RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.72 10.9948 0.143166
2 to 25 16.18 11.5326 0.172426
3 to 26 15.50 21.2087 0.782908
4 to 27 15.95 34.1807 0.992044
5 to 28 15.99 12.3468 0.221301
6 to 29 15.70 17.6260 0.587205
7 to 30 15.90 13.1014 0.270629
8 to 31 15.49 21.4487 0.793138
9 to 32 15.19 33.1673 0.989266
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.264906
Tough bday spacings test for dh-ranFile-2018-06-19_14:31: 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 31 70 99 98 83 50 34 14 4 7
(O-E)^2/E 0.1 0.9 0.1 0.0 0.0 0.3 0.1 0.6 0.1 1.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 5.298, p= 0.130
RESULTS OF GCD FOR dh-ranFile-2018-06-19_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.809530
p-value, dist. of gcd's: 0.727049
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.152 0.205 0.908 0.670 0.940 0.410 0.286 0.225
Bits 8 to 15---> 0.723 0.088 0.155 0.303 0.931 0.530 0.398 0.669
Bits 16 to 23---> 0.764 0.656 0.534 0.177 0.333 0.276 0.962 0.357
Bits 24 to 31---> 0.667 0.173 0.589 0.321 0.828 0.988 0.963 0.019
KS test for the above 32 p values: 0.186
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_14:31,
p-values for 5 runs: 0.2430, 0.2907, 0.7109, 0.4466, 0.7536
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 217 211.4 0.147 0.147
r= 29 5084 5134.0 0.487 0.635
r= 30 23160 23103.0 0.140 0.775
r= 31 11539 11551.5 0.014 0.789
chi-square = 0.789 with df = 3; p-value = 0.148
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 188 211.4 2.594 2.594
r= 30 5209 5134.0 1.095 3.689
r= 31 23227 23103.0 0.665 4.354
r= 32 11376 11551.5 2.667 7.021
chi-square = 7.021 with df = 3; p-value = 0.929
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_14:31
b-rank test for bits 1 to 8, p=0.65101
b-rank test for bits 2 to 9, p=0.37653
b-rank test for bits 3 to 10, p=0.09777
b-rank test for bits 4 to 11, p=0.49261
b-rank test for bits 5 to 12, p=0.05371
b-rank test for bits 6 to 13, p=0.77302
b-rank test for bits 7 to 14, p=0.28130
b-rank test for bits 8 to 15, p=0.80821
b-rank test for bits 9 to 16, p=0.30916
b-rank test for bits 10 to 17, p=0.12817
b-rank test for bits 11 to 18, p=0.60630
b-rank test for bits 12 to 19, p=0.84036
b-rank test for bits 13 to 20, p=0.96778
b-rank test for bits 14 to 21, p=0.91126
b-rank test for bits 15 to 22, p=0.35401
b-rank test for bits 16 to 23, p=0.85788
b-rank test for bits 17 to 24, p=0.46661
b-rank test for bits 18 to 25, p=0.71695
b-rank test for bits 19 to 26, p=0.37728
b-rank test for bits 20 to 27, p=0.16401
b-rank test for bits 21 to 28, p=0.71758
b-rank test for bits 22 to 29, p=0.92474
b-rank test for bits 23 to 30, p=0.78188
b-rank test for bits 24 to 31, p=0.00832
b-rank test for bits 25 to 32, p=0.74844
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 = 0.808655
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_14:31
(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 141229 -1.59 0.055967
2 141707 -0.47 0.318202
3 141563 -0.81 0.209205
4 141730 -0.42 0.337610
5 141986 0.18 0.571084
6 141650 -0.61 0.272287
7 142416 1.18 0.881756
8 141404 -1.18 0.118865
9 141788 -0.28 0.388404
10 141584 -0.76 0.223592
11 141727 -0.43 0.335052
12 141618 -0.68 0.248038
13 142548 1.49 0.932179
14 141764 -0.34 0.367095
15 142391 1.13 0.869790
16 141654 -0.60 0.275399
17 141945 0.08 0.533210
18 142243 0.78 0.782188
19 141526 -0.90 0.185225
20 142276 0.86 0.804196
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_14:31
Bits used No. missing words z-score p-value
23 to 32 142075 0.5713 0.716094
22 to 31 142082 0.5954 0.724217
21 to 30 141925 0.0540 0.521546
20 to 29 141771 -0.4770 0.316681
19 to 28 142124 0.7402 0.770423
18 to 27 141776 -0.4598 0.322845
17 to 26 142672 2.6299 0.995729
16 to 25 141875 -0.1184 0.452884
15 to 24 142317 1.4058 0.920102
14 to 23 142149 0.8264 0.795725
13 to 22 142177 0.9230 0.821996
12 to 21 142137 0.7851 0.783793
11 to 20 141864 -0.1563 0.437894
10 to 19 141305 -2.0839 0.018585
9 to 18 141640 -0.9287 0.176516
8 to 17 142045 0.4678 0.680046
7 to 16 141905 -0.0149 0.494044
6 to 15 142490 2.0023 0.977374
5 to 14 142024 0.3954 0.653731
4 to 13 141918 0.0299 0.511925
3 to 12 141883 -0.0908 0.463829
2 to 11 142047 0.4747 0.682508
1 to 10 141944 0.1196 0.547581
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_14:31
Bits used No. missing words z-score p-value
28 to 32 142312 1.3650 0.913871
27 to 31 141972 0.2124 0.584118
26 to 30 141843 -0.2248 0.411049
25 to 29 141742 -0.5672 0.285282
24 to 28 141993 0.2836 0.611652
23 to 27 141907 -0.0079 0.496849
22 to 26 141796 -0.3842 0.350426
21 to 25 142602 2.3480 0.990564
20 to 24 142610 2.3752 0.991229
19 to 23 141349 -1.8994 0.028754
18 to 22 141212 -2.3638 0.009044
17 to 21 142087 0.6023 0.726503
16 to 20 141702 -0.7028 0.241086
15 to 19 141612 -1.0079 0.156752
14 to 18 142275 1.2396 0.892431
13 to 17 141957 0.1616 0.564187
12 to 16 142614 2.3887 0.991546
11 to 15 141819 -0.3062 0.379725
10 to 14 142123 0.7243 0.765561
9 to 13 142090 0.6124 0.729877
8 to 12 141719 -0.6452 0.259403
7 to 11 141870 -0.1333 0.446969
6 to 10 142103 0.6565 0.744252
5 to 9 141846 -0.2147 0.415009
4 to 8 141858 -0.1740 0.430933
3 to 7 141647 -0.8893 0.186933
2 to 6 141735 -0.5909 0.277277
1 to 5 141969 0.2023 0.580148
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_14:31
Bits used No. missing words z-score p-value
31 to 32 141665 -0.7207 0.235536
30 to 31 142500 1.7424 0.959280
29 to 30 142384 1.4002 0.919274
28 to 29 141651 -0.7620 0.223019
27 to 28 142284 1.1052 0.865468
26 to 27 141381 -1.5585 0.059558
25 to 26 142191 0.8309 0.796981
24 to 25 141734 -0.5172 0.302509
23 to 24 141937 0.0816 0.532527
22 to 23 142101 0.5654 0.714099
21 to 22 141976 0.1967 0.577956
20 to 21 142460 1.6244 0.947854
19 to 20 142247 0.9961 0.840394
18 to 19 141620 -0.8535 0.196696
17 to 18 141874 -0.1042 0.458498
16 to 17 141683 -0.6676 0.252182
15 to 16 141705 -0.6027 0.273340
14 to 15 141776 -0.3933 0.347048
13 to 14 142277 1.0846 0.860944
12 to 13 141895 -0.0423 0.483141
11 to 12 142410 1.4769 0.930149
10 to 11 141380 -1.5614 0.059209
9 to 10 141873 -0.1072 0.457328
8 to 9 141920 0.0315 0.512555
7 to 8 141819 -0.2665 0.394942
6 to 7 142487 1.7040 0.955813
5 to 6 142623 2.1052 0.982364
4 to 5 141738 -0.5054 0.306640
3 to 4 142174 0.7807 0.782522
2 to 3 141350 -1.6499 0.049478
1 to 2 141961 0.1524 0.560572
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2491.67 -0.118 0.453094
Test results for specific bytes for dh-ranFile-2018-06-19_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2568.28 0.966 0.832867
2 to 9 2535.86 0.507 0.693964
3 to 10 2493.26 -0.095 0.462041
4 to 11 2530.08 0.425 0.664722
5 to 12 2560.02 0.849 0.802013
6 to 13 2504.55 0.064 0.525652
7 to 14 2521.64 0.306 0.620217
8 to 15 2497.24 -0.039 0.484453
9 to 16 2474.40 -0.362 0.358669
10 to 17 2533.93 0.480 0.684323
11 to 18 2367.44 -1.875 0.030418
12 to 19 2448.49 -0.728 0.233160
13 to 20 2466.59 -0.472 0.318313
14 to 21 2508.45 0.120 0.547584
15 to 22 2385.75 -1.616 0.053072
16 to 23 2425.50 -1.054 0.146037
17 to 24 2436.98 -0.891 0.186390
18 to 25 2510.76 0.152 0.560481
19 to 26 2367.93 -1.868 0.030902
20 to 27 2513.69 0.194 0.576746
21 to 28 2454.16 -0.648 0.258411
22 to 29 2450.99 -0.693 0.244105
23 to 30 2414.02 -1.216 0.112006
24 to 31 2504.91 0.069 0.527700
25 to 32 2529.31 0.415 0.660773
CDPARK for dh-ranFile-2018-06-19_14:31: 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
3533 0.4566 0.676028
3529 0.2740 0.607947
3498 -1.1416 0.126820
3518 -0.2283 0.409702
3498 -1.1416 0.126820
3527 0.1826 0.572463
3540 0.7763 0.781201
3537 0.6393 0.738676
3537 0.6393 0.738676
3529 0.2740 0.607947
Square side=100, avg. no. parked=3524.60 sample std.=14.55
p-value of the KSTEST for those 10 p-values: 0.429159
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_14:31
0.8974,0.0107,0.2281,0.1326,0.3635,0.3264,0.0865,0.0088,0.2868,0.6971,
The KS test for those 10 p-values: 0.027318
The 3DSPHERES test for dh-ranFile-2018-06-19_14:31
sample no r^3 equiv. uni.
1 17.024 0.433033
2 51.396 0.819711
3 1.038 0.034009
4 55.300 0.841709
5 11.711 0.323194
6 45.505 0.780591
7 0.356 0.011810
8 6.485 0.194389
9 6.073 0.183253
10 49.594 0.808554
11 15.311 0.399734
12 16.725 0.427360
13 59.983 0.864589
14 59.184 0.860933
15 32.243 0.658618
16 32.547 0.662060
17 92.296 0.953881
18 94.974 0.957819
19 18.475 0.459812
20 7.000 0.208100
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.626396
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 1.5 0.6 -1.4 -0.1
1.8 -0.7 -1.0 2.6 0.4 -0.9
0.5 -0.3 -1.4 -0.4 -0.2 0.3
-0.4 0.3 1.1 0.2 0.9 -0.3
-1.7 -0.6 1.5 -0.8 1.2 -0.6
0.6 -0.3 0.6 -0.6 1.0 -0.5
1.4 0.8 -0.4 -0.1 0.9 -1.0
-0.1
Chi-square with 42 degrees of freedom:38.466421
z-score=-0.385545, p-value=0.373128
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_14:31
Test no p-value
1 0.127051
2 0.021439
3 0.338275
4 0.194579
5 0.852895
6 0.033869
7 0.499715
8 0.001092
9 0.070535
10 0.869187
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.009006
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_14:31:
(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 66594 0.08 66528 0.29
3 25000.00 24955 0.08 25109 0.48
4 6666.67 6808 3.00 6718 0.40
5 1388.89 1355 0.83 1345 1.39
6 238.10 237 0.01 274 5.41
7 34.72 42 1.53 23 3.96
8 4.96 8 1.86 2 1.77
p=0.71270 p=0.96661
Number of rngs required: 690213, p-value: 0.984
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_14:31
No. of wins: Observed Expected
98639 98585.9
z-score= 0.238, pvalue=0.59394
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67057 66666.7 2.285 2.285
2 37806 37654.3 0.611 2.896
3 27079 26954.7 0.573 3.469
4 19223 19313.5 0.424 3.893
5 13740 13851.4 0.896 4.789
6 9847 9943.5 0.937 5.727
7 7047 7145.0 1.345 7.071
8 5133 5139.1 0.007 7.079
9 3589 3699.9 3.322 10.401
10 2688 2666.3 0.177 10.577
11 1892 1923.3 0.510 11.088
12 1355 1388.7 0.820 11.907
13 998 1003.7 0.033 11.940
14 701 726.1 0.870 12.810
15 487 525.8 2.868 15.679
16 373 381.2 0.174 15.853
17 256 276.5 1.526 17.378
18 198 200.8 0.040 17.418
19 159 146.0 1.160 18.579
20 119 106.2 1.539 20.118
21 253 287.1 4.053 24.171
Chisq= 24.17 for 20 degrees of freedom, p= 0.76499
SUMMARY of craptest
p-value for no. of wins: 0.593935
p-value for throws/game: 0.764994
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_14:31
No. of wins: Observed Expected
98827 98585.9
z-score= 1.079, pvalue=0.85960
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66503 66666.7 0.402 0.402
2 37846 37654.3 0.976 1.378
3 26760 26954.7 1.407 2.784
4 19380 19313.5 0.229 3.014
5 13755 13851.4 0.671 3.685
6 9906 9943.5 0.142 3.827
7 7206 7145.0 0.520 4.347
8 5179 5139.1 0.310 4.657
9 3717 3699.9 0.079 4.736
10 2714 2666.3 0.853 5.590
11 1886 1923.3 0.725 6.314
12 1440 1388.7 1.892 8.206
13 1084 1003.7 6.422 14.628
14 695 726.1 1.335 15.964
15 506 525.8 0.748 16.712
16 400 381.2 0.932 17.644
17 280 276.5 0.043 17.687
18 206 200.8 0.133 17.821
19 152 146.0 0.248 18.068
20 97 106.2 0.800 18.868
21 288 287.1 0.003 18.871
Chisq= 18.87 for 20 degrees of freedom, p= 0.46976
SUMMARY of craptest
p-value for no. of wins: 0.859600
p-value for throws/game: 0.469755
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0083,0.0088,0.0090,0.0090,0.0107,0.0118,0.0186,0.0190,0.0214,
0.0273,0.0288,0.0304,0.0309,0.0339,0.0340,0.0495,0.0531,0.0537,0.0560,
0.0592,0.0596,0.0705,0.0865,0.0876,0.0978,0.1120,0.1189,0.1268,0.1268,
0.1271,0.1282,0.1296,0.1326,0.1432,0.1460,0.1478,0.1518,0.1546,0.1568,
0.1640,0.1724,0.1727,0.1765,0.1774,0.1833,0.1852,0.1857,0.1864,0.1869,
0.1944,0.1946,0.1967,0.2050,0.2081,0.2092,0.2213,0.2230,0.2236,0.2251,
0.2281,0.2332,0.2355,0.2411,0.2430,0.2441,0.2480,0.2522,0.2584,0.2594,
0.2649,0.2706,0.2723,0.2733,0.2754,0.2757,0.2773,0.2813,0.2853,0.2856,
0.2868,0.2907,0.3025,0.3032,0.3066,0.3092,0.3167,0.3182,0.3183,0.3206,
0.3228,0.3232,0.3264,0.3329,0.3351,0.3376,0.3383,0.3470,0.3504,0.3540,
0.3571,0.3587,0.3635,0.3671,0.3731,0.3765,0.3773,0.3797,0.3884,0.3949,
0.3978,0.3997,0.4097,0.4103,0.4110,0.4150,0.4274,0.4292,0.4309,0.4330,
0.4379,0.4466,0.4470,0.4529,0.4531,0.4573,0.4585,0.4598,0.4620,0.4638,
0.4666,0.4698,0.4831,0.4845,0.4926,0.4940,0.4968,0.4997,0.5119,0.5126,
0.5215,0.5257,0.5277,0.5305,0.5325,0.5332,0.5341,0.5476,0.5476,0.5605,
0.5606,0.5642,0.5711,0.5725,0.5767,0.5780,0.5801,0.5841,0.5872,0.5891,
0.5939,0.6063,0.6079,0.6079,0.6117,0.6202,0.6264,0.6510,0.6537,0.6559,
0.6586,0.6608,0.6621,0.6647,0.6667,0.6693,0.6703,0.6760,0.6800,0.6825,
0.6843,0.6940,0.6971,0.7109,0.7127,0.7141,0.7161,0.7169,0.7176,0.7235,
0.7242,0.7265,0.7270,0.7299,0.7387,0.7387,0.7443,0.7484,0.7536,0.7645,
0.7650,0.7656,0.7704,0.7730,0.7806,0.7812,0.7819,0.7822,0.7825,0.7829,
0.7838,0.7931,0.7957,0.7970,0.8020,0.8042,0.8082,0.8086,0.8087,0.8095,
0.8197,0.8220,0.8278,0.8329,0.8404,0.8404,0.8417,0.8529,0.8579,0.8596,
0.8609,0.8609,0.8646,0.8655,0.8692,0.8698,0.8818,0.8924,0.8974,0.9079,
0.9113,0.9139,0.9193,0.9201,0.9247,0.9288,0.9301,0.9309,0.9322,0.9404,
0.9479,0.9539,0.9558,0.9578,0.9593,0.9618,0.9626,0.9666,0.9678,0.9774,
0.9824,0.9839,0.9883,0.9893,0.9906,0.9912,0.9915,0.9920,0.9957,
Overall p-value after applying KStest on 269 p-values = 0.835682
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.