RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.74 14.1223 0.341573
2 to 25 15.79 12.4754 0.229464
3 to 26 15.88 18.5400 0.644433
4 to 27 15.70 16.5029 0.511497
5 to 28 15.78 18.3036 0.630066
6 to 29 15.85 12.9130 0.258011
7 to 30 15.60 21.8778 0.810534
8 to 31 15.88 17.2439 0.562036
9 to 32 15.94 15.7029 0.455017
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.502247
Tough bday spacings test for dh-ranFile-2018-06-17_01:31: 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 38 76 111 94 75 48 27 12 10 2
(O-E)^2/E 0.5 0.1 0.1 1.8 0.1 0.1 0.3 0.3 0.6 1.7 1.0
Birthday Spacings: Sum(O-E)^2/E= 6.663, p= 0.243
RESULTS OF GCD FOR dh-ranFile-2018-06-17_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.226052
p-value, dist. of gcd's: 0.881015
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.433 0.479 0.637 0.420 0.510 0.708 0.564 0.159
Bits 8 to 15---> 0.251 0.859 0.311 0.916 0.841 0.043 0.914 0.763
Bits 16 to 23---> 0.400 0.610 0.347 0.098 0.627 0.595 0.172 0.823
Bits 24 to 31---> 0.871 0.324 0.155 0.096 0.460 0.974 0.430 0.921
KS test for the above 32 p values: 0.070
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_01:31,
p-values for 5 runs: 0.8334, 0.9487, 0.5277, 0.4819, 0.4743
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 185 211.4 3.301 3.301
r= 29 5191 5134.0 0.633 3.934
r= 30 23014 23103.0 0.343 4.277
r= 31 11610 11551.5 0.296 4.573
chi-square = 4.573 with df = 3; p-value = 0.794
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 238 211.4 3.342 3.342
r= 30 5285 5134.0 4.441 7.783
r= 31 22995 23103.0 0.505 8.288
r= 32 11482 11551.5 0.418 8.706
chi-square = 8.706 with df = 3; p-value = 0.967
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_01:31
b-rank test for bits 1 to 8, p=0.92663
b-rank test for bits 2 to 9, p=0.68438
b-rank test for bits 3 to 10, p=0.92869
b-rank test for bits 4 to 11, p=0.53817
b-rank test for bits 5 to 12, p=0.60865
b-rank test for bits 6 to 13, p=0.36889
b-rank test for bits 7 to 14, p=0.94889
b-rank test for bits 8 to 15, p=0.02135
b-rank test for bits 9 to 16, p=0.74745
b-rank test for bits 10 to 17, p=0.35524
b-rank test for bits 11 to 18, p=0.04081
b-rank test for bits 12 to 19, p=0.78397
b-rank test for bits 13 to 20, p=0.64172
b-rank test for bits 14 to 21, p=0.78277
b-rank test for bits 15 to 22, p=0.15037
b-rank test for bits 16 to 23, p=0.89210
b-rank test for bits 17 to 24, p=0.87042
b-rank test for bits 18 to 25, p=0.82527
b-rank test for bits 19 to 26, p=0.46997
b-rank test for bits 20 to 27, p=0.29313
b-rank test for bits 21 to 28, p=0.79786
b-rank test for bits 22 to 29, p=0.74076
b-rank test for bits 23 to 30, p=0.31507
b-rank test for bits 24 to 31, p=0.51636
b-rank test for bits 25 to 32, p=0.60556
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 = 0.153981
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_01:31
(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 142105 0.46 0.676227
2 142108 0.46 0.678741
3 141319 -1.38 0.083905
4 142500 1.38 0.916217
5 141532 -0.88 0.188993
6 141903 -0.01 0.494100
7 142276 0.86 0.804196
8 141931 0.05 0.520190
9 141641 -0.63 0.265350
10 141604 -0.71 0.237803
11 141361 -1.28 0.100071
12 143136 2.87 0.997922
13 142269 0.84 0.799644
14 142520 1.43 0.923181
15 142105 0.46 0.676227
16 143035 2.63 0.995732
17 142295 0.90 0.816232
18 142289 0.89 0.812482
19 141631 -0.65 0.257748
20 142331 0.99 0.837740
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_01:31
Bits used No. missing words z-score p-value
23 to 32 141798 -0.3839 0.350528
22 to 31 142022 0.3885 0.651183
21 to 30 141874 -0.1218 0.451518
20 to 29 141880 -0.1011 0.459721
19 to 28 142433 1.8058 0.964522
18 to 27 142330 1.4506 0.926552
17 to 26 141898 -0.0391 0.484418
16 to 25 142364 1.5678 0.941539
15 to 24 141504 -1.3977 0.081103
14 to 23 141733 -0.6080 0.271582
13 to 22 142123 0.7368 0.769376
12 to 21 141882 -0.0942 0.462459
11 to 20 141395 -1.7736 0.038069
10 to 19 142049 0.4816 0.684962
9 to 18 141858 -0.1770 0.429754
8 to 17 142065 0.5368 0.704295
7 to 16 142066 0.5402 0.705485
6 to 15 141078 -2.8667 0.002074
5 to 14 141992 0.2851 0.612204
4 to 13 142338 1.4782 0.930319
3 to 12 141651 -0.8908 0.186520
2 to 11 142065 0.5368 0.704295
1 to 10 142111 0.6954 0.756602
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_01:31
Bits used No. missing words z-score p-value
28 to 32 141539 -1.2554 0.104675
27 to 31 142161 0.8531 0.803203
26 to 30 141649 -0.8825 0.188760
25 to 29 141684 -0.7638 0.222484
24 to 28 141717 -0.6520 0.257212
23 to 27 141893 -0.0554 0.477928
22 to 26 141877 -0.1096 0.456366
21 to 25 141753 -0.5299 0.298080
20 to 24 142240 1.1209 0.868838
19 to 23 141721 -0.6384 0.261605
18 to 22 142250 1.1548 0.875917
17 to 21 141468 -1.4960 0.067322
16 to 20 142163 0.8599 0.805077
15 to 19 142191 0.9548 0.830164
14 to 18 142054 0.4904 0.688077
13 to 17 141861 -0.1638 0.434932
12 to 16 142393 1.6396 0.949452
11 to 15 141598 -1.0554 0.145631
10 to 14 141929 0.0667 0.526581
9 to 13 141624 -0.9672 0.166717
8 to 12 141993 0.2836 0.611652
7 to 11 141755 -0.5232 0.300434
6 to 10 141712 -0.6689 0.251775
5 to 9 142008 0.3345 0.630989
4 to 8 141693 -0.7333 0.231681
3 to 7 141962 0.1785 0.570852
2 to 6 142105 0.6633 0.746427
1 to 5 142535 2.1209 0.983036
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_01:31
Bits used No. missing words z-score p-value
31 to 32 141572 -0.9951 0.159850
30 to 31 141206 -2.0747 0.019006
29 to 30 141894 -0.0452 0.481966
28 to 29 141480 -1.2665 0.102674
27 to 28 141705 -0.6027 0.273340
26 to 27 142324 1.2232 0.889376
25 to 26 141944 0.1023 0.540729
24 to 25 141738 -0.5054 0.306640
23 to 24 142565 1.9341 0.973451
22 to 23 141863 -0.1367 0.445647
21 to 22 141576 -0.9833 0.162736
20 to 21 141945 0.1052 0.541900
19 to 20 141709 -0.5909 0.277279
18 to 19 142123 0.6303 0.735749
17 to 18 141550 -1.0600 0.144579
16 to 17 142160 0.7394 0.770180
15 to 16 141777 -0.3904 0.348137
14 to 15 141748 -0.4759 0.317073
13 to 14 141836 -0.2163 0.414372
12 to 13 141915 0.0167 0.506672
11 to 12 142058 0.4386 0.669508
10 to 11 141863 -0.1367 0.445647
9 to 10 141479 -1.2694 0.102147
8 to 9 141956 0.1377 0.554749
7 to 8 141850 -0.1750 0.430534
6 to 7 142354 1.3117 0.905191
5 to 6 141696 -0.6293 0.264579
4 to 5 141638 -0.8004 0.211744
3 to 4 142350 1.2999 0.903184
2 to 3 141668 -0.7119 0.238267
1 to 2 141859 -0.1485 0.440988
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2473.27 -0.378 0.352683
Test results for specific bytes for dh-ranFile-2018-06-17_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2427.81 -1.021 0.153638
2 to 9 2445.64 -0.769 0.221025
3 to 10 2461.37 -0.546 0.292422
4 to 11 2620.77 1.708 0.956182
5 to 12 2536.22 0.512 0.695741
6 to 13 2534.87 0.493 0.689062
7 to 14 2546.28 0.654 0.743583
8 to 15 2529.55 0.418 0.662015
9 to 16 2519.02 0.269 0.606011
10 to 17 2329.57 -2.410 0.007970
11 to 18 2413.29 -1.226 0.110044
12 to 19 2517.11 0.242 0.595615
13 to 20 2392.74 -1.517 0.064657
14 to 21 2610.53 1.563 0.940987
15 to 22 2535.90 0.508 0.694179
16 to 23 2439.82 -0.851 0.197368
17 to 24 2478.97 -0.297 0.383085
18 to 25 2522.52 0.318 0.624929
19 to 26 2544.71 0.632 0.736419
20 to 27 2517.15 0.243 0.595836
21 to 28 2438.92 -0.864 0.193848
22 to 29 2528.30 0.400 0.655516
23 to 30 2410.46 -1.266 0.102707
24 to 31 2471.60 -0.402 0.343991
25 to 32 2496.59 -0.048 0.480755
CDPARK for dh-ranFile-2018-06-17_01:31: 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
3476 -2.1461 0.015932
3529 0.2740 0.607947
3542 0.8676 0.807188
3503 -0.9132 0.180558
3573 2.2831 0.988788
3503 -0.9132 0.180558
3539 0.7306 0.767486
3519 -0.1826 0.427537
3527 0.1826 0.572463
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3522.40 sample std.=25.08
p-value of the KSTEST for those 10 p-values: 0.963180
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_01:31
0.4500,0.6126,0.6175,0.4508,0.4799,0.0780,0.6367,0.4436,0.4252,0.1143,
The KS test for those 10 p-values: 0.220915
The 3DSPHERES test for dh-ranFile-2018-06-17_01:31
sample no r^3 equiv. uni.
1 14.048 0.373917
2 60.799 0.868223
3 3.185 0.100721
4 70.923 0.905965
5 19.485 0.477694
6 5.627 0.171025
7 22.544 0.528321
8 6.439 0.193163
9 26.679 0.589061
10 52.960 0.828868
11 93.250 0.955325
12 29.109 0.621031
13 34.770 0.686197
14 22.953 0.534714
15 21.968 0.519183
16 41.965 0.753115
17 1.952 0.062981
18 90.747 0.951437
19 3.514 0.110530
20 49.711 0.809296
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.690977
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 0.8 -0.8 0.4 1.3
0.2 0.5 -0.6 0.7 -1.1 -0.3
0.2 0.9 0.3 0.4 0.0 1.3
-0.2 1.9 -0.7 0.2 -0.4 -0.3
-1.5 -2.3 -1.1 0.6 -1.6 -1.1
-0.3 -1.4 0.2 0.3 0.8 0.6
0.0 0.2 -1.2 -0.7 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:35.080082
z-score=-0.755025, p-value=0.233573
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_01:31
Test no p-value
1 0.108012
2 0.065136
3 0.186906
4 0.085664
5 0.499547
6 0.195578
7 0.772673
8 0.039344
9 0.505628
10 0.043056
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004717
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_01:31:
(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 66791 0.23 66539 0.24
3 25000.00 25090 0.32 25043 0.07
4 6666.67 6556 1.84 6742 0.85
5 1388.89 1318 3.62 1377 0.10
6 238.10 218 1.70 259 1.84
7 34.72 18 8.05 35 0.00
8 4.96 8 1.86 4 0.19
p=0.99275 p=0.22898
Number of rngs required: 687287, p-value: 0.097
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_01:31
No. of wins: Observed Expected
98297 98585.9
z-score=-1.292, pvalue=0.09819
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66595 66666.7 0.077 0.077
2 37604 37654.3 0.067 0.144
3 26985 26954.7 0.034 0.178
4 19424 19313.5 0.633 0.811
5 13886 13851.4 0.086 0.897
6 10034 9943.5 0.823 1.720
7 7158 7145.0 0.024 1.744
8 5206 5139.1 0.872 2.615
9 3581 3699.9 3.819 6.434
10 2622 2666.3 0.736 7.170
11 1867 1923.3 1.650 8.820
12 1341 1388.7 1.641 10.461
13 1024 1003.7 0.410 10.871
14 722 726.1 0.024 10.894
15 542 525.8 0.497 11.391
16 404 381.2 1.370 12.761
17 255 276.5 1.678 14.439
18 187 200.8 0.952 15.391
19 147 146.0 0.007 15.398
20 87 106.2 3.476 18.874
21 329 287.1 6.111 24.985
Chisq= 24.99 for 20 degrees of freedom, p= 0.79800
SUMMARY of craptest
p-value for no. of wins: 0.098188
p-value for throws/game: 0.797997
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_01:31
No. of wins: Observed Expected
98611 98585.9
z-score= 0.112, pvalue=0.54477
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66498 66666.7 0.427 0.427
2 37860 37654.3 1.123 1.550
3 26857 26954.7 0.354 1.905
4 19398 19313.5 0.370 2.275
5 13789 13851.4 0.281 2.556
6 9995 9943.5 0.266 2.822
7 7215 7145.0 0.685 3.507
8 5151 5139.1 0.028 3.535
9 3621 3699.9 1.681 5.216
10 2600 2666.3 1.648 6.865
11 1982 1923.3 1.790 8.654
12 1359 1388.7 0.637 9.291
13 1035 1003.7 0.975 10.266
14 720 726.1 0.052 10.318
15 544 525.8 0.627 10.946
16 390 381.2 0.205 11.151
17 301 276.5 2.164 13.315
18 210 200.8 0.419 13.734
19 125 146.0 3.016 16.750
20 104 106.2 0.046 16.796
21 246 287.1 5.887 22.684
Chisq= 22.68 for 20 degrees of freedom, p= 0.69540
SUMMARY of craptest
p-value for no. of wins: 0.544766
p-value for throws/game: 0.695404
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0021,0.0047,0.0080,0.0159,0.0190,0.0213,0.0381,0.0393,0.0408,0.0426,
0.0431,0.0630,0.0647,0.0651,0.0673,0.0700,0.0780,0.0811,0.0839,0.0857,
0.0961,0.0970,0.0979,0.0982,0.1001,0.1007,0.1021,0.1027,0.1027,0.1047,
0.1080,0.1100,0.1105,0.1143,0.1446,0.1456,0.1504,0.1536,0.1540,0.1555,
0.1593,0.1599,0.1627,0.1667,0.1710,0.1725,0.1806,0.1806,0.1865,0.1869,
0.1888,0.1890,0.1932,0.1938,0.1956,0.1974,0.2117,0.2209,0.2210,0.2225,
0.2261,0.2290,0.2295,0.2317,0.2336,0.2378,0.2383,0.2432,0.2510,0.2518,
0.2572,0.2577,0.2580,0.2616,0.2646,0.2653,0.2716,0.2733,0.2773,0.2924,
0.2931,0.2981,0.3004,0.3066,0.3108,0.3151,0.3171,0.3240,0.3240,0.3416,
0.3440,0.3465,0.3481,0.3505,0.3527,0.3552,0.3689,0.3739,0.3831,0.3999,
0.4144,0.4197,0.4252,0.4275,0.4298,0.4304,0.4305,0.4330,0.4349,0.4410,
0.4436,0.4456,0.4456,0.4500,0.4508,0.4515,0.4550,0.4564,0.4597,0.4597,
0.4625,0.4700,0.4743,0.4777,0.4779,0.4790,0.4799,0.4808,0.4819,0.4820,
0.4844,0.4941,0.4995,0.5022,0.5056,0.5067,0.5100,0.5115,0.5164,0.5192,
0.5202,0.5266,0.5277,0.5283,0.5347,0.5382,0.5407,0.5419,0.5448,0.5547,
0.5620,0.5635,0.5709,0.5725,0.5891,0.5952,0.5956,0.5958,0.6056,0.6060,
0.6079,0.6086,0.6099,0.6117,0.6122,0.6126,0.6175,0.6210,0.6249,0.6267,
0.6301,0.6310,0.6367,0.6370,0.6417,0.6444,0.6512,0.6555,0.6620,0.6695,
0.6762,0.6762,0.6787,0.6844,0.6850,0.6862,0.6881,0.6891,0.6910,0.6942,
0.6954,0.6957,0.7043,0.7043,0.7055,0.7076,0.7357,0.7364,0.7408,0.7436,
0.7464,0.7474,0.7531,0.7566,0.7634,0.7675,0.7694,0.7702,0.7727,0.7828,
0.7840,0.7941,0.7979,0.7980,0.7996,0.8032,0.8042,0.8051,0.8072,0.8093,
0.8105,0.8125,0.8162,0.8228,0.8253,0.8289,0.8302,0.8334,0.8377,0.8413,
0.8591,0.8682,0.8688,0.8704,0.8711,0.8759,0.8810,0.8894,0.8921,0.9032,
0.9052,0.9060,0.9138,0.9160,0.9162,0.9213,0.9232,0.9266,0.9266,0.9287,
0.9303,0.9410,0.9415,0.9487,0.9489,0.9495,0.9514,0.9553,0.9562,0.9632,
0.9645,0.9665,0.9735,0.9740,0.9830,0.9888,0.9928,0.9957,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.974347
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.