RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.75 10.4282 0.115299
2 to 25 15.94 14.8185 0.391449
3 to 26 15.65 15.4718 0.438464
4 to 27 15.80 13.4932 0.297403
5 to 28 15.81 19.9833 0.724914
6 to 29 15.51 29.2016 0.967288
7 to 30 15.98 16.0871 0.482334
8 to 31 15.76 22.3776 0.829368
9 to 32 15.70 16.7009 0.525199
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.915108
Tough bday spacings test for dh-ranFile-2018-06-17_04:31: 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 10 33 68 105 99 91 37 38 9 10 0
(O-E)^2/E 0.1 0.4 0.4 0.5 0.0 2.1 4.4 2.3 2.3 1.7 4.1
Birthday Spacings: Sum(O-E)^2/E= 18.270, p= 0.949
RESULTS OF GCD FOR dh-ranFile-2018-06-17_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.360480
p-value, dist. of gcd's: 0.778146
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.447 0.034 0.044 0.794 0.482 0.327 0.454 0.599
Bits 8 to 15---> 0.052 0.576 0.175 0.101 0.046 0.290 0.966 0.553
Bits 16 to 23---> 0.142 0.885 0.137 0.849 0.866 0.016 0.631 0.660
Bits 24 to 31---> 0.264 0.295 0.039 0.907 0.165 0.953 0.012 0.697
KS test for the above 32 p values: 0.931
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_04:31,
p-values for 5 runs: 0.1118, 0.8733, 0.3513, 0.7011, 0.4858
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5136 5134.0 0.001 0.196
r= 30 22983 23103.0 0.624 0.819
r= 31 11676 11551.5 1.341 2.161
chi-square = 2.161 with df = 3; p-value = 0.460
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5204 5134.0 0.954 1.289
r= 31 23357 23103.0 2.791 4.081
r= 32 11236 11551.5 8.618 12.699
chi-square = 12.699 with df = 3; p-value = 0.995
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_04:31
b-rank test for bits 1 to 8, p=0.00700
b-rank test for bits 2 to 9, p=0.68530
b-rank test for bits 3 to 10, p=0.90286
b-rank test for bits 4 to 11, p=0.31833
b-rank test for bits 5 to 12, p=0.26346
b-rank test for bits 6 to 13, p=0.53807
b-rank test for bits 7 to 14, p=0.30923
b-rank test for bits 8 to 15, p=0.36338
b-rank test for bits 9 to 16, p=0.91860
b-rank test for bits 10 to 17, p=0.78084
b-rank test for bits 11 to 18, p=0.89155
b-rank test for bits 12 to 19, p=0.64165
b-rank test for bits 13 to 20, p=0.41799
b-rank test for bits 14 to 21, p=0.39462
b-rank test for bits 15 to 22, p=0.02184
b-rank test for bits 16 to 23, p=0.32100
b-rank test for bits 17 to 24, p=0.43380
b-rank test for bits 18 to 25, p=0.85785
b-rank test for bits 19 to 26, p=0.30147
b-rank test for bits 20 to 27, p=0.97634
b-rank test for bits 21 to 28, p=0.86153
b-rank test for bits 22 to 29, p=0.70366
b-rank test for bits 23 to 30, p=0.15580
b-rank test for bits 24 to 31, p=0.66121
b-rank test for bits 25 to 32, p=0.70278
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 = 0.700651
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_04:31
(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 141918 0.02 0.508081
2 141960 0.12 0.547120
3 142183 0.64 0.738724
4 142181 0.63 0.737202
5 141842 -0.16 0.437499
6 141460 -1.05 0.146897
7 140985 -2.16 0.015400
8 141266 -1.50 0.066406
9 142027 0.27 0.608315
10 141671 -0.56 0.288816
11 142819 2.13 0.983223
12 141699 -0.49 0.311563
13 142208 0.70 0.757357
14 141655 -0.59 0.276180
15 142573 1.55 0.939505
16 141120 -1.84 0.032575
17 142055 0.34 0.633204
18 141601 -0.72 0.235640
19 141674 -0.55 0.291216
20 141791 -0.28 0.391093
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_04:31
Bits used No. missing words z-score p-value
23 to 32 142085 0.6058 0.727663
22 to 31 142356 1.5402 0.938249
21 to 30 142027 0.4058 0.657540
20 to 29 141745 -0.5667 0.285474
19 to 28 141566 -1.1839 0.118227
18 to 27 141930 0.0713 0.528411
17 to 26 141816 -0.3218 0.373792
16 to 25 141652 -0.8873 0.187447
15 to 24 142298 1.3402 0.909917
14 to 23 142014 0.3609 0.640925
13 to 22 141875 -0.1184 0.452884
12 to 21 142193 0.9782 0.836006
11 to 20 141681 -0.7873 0.215540
10 to 19 141754 -0.5356 0.296110
9 to 18 141648 -0.9011 0.183758
8 to 17 141922 0.0437 0.517424
7 to 16 141923 0.0471 0.518798
6 to 15 141807 -0.3529 0.362096
5 to 14 142011 0.3506 0.637051
4 to 13 141842 -0.2322 0.408202
3 to 12 142348 1.5127 0.934816
2 to 11 141813 -0.3322 0.369880
1 to 10 142432 1.8023 0.964252
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_04:31
Bits used No. missing words z-score p-value
28 to 32 141794 -0.3909 0.347917
27 to 31 141402 -1.7198 0.042738
26 to 30 141643 -0.9028 0.183312
25 to 29 141738 -0.5808 0.280695
24 to 28 141569 -1.1537 0.124320
23 to 27 142043 0.4531 0.674768
22 to 26 142247 1.1446 0.873822
21 to 25 142225 1.0701 0.857706
20 to 24 142015 0.3582 0.639905
19 to 23 141980 0.2396 0.594664
18 to 22 142136 0.7684 0.778867
17 to 21 141253 -2.2248 0.013046
16 to 20 141869 -0.1367 0.445629
15 to 19 141722 -0.6350 0.262709
14 to 18 141530 -1.2859 0.099245
13 to 17 142316 1.3785 0.915982
12 to 16 141350 -1.8960 0.028978
11 to 15 141616 -0.9943 0.160029
10 to 14 141978 0.2328 0.592034
9 to 13 142344 1.4735 0.929686
8 to 12 142174 0.8972 0.815190
7 to 11 141582 -1.1096 0.133587
6 to 10 141494 -1.4079 0.079581
5 to 9 141821 -0.2994 0.382308
4 to 8 142057 0.5006 0.691665
3 to 7 142311 1.3616 0.913337
2 to 6 142150 0.8158 0.792702
1 to 5 141981 0.2429 0.595978
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_04:31
Bits used No. missing words z-score p-value
31 to 32 141991 0.2409 0.595189
30 to 31 141690 -0.6470 0.258819
29 to 30 141752 -0.4641 0.321288
28 to 29 141698 -0.6234 0.266513
27 to 28 142049 0.4120 0.659832
26 to 27 141731 -0.5260 0.299428
25 to 26 141452 -1.3491 0.088660
24 to 25 141789 -0.3550 0.361311
23 to 24 141627 -0.8328 0.202470
22 to 23 141955 0.1347 0.553583
21 to 22 142393 1.4268 0.923175
20 to 21 141963 0.1583 0.562897
19 to 20 141759 -0.4435 0.328720
18 to 19 141858 -0.1514 0.439824
17 to 18 141844 -0.1927 0.423592
16 to 17 141535 -1.1042 0.134749
15 to 16 142258 1.0285 0.848149
14 to 15 141842 -0.1986 0.421283
13 to 14 141941 0.0934 0.537216
12 to 13 141517 -1.1573 0.123572
11 to 12 141946 0.1082 0.543070
10 to 11 142528 1.8250 0.965998
9 to 10 141683 -0.6676 0.252182
8 to 9 141954 0.1318 0.552417
7 to 8 142087 0.5241 0.699896
6 to 7 142092 0.5388 0.705005
5 to 6 142206 0.8751 0.809249
4 to 5 141932 0.0669 0.526659
3 to 4 141825 -0.2488 0.401773
2 to 3 141328 -1.7148 0.043188
1 to 2 142191 0.8309 0.796981
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2537.51 0.531 0.702122
Test results for specific bytes for dh-ranFile-2018-06-17_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2421.97 -1.104 0.134896
2 to 9 2555.61 0.786 0.784185
3 to 10 2545.65 0.646 0.740720
4 to 11 2495.45 -0.064 0.474372
5 to 12 2531.40 0.444 0.671508
6 to 13 2486.38 -0.193 0.423617
7 to 14 2547.64 0.674 0.749736
8 to 15 2373.03 -1.796 0.036273
9 to 16 2446.32 -0.759 0.223870
10 to 17 2544.42 0.628 0.735069
11 to 18 2518.30 0.259 0.602108
12 to 19 2667.13 2.364 0.990951
13 to 20 2464.08 -0.508 0.305723
14 to 21 2557.80 0.817 0.793154
15 to 22 2691.80 2.712 0.996660
16 to 23 2466.14 -0.479 0.316037
17 to 24 2388.92 -1.571 0.058094
18 to 25 2673.77 2.458 0.993005
19 to 26 2491.32 -0.123 0.451171
20 to 27 2616.23 1.644 0.949891
21 to 28 2507.02 0.099 0.539518
22 to 29 2542.99 0.608 0.728415
23 to 30 2544.57 0.630 0.735759
24 to 31 2509.87 0.140 0.555524
25 to 32 2475.97 -0.340 0.366999
CDPARK for dh-ranFile-2018-06-17_04:31: 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
3529 0.2740 0.607947
3507 -0.7306 0.232514
3533 0.4566 0.676028
3511 -0.5479 0.291865
3532 0.4110 0.659449
3524 0.0457 0.518210
3507 -0.7306 0.232514
3505 -0.8219 0.205562
3569 2.1005 0.982156
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3523.30 sample std.=18.34
p-value of the KSTEST for those 10 p-values: 0.641920
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_04:31
0.6246,0.0992,0.8817,0.2121,0.6166,0.6409,0.6741,0.5968,0.2257,0.4407,
The KS test for those 10 p-values: 0.694419
The 3DSPHERES test for dh-ranFile-2018-06-17_04:31
sample no r^3 equiv. uni.
1 4.297 0.133452
2 30.127 0.633672
3 80.584 0.931856
4 6.468 0.193940
5 79.811 0.930077
6 45.905 0.783498
7 31.412 0.649038
8 18.435 0.459081
9 73.207 0.912860
10 7.103 0.210829
11 19.491 0.477800
12 4.496 0.139164
13 98.606 0.962629
14 16.400 0.421129
15 17.723 0.446093
16 7.140 0.211785
17 24.495 0.558026
18 12.472 0.340134
19 34.889 0.687447
20 78.248 0.926338
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.536306
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.2 -1.1 0.5 -0.8 0.8
-0.9 -1.2 0.8 1.0 -1.3 -0.3
1.7 -0.5 0.1 -1.6 -0.7 -0.3
-0.6 1.6 1.3 -0.1 1.0 -1.5
-0.8 -0.1 0.6 0.8 -0.3 -0.2
0.1 2.8 1.4 0.8 -2.0 -0.3
-1.4 1.5 3.0 -1.3 -0.6 0.0
1.8
Chi-square with 42 degrees of freedom:58.834263
z-score=1.836769, p-value=0.956099
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_04:31
Test no p-value
1 0.386530
2 0.399779
3 0.361299
4 0.960378
5 0.179852
6 0.212209
7 0.031911
8 0.055418
9 0.156407
10 0.254706
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.032338
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_04:31:
(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 66597 0.07 66475 0.55
3 25000.00 25020 0.02 24957 0.07
4 6666.67 6683 0.04 6837 4.35
5 1388.89 1413 0.42 1465 4.17
6 238.10 244 0.15 229 0.35
7 34.72 39 0.53 35 0.00
8 4.96 3 0.77 1 3.16
p=0.07992 p=0.95122
Number of rngs required: 688222, p-value: 0.418
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_04:31
No. of wins: Observed Expected
98251 98585.9
z-score=-1.498, pvalue=0.06711
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66438 66666.7 0.784 0.784
2 37953 37654.3 2.369 3.153
3 26888 26954.7 0.165 3.319
4 19261 19313.5 0.143 3.461
5 14034 13851.4 2.407 5.868
6 9808 9943.5 1.848 7.715
7 7127 7145.0 0.045 7.761
8 5070 5139.1 0.928 8.689
9 3838 3699.9 5.157 13.847
10 2655 2666.3 0.048 13.894
11 1869 1923.3 1.535 15.429
12 1370 1388.7 0.253 15.682
13 1029 1003.7 0.637 16.319
14 720 726.1 0.052 16.371
15 512 525.8 0.364 16.735
16 392 381.2 0.309 17.044
17 279 276.5 0.022 17.066
18 196 200.8 0.116 17.182
19 137 146.0 0.553 17.735
20 107 106.2 0.006 17.741
21 317 287.1 3.111 20.851
Chisq= 20.85 for 20 degrees of freedom, p= 0.59408
SUMMARY of craptest
p-value for no. of wins: 0.067108
p-value for throws/game: 0.594077
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_04:31
No. of wins: Observed Expected
98206 98585.9
z-score=-1.699, pvalue=0.04466
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66464 66666.7 0.616 0.616
2 38094 37654.3 5.134 5.750
3 26728 26954.7 1.907 7.657
4 19151 19313.5 1.367 9.024
5 13891 13851.4 0.113 9.137
6 9885 9943.5 0.345 9.482
7 7231 7145.0 1.035 10.516
8 5189 5139.1 0.485 11.001
9 3685 3699.9 0.060 11.061
10 2771 2666.3 4.112 15.173
11 1934 1923.3 0.059 15.232
12 1392 1388.7 0.008 15.239
13 1009 1003.7 0.028 15.267
14 684 726.1 2.446 17.713
15 504 525.8 0.907 18.620
16 378 381.2 0.026 18.646
17 263 276.5 0.663 19.308
18 204 200.8 0.050 19.359
19 145 146.0 0.007 19.365
20 103 106.2 0.097 19.462
21 295 287.1 0.217 19.679
Chisq= 19.68 for 20 degrees of freedom, p= 0.52184
SUMMARY of craptest
p-value for no. of wins: 0.044664
p-value for throws/game: 0.521842
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0070,0.0122,0.0130,0.0154,0.0156,0.0218,0.0290,0.0319,0.0323,0.0326,
0.0335,0.0363,0.0391,0.0427,0.0432,0.0443,0.0447,0.0456,0.0522,0.0554,
0.0581,0.0664,0.0671,0.0796,0.0799,0.0887,0.0992,0.0992,0.1010,0.1118,
0.1153,0.1182,0.1236,0.1243,0.1335,0.1336,0.1347,0.1349,0.1374,0.1392,
0.1418,0.1469,0.1558,0.1564,0.1600,0.1648,0.1746,0.1799,0.1833,0.1838,
0.1874,0.1939,0.2025,0.2056,0.2108,0.2118,0.2121,0.2122,0.2155,0.2239,
0.2257,0.2325,0.2325,0.2356,0.2522,0.2547,0.2588,0.2627,0.2635,0.2641,
0.2665,0.2762,0.2807,0.2855,0.2888,0.2896,0.2912,0.2919,0.2953,0.2961,
0.2974,0.2994,0.3015,0.3057,0.3092,0.3116,0.3160,0.3183,0.3210,0.3213,
0.3273,0.3287,0.3401,0.3479,0.3513,0.3605,0.3613,0.3613,0.3621,0.3634,
0.3670,0.3699,0.3738,0.3746,0.3823,0.3865,0.3911,0.3914,0.3946,0.3998,
0.4018,0.4082,0.4175,0.4180,0.4211,0.4213,0.4236,0.4236,0.4338,0.4375,
0.4385,0.4398,0.4407,0.4456,0.4461,0.4473,0.4512,0.4529,0.4541,0.4591,
0.4603,0.4744,0.4778,0.4815,0.4823,0.4858,0.5081,0.5174,0.5182,0.5188,
0.5218,0.5252,0.5267,0.5284,0.5363,0.5372,0.5381,0.5395,0.5431,0.5471,
0.5524,0.5527,0.5536,0.5555,0.5580,0.5629,0.5762,0.5920,0.5941,0.5947,
0.5952,0.5960,0.5968,0.5994,0.6021,0.6079,0.6083,0.6166,0.6246,0.6315,
0.6332,0.6337,0.6371,0.6399,0.6409,0.6409,0.6416,0.6419,0.6490,0.6575,
0.6594,0.6598,0.6603,0.6612,0.6715,0.6741,0.6748,0.6760,0.6853,0.6874,
0.6917,0.6944,0.6974,0.6999,0.7007,0.7011,0.7021,0.7028,0.7037,0.7050,
0.7249,0.7277,0.7284,0.7351,0.7358,0.7372,0.7387,0.7407,0.7497,0.7574,
0.7781,0.7789,0.7808,0.7835,0.7842,0.7927,0.7932,0.7945,0.7970,0.8092,
0.8152,0.8294,0.8360,0.8481,0.8495,0.8577,0.8578,0.8615,0.8659,0.8733,
0.8738,0.8817,0.8854,0.8915,0.9029,0.9066,0.9099,0.9129,0.9133,0.9151,
0.9160,0.9186,0.9232,0.9263,0.9297,0.9301,0.9310,0.9319,0.9348,0.9382,
0.9395,0.9494,0.9499,0.9512,0.9526,0.9561,0.9604,0.9626,0.9643,0.9660,
0.9664,0.9673,0.9763,0.9822,0.9832,0.9910,0.9930,0.9947,0.9967,
Overall p-value after applying KStest on 269 p-values = 0.889143
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.