RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_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 15.59 34.5892 0.992959
2 to 25 15.85 9.1203 0.063588
3 to 26 15.67 20.7056 0.760262
4 to 27 15.76 21.7475 0.805373
5 to 28 15.61 22.8479 0.845731
6 to 29 15.46 18.8916 0.665211
7 to 30 15.70 9.2125 0.066641
8 to 31 15.60 15.7541 0.458669
9 to 32 15.82 31.2455 0.981358
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.108866
Tough bday spacings test for dh-ranFile-2018-06-27_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 12 40 64 86 97 93 47 34 21 5 1
(O-E)^2/E 0.9 0.3 1.2 1.4 0.0 2.8 0.5 0.6 2.5 0.4 2.3
Birthday Spacings: Sum(O-E)^2/E= 12.907, p= 0.771
RESULTS OF GCD FOR dh-ranFile-2018-06-27_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.921532
p-value, dist. of gcd's: 0.326614
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.293 0.488 0.111 0.974 0.723 0.915 0.059 0.134
Bits 8 to 15---> 0.265 0.753 0.134 0.802 0.340 0.974 0.383 0.860
Bits 16 to 23---> 0.936 0.430 0.472 0.941 0.373 0.888 0.951 0.813
Bits 24 to 31---> 0.194 0.896 0.110 0.172 0.840 0.717 0.849 0.181
KS test for the above 32 p values: 0.886
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_16:31,
p-values for 5 runs: 0.1779, 0.4245, 0.6237, 0.2209, 0.3175
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5099 5134.0 0.239 0.968
r= 30 23087 23103.0 0.011 0.979
r= 31 11615 11551.5 0.349 1.328
chi-square = 1.328 with df = 3; p-value = 0.278
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 188 211.4 2.594 2.594
r= 30 5268 5134.0 3.497 6.091
r= 31 22921 23103.0 1.435 7.525
r= 32 11623 11551.5 0.442 7.968
chi-square = 7.968 with df = 3; p-value = 0.953
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_16:31
b-rank test for bits 1 to 8, p=0.26865
b-rank test for bits 2 to 9, p=0.02493
b-rank test for bits 3 to 10, p=0.31687
b-rank test for bits 4 to 11, p=0.65445
b-rank test for bits 5 to 12, p=0.55512
b-rank test for bits 6 to 13, p=0.45147
b-rank test for bits 7 to 14, p=0.28275
b-rank test for bits 8 to 15, p=0.27611
b-rank test for bits 9 to 16, p=0.07578
b-rank test for bits 10 to 17, p=0.06776
b-rank test for bits 11 to 18, p=0.81803
b-rank test for bits 12 to 19, p=0.14014
b-rank test for bits 13 to 20, p=0.01178
b-rank test for bits 14 to 21, p=0.47332
b-rank test for bits 15 to 22, p=0.96866
b-rank test for bits 16 to 23, p=0.53722
b-rank test for bits 17 to 24, p=0.63207
b-rank test for bits 18 to 25, p=0.73186
b-rank test for bits 19 to 26, p=0.54223
b-rank test for bits 20 to 27, p=0.18244
b-rank test for bits 21 to 28, p=0.09560
b-rank test for bits 22 to 29, p=0.70172
b-rank test for bits 23 to 30, p=0.80260
b-rank test for bits 24 to 31, p=0.69394
b-rank test for bits 25 to 32, p=0.55313
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 = 0.388694
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_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 142004 0.22 0.587528
2 142417 1.19 0.882217
3 141661 -0.58 0.280886
4 142184 0.64 0.739483
5 142160 0.59 0.720954
6 142358 1.05 0.852749
7 141799 -0.26 0.398288
8 142880 2.27 0.988333
9 141982 0.17 0.567412
10 142310 0.94 0.825401
11 141674 -0.55 0.291216
12 141280 -1.47 0.070727
13 141559 -0.82 0.206528
14 142147 0.56 0.710657
15 141933 0.06 0.522052
16 141693 -0.51 0.306624
17 141530 -0.89 0.187732
18 141892 -0.04 0.483851
19 142429 1.21 0.887661
20 142557 1.51 0.934892
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_16:31
Bits used No. missing words z-score p-value
23 to 32 141628 -0.9701 0.165998
22 to 31 141993 0.2885 0.613525
21 to 30 142028 0.4092 0.658806
20 to 29 141851 -0.2011 0.420295
19 to 28 142270 1.2437 0.893193
18 to 27 141923 0.0471 0.518798
17 to 26 141711 -0.6839 0.247020
16 to 25 142111 0.6954 0.756602
15 to 24 141969 0.2058 0.581510
14 to 23 141718 -0.6598 0.254704
13 to 22 142133 0.7713 0.779728
12 to 21 142268 1.2368 0.891918
11 to 20 141303 -2.0908 0.018273
10 to 19 141966 0.1954 0.577466
9 to 18 142070 0.5540 0.710222
8 to 17 141820 -0.3080 0.379028
7 to 16 142647 2.5437 0.994516
6 to 15 141298 -2.1080 0.017514
5 to 14 141858 -0.1770 0.429754
4 to 13 141796 -0.3908 0.347975
3 to 12 141778 -0.4529 0.325324
2 to 11 142123 0.7368 0.769376
1 to 10 141914 0.0161 0.506424
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_16:31
Bits used No. missing words z-score p-value
28 to 32 141860 -0.1672 0.433598
27 to 31 141936 0.0904 0.536018
26 to 30 141774 -0.4587 0.323208
25 to 29 142352 1.5006 0.933267
24 to 28 141834 -0.2554 0.399224
23 to 27 141675 -0.7943 0.213499
22 to 26 141677 -0.7876 0.215477
21 to 25 142131 0.7514 0.773801
20 to 24 141918 0.0294 0.511723
19 to 23 142113 0.6904 0.755031
18 to 22 141738 -0.5808 0.280695
17 to 21 141836 -0.2486 0.401844
16 to 20 141741 -0.5706 0.284132
15 to 19 142018 0.3684 0.643702
14 to 18 141555 -1.2011 0.114853
13 to 17 141457 -1.5333 0.062598
12 to 16 142227 1.0768 0.859226
11 to 15 141976 0.2260 0.589399
10 to 14 141748 -0.5469 0.292230
9 to 13 141658 -0.8520 0.197116
8 to 12 142173 0.8938 0.814285
7 to 11 141355 -1.8791 0.030116
6 to 10 142181 0.9209 0.821453
5 to 9 142180 0.9175 0.820566
4 to 8 141943 0.1141 0.545435
3 to 7 141879 -0.1028 0.459056
2 to 6 142214 1.0328 0.849147
1 to 5 141989 0.2701 0.606446
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_16:31
Bits used No. missing words z-score p-value
31 to 32 141837 -0.2134 0.415522
30 to 31 142594 2.0197 0.978291
29 to 30 142439 1.5624 0.940909
28 to 29 141242 -1.9685 0.024504
27 to 28 141955 0.1347 0.553583
26 to 27 142211 0.8899 0.813235
25 to 26 141935 0.0757 0.530180
24 to 25 141905 -0.0128 0.494905
23 to 24 141780 -0.3815 0.351415
22 to 23 142030 0.3560 0.639064
21 to 22 141990 0.2380 0.594046
20 to 21 141555 -1.0452 0.147960
19 to 20 141848 -0.1809 0.428217
18 to 19 142210 0.8869 0.812442
17 to 18 142226 0.9341 0.824882
16 to 17 142082 0.5094 0.694747
15 to 16 142286 1.1111 0.866742
14 to 15 142033 0.3648 0.642373
13 to 14 142137 0.6716 0.749079
12 to 13 141961 0.1524 0.560572
11 to 12 140973 -2.7620 0.002872
10 to 11 141693 -0.6381 0.261691
9 to 10 142218 0.9105 0.818729
8 to 9 141760 -0.4405 0.329787
7 to 8 142280 1.0934 0.862896
6 to 7 141658 -0.7414 0.229230
5 to 6 142112 0.5978 0.725029
4 to 5 142679 2.2704 0.988409
3 to 4 141998 0.2616 0.603171
2 to 3 141963 0.1583 0.562897
1 to 2 141964 0.1613 0.564059
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2348.61 -2.141 0.016136
Test results for specific bytes for dh-ranFile-2018-06-27_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2473.71 -0.372 0.355034
2 to 9 2548.90 0.692 0.755376
3 to 10 2561.49 0.870 0.807756
4 to 11 2631.13 1.854 0.968160
5 to 12 2578.05 1.104 0.865150
6 to 13 2540.67 0.575 0.717427
7 to 14 2534.58 0.489 0.687581
8 to 15 2541.66 0.589 0.722133
9 to 16 2387.64 -1.589 0.056028
10 to 17 2543.14 0.610 0.729105
11 to 18 2308.96 -2.702 0.003449
12 to 19 2483.76 -0.230 0.409197
13 to 20 2526.38 0.373 0.645471
14 to 21 2465.46 -0.488 0.312633
15 to 22 2516.30 0.231 0.591182
16 to 23 2639.55 1.974 0.975782
17 to 24 2534.81 0.492 0.688747
18 to 25 2405.23 -1.340 0.090090
19 to 26 2493.46 -0.093 0.463144
20 to 27 2511.19 0.158 0.562864
21 to 28 2512.98 0.184 0.572805
22 to 29 2543.08 0.609 0.728810
23 to 30 2421.21 -1.114 0.132578
24 to 31 2499.76 -0.003 0.498662
25 to 32 2507.93 0.112 0.544627
CDPARK for dh-ranFile-2018-06-27_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
3455 -3.1050 0.000951
3550 1.2329 0.891189
3535 0.5479 0.708135
3535 0.5479 0.708135
3483 -1.8265 0.033889
3549 1.1872 0.882429
3515 -0.3653 0.357445
3491 -1.4612 0.071982
3506 -0.7763 0.218799
3538 0.6849 0.753306
Square side=100, avg. no. parked=3515.70 sample std.=29.98
p-value of the KSTEST for those 10 p-values: 0.261680
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_16:31
0.6016,0.4640,0.8744,0.6391,0.8631,0.1886,0.6564,0.9547,0.0798,0.8573,
The KS test for those 10 p-values: 0.303077
The 3DSPHERES test for dh-ranFile-2018-06-27_16:31
sample no r^3 equiv. uni.
1 45.051 0.777250
2 0.716 0.023581
3 5.538 0.168563
4 17.313 0.438481
5 4.527 0.140066
6 117.531 0.980113
7 17.774 0.447038
8 50.643 0.815132
9 37.051 0.709179
10 19.321 0.474823
11 30.936 0.643419
12 24.195 0.553580
13 86.450 0.943958
14 19.299 0.474444
15 41.428 0.748653
16 3.659 0.114813
17 49.677 0.809082
18 8.218 0.239627
19 36.372 0.702520
20 6.249 0.188045
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.965679
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.3 -1.1 1.2 -1.0 -1.6
-0.6 -2.0 0.4 -0.9 0.6 0.9
-0.7 1.3 1.7 0.3 -0.5 -0.4
0.3 -1.1 -1.1 1.0 0.1 0.5
0.1 0.4 0.0 -0.1 -1.8 -1.6
1.3 -0.5 -0.2 0.0 0.5 -0.3
0.3 -0.7 0.9 -0.7 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:37.496776
z-score=-0.491342, p-value=0.331201
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_16:31
Test no p-value
1 0.087292
2 0.389594
3 0.606977
4 0.195528
5 0.915125
6 0.010604
7 0.075000
8 0.413005
9 0.162126
10 0.528019
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.113384
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_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 66691 0.01 66527 0.29
3 25000.00 24933 0.18 25055 0.12
4 6666.67 6722 0.46 6756 1.20
5 1388.89 1377 0.10 1378 0.09
6 238.10 245 0.20 251 0.70
7 34.72 25 2.72 30 0.64
8 4.96 6 0.22 2 1.77
p=0.30829 p=0.43075
Number of rngs required: 689441, p-value: 0.886
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_16:31
No. of wins: Observed Expected
98401 98585.9
z-score=-0.827, pvalue=0.20418
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66701 66666.7 0.018 0.018
2 37691 37654.3 0.036 0.053
3 26845 26954.7 0.447 0.500
4 19306 19313.5 0.003 0.503
5 13732 13851.4 1.030 1.533
6 10077 9943.5 1.791 3.324
7 7060 7145.0 1.012 4.336
8 5120 5139.1 0.071 4.406
9 3704 3699.9 0.005 4.411
10 2741 2666.3 2.093 6.504
11 1896 1923.3 0.388 6.892
12 1393 1388.7 0.013 6.905
13 980 1003.7 0.560 7.466
14 706 726.1 0.559 8.024
15 566 525.8 3.068 11.092
16 386 381.2 0.062 11.154
17 306 276.5 3.139 14.292
18 216 200.8 1.146 15.438
19 168 146.0 3.320 18.758
20 103 106.2 0.097 18.856
21 303 287.1 0.879 19.735
Chisq= 19.73 for 20 degrees of freedom, p= 0.52537
SUMMARY of craptest
p-value for no. of wins: 0.204177
p-value for throws/game: 0.525365
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_16:31
No. of wins: Observed Expected
98864 98585.9
z-score= 1.244, pvalue=0.89325
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66405 66666.7 1.027 1.027
2 37753 37654.3 0.259 1.286
3 27017 26954.7 0.144 1.429
4 19352 19313.5 0.077 1.506
5 13713 13851.4 1.383 2.890
6 9933 9943.5 0.011 2.901
7 7162 7145.0 0.040 2.941
8 5029 5139.1 2.358 5.299
9 3838 3699.9 5.157 10.456
10 2690 2666.3 0.211 10.667
11 1969 1923.3 1.084 11.751
12 1401 1388.7 0.108 11.859
13 1025 1003.7 0.451 12.311
14 714 726.1 0.203 12.514
15 524 525.8 0.006 12.520
16 367 381.2 0.525 13.046
17 311 276.5 4.294 17.340
18 224 200.8 2.673 20.013
19 159 146.0 1.160 21.173
20 112 106.2 0.315 21.489
21 302 287.1 0.772 22.260
Chisq= 22.26 for 20 degrees of freedom, p= 0.67345
SUMMARY of craptest
p-value for no. of wins: 0.893252
p-value for throws/game: 0.673445
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0029,0.0034,0.0106,0.0118,0.0161,0.0175,0.0183,0.0236,0.0245,
0.0249,0.0301,0.0339,0.0560,0.0594,0.0626,0.0636,0.0666,0.0678,0.0707,
0.0720,0.0750,0.0758,0.0798,0.0873,0.0901,0.0956,0.1089,0.1096,0.1115,
0.1134,0.1148,0.1149,0.1326,0.1338,0.1343,0.1401,0.1401,0.1480,0.1621,
0.1660,0.1686,0.1722,0.1779,0.1805,0.1824,0.1877,0.1880,0.1886,0.1941,
0.1955,0.1971,0.2042,0.2065,0.2135,0.2155,0.2188,0.2209,0.2292,0.2396,
0.2470,0.2547,0.2617,0.2617,0.2655,0.2687,0.2761,0.2775,0.2807,0.2809,
0.2828,0.2841,0.2912,0.2922,0.2934,0.3031,0.3066,0.3083,0.3126,0.3169,
0.3175,0.3232,0.3253,0.3266,0.3298,0.3312,0.3401,0.3480,0.3514,0.3550,
0.3574,0.3728,0.3790,0.3829,0.3887,0.3896,0.3983,0.3992,0.4018,0.4092,
0.4130,0.4155,0.4203,0.4245,0.4282,0.4298,0.4298,0.4308,0.4336,0.4385,
0.4470,0.4515,0.4587,0.4591,0.4631,0.4640,0.4717,0.4733,0.4744,0.4748,
0.4839,0.4884,0.4949,0.4987,0.5064,0.5117,0.5188,0.5221,0.5254,0.5280,
0.5302,0.5360,0.5372,0.5422,0.5446,0.5454,0.5531,0.5536,0.5536,0.5551,
0.5606,0.5629,0.5629,0.5641,0.5674,0.5728,0.5775,0.5815,0.5875,0.5894,
0.5912,0.5940,0.6016,0.6032,0.6064,0.6070,0.6135,0.6237,0.6321,0.6391,
0.6391,0.6424,0.6434,0.6437,0.6455,0.6545,0.6564,0.6588,0.6652,0.6734,
0.6876,0.6887,0.6939,0.6947,0.7017,0.7025,0.7081,0.7081,0.7092,0.7102,
0.7107,0.7172,0.7174,0.7210,0.7221,0.7235,0.7250,0.7288,0.7291,0.7319,
0.7395,0.7487,0.7491,0.7529,0.7533,0.7550,0.7554,0.7566,0.7603,0.7694,
0.7711,0.7738,0.7773,0.7797,0.8022,0.8026,0.8054,0.8078,0.8091,0.8124,
0.8129,0.8132,0.8143,0.8151,0.8180,0.8187,0.8206,0.8215,0.8249,0.8254,
0.8398,0.8457,0.8491,0.8494,0.8527,0.8573,0.8592,0.8597,0.8629,0.8631,
0.8651,0.8667,0.8744,0.8822,0.8824,0.8859,0.8862,0.8877,0.8882,0.8912,
0.8919,0.8932,0.8933,0.8956,0.9146,0.9151,0.9215,0.9333,0.9349,0.9361,
0.9409,0.9409,0.9440,0.9509,0.9533,0.9547,0.9657,0.9682,0.9687,0.9740,
0.9743,0.9758,0.9783,0.9801,0.9814,0.9883,0.9884,0.9930,0.9945,
Overall p-value after applying KStest on 269 p-values = 0.357732
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.