RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.63 18.9105 0.666306
2 to 25 15.71 24.0115 0.880878
3 to 26 15.98 18.7925 0.659430
4 to 27 16.05 29.2678 0.967865
5 to 28 16.03 13.4498 0.294405
6 to 29 15.85 19.3075 0.688830
7 to 30 15.82 22.3265 0.827514
8 to 31 15.85 31.2822 0.981550
9 to 32 15.71 19.0568 0.674717
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.017204
Tough bday spacings test for dh-ranFile-2018-06-23_00:31: 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 11 40 78 88 90 90 48 32 14 5 4
(O-E)^2/E 0.4 0.3 0.3 1.0 0.6 1.8 0.3 0.2 0.1 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.286, p= 0.129
RESULTS OF GCD FOR dh-ranFile-2018-06-23_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.786414
p-value, dist. of gcd's: 0.950468
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.270 0.160 0.713 0.760 0.704 0.387 0.117 0.311
Bits 8 to 15---> 0.193 0.570 0.096 0.513 0.404 0.046 0.803 0.407
Bits 16 to 23---> 0.903 0.575 0.410 0.763 0.108 0.059 0.489 0.713
Bits 24 to 31---> 0.433 0.585 0.930 0.677 0.108 0.501 0.981 0.358
KS test for the above 32 p values: 0.203
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_00:31,
p-values for 5 runs: 0.2614, 0.4221, 0.0602, 0.7633, 0.8159
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 230 211.4 1.633 1.633
r= 29 5119 5134.0 0.044 1.677
r= 30 23090 23103.0 0.007 1.684
r= 31 11561 11551.5 0.008 1.692
chi-square = 1.692 with df = 3; p-value = 0.361
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5100 5134.0 0.225 0.226
r= 31 23044 23103.0 0.151 0.377
r= 32 11645 11551.5 0.756 1.133
chi-square = 1.133 with df = 3; p-value = 0.231
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_00:31
b-rank test for bits 1 to 8, p=0.48147
b-rank test for bits 2 to 9, p=0.14849
b-rank test for bits 3 to 10, p=0.85940
b-rank test for bits 4 to 11, p=0.27015
b-rank test for bits 5 to 12, p=0.32948
b-rank test for bits 6 to 13, p=0.34112
b-rank test for bits 7 to 14, p=0.18499
b-rank test for bits 8 to 15, p=0.55219
b-rank test for bits 9 to 16, p=0.31760
b-rank test for bits 10 to 17, p=0.28398
b-rank test for bits 11 to 18, p=0.27888
b-rank test for bits 12 to 19, p=0.26931
b-rank test for bits 13 to 20, p=0.38577
b-rank test for bits 14 to 21, p=0.74975
b-rank test for bits 15 to 22, p=0.95857
b-rank test for bits 16 to 23, p=0.95164
b-rank test for bits 17 to 24, p=0.24595
b-rank test for bits 18 to 25, p=0.73303
b-rank test for bits 19 to 26, p=0.17110
b-rank test for bits 20 to 27, p=0.17859
b-rank test for bits 21 to 28, p=0.84045
b-rank test for bits 22 to 29, p=0.60959
b-rank test for bits 23 to 30, p=0.55963
b-rank test for bits 24 to 31, p=0.41445
b-rank test for bits 25 to 32, p=0.40085
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 = 0.276611
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_00:31
(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 141835 -0.17 0.431063
2 141532 -0.88 0.188993
3 142207 0.70 0.756626
4 141908 -0.00 0.498760
5 142240 0.77 0.780119
6 142066 0.37 0.642837
7 142471 1.31 0.905293
8 141870 -0.09 0.463392
9 142011 0.24 0.593884
10 141698 -0.49 0.310737
11 142163 0.59 0.723305
12 141635 -0.64 0.260775
13 142458 1.28 0.900068
14 141709 -0.47 0.319871
15 142273 0.85 0.802253
16 141945 0.08 0.533210
17 141857 -0.12 0.451344
18 142768 2.01 0.977585
19 141139 -1.80 0.035943
20 142753 1.97 0.975649
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_00:31
Bits used No. missing words z-score p-value
23 to 32 142095 0.6402 0.738992
22 to 31 141953 0.1506 0.559849
21 to 30 141782 -0.4391 0.330306
20 to 29 142123 0.7368 0.769376
19 to 28 141920 0.0368 0.514675
18 to 27 142462 1.9058 0.971659
17 to 26 141967 0.1989 0.578815
16 to 25 141858 -0.1770 0.429754
15 to 24 141408 -1.7287 0.041929
14 to 23 142135 0.7782 0.781766
13 to 22 142143 0.8058 0.789809
12 to 21 141902 -0.0253 0.489918
11 to 20 142128 0.7540 0.774586
10 to 19 142016 0.3678 0.643499
9 to 18 141514 -1.3632 0.086409
8 to 17 142089 0.6196 0.732224
7 to 16 142332 1.4575 0.927508
6 to 15 141961 0.1782 0.570706
5 to 14 141356 -1.9080 0.028193
4 to 13 141805 -0.3598 0.359514
3 to 12 142769 2.9644 0.998484
2 to 11 142208 1.0299 0.848471
1 to 10 141698 -0.7287 0.233085
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_00:31
Bits used No. missing words z-score p-value
28 to 32 142031 0.4124 0.659992
27 to 31 141274 -2.1537 0.015633
26 to 30 142129 0.7446 0.771757
25 to 29 141718 -0.6486 0.258306
24 to 28 142060 0.5107 0.695236
23 to 27 141530 -1.2859 0.099245
22 to 26 142392 1.6362 0.949098
21 to 25 142066 0.5311 0.702320
20 to 24 141994 0.2870 0.612950
19 to 23 141823 -0.2926 0.384897
18 to 22 142016 0.3616 0.641172
17 to 21 141850 -0.2011 0.420303
16 to 20 142124 0.7277 0.766600
15 to 19 141802 -0.3638 0.357992
14 to 18 141906 -0.0113 0.495497
13 to 17 142152 0.8226 0.794635
12 to 16 141250 -2.2350 0.012708
11 to 15 142191 0.9548 0.830164
10 to 14 142053 0.4870 0.686877
9 to 13 142545 2.1548 0.984412
8 to 12 141749 -0.5435 0.293396
7 to 11 141880 -0.0994 0.460401
6 to 10 142176 0.9040 0.816993
5 to 9 141776 -0.4520 0.325647
4 to 8 142013 0.3514 0.637365
3 to 7 141429 -1.6282 0.051737
2 to 6 141778 -0.4452 0.328093
1 to 5 141909 -0.0011 0.499554
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_00:31
Bits used No. missing words z-score p-value
31 to 32 141832 -0.2281 0.409780
30 to 31 141528 -1.1249 0.130323
29 to 30 142150 0.7099 0.761130
28 to 29 142376 1.3766 0.915683
27 to 28 141747 -0.4788 0.316023
26 to 27 141756 -0.4523 0.325526
25 to 26 141499 -1.2104 0.113060
24 to 25 141901 -0.0246 0.490198
23 to 24 142399 1.4445 0.925694
22 to 23 141825 -0.2488 0.401773
21 to 22 141824 -0.2517 0.400632
20 to 21 142155 0.7247 0.765679
19 to 20 141649 -0.7679 0.221263
18 to 19 141531 -1.1160 0.132207
17 to 18 141877 -0.0954 0.462011
16 to 17 141623 -0.8446 0.199158
15 to 16 141914 0.0138 0.505496
14 to 15 142051 0.4179 0.661992
13 to 14 141856 -0.1573 0.437498
12 to 13 142080 0.5035 0.692677
11 to 12 141386 -1.5437 0.061325
10 to 11 141587 -0.9508 0.170846
9 to 10 141932 0.0669 0.526659
8 to 9 141983 0.2173 0.586019
7 to 8 142241 0.9784 0.836056
6 to 7 141691 -0.6440 0.259774
5 to 6 141986 0.2262 0.589464
4 to 5 142160 0.7394 0.770180
3 to 4 142125 0.6362 0.737675
2 to 3 141953 0.1288 0.551250
1 to 2 142759 2.5064 0.993902
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2515.78 0.223 0.588313
Test results for specific bytes for dh-ranFile-2018-06-23_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2597.67 1.381 0.916393
2 to 9 2466.86 -0.469 0.319628
3 to 10 2460.27 -0.562 0.287080
4 to 11 2496.57 -0.049 0.480631
5 to 12 2369.04 -1.852 0.032012
6 to 13 2493.06 -0.098 0.460907
7 to 14 2488.58 -0.162 0.435832
8 to 15 2601.87 1.441 0.925164
9 to 16 2600.24 1.418 0.921844
10 to 17 2361.88 -1.953 0.025393
11 to 18 2616.93 1.654 0.950893
12 to 19 2378.67 -1.716 0.043092
13 to 20 2578.64 1.112 0.866970
14 to 21 2410.34 -1.268 0.102394
15 to 22 2464.88 -0.497 0.309696
16 to 23 2428.17 -1.016 0.154845
17 to 24 2386.58 -1.604 0.054361
18 to 25 2504.21 0.060 0.523764
19 to 26 2472.26 -0.392 0.347436
20 to 27 2515.88 0.225 0.588848
21 to 28 2608.91 1.540 0.938241
22 to 29 2572.55 1.026 0.847540
23 to 30 2566.85 0.945 0.827776
24 to 31 2567.65 0.957 0.830632
25 to 32 2495.67 -0.061 0.475601
CDPARK for dh-ranFile-2018-06-23_00:31: 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
3520 -0.1370 0.445521
3540 0.7763 0.781201
3543 0.9132 0.819442
3541 0.8219 0.794438
3537 0.6393 0.738676
3519 -0.1826 0.427537
3529 0.2740 0.607947
3509 -0.6393 0.261324
3559 1.6438 0.949895
3550 1.2329 0.891189
Square side=100, avg. no. parked=3534.70 sample std.=14.57
p-value of the KSTEST for those 10 p-values: 0.094544
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_00:31
0.8806,0.4766,0.6164,0.8526,0.4628,0.6427,0.8140,0.6555,0.6612,0.7088,
The KS test for those 10 p-values: 0.041426
The 3DSPHERES test for dh-ranFile-2018-06-23_00:31
sample no r^3 equiv. uni.
1 2.396 0.076746
2 17.359 0.439336
3 18.096 0.452936
4 33.080 0.668020
5 15.541 0.404307
6 40.169 0.737887
7 25.232 0.568749
8 27.935 0.605902
9 44.998 0.776857
10 13.175 0.355417
11 23.380 0.541290
12 30.230 0.634936
13 15.381 0.401131
14 77.878 0.925424
15 23.383 0.541329
16 19.568 0.479129
17 10.916 0.305025
18 19.907 0.484989
19 22.951 0.534685
20 5.333 0.162869
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.180200
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 2.2 -1.8 0.9 -0.5 -0.4
2.1 0.5 -0.8 0.3 -0.4 0.2
0.1 1.4 0.1 0.8 0.3 -1.7
0.9 -0.0 -0.6 -0.5 0.8 -1.7
-0.5 -0.0 -0.1 0.4 0.8 0.4
-1.6 -1.5 1.5 -0.5 0.1 -0.3
-0.5 0.5 0.1 0.4 0.9 -1.0
0.8
Chi-square with 42 degrees of freedom:36.954001
z-score=-0.550564, p-value=0.308282
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_00:31
Test no p-value
1 0.962361
2 0.439077
3 0.347710
4 0.284960
5 0.018470
6 0.468859
7 0.502224
8 0.922529
9 0.308146
10 0.138902
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.579128
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_00:31:
(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 66784 0.21 66647 0.01
3 25000.00 24984 0.01 24947 0.11
4 6666.67 6576 1.23 6747 0.97
5 1388.89 1385 0.01 1379 0.07
6 238.10 231 0.21 233 0.11
7 34.72 37 0.15 40 0.80
8 4.96 2 1.77 6 0.22
p=0.26783 p=0.10845
Number of rngs required: 688704, p-value: 0.636
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_00:31
No. of wins: Observed Expected
98360 98585.9
z-score=-1.010, pvalue=0.15621
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66388 66666.7 1.165 1.165
2 37703 37654.3 0.063 1.228
3 27107 26954.7 0.860 2.088
4 19357 19313.5 0.098 2.186
5 13824 13851.4 0.054 2.240
6 9965 9943.5 0.046 2.287
7 7185 7145.0 0.224 2.510
8 5177 5139.1 0.280 2.790
9 3704 3699.9 0.005 2.795
10 2642 2666.3 0.221 3.016
11 1888 1923.3 0.649 3.665
12 1401 1388.7 0.108 3.773
13 996 1003.7 0.059 3.833
14 740 726.1 0.265 4.097
15 514 525.8 0.266 4.364
16 374 381.2 0.134 4.498
17 275 276.5 0.009 4.506
18 190 200.8 0.584 5.090
19 148 146.0 0.028 5.118
20 119 106.2 1.539 6.657
21 303 287.1 0.879 7.536
Chisq= 7.54 for 20 degrees of freedom, p= 0.00548
SUMMARY of craptest
p-value for no. of wins: 0.156207
p-value for throws/game: 0.005481
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_00:31
No. of wins: Observed Expected
98406 98585.9
z-score=-0.804, pvalue=0.21057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66865 66666.7 0.590 0.590
2 37949 37654.3 2.306 2.896
3 26768 26954.7 1.294 4.190
4 19141 19313.5 1.540 5.730
5 13796 13851.4 0.222 5.952
6 9991 9943.5 0.226 6.178
7 7159 7145.0 0.027 6.205
8 5168 5139.1 0.163 6.368
9 3655 3699.9 0.544 6.912
10 2664 2666.3 0.002 6.914
11 1860 1923.3 2.085 8.999
12 1352 1388.7 0.972 9.971
13 1031 1003.7 0.742 10.713
14 708 726.1 0.453 11.166
15 477 525.8 4.536 15.702
16 394 381.2 0.433 16.135
17 249 276.5 2.743 18.878
18 197 200.8 0.073 18.951
19 151 146.0 0.172 19.123
20 101 106.2 0.256 19.379
21 324 287.1 4.739 24.118
Chisq= 24.12 for 20 degrees of freedom, p= 0.76272
SUMMARY of craptest
p-value for no. of wins: 0.210574
p-value for throws/game: 0.762717
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0055,0.0127,0.0156,0.0172,0.0185,0.0254,0.0282,0.0320,0.0359,0.0414,
0.0419,0.0431,0.0459,0.0517,0.0544,0.0593,0.0602,0.0613,0.0767,0.0864,
0.0945,0.0964,0.0992,0.1024,0.1083,0.1083,0.1085,0.1131,0.1166,0.1288,
0.1303,0.1322,0.1389,0.1485,0.1548,0.1562,0.1602,0.1629,0.1708,0.1711,
0.1786,0.1802,0.1850,0.1890,0.1930,0.1992,0.2033,0.2106,0.2213,0.2310,
0.2331,0.2460,0.2583,0.2598,0.2608,0.2613,0.2614,0.2678,0.2693,0.2696,
0.2701,0.2766,0.2789,0.2840,0.2850,0.2871,0.2934,0.2944,0.3050,0.3081,
0.3083,0.3097,0.3107,0.3113,0.3160,0.3176,0.3196,0.3199,0.3255,0.3256,
0.3281,0.3295,0.3303,0.3411,0.3474,0.3477,0.3554,0.3580,0.3584,0.3595,
0.3613,0.3849,0.3858,0.3866,0.4006,0.4008,0.4011,0.4018,0.4037,0.4043,
0.4074,0.4098,0.4104,0.4145,0.4203,0.4221,0.4275,0.4298,0.4311,0.4327,
0.4358,0.4375,0.4391,0.4393,0.4455,0.4513,0.4529,0.4604,0.4609,0.4620,
0.4628,0.4634,0.4689,0.4756,0.4766,0.4791,0.4806,0.4815,0.4850,0.4887,
0.4899,0.4902,0.4955,0.4988,0.4996,0.5014,0.5022,0.5055,0.5130,0.5147,
0.5238,0.5267,0.5332,0.5347,0.5413,0.5413,0.5513,0.5522,0.5596,0.5598,
0.5687,0.5701,0.5707,0.5749,0.5788,0.5791,0.5849,0.5860,0.5883,0.5888,
0.5895,0.5939,0.6059,0.6079,0.6096,0.6130,0.6164,0.6349,0.6355,0.6374,
0.6412,0.6427,0.6428,0.6435,0.6555,0.6594,0.6600,0.6612,0.6620,0.6663,
0.6680,0.6747,0.6765,0.6869,0.6888,0.6927,0.6952,0.7023,0.7043,0.7088,
0.7129,0.7132,0.7233,0.7322,0.7330,0.7377,0.7379,0.7387,0.7390,0.7497,
0.7566,0.7599,0.7611,0.7627,0.7633,0.7634,0.7657,0.7666,0.7694,0.7702,
0.7718,0.7746,0.7769,0.7801,0.7812,0.7818,0.7864,0.7898,0.7944,0.7946,
0.8023,0.8034,0.8140,0.8159,0.8170,0.8194,0.8275,0.8278,0.8302,0.8306,
0.8361,0.8405,0.8475,0.8485,0.8526,0.8594,0.8670,0.8806,0.8809,0.8912,
0.9001,0.9029,0.9053,0.9157,0.9164,0.9218,0.9225,0.9252,0.9254,0.9257,
0.9275,0.9296,0.9382,0.9491,0.9499,0.9505,0.9509,0.9516,0.9586,0.9624,
0.9679,0.9717,0.9756,0.9776,0.9811,0.9816,0.9844,0.9939,0.9985,
Overall p-value after applying KStest on 269 p-values = 0.515366
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.