RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_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 15.40 24.1602 0.884854
2 to 25 15.76 30.1184 0.974496
3 to 26 15.64 23.9326 0.878722
4 to 27 15.86 24.9990 0.905267
5 to 28 15.64 15.7168 0.456006
6 to 29 15.67 28.1580 0.956875
7 to 30 16.00 24.8637 0.902198
8 to 31 15.64 31.6118 0.983192
9 to 32 15.88 18.3444 0.632567
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000132
Tough bday spacings test for dh-ranFile-2018-06-22_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 31 71 105 98 78 64 27 11 8 3
(O-E)^2/E 2.9 0.9 0.1 0.5 0.0 0.0 2.7 0.3 1.0 0.3 0.3
Birthday Spacings: Sum(O-E)^2/E= 8.950, p= 0.463
RESULTS OF GCD FOR dh-ranFile-2018-06-22_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.213398
p-value, dist. of gcd's: 0.252086
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.597 0.351 0.115 0.282 0.535 0.135 0.538 0.133
Bits 8 to 15---> 0.436 0.439 0.061 0.593 0.307 0.969 0.493 0.342
Bits 16 to 23---> 0.424 0.902 0.086 0.590 0.570 0.367 0.549 0.571
Bits 24 to 31---> 0.026 0.951 0.348 0.877 0.497 0.257 0.044 0.314
KS test for the above 32 p values: 0.852
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_08:31,
p-values for 5 runs: 0.5238, 0.1683, 0.2118, 0.4284, 0.3017
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5143 5134.0 0.016 0.288
r= 30 23020 23103.0 0.299 0.586
r= 31 11618 11551.5 0.383 0.969
chi-square = 0.969 with df = 3; p-value = 0.191
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5217 5134.0 1.341 1.613
r= 31 23179 23103.0 0.250 1.863
r= 32 11385 11551.5 2.401 4.264
chi-square = 4.264 with df = 3; p-value = 0.766
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_08:31
b-rank test for bits 1 to 8, p=0.52034
b-rank test for bits 2 to 9, p=0.98810
b-rank test for bits 3 to 10, p=0.88883
b-rank test for bits 4 to 11, p=0.87054
b-rank test for bits 5 to 12, p=0.61420
b-rank test for bits 6 to 13, p=0.19637
b-rank test for bits 7 to 14, p=0.14566
b-rank test for bits 8 to 15, p=0.75100
b-rank test for bits 9 to 16, p=0.23381
b-rank test for bits 10 to 17, p=0.01346
b-rank test for bits 11 to 18, p=0.71179
b-rank test for bits 12 to 19, p=0.87525
b-rank test for bits 13 to 20, p=0.54344
b-rank test for bits 14 to 21, p=0.03067
b-rank test for bits 15 to 22, p=0.34195
b-rank test for bits 16 to 23, p=0.78512
b-rank test for bits 17 to 24, p=0.82735
b-rank test for bits 18 to 25, p=0.29019
b-rank test for bits 19 to 26, p=0.81217
b-rank test for bits 20 to 27, p=0.83960
b-rank test for bits 21 to 28, p=0.78377
b-rank test for bits 22 to 29, p=0.02339
b-rank test for bits 23 to 30, p=0.38534
b-rank test for bits 24 to 31, p=0.35079
b-rank test for bits 25 to 32, p=0.51509
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 = 0.597118
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_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 141334 -1.34 0.089437
2 142628 1.68 0.953437
3 141559 -0.82 0.206528
4 141733 -0.41 0.340175
5 142456 1.28 0.899246
6 141983 0.17 0.568331
7 142403 1.15 0.875634
8 142475 1.32 0.906859
9 142239 0.77 0.779426
10 142325 0.97 0.834274
11 141788 -0.28 0.388404
12 142030 0.28 0.611005
13 141431 -1.12 0.131870
14 142188 0.65 0.742508
15 142189 0.65 0.743262
16 141407 -1.17 0.120264
17 142310 0.94 0.825401
18 141371 -1.26 0.104236
19 141648 -0.61 0.270738
20 141862 -0.11 0.455973
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_08:31
Bits used No. missing words z-score p-value
23 to 32 142026 0.4023 0.656272
22 to 31 142113 0.7023 0.758757
21 to 30 141767 -0.4908 0.311786
20 to 29 141435 -1.6356 0.050960
19 to 28 141940 0.1058 0.542113
18 to 27 142076 0.5747 0.717261
17 to 26 141755 -0.5322 0.297303
16 to 25 141398 -1.7632 0.038933
15 to 24 141910 0.0023 0.500922
14 to 23 141968 0.2023 0.580163
13 to 22 141813 -0.3322 0.369880
12 to 21 142286 1.2989 0.903004
11 to 20 141837 -0.2494 0.401520
10 to 19 142437 1.8196 0.965586
9 to 18 142039 0.4471 0.672612
8 to 17 141793 -0.4011 0.344159
7 to 16 141748 -0.5563 0.288999
6 to 15 141845 -0.2218 0.412224
5 to 14 141886 -0.0804 0.467940
4 to 13 141759 -0.5184 0.302097
3 to 12 142026 0.4023 0.656272
2 to 11 142431 1.7989 0.963980
1 to 10 142169 0.8954 0.814717
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_08:31
Bits used No. missing words z-score p-value
28 to 32 141856 -0.1808 0.428270
27 to 31 141915 0.0192 0.507667
26 to 30 141127 -2.6520 0.004001
25 to 29 142340 1.4599 0.927841
24 to 28 142205 1.0023 0.841894
23 to 27 141399 -1.7299 0.041821
22 to 26 142254 1.1684 0.878672
21 to 25 141811 -0.3333 0.369446
20 to 24 142293 1.3006 0.903298
19 to 23 142177 0.9074 0.817891
18 to 22 141757 -0.5164 0.302797
17 to 21 141711 -0.6723 0.250695
16 to 20 142049 0.4735 0.682057
15 to 19 141873 -0.1232 0.450993
14 to 18 141977 0.2294 0.590717
13 to 17 142133 0.7582 0.775835
12 to 16 141898 -0.0384 0.484682
11 to 15 142628 2.4362 0.992578
10 to 14 142073 0.5548 0.710489
9 to 13 141857 -0.1774 0.429601
8 to 12 141584 -1.1028 0.135054
7 to 11 141722 -0.6350 0.262709
6 to 10 141557 -1.1943 0.116173
5 to 9 142098 0.6396 0.738770
4 to 8 141897 -0.0418 0.483330
3 to 7 141928 0.0633 0.525232
2 to 6 142126 0.7345 0.768670
1 to 5 141496 -1.4011 0.080589
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_08:31
Bits used No. missing words z-score p-value
31 to 32 142246 0.9931 0.839676
30 to 31 141502 -1.2016 0.114766
29 to 30 142075 0.4887 0.687474
28 to 29 141984 0.2203 0.587168
27 to 28 141841 -0.2016 0.420129
26 to 27 141683 -0.6676 0.252182
25 to 26 141345 -1.6647 0.047987
24 to 25 141829 -0.2370 0.406343
23 to 24 142190 0.8279 0.796146
22 to 23 141585 -0.9567 0.169353
21 to 22 141677 -0.6853 0.246565
20 to 21 141989 0.2350 0.592901
19 to 20 141950 0.1200 0.547747
18 to 19 141647 -0.7738 0.219514
17 to 18 142396 1.4356 0.924443
16 to 17 141645 -0.7797 0.217774
15 to 16 141604 -0.9007 0.183880
14 to 15 141525 -1.1337 0.128457
13 to 14 141675 -0.6912 0.244708
12 to 13 142158 0.7335 0.768385
11 to 12 141925 0.0462 0.518434
10 to 11 141431 -1.4110 0.079122
9 to 10 142147 0.7011 0.758377
8 to 9 141696 -0.6293 0.264579
7 to 8 141680 -0.6765 0.249365
6 to 7 142074 0.4858 0.686429
5 to 6 141667 -0.7148 0.237355
4 to 5 142296 1.1406 0.872986
3 to 4 141958 0.1436 0.557080
2 to 3 141993 0.2468 0.597474
1 to 2 142046 0.4032 0.656583
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2402.06 -1.385 0.083009
Test results for specific bytes for dh-ranFile-2018-06-22_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2422.86 -1.091 0.137648
2 to 9 2609.42 1.547 0.939114
3 to 10 2362.05 -1.951 0.025535
4 to 11 2599.48 1.407 0.920258
5 to 12 2527.78 0.393 0.652797
6 to 13 2530.69 0.434 0.667853
7 to 14 2528.37 0.401 0.655872
8 to 15 2523.17 0.328 0.628403
9 to 16 2523.91 0.338 0.632390
10 to 17 2527.95 0.395 0.653698
11 to 18 2570.63 0.999 0.841065
12 to 19 2547.91 0.677 0.750950
13 to 20 2520.26 0.286 0.612740
14 to 21 2440.03 -0.848 0.198171
15 to 22 2615.29 1.631 0.948502
16 to 23 2526.92 0.381 0.648301
17 to 24 2477.17 -0.323 0.373378
18 to 25 2530.92 0.437 0.669047
19 to 26 2495.63 -0.062 0.475352
20 to 27 2479.73 -0.287 0.387188
21 to 28 2611.01 1.570 0.941776
22 to 29 2350.80 -2.110 0.017429
23 to 30 2431.28 -0.972 0.165560
24 to 31 2389.54 -1.562 0.059132
25 to 32 2537.85 0.535 0.703787
CDPARK for dh-ranFile-2018-06-22_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
3535 0.5479 0.708135
3523 0.0000 0.500000
3549 1.1872 0.882429
3532 0.4110 0.659449
3529 0.2740 0.607947
3508 -0.6849 0.246694
3513 -0.4566 0.323972
3527 0.1826 0.572463
3563 1.8265 0.966111
3510 -0.5936 0.276387
Square side=100, avg. no. parked=3528.90 sample std.=16.43
p-value of the KSTEST for those 10 p-values: 0.588310
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_08:31
0.9898,0.0331,0.7795,0.6813,0.9032,0.0326,0.0978,0.7962,0.4166,0.3898,
The KS test for those 10 p-values: 0.476377
The 3DSPHERES test for dh-ranFile-2018-06-22_08:31
sample no r^3 equiv. uni.
1 30.848 0.642377
2 2.217 0.071228
3 7.327 0.216699
4 34.565 0.684049
5 1.159 0.037910
6 47.492 0.794654
7 8.083 0.236179
8 2.840 0.090332
9 52.729 0.827548
10 24.832 0.562962
11 7.138 0.211735
12 84.939 0.941064
13 4.192 0.130401
14 118.855 0.980972
15 35.058 0.689197
16 12.365 0.337787
17 27.908 0.605555
18 0.069 0.002308
19 36.194 0.700751
20 84.271 0.939737
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.560673
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 1.3 -0.1 0.9 -0.6 0.5
1.2 0.8 -0.5 1.5 -0.5 -1.0
-0.7 0.2 -0.0 -0.1 1.4 0.5
0.4 -0.3 -1.4 -0.4 -0.4 -0.4
0.7 0.0 1.0 -0.8 1.1 -0.9
0.2 -1.5 0.6 0.0 0.9 -1.7
-0.2 0.5 -0.8 0.4 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:29.309082
z-score=-1.384693, p-value=0.069351
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_08:31
Test no p-value
1 0.017664
2 0.881695
3 0.475152
4 0.017123
5 0.327993
6 0.830635
7 0.635667
8 0.994894
9 0.631477
10 0.149356
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.475302
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_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 66587 0.10 66563 0.16
3 25000.00 24978 0.02 25139 0.77
4 6666.67 6762 1.36 6593 0.81
5 1388.89 1396 0.04 1411 0.35
6 238.10 237 0.01 267 3.51
7 34.72 31 0.40 24 3.31
8 4.96 8 1.86 2 1.77
p=0.29371 p=0.90140
Number of rngs required: 687900, p-value: 0.281
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_08:31
No. of wins: Observed Expected
98499 98585.9
z-score=-0.388, pvalue=0.34883
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66843 66666.7 0.466 0.466
2 37480 37654.3 0.807 1.273
3 27097 26954.7 0.751 2.024
4 19255 19313.5 0.177 2.201
5 13786 13851.4 0.309 2.510
6 9990 9943.5 0.217 2.727
7 7144 7145.0 0.000 2.727
8 5074 5139.1 0.824 3.551
9 3740 3699.9 0.435 3.987
10 2632 2666.3 0.441 4.428
11 1961 1923.3 0.738 5.166
12 1402 1388.7 0.127 5.292
13 992 1003.7 0.137 5.429
14 707 726.1 0.505 5.934
15 503 525.8 0.992 6.925
16 374 381.2 0.134 7.060
17 291 276.5 0.756 7.816
18 175 200.8 3.322 11.138
19 153 146.0 0.337 11.475
20 101 106.2 0.256 11.731
21 300 287.1 0.578 12.309
Chisq= 12.31 for 20 degrees of freedom, p= 0.09498
SUMMARY of craptest
p-value for no. of wins: 0.348830
p-value for throws/game: 0.094984
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_08:31
No. of wins: Observed Expected
98821 98585.9
z-score= 1.052, pvalue=0.85353
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66651 66666.7 0.004 0.004
2 37510 37654.3 0.553 0.557
3 27062 26954.7 0.427 0.984
4 19395 19313.5 0.344 1.328
5 13942 13851.4 0.592 1.920
6 10047 9943.5 1.076 2.997
7 7020 7145.0 2.188 5.184
8 5059 5139.1 1.248 6.432
9 3759 3699.9 0.945 7.377
10 2664 2666.3 0.002 7.379
11 1919 1923.3 0.010 7.389
12 1391 1388.7 0.004 7.393
13 976 1003.7 0.765 8.158
14 727 726.1 0.001 8.159
15 509 525.8 0.539 8.698
16 381 381.2 0.000 8.698
17 281 276.5 0.072 8.770
18 200 200.8 0.003 8.773
19 137 146.0 0.553 9.326
20 105 106.2 0.014 9.340
21 265 287.1 1.703 11.043
Chisq= 11.04 for 20 degrees of freedom, p= 0.05491
SUMMARY of craptest
p-value for no. of wins: 0.853529
p-value for throws/game: 0.054912
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0023,0.0040,0.0135,0.0171,0.0174,0.0177,0.0234,0.0255,0.0256,
0.0307,0.0326,0.0331,0.0379,0.0389,0.0418,0.0438,0.0480,0.0510,0.0549,
0.0591,0.0612,0.0694,0.0712,0.0791,0.0806,0.0830,0.0863,0.0894,0.0903,
0.0950,0.0978,0.1042,0.1148,0.1148,0.1162,0.1203,0.1285,0.1304,0.1319,
0.1332,0.1351,0.1352,0.1376,0.1457,0.1494,0.1656,0.1683,0.1694,0.1839,
0.1912,0.1964,0.1982,0.2065,0.2117,0.2118,0.2134,0.2167,0.2178,0.2195,
0.2338,0.2362,0.2374,0.2447,0.2466,0.2467,0.2494,0.2507,0.2521,0.2522,
0.2567,0.2627,0.2646,0.2707,0.2764,0.2809,0.2815,0.2890,0.2902,0.2937,
0.2973,0.3017,0.3021,0.3028,0.3067,0.3118,0.3142,0.3240,0.3280,0.3378,
0.3402,0.3419,0.3419,0.3442,0.3476,0.3488,0.3508,0.3514,0.3674,0.3694,
0.3699,0.3734,0.3853,0.3872,0.3884,0.3898,0.4015,0.4063,0.4122,0.4166,
0.4201,0.4243,0.4283,0.4284,0.4296,0.4360,0.4393,0.4510,0.4560,0.4560,
0.4631,0.4679,0.4752,0.4753,0.4754,0.4764,0.4833,0.4847,0.4927,0.4972,
0.5000,0.5009,0.5077,0.5151,0.5184,0.5203,0.5238,0.5252,0.5345,0.5384,
0.5421,0.5434,0.5477,0.5493,0.5571,0.5607,0.5630,0.5683,0.5697,0.5709,
0.5725,0.5802,0.5872,0.5883,0.5904,0.5907,0.5929,0.5930,0.5969,0.5971,
0.5975,0.6056,0.6079,0.6110,0.6127,0.6142,0.6284,0.6315,0.6324,0.6326,
0.6357,0.6424,0.6483,0.6528,0.6537,0.6559,0.6563,0.6563,0.6566,0.6594,
0.6679,0.6690,0.6726,0.6813,0.6821,0.6840,0.6864,0.6875,0.6892,0.7008,
0.7038,0.7081,0.7105,0.7118,0.7173,0.7388,0.7425,0.7433,0.7510,0.7510,
0.7584,0.7588,0.7656,0.7684,0.7687,0.7758,0.7794,0.7795,0.7838,0.7851,
0.7947,0.7961,0.7962,0.8122,0.8147,0.8179,0.8254,0.8274,0.8275,0.8306,
0.8343,0.8396,0.8397,0.8411,0.8419,0.8517,0.8535,0.8705,0.8730,0.8753,
0.8756,0.8770,0.8787,0.8787,0.8817,0.8824,0.8849,0.8888,0.8992,0.9014,
0.9020,0.9022,0.9030,0.9032,0.9033,0.9053,0.9069,0.9203,0.9244,0.9278,
0.9391,0.9397,0.9411,0.9418,0.9485,0.9513,0.9534,0.9569,0.9640,0.9656,
0.9661,0.9688,0.9745,0.9810,0.9832,0.9881,0.9898,0.9926,0.9949,
Overall p-value after applying KStest on 269 p-values = 0.949649
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.