RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-25_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.90 18.8110 0.660515
2 to 25 15.86 17.0104 0.546339
3 to 26 15.77 21.4561 0.793451
4 to 27 16.02 12.9739 0.262070
5 to 28 15.76 16.7331 0.527412
6 to 29 15.93 17.1157 0.553444
7 to 30 16.03 16.8593 0.536062
8 to 31 15.61 29.4466 0.969376
9 to 32 15.48 18.0847 0.616486
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.211192
Tough bday spacings test for dh-ranFile-2018-04-25_05:31: 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 9 48 80 86 90 61 58 37 17 9 5
(O-E)^2/E 0.0 3.5 0.6 1.4 0.6 3.8 0.7 1.8 0.3 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 13.714, p= 0.814
RESULTS OF GCD FOR dh-ranFile-2018-04-25_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.943682
p-value, dist. of gcd's: 0.276347
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-25_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.474 0.393 0.616 0.469 0.708 0.511 0.668 0.718
Bits 8 to 15---> 0.415 0.805 0.855 0.411 0.815 0.716 0.053 0.149
Bits 16 to 23---> 0.915 0.740 0.859 0.080 0.848 0.239 0.244 0.434
Bits 24 to 31---> 0.974 0.406 0.510 0.629 0.331 0.613 0.391 0.545
KS test for the above 32 p values: 0.688
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-25_05:31,
p-values for 5 runs: 0.9367, 0.6837, 0.4511, 0.3559, 0.4935
Rank test for binary matrices (31x31) for dh-ranFile-2018-04-25_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 250 211.4 7.041 7.041
r= 29 5072 5134.0 0.749 7.790
r= 30 23131 23103.0 0.034 7.824
r= 31 11547 11551.5 0.002 7.825
chi-square = 7.825 with df = 3; p-value = 0.950
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-04-25_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 4979 5134.0 4.680 4.875
r= 31 23207 23103.0 0.468 5.343
r= 32 11609 11551.5 0.286 5.629
chi-square = 5.629 with df = 3; p-value = 0.869
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-04-25_05:31
b-rank test for bits 1 to 8, p=0.96999
b-rank test for bits 2 to 9, p=0.13323
b-rank test for bits 3 to 10, p=0.69603
b-rank test for bits 4 to 11, p=0.48769
b-rank test for bits 5 to 12, p=0.43392
b-rank test for bits 6 to 13, p=0.79345
b-rank test for bits 7 to 14, p=0.46655
b-rank test for bits 8 to 15, p=0.38971
b-rank test for bits 9 to 16, p=0.06391
b-rank test for bits 10 to 17, p=0.45650
b-rank test for bits 11 to 18, p=0.99686
b-rank test for bits 12 to 19, p=0.33154
b-rank test for bits 13 to 20, p=0.04223
b-rank test for bits 14 to 21, p=0.28844
b-rank test for bits 15 to 22, p=0.68923
b-rank test for bits 16 to 23, p=0.09129
b-rank test for bits 17 to 24, p=0.26794
b-rank test for bits 18 to 25, p=0.60625
b-rank test for bits 19 to 26, p=0.00578
b-rank test for bits 20 to 27, p=0.93217
b-rank test for bits 21 to 28, p=0.07204
b-rank test for bits 22 to 29, p=0.31515
b-rank test for bits 23 to 30, p=0.70670
b-rank test for bits 24 to 31, p=0.61103
b-rank test for bits 25 to 32, p=0.70840
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 = 0.668269
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-25_05:31
(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 141720 -0.44 0.329114
2 142026 0.27 0.607417
3 141742 -0.39 0.347914
4 141655 -0.59 0.276180
5 141836 -0.17 0.431981
6 142318 0.95 0.830170
7 141733 -0.41 0.340175
8 141475 -1.01 0.155103
9 142093 0.43 0.666088
10 141483 -1.00 0.159601
11 142371 1.08 0.859632
12 141789 -0.28 0.389300
13 141903 -0.01 0.494100
14 141629 -0.65 0.256241
15 141309 -1.40 0.080362
16 141639 -0.63 0.263820
17 141294 -1.44 0.075261
18 141841 -0.16 0.436579
19 142387 1.12 0.867800
20 142536 1.46 0.928428
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-04-25_05:31
Bits used No. missing words z-score p-value
23 to 32 141583 -1.1253 0.130236
22 to 31 142178 0.9264 0.822894
21 to 30 142248 1.1678 0.878562
20 to 29 141999 0.3092 0.621418
19 to 28 142090 0.6230 0.733358
18 to 27 141627 -0.9736 0.165140
17 to 26 142063 0.5299 0.701908
16 to 25 141715 -0.6701 0.251396
15 to 24 141932 0.0782 0.531155
14 to 23 141922 0.0437 0.517424
13 to 22 142353 1.5299 0.936979
12 to 21 141810 -0.3425 0.365981
11 to 20 142119 0.7230 0.765160
10 to 19 141727 -0.6287 0.264765
9 to 18 142128 0.7540 0.774586
8 to 17 141924 0.0506 0.520172
7 to 16 141673 -0.8149 0.207556
6 to 15 142268 1.2368 0.891918
5 to 14 142164 0.8782 0.810075
4 to 13 141985 0.2609 0.602927
3 to 12 142178 0.9264 0.822894
2 to 11 142101 0.6609 0.745672
1 to 10 141230 -2.3425 0.009577
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-04-25_05:31
Bits used No. missing words z-score p-value
28 to 32 142010 0.3413 0.633544
27 to 31 141808 -0.3435 0.365614
26 to 30 141600 -1.0486 0.147187
25 to 29 142264 1.2023 0.885371
24 to 28 141969 0.2023 0.580148
23 to 27 141881 -0.0960 0.461747
22 to 26 142152 0.8226 0.794635
21 to 25 142029 0.4057 0.657504
20 to 24 141720 -0.6418 0.260503
19 to 23 141953 0.1480 0.558842
18 to 22 142206 1.0057 0.842711
17 to 21 142137 0.7718 0.779873
16 to 20 141716 -0.6554 0.256119
15 to 19 141836 -0.2486 0.401844
14 to 18 141341 -1.9265 0.027018
13 to 17 141715 -0.6587 0.255030
12 to 16 141412 -1.6859 0.045911
11 to 15 141601 -1.0452 0.147968
10 to 14 142138 0.7752 0.780875
9 to 13 142135 0.7650 0.777859
8 to 12 141592 -1.0757 0.141032
7 to 11 141792 -0.3977 0.345415
6 to 10 142269 1.2192 0.888620
5 to 9 142314 1.3718 0.914931
4 to 8 142262 1.1955 0.884053
3 to 7 141896 -0.0452 0.481979
2 to 6 141606 -1.0282 0.151919
1 to 5 141758 -0.5130 0.303982
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-04-25_05:31
Bits used No. missing words z-score p-value
31 to 32 141251 -1.9420 0.026070
30 to 31 141508 -1.1839 0.118233
29 to 30 142402 1.4533 0.926930
28 to 29 141977 0.1996 0.579110
27 to 28 141490 -1.2370 0.108051
26 to 27 141539 -1.0924 0.137325
25 to 26 141887 -0.0659 0.473741
24 to 25 141606 -0.8948 0.185453
23 to 24 141818 -0.2694 0.393807
22 to 23 141726 -0.5408 0.294324
21 to 22 141673 -0.6971 0.242858
20 to 21 142146 0.6981 0.757456
19 to 20 141510 -1.1780 0.119405
18 to 19 142157 0.7306 0.767485
17 to 18 141758 -0.4464 0.327654
16 to 17 141457 -1.3343 0.091052
15 to 16 142051 0.4179 0.661992
14 to 15 142077 0.4946 0.689559
13 to 14 141961 0.1524 0.560572
12 to 13 141755 -0.4553 0.324464
11 to 12 142329 1.2380 0.892135
10 to 11 141828 -0.2399 0.405199
9 to 10 141621 -0.8505 0.197515
8 to 9 142083 0.5123 0.695780
7 to 8 141842 -0.1986 0.421283
6 to 7 141496 -1.2193 0.111372
5 to 6 142396 1.4356 0.924443
4 to 5 142068 0.4681 0.680127
3 to 4 141619 -0.8564 0.195880
2 to 3 142262 1.0403 0.850905
1 to 2 141808 -0.2989 0.382505
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-25_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2548.22 0.682 0.752356
Test results for specific bytes for dh-ranFile-2018-04-25_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2479.35 -0.292 0.385130
2 to 9 2715.47 3.047 0.998845
3 to 10 2456.24 -0.619 0.267993
4 to 11 2427.46 -1.026 0.152486
5 to 12 2537.59 0.532 0.702501
6 to 13 2613.80 1.609 0.946236
7 to 14 2468.58 -0.444 0.328396
8 to 15 2538.86 0.550 0.708684
9 to 16 2483.15 -0.238 0.405837
10 to 17 2493.78 -0.088 0.464974
11 to 18 2564.47 0.912 0.819060
12 to 19 2483.80 -0.229 0.409388
13 to 20 2481.64 -0.260 0.397585
14 to 21 2484.93 -0.213 0.415616
15 to 22 2494.79 -0.074 0.470614
16 to 23 2511.98 0.169 0.567246
17 to 24 2620.88 1.710 0.956325
18 to 25 2496.05 -0.056 0.477728
19 to 26 2466.93 -0.468 0.320015
20 to 27 2451.42 -0.687 0.246030
21 to 28 2424.58 -1.067 0.143061
22 to 29 2496.81 -0.045 0.481993
23 to 30 2510.89 0.154 0.561177
24 to 31 2495.00 -0.071 0.471809
25 to 32 2499.06 -0.013 0.494674
CDPARK for dh-ranFile-2018-04-25_05:31: 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
3516 -0.3196 0.374623
3504 -0.8676 0.192812
3511 -0.5479 0.291865
3515 -0.3653 0.357445
3523 0.0000 0.500000
3542 0.8676 0.807188
3519 -0.1826 0.427537
3553 1.3699 0.914635
3553 1.3699 0.914635
3501 -1.0046 0.157553
Square side=100, avg. no. parked=3523.70 sample std.=18.09
p-value of the KSTEST for those 10 p-values: 0.777609
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-25_05:31
0.6821,0.5913,0.5147,0.2362,0.1055,0.2491,0.1370,0.4103,0.6078,0.7712,
The KS test for those 10 p-values: 0.577155
The 3DSPHERES test for dh-ranFile-2018-04-25_05:31
sample no r^3 equiv. uni.
1 68.240 0.897168
2 11.304 0.313954
3 2.197 0.070628
4 0.612 0.020185
5 38.566 0.723498
6 15.167 0.396843
7 2.339 0.074992
8 35.836 0.697151
9 23.950 0.549929
10 32.503 0.661573
11 4.014 0.125248
12 124.875 0.984431
13 17.753 0.446645
14 29.884 0.630692
15 34.300 0.681244
16 31.349 0.648291
17 30.232 0.634957
18 13.701 0.366632
19 17.822 0.447920
20 91.891 0.953255
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.821541
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-25_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 -0.4 0.5 -1.0 -0.2
-0.7 0.1 -0.4 0.8 1.1 -0.4
-0.3 -0.5 -1.3 -0.3 0.8 0.3
0.3 -0.5 0.8 -0.5 1.5 -0.1
0.4 0.2 -1.3 0.9 -1.1 0.4
-1.0 -0.4 -0.2 0.0 0.1 -1.4
1.7 0.8 -0.4 1.5 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:24.540403
z-score=-1.904998, p-value=0.014459
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-04-25_05:31
Test no p-value
1 0.043718
2 0.675221
3 0.931153
4 0.875338
5 0.852692
6 0.286781
7 0.122556
8 0.484948
9 0.525010
10 0.822004
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.739363
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-25_05:31:
(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 66801 0.27 66767 0.15
3 25000.00 24952 0.09 25031 0.04
4 6666.67 6584 1.03 6558 1.77
5 1388.89 1393 0.01 1360 0.60
6 238.10 233 0.11 252 0.81
7 34.72 34 0.01 22 4.66
8 4.96 2 1.77 9 3.29
p=0.22841 p=0.92115
Number of rngs required: 688172, p-value: 0.395
RESULTS OF CRAPS TEST for dh-ranFile-2018-04-25_05:31
No. of wins: Observed Expected
99040 98585.9
z-score= 2.031, pvalue=0.97888
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66809 66666.7 0.304 0.304
2 37589 37654.3 0.113 0.417
3 26749 26954.7 1.570 1.987
4 19611 19313.5 4.584 6.571
5 13709 13851.4 1.464 8.036
6 9921 9943.5 0.051 8.087
7 7226 7145.0 0.918 9.004
8 5159 5139.1 0.077 9.082
9 3643 3699.9 0.874 9.956
10 2646 2666.3 0.155 10.110
11 1851 1923.3 2.720 12.830
12 1416 1388.7 0.535 13.365
13 1020 1003.7 0.264 13.629
14 741 726.1 0.304 13.934
15 531 525.8 0.051 13.984
16 370 381.2 0.326 14.310
17 267 276.5 0.329 14.640
18 183 200.8 1.583 16.223
19 145 146.0 0.007 16.229
20 95 106.2 1.184 17.413
21 319 287.1 3.541 20.955
Chisq= 20.95 for 20 degrees of freedom, p= 0.60019
SUMMARY of craptest
p-value for no. of wins: 0.978882
p-value for throws/game: 0.600186
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-25_05:31
No. of wins: Observed Expected
98121 98585.9
z-score=-2.079, pvalue=0.01880
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66778 66666.7 0.186 0.186
2 37609 37654.3 0.055 0.240
3 26746 26954.7 1.616 1.857
4 19375 19313.5 0.196 2.053
5 13755 13851.4 0.671 2.724
6 9975 9943.5 0.100 2.824
7 7235 7145.0 1.133 3.957
8 5154 5139.1 0.043 4.000
9 3653 3699.9 0.594 4.594
10 2662 2666.3 0.007 4.601
11 1927 1923.3 0.007 4.608
12 1407 1388.7 0.240 4.848
13 990 1003.7 0.187 5.035
14 756 726.1 1.228 6.263
15 574 525.8 4.412 10.675
16 377 381.2 0.045 10.720
17 262 276.5 0.764 11.484
18 201 200.8 0.000 11.484
19 153 146.0 0.337 11.821
20 101 106.2 0.256 12.078
21 310 287.1 1.824 13.902
Chisq= 13.90 for 20 degrees of freedom, p= 0.16456
SUMMARY of craptest
p-value for no. of wins: 0.018803
p-value for throws/game: 0.164558
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0058,0.0096,0.0145,0.0188,0.0202,0.0261,0.0270,0.0422,0.0437,0.0459,
0.0533,0.0639,0.0706,0.0720,0.0750,0.0753,0.0801,0.0804,0.0911,0.0913,
0.1055,0.1081,0.1114,0.1182,0.1194,0.1226,0.1252,0.1302,0.1332,0.1370,
0.1373,0.1410,0.1431,0.1472,0.1480,0.1485,0.1519,0.1525,0.1551,0.1576,
0.1596,0.1646,0.1651,0.1855,0.1928,0.1959,0.1975,0.2076,0.2112,0.2284,
0.2362,0.2394,0.2429,0.2441,0.2460,0.2491,0.2514,0.2550,0.2561,0.2562,
0.2605,0.2621,0.2638,0.2648,0.2679,0.2680,0.2762,0.2763,0.2868,0.2884,
0.2919,0.2943,0.3040,0.3140,0.3151,0.3200,0.3245,0.3277,0.3284,0.3291,
0.3314,0.3315,0.3402,0.3454,0.3479,0.3559,0.3574,0.3656,0.3660,0.3666,
0.3746,0.3825,0.3851,0.3893,0.3897,0.3908,0.3926,0.3938,0.3952,0.3968,
0.3976,0.4018,0.4052,0.4058,0.4058,0.4094,0.4103,0.4109,0.4151,0.4156,
0.4213,0.4275,0.4320,0.4338,0.4339,0.4366,0.4466,0.4479,0.4511,0.4565,
0.4617,0.4650,0.4666,0.4690,0.4706,0.4718,0.4737,0.4740,0.4777,0.4820,
0.4820,0.4849,0.4877,0.4935,0.4941,0.4947,0.5000,0.5103,0.5105,0.5147,
0.5174,0.5202,0.5250,0.5274,0.5312,0.5361,0.5446,0.5463,0.5499,0.5534,
0.5588,0.5606,0.5612,0.5672,0.5772,0.5791,0.5801,0.5913,0.6002,0.6029,
0.6063,0.6074,0.6078,0.6110,0.6131,0.6158,0.6165,0.6214,0.6286,0.6307,
0.6335,0.6350,0.6483,0.6575,0.6605,0.6616,0.6620,0.6661,0.6683,0.6685,
0.6752,0.6801,0.6812,0.6821,0.6837,0.6875,0.6892,0.6896,0.6958,0.6960,
0.6972,0.7019,0.7025,0.7067,0.7081,0.7084,0.7087,0.7157,0.7185,0.7235,
0.7334,0.7394,0.7402,0.7457,0.7524,0.7575,0.7652,0.7675,0.7712,0.7746,
0.7776,0.7779,0.7799,0.7809,0.7934,0.7935,0.7946,0.8052,0.8072,0.8101,
0.8135,0.8153,0.8191,0.8215,0.8220,0.8229,0.8229,0.8302,0.8427,0.8475,
0.8509,0.8527,0.8549,0.8590,0.8596,0.8678,0.8689,0.8753,0.8786,0.8841,
0.8854,0.8886,0.8919,0.8921,0.8972,0.9146,0.9146,0.9149,0.9153,0.9212,
0.9244,0.9269,0.9284,0.9312,0.9322,0.9367,0.9370,0.9437,0.9462,0.9502,
0.9533,0.9563,0.9694,0.9700,0.9736,0.9789,0.9844,0.9969,0.9988,
Overall p-value after applying KStest on 269 p-values = 0.554290
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.