RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_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 15.67 27.7434 0.951973
2 to 25 15.65 30.0926 0.974315
3 to 26 15.59 18.9099 0.666272
4 to 27 15.63 27.8474 0.953247
5 to 28 15.61 27.0214 0.942246
6 to 29 15.55 19.1693 0.681096
7 to 30 15.65 16.0312 0.478374
8 to 31 15.50 13.4041 0.291260
9 to 32 15.67 32.6178 0.987404
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.001662
Tough bday spacings test for dh-ranFile-2018-06-16_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 13 39 74 101 94 79 40 27 19 8 6
(O-E)^2/E 1.6 0.2 0.0 0.1 0.1 0.0 2.8 0.3 1.1 0.3 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.447, p= 0.317
RESULTS OF GCD FOR dh-ranFile-2018-06-16_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.916060
p-value, dist. of gcd's: 0.249453
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.315 0.390 0.750 0.448 0.281 0.288 0.844 0.381
Bits 8 to 15---> 0.645 0.692 0.550 0.610 0.786 0.352 0.829 0.113
Bits 16 to 23---> 0.105 0.487 0.093 0.162 0.180 0.735 0.023 0.190
Bits 24 to 31---> 0.776 0.509 0.278 0.559 0.623 0.465 0.427 0.661
KS test for the above 32 p values: 0.694
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_18:31,
p-values for 5 runs: 0.6589, 0.5981, 0.4914, 0.5355, 0.0882
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5084 5134.0 0.487 0.586
r= 30 23138 23103.0 0.053 0.639
r= 31 11562 11551.5 0.010 0.649
chi-square = 0.649 with df = 3; p-value = 0.115
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5192 5134.0 0.655 0.990
r= 31 23162 23103.0 0.150 1.141
r= 32 11443 11551.5 1.020 2.160
chi-square = 2.160 with df = 3; p-value = 0.460
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_18:31
b-rank test for bits 1 to 8, p=0.13217
b-rank test for bits 2 to 9, p=0.55108
b-rank test for bits 3 to 10, p=0.17524
b-rank test for bits 4 to 11, p=0.27098
b-rank test for bits 5 to 12, p=0.65450
b-rank test for bits 6 to 13, p=0.15992
b-rank test for bits 7 to 14, p=0.09712
b-rank test for bits 8 to 15, p=0.21621
b-rank test for bits 9 to 16, p=0.78915
b-rank test for bits 10 to 17, p=0.73321
b-rank test for bits 11 to 18, p=0.94082
b-rank test for bits 12 to 19, p=0.46714
b-rank test for bits 13 to 20, p=0.60373
b-rank test for bits 14 to 21, p=0.81593
b-rank test for bits 15 to 22, p=0.72341
b-rank test for bits 16 to 23, p=0.33986
b-rank test for bits 17 to 24, p=0.36302
b-rank test for bits 18 to 25, p=0.32799
b-rank test for bits 19 to 26, p=0.51390
b-rank test for bits 20 to 27, p=0.23801
b-rank test for bits 21 to 28, p=0.46047
b-rank test for bits 22 to 29, p=0.15743
b-rank test for bits 23 to 30, p=0.77339
b-rank test for bits 24 to 31, p=0.51683
b-rank test for bits 25 to 32, p=0.54279
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 = 0.494464
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_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 142140 0.54 0.705039
2 141236 -1.57 0.057836
3 141841 -0.16 0.436579
4 142239 0.77 0.779426
5 141926 0.04 0.515534
6 140986 -2.16 0.015491
7 142404 1.16 0.876113
8 141709 -0.47 0.319871
9 141825 -0.20 0.421901
10 141615 -0.69 0.245825
11 141972 0.15 0.558207
12 141082 -1.93 0.026617
13 141792 -0.27 0.391990
14 142113 0.48 0.682915
15 142608 1.63 0.948703
16 141846 -0.15 0.441184
17 141761 -0.35 0.364459
18 141801 -0.25 0.400093
19 142000 0.21 0.583886
20 142802 2.09 0.981496
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_18:31
Bits used No. missing words z-score p-value
23 to 32 141697 -0.7322 0.232032
22 to 31 141675 -0.8080 0.209535
21 to 30 141930 0.0713 0.528411
20 to 29 142227 1.0954 0.863332
19 to 28 141901 -0.0287 0.488542
18 to 27 141786 -0.4253 0.335318
17 to 26 141743 -0.5736 0.283136
16 to 25 142295 1.3299 0.908224
15 to 24 141691 -0.7529 0.225766
14 to 23 142500 2.0368 0.979165
13 to 22 142228 1.0989 0.864086
12 to 21 142113 0.7023 0.758757
11 to 20 141327 -2.0080 0.022320
10 to 19 141531 -1.3046 0.096017
9 to 18 141559 -1.2080 0.113517
8 to 17 142256 1.1954 0.884037
7 to 16 141731 -0.6149 0.269300
6 to 15 142038 0.4437 0.671367
5 to 14 142199 0.9989 0.841069
4 to 13 142322 1.4230 0.922632
3 to 12 141954 0.1540 0.561209
2 to 11 141261 -2.2356 0.012688
1 to 10 141791 -0.4080 0.341624
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_18:31
Bits used No. missing words z-score p-value
28 to 32 142276 1.2429 0.893057
27 to 31 142264 1.2023 0.885371
26 to 30 142160 0.8497 0.802262
25 to 29 142082 0.5853 0.720834
24 to 28 141516 -1.3333 0.091213
23 to 27 141900 -0.0316 0.487385
22 to 26 142052 0.4836 0.685675
21 to 25 142511 2.0396 0.979303
20 to 24 141888 -0.0723 0.471180
19 to 23 141987 0.2633 0.603836
18 to 22 142269 1.2192 0.888620
17 to 21 141788 -0.4113 0.340431
16 to 20 141657 -0.8554 0.196177
15 to 19 142038 0.4362 0.668643
14 to 18 142222 1.0599 0.855405
13 to 17 141917 0.0260 0.510371
12 to 16 141839 -0.2384 0.405783
11 to 15 141732 -0.6011 0.273881
10 to 14 142012 0.3480 0.636093
9 to 13 141692 -0.7367 0.230649
8 to 12 141592 -1.0757 0.141032
7 to 11 141594 -1.0689 0.142554
6 to 10 142293 1.3006 0.903298
5 to 9 141782 -0.4316 0.333006
4 to 8 141968 0.1989 0.578822
3 to 7 141705 -0.6926 0.244267
2 to 6 141832 -0.2621 0.396609
1 to 5 141778 -0.4452 0.328093
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_18:31
Bits used No. missing words z-score p-value
31 to 32 142501 1.7453 0.959537
30 to 31 141338 -1.6853 0.045962
29 to 30 141214 -2.0511 0.020128
28 to 29 141892 -0.0511 0.479615
27 to 28 141718 -0.5644 0.286243
26 to 27 142169 0.7660 0.778158
25 to 26 142307 1.1731 0.879616
24 to 25 141889 -0.0600 0.476090
23 to 24 141583 -0.9626 0.167868
22 to 23 141531 -1.1160 0.132207
21 to 22 142505 1.7571 0.960553
20 to 21 141904 -0.0157 0.493728
19 to 20 142143 0.6893 0.754680
18 to 19 141802 -0.3166 0.375771
17 to 18 142219 0.9135 0.819505
16 to 17 142214 0.8987 0.815602
15 to 16 141692 -0.6411 0.260732
14 to 15 142230 0.9459 0.827908
13 to 14 142102 0.5683 0.715101
12 to 13 141881 -0.0836 0.466699
11 to 12 141821 -0.2606 0.397216
10 to 11 141990 0.2380 0.594046
9 to 10 142287 1.1141 0.867376
8 to 9 141760 -0.4405 0.329787
7 to 8 142029 0.3530 0.637959
6 to 7 141568 -1.0069 0.156998
5 to 6 142057 0.4356 0.668438
4 to 5 142070 0.4740 0.682233
3 to 4 141105 -2.3727 0.008830
2 to 3 141923 0.0403 0.516083
1 to 2 142053 0.4238 0.664146
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2476.76 -0.329 0.371217
Test results for specific bytes for dh-ranFile-2018-06-16_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2569.09 0.977 0.835732
2 to 9 2502.43 0.034 0.513728
3 to 10 2456.11 -0.621 0.267421
4 to 11 2558.92 0.833 0.797632
5 to 12 2560.61 0.857 0.804333
6 to 13 2449.37 -0.716 0.236986
7 to 14 2554.10 0.765 0.777879
8 to 15 2423.42 -1.083 0.139396
9 to 16 2626.21 1.785 0.962862
10 to 17 2479.89 -0.284 0.388073
11 to 18 2557.84 0.818 0.793308
12 to 19 2570.26 0.994 0.839784
13 to 20 2486.91 -0.185 0.426578
14 to 21 2435.11 -0.918 0.179386
15 to 22 2475.39 -0.348 0.363917
16 to 23 2437.12 -0.889 0.186914
17 to 24 2470.46 -0.418 0.338047
18 to 25 2427.48 -1.026 0.152547
19 to 26 2408.69 -1.291 0.098290
20 to 27 2480.18 -0.280 0.389642
21 to 28 2467.76 -0.456 0.324235
22 to 29 2466.17 -0.478 0.316153
23 to 30 2421.74 -1.107 0.134208
24 to 31 2570.64 0.999 0.841111
25 to 32 2469.64 -0.429 0.333826
CDPARK for dh-ranFile-2018-06-16_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
3524 0.0457 0.518210
3563 1.8265 0.966111
3497 -1.1872 0.117571
3502 -0.9589 0.168804
3550 1.2329 0.891189
3550 1.2329 0.891189
3470 -2.4201 0.007758
3549 1.1872 0.882429
3524 0.0457 0.518210
3543 0.9132 0.819442
Square side=100, avg. no. parked=3527.20 sample std.=28.08
p-value of the KSTEST for those 10 p-values: 0.234030
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_18:31
0.9437,0.5853,0.5728,0.1851,0.5679,0.0396,0.9594,0.0473,0.6531,0.2144,
The KS test for those 10 p-values: 0.655838
The 3DSPHERES test for dh-ranFile-2018-06-16_18:31
sample no r^3 equiv. uni.
1 34.714 0.685617
2 16.718 0.427233
3 13.701 0.366627
4 1.079 0.035316
5 8.193 0.238976
6 68.072 0.896592
7 21.420 0.510316
8 5.555 0.169022
9 12.385 0.338232
10 128.928 0.986399
11 0.382 0.012660
12 7.760 0.227932
13 67.211 0.893581
14 70.658 0.905133
15 5.179 0.158551
16 11.275 0.313294
17 3.723 0.116694
18 75.443 0.919118
19 17.616 0.444112
20 17.356 0.439288
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.477628
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 -0.6 0.3 0.0 -0.4
-0.7 1.3 0.2 0.1 -1.3 -1.2
-0.2 0.1 2.0 1.2 1.0 0.3
-0.4 0.3 -1.7 -0.7 0.4 0.8
0.5 -1.1 -0.3 -0.7 -0.9 0.3
-1.9 -0.5 0.8 -1.0 -0.5 -1.0
0.5 -0.4 -1.6 -1.3 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:33.050459
z-score=-0.976475, p-value=0.163104
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_18:31
Test no p-value
1 0.432586
2 0.001597
3 0.107338
4 0.611586
5 0.411339
6 0.344789
7 0.055644
8 0.691538
9 0.047734
10 0.094212
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.013027
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_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 66666 0.00 66734 0.07
3 25000.00 24950 0.10 24898 0.42
4 6666.67 6688 0.07 6713 0.32
5 1388.89 1414 0.45 1349 1.15
6 238.10 240 0.02 270 4.28
7 34.72 35 0.00 29 0.94
8 4.96 6 0.22 6 0.22
p=0.00957 p=0.71350
Number of rngs required: 687584, p-value: 0.172
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_18:31
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 66723 66666.7 0.048 0.048
2 37828 37654.3 0.801 0.849
3 26762 26954.7 1.378 2.227
4 19382 19313.5 0.243 2.470
5 13752 13851.4 0.714 3.184
6 9873 9943.5 0.500 3.684
7 7170 7145.0 0.087 3.771
8 5036 5139.1 2.067 5.839
9 3818 3699.9 3.772 9.611
10 2682 2666.3 0.092 9.703
11 1884 1923.3 0.804 10.507
12 1385 1388.7 0.010 10.517
13 1025 1003.7 0.451 10.969
14 752 726.1 0.921 11.890
15 523 525.8 0.015 11.905
16 382 381.2 0.002 11.907
17 285 276.5 0.259 12.166
18 202 200.8 0.007 12.173
19 151 146.0 0.172 12.345
20 111 106.2 0.216 12.560
21 274 287.1 0.599 13.159
Chisq= 13.16 for 20 degrees of freedom, p= 0.12956
SUMMARY of craptest
p-value for no. of wins: 0.597401
p-value for throws/game: 0.129558
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_18:31
No. of wins: Observed Expected
98279 98585.9
z-score=-1.372, pvalue=0.08496
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66724 66666.7 0.049 0.049
2 37485 37654.3 0.761 0.811
3 27006 26954.7 0.098 0.908
4 19324 19313.5 0.006 0.914
5 13802 13851.4 0.176 1.090
6 9945 9943.5 0.000 1.090
7 7167 7145.0 0.068 1.158
8 5206 5139.1 0.872 2.030
9 3712 3699.9 0.040 2.069
10 2553 2666.3 4.814 6.884
11 1936 1923.3 0.083 6.967
12 1410 1388.7 0.325 7.293
13 1039 1003.7 1.240 8.533
14 762 726.1 1.771 10.304
15 499 525.8 1.370 11.674
16 380 381.2 0.003 11.677
17 278 276.5 0.008 11.685
18 194 200.8 0.232 11.917
19 140 146.0 0.245 12.162
20 135 106.2 7.801 19.963
21 303 287.1 0.879 20.842
Chisq= 20.84 for 20 degrees of freedom, p= 0.59352
SUMMARY of craptest
p-value for no. of wins: 0.084962
p-value for throws/game: 0.593521
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0017,0.0078,0.0088,0.0096,0.0127,0.0127,0.0130,0.0155,0.0201,
0.0223,0.0233,0.0266,0.0353,0.0396,0.0460,0.0473,0.0477,0.0556,0.0578,
0.0850,0.0882,0.0912,0.0927,0.0942,0.0960,0.0971,0.0983,0.1053,0.1073,
0.1127,0.1135,0.1148,0.1167,0.1176,0.1296,0.1322,0.1322,0.1342,0.1394,
0.1410,0.1426,0.1525,0.1570,0.1574,0.1586,0.1599,0.1619,0.1631,0.1679,
0.1688,0.1690,0.1715,0.1752,0.1794,0.1801,0.1851,0.1869,0.1904,0.1962,
0.2095,0.2144,0.2162,0.2258,0.2279,0.2306,0.2320,0.2340,0.2370,0.2380,
0.2390,0.2443,0.2458,0.2495,0.2607,0.2674,0.2693,0.2710,0.2739,0.2775,
0.2808,0.2831,0.2862,0.2880,0.2913,0.3133,0.3150,0.3162,0.3174,0.3199,
0.3242,0.3280,0.3281,0.3298,0.3330,0.3338,0.3353,0.3380,0.3382,0.3399,
0.3404,0.3416,0.3448,0.3524,0.3630,0.3639,0.3645,0.3666,0.3712,0.3758,
0.3815,0.3881,0.3896,0.3896,0.3920,0.3966,0.3972,0.4001,0.4058,0.4113,
0.4219,0.4266,0.4270,0.4272,0.4326,0.4366,0.4393,0.4412,0.4441,0.4485,
0.4602,0.4605,0.4645,0.4667,0.4671,0.4712,0.4761,0.4776,0.4784,0.4796,
0.4868,0.4874,0.4885,0.4914,0.4937,0.4945,0.5095,0.5103,0.5104,0.5137,
0.5139,0.5155,0.5161,0.5168,0.5182,0.5182,0.5284,0.5355,0.5428,0.5504,
0.5511,0.5582,0.5587,0.5612,0.5679,0.5728,0.5788,0.5839,0.5853,0.5935,
0.5940,0.5974,0.5981,0.6037,0.6038,0.6096,0.6116,0.6227,0.6361,0.6380,
0.6455,0.6531,0.6545,0.6558,0.6589,0.6613,0.6641,0.6663,0.6684,0.6686,
0.6714,0.6811,0.6822,0.6829,0.6856,0.6857,0.6915,0.6922,0.6941,0.7050,
0.7135,0.7151,0.7208,0.7234,0.7332,0.7354,0.7501,0.7547,0.7588,0.7734,
0.7756,0.7779,0.7782,0.7794,0.7861,0.7892,0.7933,0.7976,0.8023,0.8043,
0.8156,0.8159,0.8194,0.8195,0.8279,0.8290,0.8357,0.8398,0.8411,0.8411,
0.8441,0.8554,0.8633,0.8641,0.8674,0.8761,0.8796,0.8824,0.8840,0.8854,
0.8886,0.8912,0.8912,0.8931,0.8936,0.8966,0.9033,0.9051,0.9082,0.9161,
0.9191,0.9226,0.9408,0.9422,0.9437,0.9487,0.9520,0.9532,0.9594,0.9595,
0.9606,0.9629,0.9661,0.9743,0.9792,0.9793,0.9815,0.9864,0.9874,
Overall p-value after applying KStest on 269 p-values = 0.386360
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.