RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_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 15.79 23.5560 0.867992
2 to 25 15.71 10.3766 0.112921
3 to 26 15.64 29.2290 0.967528
4 to 27 15.70 18.7128 0.654737
5 to 28 15.30 37.3007 0.996937
6 to 29 15.72 33.8652 0.991261
7 to 30 15.78 9.7720 0.087102
8 to 31 15.61 14.5719 0.373713
9 to 32 15.56 17.8669 0.602719
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.046926
Tough bday spacings test for dh-ranFile-2018-06-23_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 11 36 78 101 97 78 51 28 16 2 2
(O-E)^2/E 0.4 0.0 0.3 0.1 0.0 0.0 0.0 0.1 0.1 3.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 5.287, p= 0.129
RESULTS OF GCD FOR dh-ranFile-2018-06-23_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.664147
p-value, dist. of gcd's: 0.248403
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.699 0.003 0.614 0.892 0.583 0.009 0.313 0.813
Bits 8 to 15---> 0.641 0.070 0.191 0.673 0.352 0.929 0.382 0.043
Bits 16 to 23---> 0.201 0.824 0.888 0.649 0.192 0.240 0.367 0.465
Bits 24 to 31---> 0.239 0.221 0.937 0.754 0.582 0.436 0.784 0.505
KS test for the above 32 p values: 0.094
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_11:31,
p-values for 5 runs: 0.2019, 0.9732, 0.6473, 0.6241, 0.9923
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5228 5134.0 1.721 1.926
r= 30 22959 23103.0 0.898 2.824
r= 31 11595 11551.5 0.164 2.987
chi-square = 2.987 with df = 3; p-value = 0.606
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 5190 5134.0 0.611 0.805
r= 31 23329 23103.0 2.210 3.015
r= 32 11276 11551.5 6.572 9.587
chi-square = 9.587 with df = 3; p-value = 0.978
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_11:31
b-rank test for bits 1 to 8, p=0.70653
b-rank test for bits 2 to 9, p=0.53454
b-rank test for bits 3 to 10, p=0.84294
b-rank test for bits 4 to 11, p=0.96730
b-rank test for bits 5 to 12, p=0.90405
b-rank test for bits 6 to 13, p=0.36247
b-rank test for bits 7 to 14, p=0.15977
b-rank test for bits 8 to 15, p=0.54764
b-rank test for bits 9 to 16, p=0.37915
b-rank test for bits 10 to 17, p=0.10398
b-rank test for bits 11 to 18, p=0.60557
b-rank test for bits 12 to 19, p=0.36726
b-rank test for bits 13 to 20, p=0.92615
b-rank test for bits 14 to 21, p=0.49432
b-rank test for bits 15 to 22, p=0.30008
b-rank test for bits 16 to 23, p=0.41582
b-rank test for bits 17 to 24, p=0.63355
b-rank test for bits 18 to 25, p=0.27069
b-rank test for bits 19 to 26, p=0.37088
b-rank test for bits 20 to 27, p=0.44999
b-rank test for bits 21 to 28, p=0.73159
b-rank test for bits 22 to 29, p=0.22908
b-rank test for bits 23 to 30, p=0.31616
b-rank test for bits 24 to 31, p=0.52517
b-rank test for bits 25 to 32, p=0.26064
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 = 0.444838
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_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 141600 -0.72 0.234922
2 141108 -1.87 0.030585
3 141307 -1.41 0.079667
4 141355 -1.30 0.097632
5 142312 0.94 0.826601
6 140847 -2.48 0.006531
7 142285 0.88 0.809956
8 141752 -0.37 0.356588
9 141573 -0.79 0.215987
10 142560 1.52 0.935777
11 142845 2.19 0.985597
12 142109 0.47 0.679578
13 141301 -1.42 0.077610
14 141000 -2.12 0.016810
15 142049 0.33 0.627913
16 141720 -0.44 0.329114
17 142590 1.59 0.944122
18 142279 0.86 0.806128
19 141907 -0.01 0.497828
20 142519 1.42 0.922844
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_11:31
Bits used No. missing words z-score p-value
23 to 32 141770 -0.4804 0.315454
22 to 31 142507 2.0609 0.980345
21 to 30 142014 0.3609 0.640925
20 to 29 141709 -0.6908 0.244848
19 to 28 142001 0.3161 0.624038
18 to 27 142028 0.4092 0.658806
17 to 26 141883 -0.0908 0.463829
16 to 25 141997 0.3023 0.618792
15 to 24 141836 -0.2529 0.400187
14 to 23 141607 -1.0425 0.148586
13 to 22 142152 0.8368 0.798646
12 to 21 141540 -1.2736 0.101411
11 to 20 141441 -1.6149 0.053163
10 to 19 141733 -0.6080 0.271582
9 to 18 141812 -0.3356 0.368579
8 to 17 142080 0.5885 0.721907
7 to 16 141754 -0.5356 0.296110
6 to 15 141538 -1.2804 0.100194
5 to 14 142054 0.4989 0.691062
4 to 13 141809 -0.3460 0.364684
3 to 12 142596 2.3678 0.991054
2 to 11 141655 -0.8770 0.190243
1 to 10 141641 -0.9253 0.177411
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_11:31
Bits used No. missing words z-score p-value
28 to 32 142178 0.9107 0.818785
27 to 31 141455 -1.5401 0.061768
26 to 30 141673 -0.8011 0.211532
25 to 29 142120 0.7141 0.762428
24 to 28 141711 -0.6723 0.250695
23 to 27 142002 0.3141 0.623291
22 to 26 142310 1.3582 0.912800
21 to 25 142276 1.2429 0.893057
20 to 24 141778 -0.4452 0.328093
19 to 23 141389 -1.7638 0.038880
18 to 22 142030 0.4091 0.658749
17 to 21 142143 0.7921 0.785849
16 to 20 141647 -0.8893 0.186933
15 to 19 142014 0.3548 0.638635
14 to 18 141364 -1.8486 0.032260
13 to 17 142123 0.7243 0.765561
12 to 16 141620 -0.9808 0.163351
11 to 15 141940 0.1040 0.541402
10 to 14 141957 0.1616 0.564187
9 to 13 142449 1.8294 0.966329
8 to 12 141388 -1.7672 0.038596
7 to 11 141858 -0.1740 0.430933
6 to 10 141981 0.2429 0.595978
5 to 9 141719 -0.6452 0.259403
4 to 8 141467 -1.4994 0.066882
3 to 7 141740 -0.5740 0.282984
2 to 6 142321 1.3955 0.918566
1 to 5 141896 -0.0452 0.481979
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_11:31
Bits used No. missing words z-score p-value
31 to 32 142028 0.3501 0.636853
30 to 31 142494 1.7247 0.957708
29 to 30 141786 -0.3638 0.358002
28 to 29 141764 -0.4287 0.334070
27 to 28 141431 -1.4110 0.079122
26 to 27 141688 -0.6529 0.256913
25 to 26 141725 -0.5437 0.293308
24 to 25 141512 -1.1721 0.120586
23 to 24 141546 -1.0718 0.141912
22 to 23 142174 0.7807 0.782522
21 to 22 142051 0.4179 0.661992
20 to 21 141115 -2.3432 0.009561
19 to 20 141787 -0.3609 0.359104
18 to 19 142502 1.7483 0.959793
17 to 18 142336 1.2586 0.895915
16 to 17 141899 -0.0305 0.487845
15 to 16 142146 0.6981 0.757456
14 to 15 141780 -0.3815 0.351415
13 to 14 141521 -1.1455 0.125998
12 to 13 142130 0.6509 0.742459
11 to 12 141549 -1.0629 0.143909
10 to 11 142397 1.4386 0.924862
9 to 10 141226 -2.0157 0.021914
8 to 9 141620 -0.8535 0.196696
7 to 8 141852 -0.1691 0.432853
6 to 7 142097 0.5536 0.710073
5 to 6 142364 1.3412 0.910074
4 to 5 142234 0.9577 0.830900
3 to 4 142357 1.3206 0.906676
2 to 3 141907 -0.0069 0.497258
1 to 2 141508 -1.1839 0.118233
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2501.34 0.019 0.507554
Test results for specific bytes for dh-ranFile-2018-06-23_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2414.87 -1.204 0.114300
2 to 9 2573.63 1.041 0.851114
3 to 10 2479.57 -0.289 0.386302
4 to 11 2523.46 0.332 0.629962
5 to 12 2420.60 -1.123 0.130748
6 to 13 2605.07 1.486 0.931340
7 to 14 2350.88 -2.109 0.017479
8 to 15 2483.87 -0.228 0.409771
9 to 16 2496.61 -0.048 0.480869
10 to 17 2470.19 -0.422 0.336643
11 to 18 2493.57 -0.091 0.463777
12 to 19 2455.96 -0.623 0.266712
13 to 20 2441.75 -0.824 0.205028
14 to 21 2568.61 0.970 0.834064
15 to 22 2402.98 -1.372 0.085014
16 to 23 2510.77 0.152 0.560553
17 to 24 2491.49 -0.120 0.452080
18 to 25 2489.21 -0.153 0.439363
19 to 26 2505.82 0.082 0.532803
20 to 27 2398.43 -1.436 0.075446
21 to 28 2667.43 2.368 0.991052
22 to 29 2450.22 -0.704 0.240739
23 to 30 2486.30 -0.194 0.423208
24 to 31 2502.86 0.040 0.516138
25 to 32 2457.76 -0.597 0.275133
CDPARK for dh-ranFile-2018-06-23_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
3510 -0.5936 0.276387
3539 0.7306 0.767486
3528 0.2283 0.590298
3521 -0.0913 0.463617
3546 1.0502 0.853193
3555 1.4612 0.928018
3512 -0.5023 0.307734
3498 -1.1416 0.126820
3517 -0.2740 0.392053
3552 1.3242 0.907282
Square side=100, avg. no. parked=3527.80 sample std.=18.44
p-value of the KSTEST for those 10 p-values: 0.798250
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_11:31
0.1999,0.5951,0.7584,0.1513,0.3937,0.6620,0.8290,0.9118,0.5805,0.4928,
The KS test for those 10 p-values: 0.773014
The 3DSPHERES test for dh-ranFile-2018-06-23_11:31
sample no r^3 equiv. uni.
1 11.078 0.308755
2 5.783 0.175332
3 41.078 0.745709
4 60.840 0.868402
5 20.267 0.491125
6 2.567 0.082003
7 1.617 0.052462
8 49.974 0.810961
9 45.108 0.777671
10 6.154 0.185468
11 17.143 0.435292
12 4.825 0.148568
13 11.321 0.314326
14 30.457 0.637686
15 8.609 0.249470
16 102.954 0.967671
17 0.525 0.017351
18 2.874 0.091339
19 34.466 0.683002
20 9.810 0.278928
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.312789
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 0.8 -0.3 1.1 -1.0
-0.5 0.4 0.1 1.5 0.8 -0.9
-1.0 -1.2 -0.5 1.0 0.3 -1.4
0.9 -1.4 0.8 -1.2 2.3 1.4
0.4 0.8 0.4 0.4 -2.0 0.1
-0.6 -0.3 0.0 -0.6 -0.2 -0.8
-1.2 -1.3 0.9 -0.7 0.1 2.0
-1.1
Chi-square with 42 degrees of freedom:42.448627
z-score=0.048949, p-value=0.548365
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_11:31
Test no p-value
1 0.154158
2 0.091776
3 0.266087
4 0.030486
5 0.977007
6 0.180567
7 0.188590
8 0.978835
9 0.008963
10 0.666402
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.029739
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_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 66613 0.04 66816 0.33
3 25000.00 24990 0.00 24803 1.55
4 6666.67 6726 0.53 6718 0.40
5 1388.89 1361 0.56 1377 0.10
6 238.10 267 3.51 235 0.04
7 34.72 33 0.09 43 1.97
8 4.96 9 3.29 7 0.84
p=0.76337 p=0.48630
Number of rngs required: 688377, p-value: 0.488
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_11:31
No. of wins: Observed Expected
98084 98585.9
z-score=-2.245, pvalue=0.01240
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66613 66666.7 0.043 0.043
2 37633 37654.3 0.012 0.055
3 26930 26954.7 0.023 0.078
4 19414 19313.5 0.523 0.601
5 13959 13851.4 0.836 1.437
6 9867 9943.5 0.589 2.026
7 7076 7145.0 0.667 2.693
8 5185 5139.1 0.410 3.103
9 3700 3699.9 0.000 3.103
10 2722 2666.3 1.164 4.267
11 1954 1923.3 0.489 4.756
12 1394 1388.7 0.020 4.776
13 1019 1003.7 0.233 5.009
14 693 726.1 1.513 6.521
15 501 525.8 1.173 7.694
16 349 381.2 2.712 10.406
17 275 276.5 0.009 10.415
18 187 200.8 0.952 11.367
19 144 146.0 0.027 11.394
20 101 106.2 0.256 11.650
21 284 287.1 0.034 11.684
Chisq= 11.68 for 20 degrees of freedom, p= 0.07348
SUMMARY of craptest
p-value for no. of wins: 0.012397
p-value for throws/game: 0.073481
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_11:31
No. of wins: Observed Expected
98713 98585.9
z-score= 0.569, pvalue=0.71520
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66555 66666.7 0.187 0.187
2 37907 37654.3 1.696 1.883
3 26952 26954.7 0.000 1.883
4 19218 19313.5 0.472 2.355
5 13816 13851.4 0.091 2.445
6 9979 9943.5 0.126 2.572
7 7209 7145.0 0.573 3.145
8 5142 5139.1 0.002 3.146
9 3631 3699.9 1.282 4.428
10 2653 2666.3 0.066 4.494
11 1908 1923.3 0.122 4.617
12 1362 1388.7 0.515 5.131
13 970 1003.7 1.132 6.264
14 705 726.1 0.615 6.879
15 523 525.8 0.015 6.895
16 405 381.2 1.492 8.387
17 302 276.5 2.344 10.731
18 196 200.8 0.116 10.847
19 149 146.0 0.062 10.910
20 118 106.2 1.308 12.217
21 300 287.1 0.578 12.795
Chisq= 12.80 for 20 degrees of freedom, p= 0.11401
SUMMARY of craptest
p-value for no. of wins: 0.715203
p-value for throws/game: 0.114012
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0030,0.0065,0.0090,0.0092,0.0096,0.0124,0.0168,0.0174,0.0175,0.0219,
0.0297,0.0305,0.0306,0.0323,0.0386,0.0389,0.0429,0.0469,0.0525,0.0532,
0.0618,0.0669,0.0704,0.0735,0.0754,0.0776,0.0791,0.0797,0.0820,0.0850,
0.0871,0.0913,0.0918,0.0942,0.0976,0.1002,0.1014,0.1040,0.1129,0.1140,
0.1143,0.1182,0.1206,0.1260,0.1268,0.1288,0.1307,0.1419,0.1439,0.1486,
0.1486,0.1513,0.1542,0.1598,0.1634,0.1753,0.1774,0.1806,0.1855,0.1869,
0.1886,0.1902,0.1914,0.1924,0.1967,0.1999,0.2006,0.2019,0.2050,0.2115,
0.2160,0.2214,0.2291,0.2349,0.2386,0.2398,0.2407,0.2448,0.2484,0.2495,
0.2507,0.2569,0.2594,0.2606,0.2661,0.2667,0.2707,0.2716,0.2751,0.2764,
0.2789,0.2830,0.2933,0.2961,0.3001,0.3077,0.3088,0.3128,0.3131,0.3143,
0.3155,0.3162,0.3281,0.3291,0.3341,0.3366,0.3514,0.3523,0.3566,0.3580,
0.3591,0.3625,0.3647,0.3672,0.3673,0.3686,0.3709,0.3737,0.3791,0.3820,
0.3863,0.3921,0.3937,0.4002,0.4098,0.4158,0.4232,0.4309,0.4329,0.4353,
0.4357,0.4394,0.4448,0.4500,0.4521,0.4636,0.4638,0.4638,0.4652,0.4809,
0.4820,0.4863,0.4878,0.4881,0.4911,0.4928,0.4943,0.4973,0.4978,0.5054,
0.5076,0.5161,0.5252,0.5328,0.5345,0.5414,0.5476,0.5484,0.5606,0.5642,
0.5805,0.5817,0.5833,0.5903,0.5951,0.5960,0.6027,0.6056,0.6064,0.6143,
0.6188,0.6233,0.6240,0.6241,0.6279,0.6300,0.6336,0.6369,0.6377,0.6386,
0.6409,0.6410,0.6473,0.6495,0.6547,0.6587,0.6588,0.6620,0.6620,0.6641,
0.6664,0.6732,0.6796,0.6830,0.6911,0.6985,0.7065,0.7101,0.7152,0.7219,
0.7316,0.7425,0.7457,0.7542,0.7575,0.7584,0.7624,0.7634,0.7656,0.7675,
0.7730,0.7777,0.7825,0.7837,0.7858,0.7983,0.7986,0.8061,0.8100,0.8110,
0.8132,0.8188,0.8240,0.8266,0.8290,0.8309,0.8341,0.8429,0.8511,0.8532,
0.8680,0.8684,0.8885,0.8924,0.8931,0.8959,0.9041,0.9067,0.9073,0.9101,
0.9118,0.9128,0.9186,0.9228,0.9249,0.9262,0.9280,0.9288,0.9313,0.9358,
0.9371,0.9441,0.9577,0.9598,0.9663,0.9673,0.9675,0.9677,0.9732,0.9770,
0.9776,0.9788,0.9803,0.9856,0.9911,0.9911,0.9913,0.9923,0.9969,
Overall p-value after applying KStest on 269 p-values = 0.116291
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.