RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-01_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.93 21.3794 0.790221
2 to 25 15.96 15.3874 0.432402
3 to 26 15.79 19.2099 0.683380
4 to 27 15.71 15.6250 0.449445
5 to 28 15.97 19.5131 0.700113
6 to 29 15.60 18.1238 0.618927
7 to 30 15.66 14.9044 0.397636
8 to 31 15.50 24.9950 0.905177
9 to 32 15.36 31.7277 0.983736
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.136295
Tough bday spacings test for dh-ranFile-2018-07-01_10:31: 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 15 38 64 111 91 66 57 30 12 10 6
(O-E)^2/E 3.7 0.1 1.2 1.8 0.5 1.9 0.5 0.0 0.6 1.7 0.9
Birthday Spacings: Sum(O-E)^2/E= 12.783, p= 0.764
RESULTS OF GCD FOR dh-ranFile-2018-07-01_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.484318
p-value, dist. of gcd's: 0.829865
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-01_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.676 0.418 0.885 0.250 0.644 0.768 0.939 0.917
Bits 8 to 15---> 0.484 0.075 0.319 0.968 0.995 0.219 0.961 0.061
Bits 16 to 23---> 0.451 0.728 0.180 0.448 0.845 0.145 0.880 0.439
Bits 24 to 31---> 0.666 0.944 0.968 0.087 0.051 0.527 0.711 0.540
KS test for the above 32 p values: 0.835
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-01_10:31,
p-values for 5 runs: 0.9815, 0.8826, 0.1268, 0.4098, 0.7483
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-01_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5024 5134.0 2.357 2.871
r= 30 23111 23103.0 0.003 2.873
r= 31 11664 11551.5 1.095 3.969
chi-square = 3.969 with df = 3; p-value = 0.735
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-01_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 180 211.4 4.669 4.669
r= 30 5138 5134.0 0.003 4.672
r= 31 22940 23103.0 1.151 5.823
r= 32 11742 11551.5 3.141 8.964
chi-square = 8.964 with df = 3; p-value = 0.970
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-01_10:31
b-rank test for bits 1 to 8, p=0.84506
b-rank test for bits 2 to 9, p=0.10848
b-rank test for bits 3 to 10, p=0.87957
b-rank test for bits 4 to 11, p=0.03766
b-rank test for bits 5 to 12, p=0.39379
b-rank test for bits 6 to 13, p=0.06092
b-rank test for bits 7 to 14, p=0.47541
b-rank test for bits 8 to 15, p=0.25546
b-rank test for bits 9 to 16, p=0.97815
b-rank test for bits 10 to 17, p=0.20839
b-rank test for bits 11 to 18, p=0.43412
b-rank test for bits 12 to 19, p=0.20469
b-rank test for bits 13 to 20, p=0.21199
b-rank test for bits 14 to 21, p=0.21135
b-rank test for bits 15 to 22, p=0.23121
b-rank test for bits 16 to 23, p=0.00443
b-rank test for bits 17 to 24, p=0.74010
b-rank test for bits 18 to 25, p=0.89507
b-rank test for bits 19 to 26, p=0.47470
b-rank test for bits 20 to 27, p=0.04649
b-rank test for bits 21 to 28, p=0.13536
b-rank test for bits 22 to 29, p=0.49205
b-rank test for bits 23 to 30, p=0.65051
b-rank test for bits 24 to 31, p=0.29748
b-rank test for bits 25 to 32, p=0.61781
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 = 0.098831
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-01_10:31
(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 141200 -1.66 0.048728
2 142377 1.09 0.862734
3 142084 0.41 0.658403
4 142386 1.11 0.867299
5 141633 -0.65 0.259259
6 141710 -0.47 0.320706
7 142244 0.78 0.782875
8 141602 -0.72 0.236360
9 141943 0.08 0.531352
10 141916 0.02 0.506217
11 141907 -0.01 0.497828
12 140972 -2.19 0.014261
13 141984 0.17 0.569249
14 142263 0.83 0.795692
15 141755 -0.36 0.359205
16 142032 0.29 0.612795
17 141190 -1.68 0.046413
18 141349 -1.31 0.095236
19 142180 0.63 0.736439
20 141693 -0.51 0.306624
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-01_10:31
Bits used No. missing words z-score p-value
23 to 32 141944 0.1196 0.547581
22 to 31 142263 1.2196 0.888683
21 to 30 142383 1.6333 0.948802
20 to 29 141752 -0.5425 0.293731
19 to 28 141787 -0.4218 0.336575
18 to 27 141709 -0.6908 0.244848
17 to 26 141578 -1.1425 0.126620
16 to 25 142218 1.0644 0.856422
15 to 24 142057 0.5092 0.694696
14 to 23 141876 -0.1149 0.454250
13 to 22 142183 0.9437 0.827336
12 to 21 142140 0.7954 0.786814
11 to 20 141861 -0.1667 0.433821
10 to 19 142016 0.3678 0.643499
9 to 18 142137 0.7851 0.783793
8 to 17 141429 -1.6563 0.048830
7 to 16 141568 -1.1770 0.119598
6 to 15 141702 -0.7149 0.237326
5 to 14 142072 0.5609 0.712578
4 to 13 141735 -0.6011 0.273874
3 to 12 142149 0.8264 0.795725
2 to 11 142054 0.4989 0.691062
1 to 10 141940 0.1058 0.542113
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-01_10:31
Bits used No. missing words z-score p-value
28 to 32 141738 -0.5808 0.280695
27 to 31 141695 -0.7265 0.233753
26 to 30 141451 -1.5537 0.060133
25 to 29 141592 -1.0757 0.141032
24 to 28 142421 1.7345 0.958583
23 to 27 141951 0.1413 0.556166
22 to 26 142093 0.6226 0.733230
21 to 25 141413 -1.6825 0.046238
20 to 24 141996 0.2938 0.615543
19 to 23 141809 -0.3401 0.366890
18 to 22 141801 -0.3672 0.356727
17 to 21 142250 1.1548 0.875917
16 to 20 141268 -2.1740 0.014853
15 to 19 141537 -1.2621 0.103450
14 to 18 141969 0.2023 0.580148
13 to 17 141672 -0.8045 0.210552
12 to 16 142489 1.9650 0.975292
11 to 15 141826 -0.2825 0.388790
10 to 14 141851 -0.1977 0.421629
9 to 13 142065 0.5277 0.701145
8 to 12 142374 1.5752 0.942389
7 to 11 141441 -1.5876 0.056193
6 to 10 141847 -0.2113 0.416331
5 to 9 142272 1.2294 0.890537
4 to 8 141709 -0.6791 0.248542
3 to 7 141523 -1.3096 0.095167
2 to 6 141928 0.0633 0.525232
1 to 5 141665 -0.8282 0.203768
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-01_10:31
Bits used No. missing words z-score p-value
31 to 32 141671 -0.7030 0.241016
30 to 31 141902 -0.0216 0.491375
29 to 30 141710 -0.5880 0.278268
28 to 29 141935 0.0757 0.530180
27 to 28 142520 1.8014 0.964179
26 to 27 142300 1.1524 0.875426
25 to 26 142118 0.6155 0.730903
24 to 25 141940 0.0905 0.536044
23 to 24 141880 -0.0865 0.465527
22 to 23 141750 -0.4700 0.319178
21 to 22 142610 2.0669 0.980627
20 to 21 141823 -0.2547 0.399493
19 to 20 142580 1.9784 0.976057
18 to 19 142552 1.8958 0.971006
17 to 18 141473 -1.2871 0.099028
16 to 17 141680 -0.6765 0.249365
15 to 16 141988 0.2321 0.591756
14 to 15 142110 0.5919 0.723057
13 to 14 142080 0.5035 0.692677
12 to 13 142341 1.2734 0.898555
11 to 12 141975 0.1937 0.576801
10 to 11 141876 -0.0983 0.460840
9 to 10 141679 -0.6794 0.248430
8 to 9 141755 -0.4553 0.324464
7 to 8 142149 0.7070 0.760214
6 to 7 141989 0.2350 0.592901
5 to 6 142456 1.6126 0.946584
4 to 5 141862 -0.1396 0.444482
3 to 4 142372 1.3648 0.913843
2 to 3 141209 -2.0659 0.019420
1 to 2 141684 -0.6647 0.253124
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-01_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2467.22 -0.464 0.321466
Test results for specific bytes for dh-ranFile-2018-07-01_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2548.22 0.682 0.752377
2 to 9 2621.57 1.719 0.957220
3 to 10 2666.86 2.360 0.990855
4 to 11 2452.89 -0.666 0.252650
5 to 12 2512.05 0.170 0.567637
6 to 13 2499.73 -0.004 0.498496
7 to 14 2572.43 1.024 0.847162
8 to 15 2453.17 -0.662 0.253888
9 to 16 2465.35 -0.490 0.312046
10 to 17 2488.04 -0.169 0.432823
11 to 18 2480.30 -0.279 0.390260
12 to 19 2460.57 -0.558 0.288562
13 to 20 2551.63 0.730 0.767370
14 to 21 2503.67 0.052 0.520712
15 to 22 2572.16 1.020 0.846253
16 to 23 2397.47 -1.450 0.073524
17 to 24 2542.67 0.604 0.726913
18 to 25 2370.65 -1.829 0.033680
19 to 26 2378.82 -1.714 0.043291
20 to 27 2580.40 1.137 0.872244
21 to 28 2518.94 0.268 0.605571
22 to 29 2467.63 -0.458 0.323576
23 to 30 2478.53 -0.304 0.380706
24 to 31 2535.86 0.507 0.693987
25 to 32 2631.54 1.860 0.968580
CDPARK for dh-ranFile-2018-07-01_10:31: 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
3517 -0.2740 0.392053
3536 0.5936 0.723613
3535 0.5479 0.708135
3526 0.1370 0.554479
3514 -0.4110 0.340551
3528 0.2283 0.590298
3535 0.5479 0.708135
3499 -1.0959 0.136563
3501 -1.0046 0.157553
3503 -0.9132 0.180558
Square side=100, avg. no. parked=3519.40 sample std.=13.92
p-value of the KSTEST for those 10 p-values: 0.573137
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-01_10:31
0.0138,0.3858,0.6190,0.9185,0.3792,0.7491,0.7731,0.9205,0.2385,0.5435,
The KS test for those 10 p-values: 0.814653
The 3DSPHERES test for dh-ranFile-2018-07-01_10:31
sample no r^3 equiv. uni.
1 27.280 0.597203
2 5.538 0.168563
3 3.837 0.120062
4 0.759 0.024980
5 72.037 0.909393
6 1.288 0.042032
7 25.275 0.569365
8 48.970 0.804527
9 77.309 0.923995
10 25.203 0.568333
11 7.187 0.213032
12 0.207 0.006875
13 3.821 0.119579
14 1.396 0.045474
15 21.888 0.517904
16 63.202 0.878366
17 19.267 0.473887
18 17.341 0.439005
19 20.587 0.496537
20 45.897 0.783446
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.255432
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-01_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 -0.6 -1.1 2.0 0.9
1.1 1.6 0.5 -0.8 -0.7 -0.7
-1.5 -1.5 0.3 1.6 0.3 0.4
-0.4 0.0 -1.1 -1.7 1.8 1.3
-0.1 0.2 1.8 2.0 -0.5 -1.4
-1.1 0.4 -0.8 0.9 -0.4 -1.0
-0.9 -1.7 0.9 -0.7 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:49.492523
z-score=0.817501, p-value=0.800999
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-01_10:31
Test no p-value
1 0.000552
2 0.832204
3 0.494107
4 0.093727
5 0.339556
6 0.154206
7 0.374082
8 0.465006
9 0.319220
10 0.007631
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.024503
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-01_10:31:
(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 66944 1.15 66548 0.21
3 25000.00 24883 0.55 25024 0.02
4 6666.67 6597 0.73 6711 0.29
5 1388.89 1342 1.58 1418 0.61
6 238.10 201 5.78 249 0.50
7 34.72 30 0.64 42 1.53
8 4.96 2 1.77 7 0.84
p=0.94235 p=0.32388
Number of rngs required: 689614, p-value: 0.921
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-01_10:31
No. of wins: Observed Expected
98476 98585.9
z-score=-0.491, pvalue=0.31159
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66847 66666.7 0.488 0.488
2 37698 37654.3 0.051 0.538
3 26806 26954.7 0.821 1.359
4 19255 19313.5 0.177 1.536
5 13649 13851.4 2.958 4.494
6 10173 9943.5 5.295 9.789
7 7159 7145.0 0.027 9.816
8 5141 5139.1 0.001 9.817
9 3819 3699.9 3.836 13.653
10 2593 2666.3 2.015 15.668
11 1933 1923.3 0.049 15.717
12 1358 1388.7 0.680 16.397
13 976 1003.7 0.765 17.163
14 747 726.1 0.599 17.762
15 497 525.8 1.581 19.343
16 382 381.2 0.002 19.345
17 265 276.5 0.482 19.827
18 181 200.8 1.958 21.785
19 130 146.0 1.750 23.535
20 114 106.2 0.571 24.105
21 277 287.1 0.356 24.462
Chisq= 24.46 for 20 degrees of freedom, p= 0.77719
SUMMARY of craptest
p-value for no. of wins: 0.311589
p-value for throws/game: 0.777192
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-01_10:31
No. of wins: Observed Expected
98682 98585.9
z-score= 0.430, pvalue=0.66640
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66846 66666.7 0.482 0.482
2 37884 37654.3 1.401 1.883
3 26754 26954.7 1.495 3.378
4 19387 19313.5 0.280 3.658
5 14012 13851.4 1.862 5.520
6 9753 9943.5 3.651 9.171
7 7022 7145.0 2.118 11.289
8 5063 5139.1 1.126 12.415
9 3766 3699.9 1.182 13.598
10 2677 2666.3 0.043 13.641
11 1889 1923.3 0.613 14.253
12 1378 1388.7 0.083 14.336
13 941 1003.7 3.919 18.255
14 692 726.1 1.605 19.860
15 555 525.8 1.618 21.478
16 375 381.2 0.099 21.577
17 264 276.5 0.569 22.146
18 213 200.8 0.737 22.883
19 140 146.0 0.245 23.128
20 99 106.2 0.490 23.619
21 290 287.1 0.029 23.648
Chisq= 23.65 for 20 degrees of freedom, p= 0.74187
SUMMARY of craptest
p-value for no. of wins: 0.666402
p-value for throws/game: 0.741872
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0044,0.0069,0.0076,0.0138,0.0143,0.0149,0.0194,0.0245,0.0250,
0.0337,0.0377,0.0420,0.0433,0.0455,0.0462,0.0464,0.0465,0.0487,0.0488,
0.0509,0.0562,0.0601,0.0609,0.0614,0.0735,0.0748,0.0874,0.0937,0.0952,
0.0952,0.0988,0.0990,0.1035,0.1085,0.1196,0.1196,0.1201,0.1266,0.1268,
0.1354,0.1363,0.1366,0.1410,0.1450,0.1542,0.1576,0.1686,0.1799,0.1806,
0.2038,0.2047,0.2084,0.2106,0.2114,0.2120,0.2130,0.2186,0.2312,0.2338,
0.2364,0.2373,0.2385,0.2410,0.2448,0.2484,0.2485,0.2494,0.2504,0.2526,
0.2531,0.2539,0.2554,0.2555,0.2593,0.2739,0.2783,0.2807,0.2886,0.2937,
0.2975,0.3066,0.3116,0.3120,0.3189,0.3192,0.3192,0.3207,0.3215,0.3236,
0.3239,0.3245,0.3366,0.3396,0.3406,0.3567,0.3592,0.3669,0.3741,0.3792,
0.3807,0.3858,0.3888,0.3903,0.3921,0.3938,0.3976,0.3995,0.4098,0.4163,
0.4180,0.4216,0.4324,0.4328,0.4338,0.4341,0.4385,0.4390,0.4445,0.4484,
0.4494,0.4514,0.4542,0.4608,0.4650,0.4655,0.4739,0.4747,0.4754,0.4841,
0.4843,0.4914,0.4920,0.4941,0.4965,0.4978,0.4985,0.5062,0.5179,0.5207,
0.5252,0.5273,0.5302,0.5314,0.5360,0.5404,0.5421,0.5435,0.5476,0.5545,
0.5562,0.5676,0.5683,0.5692,0.5694,0.5731,0.5768,0.5801,0.5903,0.5918,
0.5929,0.5972,0.6056,0.6128,0.6155,0.6178,0.6189,0.6190,0.6435,0.6441,
0.6505,0.6584,0.6663,0.6664,0.6764,0.6834,0.6911,0.6927,0.6940,0.6947,
0.7001,0.7011,0.7081,0.7081,0.7110,0.7126,0.7231,0.7236,0.7269,0.7277,
0.7309,0.7332,0.7351,0.7364,0.7401,0.7419,0.7483,0.7491,0.7524,0.7602,
0.7640,0.7674,0.7681,0.7731,0.7772,0.7829,0.7834,0.7838,0.7868,0.7902,
0.7957,0.7957,0.8010,0.8045,0.8147,0.8273,0.8299,0.8322,0.8349,0.8450,
0.8451,0.8463,0.8472,0.8564,0.8627,0.8673,0.8722,0.8754,0.8759,0.8784,
0.8796,0.8803,0.8826,0.8848,0.8887,0.8905,0.8951,0.8986,0.9052,0.9094,
0.9138,0.9171,0.9185,0.9205,0.9211,0.9240,0.9389,0.9423,0.9424,0.9444,
0.9466,0.9488,0.9572,0.9586,0.9605,0.9642,0.9680,0.9684,0.9686,0.9702,
0.9710,0.9753,0.9761,0.9781,0.9806,0.9815,0.9837,0.9909,0.9951,
Overall p-value after applying KStest on 269 p-values = 0.708906
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.