RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-08-30_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 15.80 21.2650 0.785339
2 to 25 15.90 19.1961 0.682606
3 to 26 15.60 15.5133 0.441436
4 to 27 15.60 15.7686 0.459709
5 to 28 15.96 12.8138 0.251443
6 to 29 15.34 27.0575 0.942770
7 to 30 15.46 22.0519 0.817268
8 to 31 15.73 13.1570 0.274386
9 to 32 15.73 15.4827 0.439244
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.653141
Tough bday spacings test for dh-ranFile-2018-08-30_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 12 32 74 97 102 82 58 29 7 6 1
(O-E)^2/E 0.9 0.6 0.0 0.0 0.2 0.2 0.7 0.0 4.2 0.1 2.3
Birthday Spacings: Sum(O-E)^2/E= 9.095, p= 0.477
RESULTS OF GCD FOR dh-ranFile-2018-08-30_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.950288
p-value, dist. of gcd's: 0.225031
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-08-30_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.143 0.645 0.903 0.648 0.848 0.793 0.302 0.961
Bits 8 to 15---> 0.914 0.771 0.522 0.541 0.737 0.302 0.236 0.668
Bits 16 to 23---> 0.542 0.099 0.767 0.313 0.947 0.597 0.932 0.665
Bits 24 to 31---> 0.511 0.173 0.869 0.031 0.768 0.200 0.026 0.578
KS test for the above 32 p values: 0.632
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-08-30_00:31,
p-values for 5 runs: 0.8721, 0.3752, 0.5720, 0.4511, 0.3148
Rank test for binary matrices (31x31) for dh-ranFile-2018-08-30_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 223 211.4 0.634 0.634
r= 29 5171 5134.0 0.267 0.901
r= 30 23010 23103.0 0.375 1.276
r= 31 11596 11551.5 0.171 1.447
chi-square = 1.447 with df = 3; p-value = 0.305
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-08-30_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5074 5134.0 0.701 0.906
r= 31 23180 23103.0 0.256 1.163
r= 32 11528 11551.5 0.048 1.211
chi-square = 1.211 with df = 3; p-value = 0.250
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-08-30_00:31
b-rank test for bits 1 to 8, p=0.33079
b-rank test for bits 2 to 9, p=0.13157
b-rank test for bits 3 to 10, p=0.18327
b-rank test for bits 4 to 11, p=0.38187
b-rank test for bits 5 to 12, p=0.57965
b-rank test for bits 6 to 13, p=0.47462
b-rank test for bits 7 to 14, p=0.02802
b-rank test for bits 8 to 15, p=0.64496
b-rank test for bits 9 to 16, p=0.29318
b-rank test for bits 10 to 17, p=0.57866
b-rank test for bits 11 to 18, p=0.87149
b-rank test for bits 12 to 19, p=0.61968
b-rank test for bits 13 to 20, p=0.07704
b-rank test for bits 14 to 21, p=0.84485
b-rank test for bits 15 to 22, p=0.43219
b-rank test for bits 16 to 23, p=0.01501
b-rank test for bits 17 to 24, p=0.08304
b-rank test for bits 18 to 25, p=0.24816
b-rank test for bits 19 to 26, p=0.96731
b-rank test for bits 20 to 27, p=0.41017
b-rank test for bits 21 to 28, p=0.92191
b-rank test for bits 22 to 29, p=0.78570
b-rank test for bits 23 to 30, p=0.09355
b-rank test for bits 24 to 31, p=0.14957
b-rank test for bits 25 to 32, p=0.86367
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 = 0.488968
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-08-30_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 141615 -0.69 0.245825
2 140894 -2.37 0.008840
3 141621 -0.67 0.250261
4 142297 0.91 0.817471
5 142540 1.47 0.929696
6 141717 -0.45 0.326583
7 142020 0.26 0.602018
8 142617 1.65 0.950879
9 141156 -1.76 0.039194
10 142622 1.67 0.952055
11 142433 1.22 0.889435
12 141856 -0.12 0.450419
13 141989 0.19 0.573834
14 141504 -0.95 0.171811
15 141174 -1.72 0.042893
16 141614 -0.69 0.245090
17 142314 0.95 0.827796
18 141704 -0.48 0.315705
19 142528 1.45 0.925840
20 142623 1.67 0.952288
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-08-30_00:31
Bits used No. missing words z-score p-value
23 to 32 142091 0.6264 0.734490
22 to 31 142288 1.3058 0.904183
21 to 30 141764 -0.5011 0.308137
20 to 29 141659 -0.8632 0.194012
19 to 28 141767 -0.4908 0.311786
18 to 27 141750 -0.5494 0.291361
17 to 26 141752 -0.5425 0.293731
16 to 25 141889 -0.0701 0.472056
15 to 24 142138 0.7885 0.784803
14 to 23 141892 -0.0598 0.476174
13 to 22 141144 -2.6391 0.004157
12 to 21 141719 -0.6563 0.255812
11 to 20 142374 1.6023 0.945457
10 to 19 142506 2.0575 0.980180
9 to 18 141856 -0.1839 0.427047
8 to 17 142039 0.4471 0.672612
7 to 16 142239 1.1368 0.872188
6 to 15 141929 0.0678 0.527039
5 to 14 142260 1.2092 0.886708
4 to 13 142123 0.7368 0.769376
3 to 12 142009 0.3437 0.634460
2 to 11 142268 1.2368 0.891918
1 to 10 141988 0.2713 0.606911
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-08-30_00:31
Bits used No. missing words z-score p-value
28 to 32 142315 1.3752 0.915458
27 to 31 142406 1.6836 0.953873
26 to 30 141490 -1.4215 0.077592
25 to 29 141643 -0.9028 0.183312
24 to 28 141649 -0.8825 0.188760
23 to 27 142416 1.7175 0.957058
22 to 26 141825 -0.2859 0.387491
21 to 25 141699 -0.7130 0.237928
20 to 24 141680 -0.7774 0.218464
19 to 23 141446 -1.5706 0.058137
18 to 22 142094 0.6260 0.734343
17 to 21 142002 0.3141 0.623291
16 to 20 141785 -0.4215 0.336711
15 to 19 142312 1.3650 0.913871
14 to 18 142010 0.3413 0.633544
13 to 17 142486 1.9548 0.974697
12 to 16 142018 0.3684 0.643702
11 to 15 141897 -0.0418 0.483330
10 to 14 142176 0.9040 0.816993
9 to 13 141648 -0.8859 0.187845
8 to 12 141408 -1.6994 0.044620
7 to 11 141821 -0.2994 0.382308
6 to 10 141853 -0.1909 0.424283
5 to 9 142062 0.5175 0.697605
4 to 8 141370 -1.8282 0.033757
3 to 7 141753 -0.5299 0.298080
2 to 6 141655 -0.8621 0.194306
1 to 5 141587 -1.0926 0.137275
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-08-30_00:31
Bits used No. missing words z-score p-value
31 to 32 142090 0.5329 0.702966
30 to 31 141753 -0.4612 0.322345
29 to 30 142126 0.6391 0.738636
28 to 29 141820 -0.2635 0.396079
27 to 28 140975 -2.7561 0.002924
26 to 27 142386 1.4061 0.920154
25 to 26 142116 0.6096 0.728952
24 to 25 141767 -0.4199 0.337297
23 to 24 142036 0.3737 0.645671
22 to 23 142191 0.8309 0.796981
21 to 22 141690 -0.6470 0.258819
20 to 21 141502 -1.2016 0.114766
19 to 20 141980 0.2085 0.582568
18 to 19 142203 0.8663 0.806833
17 to 18 141738 -0.5054 0.306640
16 to 17 141546 -1.0718 0.141912
15 to 16 141967 0.1701 0.567541
14 to 15 141645 -0.7797 0.217774
13 to 14 142190 0.8279 0.796146
12 to 13 142033 0.3648 0.642373
11 to 12 141679 -0.6794 0.248430
10 to 11 141925 0.0462 0.518434
9 to 10 141317 -1.7473 0.040294
8 to 9 142242 0.9813 0.836784
7 to 8 142210 0.8869 0.812442
6 to 7 142196 0.8456 0.801122
5 to 6 142518 1.7955 0.963712
4 to 5 142166 0.7571 0.775517
3 to 4 142521 1.8043 0.964411
2 to 3 142317 1.2026 0.885428
1 to 2 141933 0.0698 0.527833
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-08-30_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2517.88 0.253 0.599786
Test results for specific bytes for dh-ranFile-2018-08-30_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2434.74 -0.923 0.178041
2 to 9 2366.77 -1.884 0.029774
3 to 10 2538.01 0.538 0.704564
4 to 11 2575.81 1.072 0.858172
5 to 12 2393.60 -1.505 0.066204
6 to 13 2528.29 0.400 0.655448
7 to 14 2481.31 -0.264 0.395794
8 to 15 2529.03 0.411 0.659312
9 to 16 2497.03 -0.042 0.483258
10 to 17 2585.70 1.212 0.887236
11 to 18 2604.87 1.483 0.930971
12 to 19 2503.85 0.054 0.521683
13 to 20 2582.84 1.171 0.879294
14 to 21 2499.59 -0.006 0.497679
15 to 22 2550.02 0.707 0.760323
16 to 23 2443.89 -0.794 0.213738
17 to 24 2573.39 1.038 0.850330
18 to 25 2377.36 -1.734 0.041421
19 to 26 2546.10 0.652 0.742775
20 to 27 2438.04 -0.876 0.190456
21 to 28 2495.65 -0.061 0.475495
22 to 29 2369.49 -1.846 0.032466
23 to 30 2646.49 2.072 0.980850
24 to 31 2544.51 0.629 0.735475
25 to 32 2654.60 2.186 0.985603
CDPARK for dh-ranFile-2018-08-30_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
3513 -0.4566 0.323972
3502 -0.9589 0.168804
3604 3.6986 0.999892
3551 1.2785 0.899470
3509 -0.6393 0.261324
3512 -0.5023 0.307734
3533 0.4566 0.676028
3532 0.4110 0.659449
3521 -0.0913 0.463617
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3529.60 sample std.=28.23
p-value of the KSTEST for those 10 p-values: 0.414943
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-08-30_00:31
0.1762,0.2161,0.3800,0.8169,0.2034,0.6892,0.8273,0.5985,0.3110,0.5613,
The KS test for those 10 p-values: 0.797564
The 3DSPHERES test for dh-ranFile-2018-08-30_00:31
sample no r^3 equiv. uni.
1 4.262 0.132428
2 85.434 0.942029
3 34.770 0.686200
4 78.601 0.927198
5 19.535 0.478564
6 2.984 0.094665
7 35.249 0.691173
8 56.953 0.850199
9 77.537 0.924571
10 15.012 0.393710
11 31.479 0.649816
12 82.093 0.935198
13 0.758 0.024946
14 4.054 0.126410
15 55.260 0.841499
16 0.829 0.027252
17 5.541 0.168651
18 43.204 0.763103
19 26.079 0.580758
20 16.557 0.424151
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.462183
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-08-30_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.5 1.1 -0.3 1.0 1.3
2.2 -1.5 1.1 1.9 0.4 -0.4
0.9 0.5 -0.1 -1.3 -1.4 -0.7
-0.4 0.8 0.6 -0.8 -0.2 -0.6
-0.4 2.1 -1.0 0.4 -0.7 -0.2
-0.1 -0.2 2.0 0.1 -0.6 2.0
0.3 -0.1 3.0 -0.1 0.1 1.0
-0.1
Chi-square with 42 degrees of freedom:49.166113
z-score=0.781887, p-value=0.791954
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-08-30_00:31
Test no p-value
1 0.424857
2 0.920478
3 0.252335
4 0.553311
5 0.474655
6 0.002858
7 0.332870
8 0.673718
9 0.019386
10 0.628258
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.384679
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-08-30_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 66794 0.24 66877 0.66
3 25000.00 24828 1.18 24838 1.05
4 6666.67 6644 0.08 6689 0.07
5 1388.89 1455 3.15 1311 4.37
6 238.10 238 0.00 244 0.15
7 34.72 36 0.05 35 0.00
8 4.96 4 0.19 5 0.00
p=0.44115 p=0.61013
Number of rngs required: 689481, p-value: 0.895
RESULTS OF CRAPS TEST for dh-ranFile-2018-08-30_00:31
No. of wins: Observed Expected
98504 98585.9
z-score=-0.366, pvalue=0.35714
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66849 66666.7 0.499 0.499
2 37601 37654.3 0.076 0.574
3 26959 26954.7 0.001 0.575
4 19171 19313.5 1.051 1.626
5 13733 13851.4 1.012 2.638
6 10012 9943.5 0.471 3.109
7 7134 7145.0 0.017 3.126
8 5136 5139.1 0.002 3.128
9 3674 3699.9 0.181 3.309
10 2601 2666.3 1.599 4.908
11 2007 1923.3 3.640 8.548
12 1433 1388.7 1.411 9.959
13 1040 1003.7 1.312 11.270
14 728 726.1 0.005 11.275
15 528 525.8 0.009 11.284
16 373 381.2 0.174 11.458
17 211 276.5 15.533 26.991
18 205 200.8 0.087 27.078
19 177 146.0 6.590 33.667
20 106 106.2 0.000 33.668
21 322 287.1 4.239 37.907
Chisq= 37.91 for 20 degrees of freedom, p= 0.99091
SUMMARY of craptest
p-value for no. of wins: 0.357138
p-value for throws/game: 0.990909
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-08-30_00:31
No. of wins: Observed Expected
98821 98585.9
z-score= 1.052, pvalue=0.85353
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66728 66666.7 0.056 0.056
2 37568 37654.3 0.198 0.254
3 27097 26954.7 0.751 1.005
4 19271 19313.5 0.093 1.099
5 13907 13851.4 0.223 1.322
6 9889 9943.5 0.299 1.621
7 7153 7145.0 0.009 1.630
8 5161 5139.1 0.094 1.723
9 3748 3699.9 0.626 2.349
10 2623 2666.3 0.703 3.053
11 1959 1923.3 0.662 3.714
12 1357 1388.7 0.725 4.440
13 941 1003.7 3.919 8.358
14 731 726.1 0.033 8.391
15 495 525.8 1.808 10.199
16 401 381.2 1.034 11.233
17 274 276.5 0.023 11.256
18 179 200.8 2.373 13.629
19 128 146.0 2.216 15.844
20 108 106.2 0.030 15.874
21 282 287.1 0.091 15.966
Chisq= 15.97 for 20 degrees of freedom, p= 0.28124
SUMMARY of craptest
p-value for no. of wins: 0.853529
p-value for throws/game: 0.281239
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0029,0.0029,0.0042,0.0088,0.0150,0.0194,0.0249,0.0262,0.0273,0.0280,
0.0298,0.0307,0.0325,0.0338,0.0392,0.0403,0.0414,0.0429,0.0446,0.0581,
0.0662,0.0770,0.0776,0.0830,0.0936,0.0947,0.0989,0.1148,0.1264,0.1316,
0.1324,0.1373,0.1419,0.1426,0.1496,0.1687,0.1688,0.1718,0.1730,0.1762,
0.1780,0.1833,0.1833,0.1878,0.1888,0.1905,0.1940,0.1943,0.2002,0.2034,
0.2137,0.2161,0.2178,0.2185,0.2250,0.2359,0.2379,0.2451,0.2458,0.2482,
0.2484,0.2495,0.2503,0.2514,0.2523,0.2558,0.2588,0.2613,0.2744,0.2812,
0.2914,0.2932,0.2937,0.2981,0.3016,0.3020,0.3054,0.3066,0.3077,0.3081,
0.3110,0.3118,0.3127,0.3148,0.3157,0.3223,0.3240,0.3266,0.3308,0.3329,
0.3367,0.3373,0.3571,0.3752,0.3800,0.3819,0.3823,0.3847,0.3875,0.3937,
0.3958,0.3961,0.4102,0.4149,0.4242,0.4243,0.4249,0.4270,0.4275,0.4322,
0.4392,0.4412,0.4414,0.4504,0.4511,0.4597,0.4622,0.4636,0.4721,0.4746,
0.4747,0.4755,0.4762,0.4769,0.4786,0.4833,0.4833,0.4890,0.4977,0.5115,
0.5184,0.5217,0.5218,0.5270,0.5278,0.5405,0.5417,0.5533,0.5613,0.5675,
0.5720,0.5738,0.5781,0.5787,0.5797,0.5808,0.5826,0.5966,0.5985,0.5998,
0.6020,0.6069,0.6101,0.6197,0.6233,0.6283,0.6323,0.6335,0.6345,0.6424,
0.6437,0.6450,0.6451,0.6457,0.6478,0.6498,0.6531,0.6554,0.6593,0.6594,
0.6648,0.6682,0.6726,0.6737,0.6760,0.6826,0.6862,0.6892,0.6912,0.6976,
0.7030,0.7046,0.7290,0.7343,0.7345,0.7355,0.7373,0.7386,0.7428,0.7603,
0.7631,0.7674,0.7677,0.7694,0.7714,0.7755,0.7848,0.7853,0.7857,0.7920,
0.7932,0.7961,0.7970,0.7976,0.8011,0.8068,0.8124,0.8169,0.8170,0.8173,
0.8175,0.8273,0.8278,0.8368,0.8415,0.8448,0.8477,0.8502,0.8503,0.8535,
0.8582,0.8637,0.8689,0.8715,0.8721,0.8722,0.8793,0.8854,0.8867,0.8872,
0.8894,0.8919,0.8951,0.8995,0.9025,0.9042,0.9139,0.9144,0.9155,0.9202,
0.9205,0.9219,0.9246,0.9258,0.9272,0.9297,0.9310,0.9317,0.9352,0.9420,
0.9428,0.9455,0.9468,0.9503,0.9509,0.9521,0.9523,0.9539,0.9571,0.9606,
0.9637,0.9644,0.9673,0.9747,0.9802,0.9808,0.9856,0.9909,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.180813
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.