0.5182,0.5216,0.5284,0.5288,0.5290,0.5372,0.5414,0.5425,0.5435,0.5591,
0.5605,0.5674,0.5683,0.5801,0.5815,0.5835,0.5848,0.5868,0.5903,0.5920,
0.5938,0.5966,0.5970,0.5974,0.6045,0.6079,0.6137,0.6161,0.6177,0.6194,
0.6246,0.6254,0.6254,0.6343,0.6357,0.6447,0.6525,0.6556,0.6578,0.6639,
0.6651,0.6661,0.6772,0.6884,0.6900,0.6939,0.6943,0.6973,0.7004,0.7027,
0.7031,0.7091,0.7106,0.7138,0.7165,0.7208,0.7345,0.7356,0.7386,0.7560,
0.7580,0.7583,0.7603,0.7675,0.7684,0.7695,0.7726,0.7768,0.7789,0.7825,
0.7830,0.7924,0.8025,0.8042,0.8088,0.8110,0.8167,0.8184,0.8223,0.8226,
0.8241,0.8241,0.8293,0.8331,0.8336,0.8336,0.8346,0.8395,0.8444,0.8494,
0.8530,0.8655,0.8666,0.8746,0.8762,0.8765,0.8805,0.8820,0.8844,0.8877,
0.8921,0.8921,0.8937,0.8955,0.8996,0.8998,0.9081,0.9083,0.9107,0.9139,
0.9205,0.9213,0.9215,0.9231,0.9264,0.9324,0.9333,0.9423,0.9449,0.9507,
0.9541,0.9548,0.9569,0.9619,0.9653,0.9673,0.9701,0.9703,0.9729,0.9755,
0.9756,0.9757,0.9807,0.9810,0.9816,0.9858,0.9916,0.9983,0.9985,
Overall p-value after applying KStest on 269 p-values = 0.243630
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.