RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.96 15.7173 0.456043
2 to 25 15.84 14.8038 0.390390
3 to 26 15.84 15.5644 0.445100
4 to 27 15.90 16.3514 0.500923
5 to 28 15.89 15.3035 0.426367
6 to 29 15.76 8.3694 0.042004
7 to 30 15.52 24.1661 0.885008
8 to 31 15.88 15.5905 0.446974
9 to 32 15.83 16.3997 0.504299
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.246039
Tough bday spacings test for dh-ranFile-2018-07-04_08:31: 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 9 36 80 102 99 81 47 19 12 6 9
(O-E)^2/E 0.0 0.0 0.6 0.2 0.0 0.1 0.5 3.9 0.6 0.1 6.0
Birthday Spacings: Sum(O-E)^2/E= 11.944, p= 0.711
RESULTS OF GCD FOR dh-ranFile-2018-07-04_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.688214
p-value, dist. of gcd's: 0.118450
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.430 0.436 0.635 0.409 0.455 0.123 0.503 0.331
Bits 8 to 15---> 0.452 0.870 0.405 0.870 0.269 0.008 0.555 0.747
Bits 16 to 23---> 0.424 0.526 0.458 0.969 0.331 0.880 0.096 0.984
Bits 24 to 31---> 0.622 0.697 0.277 0.490 0.219 0.754 0.868 0.765
KS test for the above 32 p values: 0.491
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_08:31,
p-values for 5 runs: 0.4046, 0.5861, 0.9676, 0.2749, 0.7381
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5219 5134.0 1.407 1.408
r= 30 22864 23103.0 2.473 3.881
r= 31 11706 11551.5 2.066 5.947
chi-square = 5.947 with df = 3; p-value = 0.886
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 222 211.4 0.530 0.530
r= 30 5186 5134.0 0.526 1.056
r= 31 23254 23103.0 0.986 2.042
r= 32 11338 11551.5 3.947 5.989
chi-square = 5.989 with df = 3; p-value = 0.888
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_08:31
b-rank test for bits 1 to 8, p=0.75216
b-rank test for bits 2 to 9, p=0.96628
b-rank test for bits 3 to 10, p=0.80910
b-rank test for bits 4 to 11, p=0.11149
b-rank test for bits 5 to 12, p=0.26660
b-rank test for bits 6 to 13, p=0.52396
b-rank test for bits 7 to 14, p=0.09516
b-rank test for bits 8 to 15, p=0.00499
b-rank test for bits 9 to 16, p=0.69670
b-rank test for bits 10 to 17, p=0.56673
b-rank test for bits 11 to 18, p=0.09843
b-rank test for bits 12 to 19, p=0.96443
b-rank test for bits 13 to 20, p=0.73757
b-rank test for bits 14 to 21, p=0.10820
b-rank test for bits 15 to 22, p=0.00668
b-rank test for bits 16 to 23, p=0.02359
b-rank test for bits 17 to 24, p=0.09152
b-rank test for bits 18 to 25, p=0.56524
b-rank test for bits 19 to 26, p=0.64197
b-rank test for bits 20 to 27, p=0.04914
b-rank test for bits 21 to 28, p=0.64061
b-rank test for bits 22 to 29, p=0.62894
b-rank test for bits 23 to 30, p=0.57034
b-rank test for bits 24 to 31, p=0.26920
b-rank test for bits 25 to 32, p=0.84880
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 = 0.107249
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_08:31
(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 141635 -0.64 0.260775
2 141817 -0.22 0.414601
3 141937 0.06 0.525774
4 141972 0.15 0.558207
5 142217 0.72 0.763885
6 141421 -1.14 0.126944
7 142893 2.30 0.989227
8 142303 0.92 0.821159
9 141384 -1.23 0.109835
10 142419 1.19 0.883137
11 141169 -1.73 0.041838
12 141731 -0.42 0.338464
13 141413 -1.16 0.123096
14 142416 1.18 0.881756
15 142051 0.33 0.629680
16 142341 1.01 0.843411
17 141282 -1.47 0.071362
18 141604 -0.71 0.237803
19 142439 1.24 0.892058
20 141896 -0.03 0.487577
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_08:31
Bits used No. missing words z-score p-value
23 to 32 142452 1.8713 0.969347
22 to 31 141966 0.1954 0.577466
21 to 30 142225 1.0885 0.861817
20 to 29 142174 0.9127 0.819288
19 to 28 141641 -0.9253 0.177411
18 to 27 141805 -0.3598 0.359514
17 to 26 142261 1.2127 0.887369
16 to 25 141968 0.2023 0.580163
15 to 24 142258 1.2023 0.885378
14 to 23 142064 0.5333 0.703103
13 to 22 141935 0.0885 0.535267
12 to 21 142020 0.3816 0.648629
11 to 20 141777 -0.4563 0.324083
10 to 19 142226 1.0920 0.862576
9 to 18 141292 -2.1287 0.016639
8 to 17 141610 -1.0322 0.150996
7 to 16 141868 -0.1425 0.443336
6 to 15 141789 -0.4149 0.339096
5 to 14 141510 -1.3770 0.084256
4 to 13 141988 0.2713 0.606911
3 to 12 142377 1.6127 0.946590
2 to 11 142419 1.7575 0.960582
1 to 10 141710 -0.6873 0.245933
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_08:31
Bits used No. missing words z-score p-value
28 to 32 142333 1.4362 0.924523
27 to 31 141784 -0.4248 0.335474
26 to 30 142083 0.5887 0.721973
25 to 29 141881 -0.0960 0.461747
24 to 28 142001 0.3107 0.622003
23 to 27 142211 1.0226 0.846754
22 to 26 141502 -1.3808 0.083673
21 to 25 141570 -1.1503 0.125016
20 to 24 142093 0.6226 0.733230
19 to 23 141969 0.2023 0.580148
18 to 22 141988 0.2667 0.605141
17 to 21 141927 0.0599 0.523882
16 to 20 142107 0.6701 0.748593
15 to 19 141713 -0.6655 0.252857
14 to 18 141488 -1.4282 0.076612
13 to 17 141798 -0.3774 0.352942
12 to 16 142598 2.3345 0.990215
11 to 15 142000 0.3074 0.620714
10 to 14 142202 0.9921 0.839426
9 to 13 142258 1.1819 0.881384
8 to 12 141573 -1.1401 0.127122
7 to 11 141740 -0.5740 0.282984
6 to 10 142372 1.5684 0.941603
5 to 9 141606 -1.0282 0.151919
4 to 8 141617 -0.9909 0.160855
3 to 7 141645 -0.8960 0.185117
2 to 6 141957 0.1616 0.564187
1 to 5 141556 -1.1977 0.115511
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_08:31
Bits used No. missing words z-score p-value
31 to 32 141555 -1.0452 0.147960
30 to 31 141554 -1.0482 0.147280
29 to 30 142276 1.0816 0.860290
28 to 29 141983 0.2173 0.586019
27 to 28 142330 1.2409 0.892681
26 to 27 141855 -0.1603 0.436336
25 to 26 142164 0.7512 0.773746
24 to 25 141892 -0.0511 0.479615
23 to 24 141016 -2.6352 0.004204
22 to 23 141531 -1.1160 0.132207
21 to 22 142266 1.0521 0.853629
20 to 21 141933 0.0698 0.527833
19 to 20 142000 0.2675 0.605444
18 to 19 141947 0.1111 0.544240
17 to 18 141926 0.0492 0.519610
16 to 17 141800 -0.3225 0.373534
15 to 16 141839 -0.2075 0.417824
14 to 15 141868 -0.1219 0.451482
13 to 14 141857 -0.1544 0.438661
12 to 13 141501 -1.2045 0.114196
11 to 12 142177 0.7896 0.785116
10 to 11 142715 2.3766 0.991264
9 to 10 141908 -0.0039 0.498435
8 to 9 142161 0.7424 0.771074
7 to 8 142020 0.3265 0.627962
6 to 7 142084 0.5153 0.696811
5 to 6 141561 -1.0275 0.152087
4 to 5 141667 -0.7148 0.237355
3 to 4 142243 0.9843 0.837510
2 to 3 142064 0.4563 0.675896
1 to 2 142040 0.3855 0.650051
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2391.02 -1.541 0.061625
Test results for specific bytes for dh-ranFile-2018-07-04_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2536.01 0.509 0.694715
2 to 9 2510.01 0.142 0.556276
3 to 10 2552.27 0.739 0.770099
4 to 11 2568.58 0.970 0.833948
5 to 12 2564.81 0.917 0.820306
6 to 13 2340.61 -2.254 0.012092
7 to 14 2622.45 1.732 0.958339
8 to 15 2471.58 -0.402 0.343875
9 to 16 2457.47 -0.601 0.273754
10 to 17 2601.91 1.441 0.925233
11 to 18 2518.58 0.263 0.603632
12 to 19 2527.38 0.387 0.650675
13 to 20 2353.06 -2.078 0.018854
14 to 21 2396.02 -1.471 0.070709
15 to 22 2368.54 -1.859 0.031502
16 to 23 2490.45 -0.135 0.446277
17 to 24 2500.57 0.008 0.503236
18 to 25 2433.92 -0.934 0.175035
19 to 26 2491.65 -0.118 0.452978
20 to 27 2500.72 0.010 0.504068
21 to 28 2661.85 2.289 0.988960
22 to 29 2521.02 0.297 0.616878
23 to 30 2321.81 -2.520 0.005869
24 to 31 2599.45 1.406 0.920202
25 to 32 2442.00 -0.820 0.206020
CDPARK for dh-ranFile-2018-07-04_08:31: 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
3522 -0.0457 0.481790
3507 -0.7306 0.232514
3577 2.4658 0.993164
3529 0.2740 0.607947
3519 -0.1826 0.427537
3557 1.5525 0.939730
3543 0.9132 0.819442
3498 -1.1416 0.126820
3509 -0.6393 0.261324
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3527.90 sample std.=23.21
p-value of the KSTEST for those 10 p-values: 0.770264
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_08:31
0.6926,0.2814,0.2611,0.9966,0.0641,0.0762,0.3809,0.9900,0.2342,0.7008,
The KS test for those 10 p-values: 0.275870
The 3DSPHERES test for dh-ranFile-2018-07-04_08:31
sample no r^3 equiv. uni.
1 24.091 0.552025
2 127.593 0.985780
3 50.034 0.811338
4 8.410 0.244473
5 42.376 0.756476
6 11.044 0.307975
7 35.923 0.698028
8 103.949 0.968726
9 45.966 0.783941
10 8.724 0.252342
11 5.439 0.165808
12 3.686 0.115631
13 32.455 0.661021
14 6.452 0.193514
15 13.909 0.371016
16 46.084 0.784789
17 15.386 0.401226
18 23.285 0.539828
19 40.547 0.741163
20 76.128 0.920945
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.531751
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.5 1.1 1.2 0.0 -0.1
-0.6 -1.0 0.2 1.5 -0.8 0.6
1.7 -0.6 0.4 -1.8 0.2 -0.3
0.1 -1.5 0.3 0.9 0.5 0.3
0.3 -1.1 -0.0 -0.2 0.5 -0.3
1.6 0.0 -0.1 0.0 -0.6 1.3
1.2 0.5 -0.4 -0.1 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:30.660526
z-score=-1.237238, p-value=0.097544
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_08:31
Test no p-value
1 0.298930
2 0.075867
3 0.071932
4 0.503799
5 0.734904
6 0.994435
7 0.176712
8 0.469182
9 0.000351
10 0.750050
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.199793
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_08:31:
(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 66806 0.29 66564 0.16
3 25000.00 24895 0.44 25182 1.32
4 6666.67 6637 0.13 6588 0.93
5 1388.89 1397 0.05 1410 0.32
6 238.10 221 1.23 222 1.09
7 34.72 34 0.01 29 0.94
8 4.96 9 3.29 4 0.19
p=0.51182 p=0.44956
Number of rngs required: 687846, p-value: 0.260
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_08:31
No. of wins: Observed Expected
98535 98585.9
z-score=-0.227, pvalue=0.41003
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66567 66666.7 0.149 0.149
2 37750 37654.3 0.243 0.392
3 27110 26954.7 0.894 1.287
4 19291 19313.5 0.026 1.313
5 13806 13851.4 0.149 1.462
6 9931 9943.5 0.016 1.477
7 7083 7145.0 0.538 2.016
8 5171 5139.1 0.198 2.214
9 3706 3699.9 0.010 2.224
10 2683 2666.3 0.105 2.329
11 1913 1923.3 0.055 2.384
12 1387 1388.7 0.002 2.387
13 977 1003.7 0.711 3.098
14 705 726.1 0.615 3.713
15 542 525.8 0.497 4.210
16 410 381.2 2.184 6.394
17 264 276.5 0.569 6.962
18 198 200.8 0.040 7.002
19 122 146.0 3.940 10.943
20 125 106.2 3.322 14.265
21 259 287.1 2.753 17.018
Chisq= 17.02 for 20 degrees of freedom, p= 0.34818
SUMMARY of craptest
p-value for no. of wins: 0.410029
p-value for throws/game: 0.348179
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_08:31
No. of wins: Observed Expected
98360 98585.9
z-score=-1.010, pvalue=0.15621
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66484 66666.7 0.501 0.501
2 37374 37654.3 2.087 2.587
3 27307 26954.7 4.604 7.191
4 19242 19313.5 0.264 7.456
5 13923 13851.4 0.370 7.825
6 10069 9943.5 1.583 9.408
7 7075 7145.0 0.686 10.095
8 5146 5139.1 0.009 10.104
9 3715 3699.9 0.062 10.166
10 2726 2666.3 1.337 11.503
11 1957 1923.3 0.589 12.092
12 1389 1388.7 0.000 12.092
13 1002 1003.7 0.003 12.095
14 728 726.1 0.005 12.100
15 521 525.8 0.044 12.144
16 370 381.2 0.326 12.471
17 257 276.5 1.381 13.851
18 193 200.8 0.305 14.156
19 143 146.0 0.061 14.217
20 97 106.2 0.800 15.017
21 282 287.1 0.091 15.108
Chisq= 15.11 for 20 degrees of freedom, p= 0.22981
SUMMARY of craptest
p-value for no. of wins: 0.156207
p-value for throws/game: 0.229810
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0042,0.0050,0.0059,0.0067,0.0075,0.0121,0.0166,0.0189,0.0236,
0.0315,0.0418,0.0420,0.0491,0.0616,0.0641,0.0707,0.0714,0.0719,0.0759,
0.0762,0.0766,0.0837,0.0843,0.0915,0.0952,0.0963,0.0975,0.0984,0.1072,
0.1082,0.1098,0.1115,0.1142,0.1155,0.1156,0.1184,0.1229,0.1231,0.1250,
0.1268,0.1269,0.1271,0.1322,0.1473,0.1480,0.1510,0.1519,0.1521,0.1562,
0.1609,0.1658,0.1750,0.1767,0.1774,0.1851,0.1935,0.1998,0.2060,0.2194,
0.2298,0.2325,0.2342,0.2374,0.2378,0.2445,0.2459,0.2460,0.2523,0.2529,
0.2602,0.2608,0.2611,0.2613,0.2666,0.2692,0.2693,0.2738,0.2749,0.2759,
0.2767,0.2814,0.2830,0.2989,0.3080,0.3241,0.3308,0.3311,0.3355,0.3385,
0.3391,0.3439,0.3482,0.3529,0.3595,0.3710,0.3735,0.3809,0.3904,0.4012,
0.4046,0.4052,0.4087,0.4097,0.4100,0.4146,0.4178,0.4237,0.4264,0.4275,
0.4296,0.4363,0.4364,0.4387,0.4433,0.4451,0.4463,0.4470,0.4496,0.4515,
0.4525,0.4530,0.4554,0.4560,0.4579,0.4617,0.4692,0.4796,0.4818,0.4876,
0.4900,0.4913,0.4984,0.5009,0.5032,0.5033,0.5038,0.5041,0.5043,0.5118,
0.5196,0.5239,0.5240,0.5258,0.5259,0.5278,0.5318,0.5353,0.5398,0.5442,
0.5520,0.5554,0.5563,0.5582,0.5642,0.5652,0.5667,0.5703,0.5775,0.5801,
0.5802,0.5860,0.5861,0.6036,0.6051,0.6054,0.6069,0.6079,0.6169,0.6207,
0.6218,0.6220,0.6280,0.6289,0.6297,0.6354,0.6406,0.6420,0.6486,0.6501,
0.6507,0.6610,0.6759,0.6882,0.6926,0.6947,0.6967,0.6968,0.6973,0.6980,
0.7008,0.7031,0.7112,0.7220,0.7332,0.7349,0.7376,0.7381,0.7412,0.7472,
0.7486,0.7501,0.7522,0.7539,0.7565,0.7639,0.7649,0.7701,0.7703,0.7711,
0.7737,0.7839,0.7848,0.7851,0.8091,0.8113,0.8193,0.8194,0.8203,0.8212,
0.8339,0.8375,0.8394,0.8434,0.8468,0.8488,0.8536,0.8603,0.8618,0.8626,
0.8682,0.8702,0.8702,0.8800,0.8814,0.8818,0.8831,0.8850,0.8854,0.8858,
0.8874,0.8879,0.8921,0.8927,0.9202,0.9209,0.9245,0.9252,0.9397,0.9416,
0.9466,0.9583,0.9606,0.9644,0.9663,0.9676,0.9687,0.9690,0.9693,0.9845,
0.9858,0.9890,0.9892,0.9900,0.9902,0.9913,0.9932,0.9944,0.9966,
Overall p-value after applying KStest on 269 p-values = 0.779418
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.