RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.89 12.9923 0.263296
2 to 25 15.83 15.0869 0.410777
3 to 26 16.05 16.5502 0.514780
4 to 27 15.90 16.3797 0.502904
5 to 28 15.98 23.6363 0.870340
6 to 29 16.00 13.9534 0.329604
7 to 30 15.64 28.6578 0.962185
8 to 31 15.72 6.9437 0.015734
9 to 32 15.56 24.5767 0.895408
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.800794
Tough bday spacings test for dh-ranFile-2018-07-08_11:31: 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 17 42 60 101 88 80 48 32 22 7 3
(O-E)^2/E 6.7 0.8 2.4 0.1 1.0 0.0 0.3 0.2 3.4 0.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 15.212, p= 0.875
RESULTS OF GCD FOR dh-ranFile-2018-07-08_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.485880
p-value, dist. of gcd's: 0.877443
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.401 0.888 0.817 0.512 0.371 0.519 0.206 0.454
Bits 8 to 15---> 0.383 0.632 0.576 0.356 0.493 0.537 0.225 0.935
Bits 16 to 23---> 0.072 0.145 0.527 0.310 0.289 0.320 0.325 0.752
Bits 24 to 31---> 0.126 0.983 0.835 0.158 0.334 0.333 0.976 0.757
KS test for the above 32 p values: 0.511
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_11:31,
p-values for 5 runs: 0.0811, 0.3034, 0.3323, 0.3651, 0.9157
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 210 211.4 0.010 0.010
r= 29 5113 5134.0 0.086 0.095
r= 30 23118 23103.0 0.010 0.105
r= 31 11559 11551.5 0.005 0.110
chi-square = 0.110 with df = 3; p-value = 0.009
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 236 211.4 2.858 2.858
r= 30 5158 5134.0 0.112 2.970
r= 31 22998 23103.0 0.478 3.448
r= 32 11608 11551.5 0.276 3.724
chi-square = 3.724 with df = 3; p-value = 0.707
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_11:31
b-rank test for bits 1 to 8, p=0.79055
b-rank test for bits 2 to 9, p=0.62476
b-rank test for bits 3 to 10, p=0.31031
b-rank test for bits 4 to 11, p=0.80010
b-rank test for bits 5 to 12, p=0.98985
b-rank test for bits 6 to 13, p=0.39909
b-rank test for bits 7 to 14, p=0.58069
b-rank test for bits 8 to 15, p=0.22731
b-rank test for bits 9 to 16, p=0.93642
b-rank test for bits 10 to 17, p=0.59465
b-rank test for bits 11 to 18, p=0.03005
b-rank test for bits 12 to 19, p=0.99495
b-rank test for bits 13 to 20, p=0.63295
b-rank test for bits 14 to 21, p=0.07848
b-rank test for bits 15 to 22, p=0.22204
b-rank test for bits 16 to 23, p=0.59226
b-rank test for bits 17 to 24, p=0.26141
b-rank test for bits 18 to 25, p=0.57653
b-rank test for bits 19 to 26, p=0.35309
b-rank test for bits 20 to 27, p=0.39127
b-rank test for bits 21 to 28, p=0.16358
b-rank test for bits 22 to 29, p=0.18572
b-rank test for bits 23 to 30, p=0.44244
b-rank test for bits 24 to 31, p=0.03695
b-rank test for bits 25 to 32, p=0.50921
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 = 0.701671
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_11:31
(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 141356 -1.29 0.098035
2 142022 0.26 0.603820
3 141747 -0.38 0.352242
4 142119 0.49 0.687892
5 142375 1.09 0.861706
6 141639 -0.63 0.263820
7 141728 -0.42 0.335904
8 142368 1.07 0.858063
9 142107 0.46 0.677904
10 142220 0.73 0.766039
11 141521 -0.91 0.182121
12 141220 -1.61 0.053635
13 141416 -1.15 0.124529
14 142194 0.67 0.747012
15 141967 0.13 0.553593
16 141391 -1.21 0.112938
17 141052 -2.00 0.022583
18 141975 0.15 0.560972
19 142289 0.89 0.812482
20 141652 -0.60 0.273841
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_11:31
Bits used No. missing words z-score p-value
23 to 32 142037 0.4402 0.670119
22 to 31 142075 0.5713 0.716094
21 to 30 141688 -0.7632 0.222670
20 to 29 142011 0.3506 0.637051
19 to 28 141806 -0.3563 0.360804
18 to 27 141904 -0.0184 0.492668
17 to 26 141981 0.2471 0.597599
16 to 25 142102 0.6644 0.746776
15 to 24 141785 -0.4287 0.334062
14 to 23 141978 0.2368 0.593591
13 to 22 141995 0.2954 0.616161
12 to 21 141831 -0.2701 0.393540
11 to 20 142482 1.9747 0.975850
10 to 19 141866 -0.1494 0.440614
9 to 18 142166 0.8851 0.811940
8 to 17 141642 -0.9218 0.178309
7 to 16 141760 -0.5149 0.303301
6 to 15 141708 -0.6942 0.243765
5 to 14 142484 1.9816 0.976239
4 to 13 142269 1.2402 0.892557
3 to 12 141706 -0.7011 0.241609
2 to 11 141688 -0.7632 0.222670
1 to 10 142119 0.7230 0.765160
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_11:31
Bits used No. missing words z-score p-value
28 to 32 141397 -1.7367 0.041219
27 to 31 141664 -0.8316 0.202810
26 to 30 141970 0.2057 0.581472
25 to 29 141868 -0.1401 0.444290
24 to 28 141887 -0.0757 0.469831
23 to 27 142034 0.4226 0.663710
22 to 26 141634 -0.9333 0.175327
21 to 25 141812 -0.3299 0.370726
20 to 24 142037 0.4328 0.667413
19 to 23 142057 0.5006 0.691665
18 to 22 142071 0.5480 0.708166
17 to 21 141858 -0.1740 0.430933
16 to 20 141922 0.0429 0.517129
15 to 19 141686 -0.7571 0.224510
14 to 18 142113 0.6904 0.755031
13 to 17 141837 -0.2452 0.403156
12 to 16 141323 -1.9876 0.023430
11 to 15 141921 0.0396 0.515778
10 to 14 141376 -1.8079 0.035311
9 to 13 141817 -0.3130 0.377147
8 to 12 141910 0.0023 0.500906
7 to 11 142283 1.2667 0.897365
6 to 10 142028 0.4023 0.656258
5 to 9 142249 1.1514 0.875221
4 to 8 141739 -0.5774 0.281838
3 to 7 141829 -0.2723 0.392694
2 to 6 141542 -1.2452 0.106532
1 to 5 141909 -0.0011 0.499554
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_11:31
Bits used No. missing words z-score p-value
31 to 32 142313 1.1908 0.883127
30 to 31 141815 -0.2783 0.390407
29 to 30 142290 1.1229 0.869264
28 to 29 141999 0.2645 0.604308
27 to 28 142157 0.7306 0.767485
26 to 27 141225 -2.0187 0.021761
25 to 26 142050 0.4150 0.660913
24 to 25 142450 1.5949 0.944632
23 to 24 141614 -0.8712 0.191828
22 to 23 142027 0.3471 0.635745
21 to 22 141510 -1.1780 0.119405
20 to 21 142046 0.4032 0.656583
19 to 20 141575 -0.9862 0.162012
18 to 19 142018 0.3206 0.625728
17 to 18 142085 0.5182 0.697841
16 to 17 141589 -0.9449 0.172348
15 to 16 142383 1.3973 0.918832
14 to 15 142247 0.9961 0.840394
13 to 14 142561 1.9223 0.972718
12 to 13 142013 0.3058 0.620126
11 to 12 141217 -2.0423 0.020562
10 to 11 142425 1.5212 0.935889
9 to 10 141911 0.0049 0.501965
8 to 9 141261 -1.9125 0.027907
7 to 8 141949 0.1170 0.546578
6 to 7 141327 -1.7178 0.042918
5 to 6 142556 1.9076 0.971777
4 to 5 141548 -1.0659 0.143241
3 to 4 142528 1.8250 0.965998
2 to 3 142123 0.6303 0.735749
1 to 2 141464 -1.3137 0.094481
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2474.84 -0.356 0.360990
Test results for specific bytes for dh-ranFile-2018-07-08_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2449.38 -0.716 0.237046
2 to 9 2395.61 -1.476 0.069931
3 to 10 2482.24 -0.251 0.400837
4 to 11 2570.95 1.003 0.842148
5 to 12 2569.84 0.988 0.838331
6 to 13 2518.51 0.262 0.603232
7 to 14 2504.53 0.064 0.525568
8 to 15 2561.86 0.875 0.809173
9 to 16 2571.63 1.013 0.844468
10 to 17 2520.21 0.286 0.612499
11 to 18 2435.36 -0.914 0.180328
12 to 19 2410.74 -1.262 0.103423
13 to 20 2407.63 -1.306 0.095720
14 to 21 2452.27 -0.675 0.249820
15 to 22 2588.46 1.251 0.894539
16 to 23 2467.51 -0.459 0.322948
17 to 24 2509.59 0.136 0.553967
18 to 25 2463.65 -0.514 0.303598
19 to 26 2492.62 -0.104 0.458432
20 to 27 2410.33 -1.268 0.102371
21 to 28 2465.68 -0.485 0.313723
22 to 29 2452.58 -0.671 0.251227
23 to 30 2440.75 -0.838 0.201041
24 to 31 2581.72 1.156 0.876092
25 to 32 2487.34 -0.179 0.428979
CDPARK for dh-ranFile-2018-07-08_11:31: 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
3512 -0.5023 0.307734
3506 -0.7763 0.218799
3532 0.4110 0.659449
3495 -1.2785 0.100530
3536 0.5936 0.723613
3513 -0.4566 0.323972
3526 0.1370 0.554479
3538 0.6849 0.753306
3493 -1.3699 0.085365
3537 0.6393 0.738676
Square side=100, avg. no. parked=3518.80 sample std.=16.42
p-value of the KSTEST for those 10 p-values: 0.687667
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_11:31
0.0925,0.8966,0.6627,0.4886,0.7594,0.0245,0.4478,0.1801,0.5169,0.0075,
The KS test for those 10 p-values: 0.319214
The 3DSPHERES test for dh-ranFile-2018-07-08_11:31
sample no r^3 equiv. uni.
1 0.498 0.016466
2 33.224 0.669609
3 3.640 0.114264
4 23.350 0.540822
5 28.251 0.610041
6 21.302 0.508392
7 9.436 0.269870
8 44.269 0.771363
9 4.305 0.133690
10 21.808 0.516607
11 37.895 0.717244
12 22.241 0.523537
13 2.938 0.093280
14 43.880 0.768382
15 49.034 0.804942
16 2.349 0.075313
17 7.298 0.215925
18 43.205 0.763112
19 11.337 0.314698
20 3.839 0.120110
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.302387
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.9 -0.1 -1.0 0.4 -0.8
-0.5 -1.2 -1.1 0.5 -0.2 0.7
-0.7 -0.6 -1.2 0.5 0.8 -0.0
1.1 0.3 0.2 1.6 0.0 -2.6
-0.2 0.2 1.2 -0.8 0.2 -1.1
-0.1 1.1 0.4 0.3 0.9 0.6
1.0 -0.7 1.7 -0.7 -0.6 2.0
-0.1
Chi-square with 42 degrees of freedom:36.164999
z-score=-0.636651, p-value=0.275893
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_11:31
Test no p-value
1 0.073972
2 0.279807
3 0.583294
4 0.477914
5 0.231206
6 0.049695
7 0.306425
8 0.432295
9 0.654097
10 0.033414
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.061356
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_11:31:
(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 66651 0.00 66528 0.29
3 25000.00 24901 0.39 25167 1.12
4 6666.67 6725 0.51 6670 0.00
5 1388.89 1426 0.99 1341 1.65
6 238.10 259 1.84 247 0.33
7 34.72 32 0.21 40 0.80
8 4.96 5 0.00 6 0.22
p=0.31608 p=0.37876
Number of rngs required: 688810, p-value: 0.680
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_11:31
No. of wins: Observed Expected
98599 98585.9
z-score= 0.059, pvalue=0.52343
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66529 66666.7 0.284 0.284
2 38024 37654.3 3.629 3.914
3 26910 26954.7 0.074 3.988
4 19349 19313.5 0.065 4.053
5 13703 13851.4 1.590 5.644
6 9886 9943.5 0.333 5.977
7 7174 7145.0 0.117 6.094
8 5167 5139.1 0.152 6.246
9 3625 3699.9 1.515 7.761
10 2628 2666.3 0.550 8.311
11 1888 1923.3 0.649 8.960
12 1445 1388.7 2.279 11.239
13 1031 1003.7 0.742 11.981
14 744 726.1 0.439 12.420
15 524 525.8 0.006 12.426
16 417 381.2 3.372 15.798
17 247 276.5 3.155 18.954
18 191 200.8 0.481 19.435
19 152 146.0 0.248 19.683
20 86 106.2 3.847 23.530
21 280 287.1 0.176 23.706
Chisq= 23.71 for 20 degrees of freedom, p= 0.74454
SUMMARY of craptest
p-value for no. of wins: 0.523435
p-value for throws/game: 0.744541
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_11:31
No. of wins: Observed Expected
98333 98585.9
z-score=-1.131, pvalue=0.12904
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66645 66666.7 0.007 0.007
2 37600 37654.3 0.078 0.085
3 27001 26954.7 0.079 0.165
4 19317 19313.5 0.001 0.165
5 13931 13851.4 0.457 0.623
6 9892 9943.5 0.267 0.890
7 7115 7145.0 0.126 1.016
8 5255 5139.1 2.615 3.631
9 3716 3699.9 0.070 3.702
10 2692 2666.3 0.248 3.949
11 1894 1923.3 0.447 4.397
12 1366 1388.7 0.372 4.769
13 997 1003.7 0.045 4.814
14 697 726.1 1.169 5.983
15 522 525.8 0.028 6.011
16 382 381.2 0.002 6.013
17 255 276.5 1.678 7.691
18 206 200.8 0.133 7.824
19 134 146.0 0.984 8.808
20 104 106.2 0.046 8.854
21 279 287.1 0.229 9.083
Chisq= 9.08 for 20 degrees of freedom, p= 0.01808
SUMMARY of craptest
p-value for no. of wins: 0.129042
p-value for throws/game: 0.018077
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0075,0.0094,0.0157,0.0165,0.0181,0.0206,0.0218,0.0226,0.0234,0.0245,
0.0279,0.0301,0.0334,0.0353,0.0369,0.0412,0.0429,0.0497,0.0536,0.0614,
0.0699,0.0717,0.0740,0.0753,0.0785,0.0811,0.0854,0.0925,0.0933,0.0945,
0.0957,0.0980,0.1005,0.1024,0.1034,0.1065,0.1129,0.1143,0.1194,0.1201,
0.1245,0.1259,0.1290,0.1337,0.1432,0.1453,0.1577,0.1620,0.1636,0.1723,
0.1753,0.1783,0.1801,0.1803,0.1821,0.1857,0.1918,0.2010,0.2028,0.2061,
0.2159,0.2188,0.2220,0.2227,0.2227,0.2245,0.2250,0.2273,0.2312,0.2370,
0.2416,0.2438,0.2498,0.2512,0.2614,0.2633,0.2638,0.2699,0.2738,0.2759,
0.2798,0.2818,0.2887,0.3024,0.3033,0.3034,0.3036,0.3064,0.3077,0.3103,
0.3103,0.3137,0.3147,0.3161,0.3192,0.3200,0.3229,0.3240,0.3255,0.3296,
0.3323,0.3334,0.3338,0.3341,0.3359,0.3522,0.3531,0.3561,0.3608,0.3610,
0.3651,0.3707,0.3710,0.3771,0.3788,0.3834,0.3904,0.3913,0.3927,0.3935,
0.3991,0.4008,0.4013,0.4032,0.4108,0.4290,0.4309,0.4323,0.4406,0.4424,
0.4443,0.4478,0.4536,0.4584,0.4698,0.4779,0.4859,0.4886,0.4927,0.4930,
0.4996,0.5009,0.5020,0.5029,0.5084,0.5092,0.5113,0.5118,0.5148,0.5158,
0.5166,0.5169,0.5171,0.5190,0.5234,0.5235,0.5256,0.5269,0.5371,0.5408,
0.5466,0.5536,0.5540,0.5545,0.5610,0.5756,0.5765,0.5807,0.5815,0.5833,
0.5923,0.5936,0.5947,0.5976,0.6032,0.6038,0.6043,0.6100,0.6125,0.6162,
0.6201,0.6248,0.6257,0.6315,0.6330,0.6357,0.6371,0.6541,0.6563,0.6566,
0.6594,0.6609,0.6627,0.6637,0.6674,0.6696,0.6701,0.6779,0.6804,0.6877,
0.6879,0.6917,0.6978,0.7017,0.7072,0.7082,0.7161,0.7172,0.7236,0.7357,
0.7387,0.7445,0.7468,0.7470,0.7524,0.7533,0.7550,0.7571,0.7594,0.7631,
0.7652,0.7660,0.7675,0.7684,0.7714,0.7906,0.8001,0.8008,0.8049,0.8092,
0.8119,0.8125,0.8169,0.8348,0.8383,0.8404,0.8421,0.8445,0.8581,0.8617,
0.8693,0.8703,0.8752,0.8755,0.8761,0.8774,0.8831,0.8877,0.8926,0.8945,
0.8954,0.8966,0.8974,0.9157,0.9188,0.9352,0.9359,0.9364,0.9446,0.9622,
0.9660,0.9718,0.9727,0.9757,0.9759,0.9762,0.9827,0.9899,0.9949,
Overall p-value after applying KStest on 269 p-values = 0.094349
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.