RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.02 10.6645 0.126537
2 to 25 15.59 14.0583 0.337031
3 to 26 15.81 27.8985 0.953861
4 to 27 15.89 15.5436 0.443613
5 to 28 15.73 19.5867 0.704085
6 to 29 15.77 9.6760 0.083354
7 to 30 15.70 12.8085 0.251092
8 to 31 15.85 19.7640 0.713521
9 to 32 16.14 14.0269 0.334803
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.817146
Tough bday spacings test for dh-ranFile-2018-06-22_16:31: 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 42 74 107 102 68 53 20 15 7 2
(O-E)^2/E 0.1 0.8 0.0 0.9 0.2 1.3 0.0 3.2 0.0 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 7.564, p= 0.329
RESULTS OF GCD FOR dh-ranFile-2018-06-22_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.184603
p-value, dist. of gcd's: 0.145941
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.638 0.403 0.736 0.981 0.010 0.901 0.581 0.845
Bits 8 to 15---> 0.349 0.332 0.845 0.834 0.393 0.606 0.571 0.439
Bits 16 to 23---> 0.857 0.106 0.579 0.755 0.430 0.527 0.430 0.526
Bits 24 to 31---> 0.742 0.364 0.224 0.252 0.100 0.124 0.570 0.526
KS test for the above 32 p values: 0.389
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_16:31,
p-values for 5 runs: 0.2678, 0.7908, 0.3951, 0.9872, 0.7099
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 190 211.4 2.170 2.170
r= 29 5116 5134.0 0.063 2.233
r= 30 23118 23103.0 0.010 2.243
r= 31 11576 11551.5 0.052 2.295
chi-square = 2.295 with df = 3; p-value = 0.486
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5038 5134.0 1.795 3.767
r= 31 23195 23103.0 0.366 4.133
r= 32 11576 11551.5 0.052 4.185
chi-square = 4.185 with df = 3; p-value = 0.758
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_16:31
b-rank test for bits 1 to 8, p=0.96321
b-rank test for bits 2 to 9, p=0.33154
b-rank test for bits 3 to 10, p=0.58118
b-rank test for bits 4 to 11, p=0.49766
b-rank test for bits 5 to 12, p=0.55427
b-rank test for bits 6 to 13, p=0.05561
b-rank test for bits 7 to 14, p=0.51873
b-rank test for bits 8 to 15, p=0.83566
b-rank test for bits 9 to 16, p=0.52389
b-rank test for bits 10 to 17, p=0.27989
b-rank test for bits 11 to 18, p=0.04377
b-rank test for bits 12 to 19, p=0.70197
b-rank test for bits 13 to 20, p=0.01929
b-rank test for bits 14 to 21, p=0.08079
b-rank test for bits 15 to 22, p=0.23475
b-rank test for bits 16 to 23, p=0.76140
b-rank test for bits 17 to 24, p=0.83475
b-rank test for bits 18 to 25, p=0.38353
b-rank test for bits 19 to 26, p=0.67793
b-rank test for bits 20 to 27, p=0.69090
b-rank test for bits 21 to 28, p=0.82308
b-rank test for bits 22 to 29, p=0.83318
b-rank test for bits 23 to 30, p=0.37928
b-rank test for bits 24 to 31, p=0.58999
b-rank test for bits 25 to 32, p=0.47271
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 = 0.798316
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_16:31
(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 142524 1.44 0.924519
2 142338 1.00 0.841723
3 141864 -0.11 0.457826
4 141934 0.06 0.522982
5 142041 0.31 0.620822
6 141883 -0.06 0.475473
7 141629 -0.65 0.256241
8 141789 -0.28 0.389300
9 141608 -0.70 0.240703
10 142076 0.39 0.651516
11 141129 -1.82 0.034136
12 141828 -0.19 0.424645
13 141987 0.18 0.572001
14 141820 -0.21 0.417335
15 141374 -1.25 0.105509
16 142188 0.65 0.742508
17 142209 0.70 0.758087
18 140940 -2.26 0.011763
19 141195 -1.67 0.047559
20 142331 0.99 0.837740
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_16:31
Bits used No. missing words z-score p-value
23 to 32 141629 -0.9667 0.166858
22 to 31 141690 -0.7563 0.224732
21 to 30 141637 -0.9391 0.173848
20 to 29 141852 -0.1977 0.421644
19 to 28 141513 -1.3667 0.085867
18 to 27 142164 0.8782 0.810075
17 to 26 142065 0.5368 0.704295
16 to 25 142005 0.3299 0.629261
15 to 24 142018 0.3747 0.646067
14 to 23 141709 -0.6908 0.244848
13 to 22 142336 1.4713 0.929392
12 to 21 142085 0.6058 0.727663
11 to 20 142314 1.3954 0.918554
10 to 19 142149 0.8264 0.795725
9 to 18 141905 -0.0149 0.494044
8 to 17 142016 0.3678 0.643499
7 to 16 141442 -1.6115 0.053537
6 to 15 142024 0.3954 0.653731
5 to 14 142276 1.2644 0.896953
4 to 13 141818 -0.3149 0.376407
3 to 12 142048 0.4782 0.683736
2 to 11 141823 -0.2977 0.382970
1 to 10 142009 0.3437 0.634460
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_16:31
Bits used No. missing words z-score p-value
28 to 32 141809 -0.3401 0.366890
27 to 31 141618 -0.9876 0.161684
26 to 30 142143 0.7921 0.785849
25 to 29 141826 -0.2825 0.388790
24 to 28 141915 0.0192 0.507667
23 to 27 142036 0.4294 0.666180
22 to 26 142056 0.4972 0.690471
21 to 25 141361 -1.8587 0.031532
20 to 24 142374 1.5752 0.942389
19 to 23 142111 0.6836 0.752895
18 to 22 141880 -0.0994 0.460401
17 to 21 142486 1.9548 0.974697
16 to 20 142133 0.7582 0.775835
15 to 19 141866 -0.1469 0.441613
14 to 18 142034 0.4226 0.663710
13 to 17 141778 -0.4452 0.328093
12 to 16 142282 1.2633 0.896757
11 to 15 141493 -1.4113 0.079080
10 to 14 142150 0.8158 0.792702
9 to 13 141378 -1.8011 0.035842
8 to 12 141528 -1.2926 0.098067
7 to 11 142028 0.4023 0.656258
6 to 10 142073 0.5548 0.710489
5 to 9 141909 -0.0011 0.499554
4 to 8 142386 1.6158 0.946935
3 to 7 142288 1.2836 0.900364
2 to 6 142235 1.1040 0.865196
1 to 5 142026 0.3955 0.653760
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_16:31
Bits used No. missing words z-score p-value
31 to 32 142841 2.7483 0.997005
30 to 31 142237 0.9666 0.833123
29 to 30 141760 -0.4405 0.329787
28 to 29 142181 0.8014 0.788546
27 to 28 141660 -0.7355 0.231022
26 to 27 141896 -0.0393 0.484317
25 to 26 142202 0.8633 0.806023
24 to 25 142581 1.9813 0.976223
23 to 24 141941 0.0934 0.537216
22 to 23 142036 0.3737 0.645671
21 to 22 141210 -2.0629 0.019560
20 to 21 141889 -0.0600 0.476090
19 to 20 142029 0.3530 0.637959
18 to 19 141251 -1.9420 0.026070
17 to 18 141660 -0.7355 0.231022
16 to 17 141965 0.1642 0.565220
15 to 16 142265 1.0492 0.852951
14 to 15 141903 -0.0187 0.492551
13 to 14 141576 -0.9833 0.162736
12 to 13 142957 3.0905 0.999001
11 to 12 142079 0.5005 0.691639
10 to 11 141839 -0.2075 0.417824
9 to 10 141867 -0.1249 0.450314
8 to 9 141944 0.1023 0.540729
7 to 8 141992 0.2439 0.596332
6 to 7 141332 -1.7030 0.044280
5 to 6 141869 -0.1190 0.452651
4 to 5 141684 -0.6647 0.253124
3 to 4 141817 -0.2724 0.392673
2 to 3 141770 -0.4110 0.340535
1 to 2 141766 -0.4228 0.336220
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2530.92 0.437 0.669046
Test results for specific bytes for dh-ranFile-2018-06-22_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2475.62 -0.345 0.365133
2 to 9 2432.79 -0.951 0.170914
3 to 10 2490.44 -0.135 0.446246
4 to 11 2487.02 -0.184 0.427191
5 to 12 2495.73 -0.060 0.475896
6 to 13 2515.38 0.218 0.586092
7 to 14 2533.62 0.475 0.682752
8 to 15 2472.91 -0.383 0.350796
9 to 16 2578.90 1.116 0.867757
10 to 17 2563.42 0.897 0.815118
11 to 18 2495.00 -0.071 0.471807
12 to 19 2340.09 -2.261 0.011866
13 to 20 2416.94 -1.175 0.120077
14 to 21 2483.58 -0.232 0.408181
15 to 22 2624.13 1.755 0.960405
16 to 23 2572.88 1.031 0.848663
17 to 24 2564.98 0.919 0.820949
18 to 25 2397.04 -1.456 0.072691
19 to 26 2516.20 0.229 0.590628
20 to 27 2646.95 2.078 0.981152
21 to 28 2602.44 1.449 0.926283
22 to 29 2357.07 -2.021 0.021622
23 to 30 2610.25 1.559 0.940527
24 to 31 2474.70 -0.358 0.360258
25 to 32 2570.90 1.003 0.841986
CDPARK for dh-ranFile-2018-06-22_16:31: 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
3562 1.7808 0.962529
3497 -1.1872 0.117571
3545 1.0046 0.842447
3482 -1.8721 0.030593
3466 -2.6027 0.004624
3515 -0.3653 0.357445
3494 -1.3242 0.092718
3525 0.0913 0.536383
3540 0.7763 0.781201
3488 -1.5982 0.055002
Square side=100, avg. no. parked=3511.40 sample std.=29.48
p-value of the KSTEST for those 10 p-values: 0.063960
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_16:31
0.6699,0.5713,0.9889,0.7028,0.5724,0.9469,0.0234,0.9921,0.1927,0.3598,
The KS test for those 10 p-values: 0.164478
The 3DSPHERES test for dh-ranFile-2018-06-22_16:31
sample no r^3 equiv. uni.
1 3.905 0.122051
2 57.236 0.851604
3 27.494 0.600074
4 34.661 0.685057
5 20.948 0.502558
6 8.208 0.239367
7 10.682 0.299584
8 69.937 0.902824
9 1.557 0.050579
10 31.957 0.655349
11 16.998 0.432542
12 50.346 0.813288
13 19.003 0.469233
14 11.252 0.312751
15 1.403 0.045704
16 37.771 0.716068
17 54.122 0.835372
18 53.571 0.832318
19 2.314 0.074230
20 5.704 0.173163
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.913329
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 1.8 -0.1 0.8 -0.8
0.0 -0.3 0.0 1.0 -0.6 -0.9
-0.7 -1.2 1.8 0.2 0.2 -1.0
1.6 -0.3 0.9 -1.2 -0.4 -0.2
-0.0 -0.8 1.0 -0.0 0.9 0.0
1.2 0.7 -0.2 -0.6 -0.8 -0.3
-1.4 -0.1 -0.4 -1.3 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:30.627082
z-score=-1.240887, p-value=0.096769
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_16:31
Test no p-value
1 0.419577
2 0.640822
3 0.239071
4 0.613772
5 0.060136
6 0.166029
7 0.784925
8 0.522697
9 0.153307
10 0.388732
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.443127
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_16:31:
(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 66410 0.99 66628 0.02
3 25000.00 25130 0.68 24921 0.25
4 6666.67 6727 0.55 6750 1.04
5 1388.89 1473 5.09 1399 0.07
6 238.10 222 1.09 256 1.35
7 34.72 35 0.00 40 0.80
8 4.96 2 1.77 5 0.00
p=0.88195 p=0.26095
Number of rngs required: 688850, p-value: 0.697
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_16:31
No. of wins: Observed Expected
98371 98585.9
z-score=-0.961, pvalue=0.16828
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66267 66666.7 2.396 2.396
2 37656 37654.3 0.000 2.396
3 27113 26954.7 0.929 3.325
4 19375 19313.5 0.196 3.521
5 14010 13851.4 1.816 5.337
6 9900 9943.5 0.191 5.528
7 7310 7145.0 3.809 9.337
8 5116 5139.1 0.104 9.440
9 3730 3699.9 0.245 9.686
10 2703 2666.3 0.505 10.191
11 1957 1923.3 0.589 10.781
12 1387 1388.7 0.002 10.783
13 942 1003.7 3.795 14.577
14 708 726.1 0.453 15.031
15 501 525.8 1.173 16.204
16 358 381.2 1.406 17.610
17 261 276.5 0.873 18.483
18 187 200.8 0.952 19.435
19 120 146.0 4.625 24.060
20 115 106.2 0.727 24.787
21 284 287.1 0.034 24.821
Chisq= 24.82 for 20 degrees of freedom, p= 0.79162
SUMMARY of craptest
p-value for no. of wins: 0.168283
p-value for throws/game: 0.791623
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_16:31
No. of wins: Observed Expected
98389 98585.9
z-score=-0.880, pvalue=0.18930
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66734 66666.7 0.068 0.068
2 37630 37654.3 0.016 0.084
3 27061 26954.7 0.419 0.503
4 18985 19313.5 5.586 6.089
5 13975 13851.4 1.103 7.191
6 9899 9943.5 0.200 7.391
7 7189 7145.0 0.271 7.662
8 5208 5139.1 0.924 8.586
9 3725 3699.9 0.171 8.757
10 2710 2666.3 0.716 9.473
11 1921 1923.3 0.003 9.476
12 1336 1388.7 2.003 11.479
13 946 1003.7 3.319 14.798
14 719 726.1 0.070 14.868
15 532 525.8 0.072 14.940
16 414 381.2 2.831 17.771
17 258 276.5 1.243 19.014
18 205 200.8 0.087 19.101
19 151 146.0 0.172 19.273
20 111 106.2 0.216 19.489
21 291 287.1 0.053 19.541
Chisq= 19.54 for 20 degrees of freedom, p= 0.51305
SUMMARY of craptest
p-value for no. of wins: 0.189303
p-value for throws/game: 0.513055
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0046,0.0105,0.0118,0.0119,0.0193,0.0196,0.0216,0.0234,0.0261,0.0306,
0.0315,0.0341,0.0358,0.0438,0.0443,0.0457,0.0476,0.0506,0.0535,0.0550,
0.0556,0.0601,0.0640,0.0727,0.0742,0.0791,0.0808,0.0834,0.0859,0.0927,
0.0968,0.0981,0.0997,0.1055,0.1062,0.1176,0.1201,0.1221,0.1239,0.1265,
0.1459,0.1533,0.1617,0.1627,0.1645,0.1660,0.1669,0.1683,0.1709,0.1732,
0.1738,0.1846,0.1893,0.1927,0.2242,0.2247,0.2310,0.2310,0.2347,0.2391,
0.2394,0.2407,0.2448,0.2511,0.2523,0.2531,0.2562,0.2610,0.2678,0.2799,
0.2996,0.3128,0.3281,0.3286,0.3298,0.3315,0.3315,0.3348,0.3362,0.3370,
0.3405,0.3487,0.3508,0.3574,0.3598,0.3603,0.3641,0.3651,0.3669,0.3764,
0.3793,0.3830,0.3835,0.3887,0.3888,0.3892,0.3893,0.3927,0.3928,0.3951,
0.4026,0.4082,0.4173,0.4178,0.4196,0.4216,0.4246,0.4272,0.4298,0.4302,
0.4325,0.4385,0.4416,0.4431,0.4436,0.4462,0.4503,0.4527,0.4578,0.4604,
0.4692,0.4718,0.4727,0.4755,0.4759,0.4761,0.4843,0.4864,0.4926,0.4940,
0.4977,0.4996,0.5026,0.5077,0.5131,0.5187,0.5227,0.5230,0.5239,0.5261,
0.5264,0.5274,0.5364,0.5372,0.5407,0.5543,0.5652,0.5699,0.5711,0.5713,
0.5720,0.5724,0.5786,0.5810,0.5812,0.5861,0.5900,0.5906,0.5963,0.6001,
0.6062,0.6138,0.6208,0.6293,0.6345,0.6380,0.6382,0.6408,0.6435,0.6457,
0.6461,0.6515,0.6537,0.6538,0.6553,0.6563,0.6637,0.6662,0.6690,0.6699,
0.6779,0.6828,0.6837,0.6851,0.6905,0.6909,0.6916,0.6968,0.7020,0.7028,
0.7041,0.7043,0.7099,0.7105,0.7135,0.7161,0.7277,0.7359,0.7416,0.7425,
0.7529,0.7552,0.7579,0.7581,0.7614,0.7758,0.7812,0.7849,0.7858,0.7885,
0.7908,0.7916,0.7927,0.7957,0.7983,0.8060,0.8101,0.8133,0.8151,0.8171,
0.8209,0.8231,0.8323,0.8331,0.8332,0.8337,0.8348,0.8354,0.8357,0.8377,
0.8417,0.8420,0.8424,0.8445,0.8454,0.8487,0.8516,0.8530,0.8567,0.8652,
0.8678,0.8819,0.8968,0.8970,0.9004,0.9010,0.9028,0.9133,0.9186,0.9245,
0.9263,0.9294,0.9405,0.9424,0.9469,0.9469,0.9539,0.9604,0.9625,0.9632,
0.9747,0.9762,0.9806,0.9812,0.9872,0.9889,0.9921,0.9970,0.9990,
Overall p-value after applying KStest on 269 p-values = 0.664609
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.