RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 21.7270 0.804553
2 to 25 15.50 15.7981 0.461806
3 to 26 15.60 27.1189 0.943653
4 to 27 15.88 11.2434 0.156363
5 to 28 16.26 23.1160 0.854486
6 to 29 15.91 20.8113 0.765156
7 to 30 15.76 14.3506 0.357854
8 to 31 15.86 17.4163 0.573474
9 to 32 15.57 18.5744 0.646501
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.419745
Tough bday spacings test for dh-ranFile-2018-07-11_10:31: 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 8 45 80 92 90 83 53 27 16 5 1
(O-E)^2/E 0.1 1.9 0.6 0.3 0.6 0.3 0.0 0.3 0.1 0.4 2.3
Birthday Spacings: Sum(O-E)^2/E= 6.978, p= 0.272
RESULTS OF GCD FOR dh-ranFile-2018-07-11_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.148083
p-value, dist. of gcd's: 0.976993
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.487 0.320 0.269 0.805 0.949 0.499 0.686 0.617
Bits 8 to 15---> 0.693 0.044 0.786 0.580 0.242 0.188 0.966 0.396
Bits 16 to 23---> 0.218 0.775 0.143 0.758 0.444 0.167 0.162 0.668
Bits 24 to 31---> 0.947 0.418 0.258 0.430 0.713 0.658 0.847 0.795
KS test for the above 32 p values: 0.253
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_10:31,
p-values for 5 runs: 0.8540, 0.5470, 0.7685, 0.4158, 0.0703
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5057 5134.0 1.155 1.415
r= 30 23048 23103.0 0.131 1.547
r= 31 11691 11551.5 1.684 3.231
chi-square = 3.231 with df = 3; p-value = 0.643
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 207 211.4 0.092 0.092
r= 30 5240 5134.0 2.188 2.280
r= 31 23031 23103.0 0.225 2.505
r= 32 11522 11551.5 0.075 2.581
chi-square = 2.581 with df = 3; p-value = 0.539
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_10:31
b-rank test for bits 1 to 8, p=0.50364
b-rank test for bits 2 to 9, p=0.06338
b-rank test for bits 3 to 10, p=0.95323
b-rank test for bits 4 to 11, p=0.04269
b-rank test for bits 5 to 12, p=0.68490
b-rank test for bits 6 to 13, p=0.57855
b-rank test for bits 7 to 14, p=0.43848
b-rank test for bits 8 to 15, p=0.33428
b-rank test for bits 9 to 16, p=0.10594
b-rank test for bits 10 to 17, p=0.80656
b-rank test for bits 11 to 18, p=0.79532
b-rank test for bits 12 to 19, p=0.15470
b-rank test for bits 13 to 20, p=0.50662
b-rank test for bits 14 to 21, p=0.11347
b-rank test for bits 15 to 22, p=0.61715
b-rank test for bits 16 to 23, p=0.43637
b-rank test for bits 17 to 24, p=0.32968
b-rank test for bits 18 to 25, p=0.31349
b-rank test for bits 19 to 26, p=0.41149
b-rank test for bits 20 to 27, p=0.53587
b-rank test for bits 21 to 28, p=0.81884
b-rank test for bits 22 to 29, p=0.65934
b-rank test for bits 23 to 30, p=0.16720
b-rank test for bits 24 to 31, p=0.28718
b-rank test for bits 25 to 32, p=0.01760
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 = 0.365548
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_10:31
(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 142673 1.78 0.962811
2 141066 -1.97 0.024396
3 142068 0.37 0.644579
4 141889 -0.05 0.481057
5 142117 0.49 0.686236
6 141322 -1.37 0.084990
7 141913 0.01 0.503421
8 142038 0.30 0.618152
9 141914 0.01 0.504353
10 142283 0.87 0.808685
11 141664 -0.57 0.283254
12 141345 -1.32 0.093663
13 142055 0.34 0.633204
14 142174 0.62 0.731840
15 141950 0.10 0.537852
16 141971 0.14 0.557285
17 141405 -1.18 0.119330
18 141568 -0.80 0.212580
19 142446 1.25 0.895061
20 141827 -0.19 0.423730
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_10:31
Bits used No. missing words z-score p-value
23 to 32 141824 -0.2942 0.384287
22 to 31 142198 0.9954 0.840233
21 to 30 142657 2.5782 0.995034
20 to 29 141646 -0.9080 0.181930
19 to 28 142468 1.9264 0.972976
18 to 27 142796 3.0575 0.998884
17 to 26 141740 -0.5839 0.279645
16 to 25 141336 -1.9770 0.024021
15 to 24 141960 0.1747 0.569352
14 to 23 142509 2.0678 0.980672
13 to 22 141614 -1.0184 0.154249
12 to 21 141927 0.0609 0.524293
11 to 20 141733 -0.6080 0.271582
10 to 19 141832 -0.2667 0.394867
9 to 18 141930 0.0713 0.528411
8 to 17 141682 -0.7839 0.216550
7 to 16 141552 -1.2322 0.108942
6 to 15 141954 0.1540 0.561209
5 to 14 141957 0.1644 0.565284
4 to 13 142409 1.7230 0.957556
3 to 12 142105 0.6747 0.750075
2 to 11 142386 1.6437 0.949880
1 to 10 141916 0.0230 0.509175
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_10:31
Bits used No. missing words z-score p-value
28 to 32 142017 0.3650 0.642438
27 to 31 141912 0.0091 0.503611
26 to 30 141925 0.0531 0.521181
25 to 29 141955 0.1548 0.561516
24 to 28 142215 1.0362 0.849938
23 to 27 141699 -0.7130 0.237928
22 to 26 141862 -0.1604 0.436267
21 to 25 142119 0.7107 0.761379
20 to 24 141784 -0.4248 0.335474
19 to 23 141826 -0.2825 0.388790
18 to 22 141300 -2.0655 0.019437
17 to 21 141997 0.2972 0.616838
16 to 20 141598 -1.0554 0.145631
15 to 19 141905 -0.0147 0.494145
14 to 18 142202 0.9921 0.839426
13 to 17 141868 -0.1401 0.444290
12 to 16 141595 -1.0655 0.143319
11 to 15 141965 0.1887 0.574841
10 to 14 141954 0.1514 0.560179
9 to 13 141972 0.2124 0.584118
8 to 12 141588 -1.0893 0.138021
7 to 11 141571 -1.1469 0.125715
6 to 10 142356 1.5141 0.935004
5 to 9 141567 -1.1604 0.122935
4 to 8 142058 0.5040 0.692857
3 to 7 142040 0.4429 0.671099
2 to 6 142271 1.2260 0.889901
1 to 5 141636 -0.9265 0.177082
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_10:31
Bits used No. missing words z-score p-value
31 to 32 141779 -0.3845 0.350321
30 to 31 141615 -0.8682 0.192634
29 to 30 141729 -0.5319 0.297381
28 to 29 141466 -1.3078 0.095478
27 to 28 142568 1.9430 0.973991
26 to 27 141730 -0.5290 0.298404
25 to 26 142820 2.6863 0.996388
24 to 25 141751 -0.4671 0.320232
23 to 24 142020 0.3265 0.627962
22 to 23 142320 1.2114 0.887132
21 to 22 142106 0.5801 0.719092
20 to 21 141869 -0.1190 0.452651
19 to 20 141900 -0.0275 0.489022
18 to 19 141625 -0.8387 0.200810
17 to 18 142221 0.9194 0.821052
16 to 17 141387 -1.5408 0.061683
15 to 16 141738 -0.5054 0.306640
14 to 15 141808 -0.2989 0.382505
13 to 14 142378 1.3825 0.916592
12 to 13 141904 -0.0157 0.493728
11 to 12 141872 -0.1101 0.456158
10 to 11 141718 -0.5644 0.286243
9 to 10 141812 -0.2871 0.387014
8 to 9 141973 0.1878 0.574490
7 to 8 141525 -1.1337 0.128457
6 to 7 142489 1.7099 0.956362
5 to 6 141393 -1.5231 0.063867
4 to 5 141916 0.0197 0.507849
3 to 4 142298 1.1465 0.874210
2 to 3 142741 2.4533 0.992922
1 to 2 142069 0.4710 0.681181
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2547.80 0.676 0.750459
Test results for specific bytes for dh-ranFile-2018-07-11_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2460.23 -0.562 0.286929
2 to 9 2474.53 -0.360 0.359344
3 to 10 2435.82 -0.908 0.182038
4 to 11 2618.12 1.670 0.952585
5 to 12 2456.87 -0.610 0.270942
6 to 13 2467.78 -0.456 0.324320
7 to 14 2460.47 -0.559 0.288088
8 to 15 2603.52 1.464 0.928393
9 to 16 2505.47 0.077 0.530849
10 to 17 2454.27 -0.647 0.258908
11 to 18 2566.48 0.940 0.826427
12 to 19 2401.94 -1.387 0.082758
13 to 20 2575.78 1.072 0.858068
14 to 21 2581.74 1.156 0.876169
15 to 22 2425.05 -1.060 0.144586
16 to 23 2515.83 0.224 0.588554
17 to 24 2473.87 -0.370 0.355853
18 to 25 2577.63 1.098 0.863873
19 to 26 2519.83 0.280 0.610443
20 to 27 2443.25 -0.803 0.211100
21 to 28 2563.48 0.898 0.815333
22 to 29 2465.20 -0.492 0.311322
23 to 30 2415.27 -1.198 0.115397
24 to 31 2523.86 0.337 0.632087
25 to 32 2519.16 0.271 0.606812
CDPARK for dh-ranFile-2018-07-11_10:31: 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
3539 0.7306 0.767486
3531 0.3653 0.642555
3531 0.3653 0.642555
3512 -0.5023 0.307734
3563 1.8265 0.966111
3537 0.6393 0.738676
3511 -0.5479 0.291865
3509 -0.6393 0.261324
3498 -1.1416 0.126820
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3524.90 sample std.=18.04
p-value of the KSTEST for those 10 p-values: 0.917821
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_10:31
0.7349,0.1120,0.7093,0.1700,0.3213,0.2199,0.9698,0.3647,0.8023,0.7587,
The KS test for those 10 p-values: 0.903695
The 3DSPHERES test for dh-ranFile-2018-07-11_10:31
sample no r^3 equiv. uni.
1 38.821 0.725841
2 9.845 0.279753
3 38.678 0.724531
4 7.465 0.220282
5 7.324 0.216626
6 19.754 0.482348
7 0.554 0.018283
8 108.452 0.973085
9 41.720 0.751088
10 57.533 0.853065
11 16.787 0.428534
12 2.207 0.070920
13 53.947 0.834408
14 26.662 0.588823
15 45.675 0.781835
16 7.841 0.229991
17 9.437 0.269887
18 39.196 0.729240
19 38.481 0.722712
20 12.086 0.331604
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.862083
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.7 0.1 0.3 1.4 1.1 0.9
0.5 -0.4 0.8 -0.0 1.4 -0.9
-0.2 0.9 -2.0 -0.2 -0.6 -0.2
-0.9 1.7 0.2 0.5 2.0 0.3
-1.5 -0.2 -0.9 -0.2 -0.1 -1.7
0.7 0.4 -0.1 0.3 0.8 -0.7
-0.7 0.2 -1.2 -0.1 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:39.608819
z-score=-0.260899, p-value=0.423538
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_10:31
Test no p-value
1 0.768392
2 0.762629
3 0.393775
4 0.145013
5 0.680934
6 0.048195
7 0.580227
8 0.023716
9 0.967817
10 0.288505
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.835552
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_10:31:
(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 66866 0.60 66367 1.35
3 25000.00 24876 0.62 25163 1.06
4 6666.67 6592 0.84 6819 3.48
5 1388.89 1383 0.02 1342 1.58
6 238.10 245 0.20 266 3.27
7 34.72 33 0.09 36 0.05
8 4.96 4 0.19 6 0.22
p=0.13644 p=0.91191
Number of rngs required: 689854, p-value: 0.956
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_10:31
No. of wins: Observed Expected
98596 98585.9
z-score= 0.045, pvalue=0.51809
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66923 66666.7 0.986 0.986
2 37600 37654.3 0.078 1.064
3 27026 26954.7 0.188 1.252
4 19184 19313.5 0.868 2.120
5 13960 13851.4 0.851 2.971
6 10026 9943.5 0.684 3.655
7 7067 7145.0 0.852 4.507
8 5083 5139.1 0.612 5.119
9 3730 3699.9 0.245 5.364
10 2603 2666.3 1.503 6.867
11 1875 1923.3 1.214 8.082
12 1323 1388.7 3.112 11.194
13 988 1003.7 0.246 11.440
14 709 726.1 0.405 11.844
15 533 525.8 0.098 11.942
16 387 381.2 0.090 12.032
17 268 276.5 0.264 12.295
18 208 200.8 0.256 12.551
19 122 146.0 3.940 16.492
20 108 106.2 0.030 16.522
21 277 287.1 0.356 16.878
Chisq= 16.88 for 20 degrees of freedom, p= 0.33912
SUMMARY of craptest
p-value for no. of wins: 0.518089
p-value for throws/game: 0.339120
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_10:31
No. of wins: Observed Expected
98660 98585.9
z-score= 0.332, pvalue=0.62991
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66778 66666.7 0.186 0.186
2 37672 37654.3 0.008 0.194
3 26937 26954.7 0.012 0.206
4 19128 19313.5 1.781 1.987
5 13763 13851.4 0.564 2.551
6 10036 9943.5 0.860 3.411
7 7204 7145.0 0.487 3.898
8 5066 5139.1 1.039 4.937
9 3718 3699.9 0.089 5.026
10 2629 2666.3 0.522 5.547
11 1997 1923.3 2.822 8.369
12 1378 1388.7 0.083 8.452
13 1027 1003.7 0.540 8.992
14 742 726.1 0.346 9.339
15 539 525.8 0.330 9.668
16 361 381.2 1.065 10.734
17 270 276.5 0.155 10.888
18 216 200.8 1.146 12.034
19 147 146.0 0.007 12.041
20 100 106.2 0.364 12.405
21 292 287.1 0.083 12.488
Chisq= 12.49 for 20 degrees of freedom, p= 0.10175
SUMMARY of craptest
p-value for no. of wins: 0.629906
p-value for throws/game: 0.101750
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0176,0.0183,0.0194,0.0237,0.0240,0.0244,0.0427,0.0443,0.0482,0.0617,
0.0634,0.0639,0.0703,0.0709,0.0828,0.0850,0.0937,0.0955,0.1018,0.1059,
0.1089,0.1120,0.1135,0.1154,0.1193,0.1229,0.1257,0.1268,0.1285,0.1364,
0.1380,0.1433,0.1433,0.1446,0.1450,0.1456,0.1481,0.1542,0.1547,0.1564,
0.1621,0.1671,0.1672,0.1700,0.1771,0.1819,0.1820,0.1877,0.1926,0.2008,
0.2111,0.2126,0.2166,0.2166,0.2175,0.2199,0.2203,0.2300,0.2379,0.2417,
0.2531,0.2577,0.2589,0.2613,0.2695,0.2699,0.2709,0.2716,0.2725,0.2796,
0.2798,0.2833,0.2862,0.2869,0.2872,0.2881,0.2885,0.2919,0.2974,0.2984,
0.3066,0.3077,0.3113,0.3135,0.3200,0.3202,0.3213,0.3243,0.3297,0.3316,
0.3343,0.3355,0.3391,0.3503,0.3559,0.3579,0.3593,0.3647,0.3655,0.3825,
0.3843,0.3870,0.3888,0.3938,0.3949,0.3962,0.4097,0.4115,0.4158,0.4177,
0.4197,0.4235,0.4237,0.4285,0.4299,0.4363,0.4364,0.4385,0.4443,0.4445,
0.4527,0.4562,0.4618,0.4811,0.4823,0.4872,0.4890,0.4937,0.4941,0.4991,
0.5034,0.5036,0.5036,0.5044,0.5066,0.5078,0.5092,0.5181,0.5212,0.5243,
0.5284,0.5308,0.5359,0.5379,0.5391,0.5470,0.5573,0.5602,0.5612,0.5615,
0.5653,0.5694,0.5735,0.5745,0.5748,0.5785,0.5802,0.5803,0.5841,0.5886,
0.5888,0.6068,0.6104,0.6168,0.6171,0.6175,0.6182,0.6280,0.6299,0.6321,
0.6332,0.6424,0.6426,0.6426,0.6426,0.6446,0.6465,0.6583,0.6593,0.6677,
0.6711,0.6809,0.6812,0.6849,0.6859,0.6862,0.6925,0.6929,0.7093,0.7126,
0.7191,0.7227,0.7245,0.7258,0.7292,0.7318,0.7349,0.7387,0.7501,0.7505,
0.7511,0.7581,0.7587,0.7614,0.7626,0.7652,0.7675,0.7684,0.7685,0.7746,
0.7818,0.7859,0.7945,0.7953,0.8023,0.8046,0.8046,0.8066,0.8087,0.8153,
0.8188,0.8211,0.8264,0.8344,0.8356,0.8394,0.8402,0.8467,0.8499,0.8531,
0.8540,0.8545,0.8581,0.8621,0.8639,0.8742,0.8762,0.8871,0.8899,0.8951,
0.9037,0.9119,0.9166,0.9178,0.9284,0.9350,0.9437,0.9472,0.9487,0.9499,
0.9526,0.9532,0.9556,0.9564,0.9576,0.9628,0.9656,0.9661,0.9678,0.9698,
0.9730,0.9731,0.9740,0.9770,0.9807,0.9929,0.9950,0.9964,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.706557
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.