RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.69 23.7479 0.873552
2 to 25 15.83 18.0924 0.616968
3 to 26 15.94 13.0451 0.266841
4 to 27 15.97 14.6632 0.380275
5 to 28 15.44 21.3917 0.790741
6 to 29 15.60 14.7099 0.383634
7 to 30 15.56 21.0974 0.778038
8 to 31 15.78 7.9388 0.032162
9 to 32 15.52 29.3291 0.968391
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.794449
Tough bday spacings test for dh-ranFile-2018-06-16_10:31: 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 42 64 103 90 78 57 30 15 6 6
(O-E)^2/E 0.0 0.8 1.2 0.3 0.6 0.0 0.5 0.0 0.0 0.1 0.9
Birthday Spacings: Sum(O-E)^2/E= 4.296, p= 0.067
RESULTS OF GCD FOR dh-ranFile-2018-06-16_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.975475
p-value, dist. of gcd's: 0.770144
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.596 0.476 0.324 0.719 0.340 0.355 0.021 0.920
Bits 8 to 15---> 0.283 0.692 0.168 0.818 0.146 0.490 0.036 0.489
Bits 16 to 23---> 0.147 0.296 0.508 0.509 0.583 0.544 0.987 0.948
Bits 24 to 31---> 0.018 0.968 0.283 0.467 0.401 0.520 0.319 0.663
KS test for the above 32 p values: 0.466
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_10:31,
p-values for 5 runs: 0.0985, 0.0883, 0.4853, 0.4189, 0.1565
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 227 211.4 1.148 1.148
r= 29 5092 5134.0 0.344 1.492
r= 30 23089 23103.0 0.009 1.501
r= 31 11592 11551.5 0.142 1.643
chi-square = 1.643 with df = 3; p-value = 0.350
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5078 5134.0 0.611 0.959
r= 31 23088 23103.0 0.010 0.969
r= 32 11614 11551.5 0.338 1.307
chi-square = 1.307 with df = 3; p-value = 0.273
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_10:31
b-rank test for bits 1 to 8, p=0.09610
b-rank test for bits 2 to 9, p=0.28859
b-rank test for bits 3 to 10, p=0.25051
b-rank test for bits 4 to 11, p=0.29635
b-rank test for bits 5 to 12, p=0.91881
b-rank test for bits 6 to 13, p=0.75427
b-rank test for bits 7 to 14, p=0.88675
b-rank test for bits 8 to 15, p=0.63318
b-rank test for bits 9 to 16, p=0.47929
b-rank test for bits 10 to 17, p=0.29328
b-rank test for bits 11 to 18, p=0.84186
b-rank test for bits 12 to 19, p=0.88321
b-rank test for bits 13 to 20, p=0.24688
b-rank test for bits 14 to 21, p=0.23560
b-rank test for bits 15 to 22, p=0.10109
b-rank test for bits 16 to 23, p=0.36037
b-rank test for bits 17 to 24, p=0.71810
b-rank test for bits 18 to 25, p=0.92304
b-rank test for bits 19 to 26, p=0.67364
b-rank test for bits 20 to 27, p=0.42849
b-rank test for bits 21 to 28, p=0.70834
b-rank test for bits 22 to 29, p=0.31067
b-rank test for bits 23 to 30, p=0.15859
b-rank test for bits 24 to 31, p=0.75683
b-rank test for bits 25 to 32, p=0.97528
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 = 0.700182
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_10:31
(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 141979 0.16 0.564654
2 141239 -1.57 0.058652
3 141792 -0.27 0.391990
4 140855 -2.46 0.006882
5 142240 0.77 0.780119
6 142486 1.35 0.911068
7 141508 -0.94 0.174203
8 141863 -0.11 0.456900
9 141771 -0.32 0.373272
10 141925 0.04 0.514603
11 141876 -0.08 0.468964
12 142569 1.54 0.938376
13 141618 -0.68 0.248038
14 142232 0.75 0.774546
15 142272 0.85 0.801603
16 141570 -0.79 0.213939
17 141818 -0.21 0.415512
18 141649 -0.61 0.271512
19 142540 1.47 0.929696
20 142372 1.08 0.860153
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_10:31
Bits used No. missing words z-score p-value
23 to 32 142064 0.5333 0.703103
22 to 31 141781 -0.4425 0.329058
21 to 30 142266 1.2299 0.890632
20 to 29 142109 0.6885 0.754436
19 to 28 141817 -0.3184 0.375099
18 to 27 141460 -1.5494 0.060641
17 to 26 141406 -1.7356 0.041315
16 to 25 141524 -1.3287 0.091970
15 to 24 141779 -0.4494 0.326567
14 to 23 142307 1.3713 0.914856
13 to 22 141646 -0.9080 0.181930
12 to 21 141828 -0.2804 0.389567
11 to 20 141867 -0.1460 0.441974
10 to 19 141699 -0.7253 0.234141
9 to 18 142168 0.8920 0.813794
8 to 17 142242 1.1471 0.874338
7 to 16 141647 -0.9046 0.182842
6 to 15 141843 -0.2287 0.409542
5 to 14 142077 0.5782 0.718426
4 to 13 141899 -0.0356 0.485792
3 to 12 141456 -1.5632 0.059002
2 to 11 141937 0.0954 0.538007
1 to 10 141549 -1.2425 0.107023
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_10:31
Bits used No. missing words z-score p-value
28 to 32 142044 0.4565 0.675988
27 to 31 141760 -0.5062 0.306357
26 to 30 141884 -0.0859 0.465787
25 to 29 141941 0.1074 0.542747
24 to 28 141684 -0.7638 0.222484
23 to 27 141609 -1.0181 0.154323
22 to 26 141497 -1.3977 0.081097
21 to 25 141571 -1.1469 0.125715
20 to 24 142039 0.4396 0.669872
19 to 23 141966 0.1921 0.576169
18 to 22 142185 0.9345 0.824970
17 to 21 142147 0.8057 0.789781
16 to 20 141540 -1.2520 0.105291
15 to 19 141762 -0.4994 0.308741
14 to 18 141989 0.2701 0.606446
13 to 17 141570 -1.1503 0.125016
12 to 16 142172 0.8904 0.813376
11 to 15 142112 0.6870 0.753964
10 to 14 141725 -0.6248 0.266036
9 to 13 142314 1.3718 0.914931
8 to 12 141795 -0.3876 0.349171
7 to 11 141982 0.2463 0.597290
6 to 10 141465 -1.5062 0.066008
5 to 9 142145 0.7989 0.787820
4 to 8 141669 -0.8147 0.207628
3 to 7 141865 -0.1503 0.440275
2 to 6 141909 -0.0011 0.499554
1 to 5 141987 0.2633 0.603836
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_10:31
Bits used No. missing words z-score p-value
31 to 32 141716 -0.5703 0.284239
30 to 31 142412 1.4828 0.930937
29 to 30 141754 -0.4582 0.323404
28 to 29 141582 -0.9656 0.167128
27 to 28 142024 0.3383 0.632416
26 to 27 141788 -0.3579 0.360207
25 to 26 141551 -1.0570 0.145251
24 to 25 141735 -0.5142 0.303539
23 to 24 141680 -0.6765 0.249365
22 to 23 141624 -0.8417 0.199983
21 to 22 142412 1.4828 0.930937
20 to 21 142105 0.5772 0.718097
19 to 20 142181 0.8014 0.788546
18 to 19 142011 0.2999 0.617878
17 to 18 142208 0.8810 0.810850
16 to 17 142154 0.7217 0.764773
15 to 16 142243 0.9843 0.837510
14 to 15 141547 -1.0688 0.142575
13 to 14 142588 2.0020 0.977356
12 to 13 141323 -1.7296 0.041852
11 to 12 141865 -0.1308 0.447980
10 to 11 142130 0.6509 0.742459
9 to 10 142193 0.8368 0.798643
8 to 9 141481 -1.2635 0.103203
7 to 8 141885 -0.0718 0.471393
6 to 7 141959 0.1465 0.558244
5 to 6 141604 -0.9007 0.183880
4 to 5 142286 1.1111 0.866742
3 to 4 141656 -0.7473 0.227445
2 to 3 142122 0.6273 0.734784
1 to 2 141246 -1.9567 0.025190
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2593.62 1.324 0.907239
Test results for specific bytes for dh-ranFile-2018-06-16_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2543.21 0.611 0.729428
2 to 9 2637.36 1.943 0.973963
3 to 10 2419.31 -1.141 0.126909
4 to 11 2541.50 0.587 0.721367
5 to 12 2484.17 -0.224 0.411410
6 to 13 2531.87 0.451 0.673898
7 to 14 2536.55 0.517 0.697386
8 to 15 2561.79 0.874 0.808888
9 to 16 2527.39 0.387 0.650759
10 to 17 2482.47 -0.248 0.402122
11 to 18 2569.63 0.985 0.837605
12 to 19 2532.58 0.461 0.677514
13 to 20 2635.51 1.916 0.972345
14 to 21 2487.81 -0.172 0.431581
15 to 22 2530.46 0.431 0.666679
16 to 23 2585.81 1.214 0.887540
17 to 24 2551.99 0.735 0.768908
18 to 25 2492.11 -0.112 0.455561
19 to 26 2583.79 1.185 0.881978
20 to 27 2512.26 0.173 0.568847
21 to 28 2504.31 0.061 0.524303
22 to 29 2535.61 0.504 0.692738
23 to 30 2498.72 -0.018 0.492775
24 to 31 2469.72 -0.428 0.334251
25 to 32 2460.55 -0.558 0.288449
CDPARK for dh-ranFile-2018-06-16_10:31: 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
3562 1.7808 0.962529
3523 0.0000 0.500000
3527 0.1826 0.572463
3545 1.0046 0.842447
3502 -0.9589 0.168804
3514 -0.4110 0.340551
3517 -0.2740 0.392053
3530 0.3196 0.625377
3551 1.2785 0.899470
3528 0.2283 0.590298
Square side=100, avg. no. parked=3529.90 sample std.=17.21
p-value of the KSTEST for those 10 p-values: 0.534436
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_10:31
0.9541,0.3195,0.7254,0.1471,0.4643,0.1962,0.5383,0.9861,0.6722,0.1220,
The KS test for those 10 p-values: 0.866819
The 3DSPHERES test for dh-ranFile-2018-06-16_10:31
sample no r^3 equiv. uni.
1 5.485 0.167088
2 24.639 0.560141
3 26.389 0.585064
4 6.766 0.201901
5 24.701 0.561051
6 42.728 0.759313
7 60.162 0.865392
8 18.119 0.453364
9 95.312 0.958292
10 10.109 0.286068
11 29.065 0.620479
12 7.852 0.230275
13 16.953 0.431691
14 29.167 0.621759
15 86.804 0.944615
16 37.390 0.712446
17 1.084 0.035495
18 7.135 0.211668
19 3.097 0.098073
20 15.595 0.405388
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.979395
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 2.3 0.6 -0.8 -1.9
0.4 0.7 -1.7 1.2 0.3 -0.1
0.2 0.9 1.5 0.8 -1.4 -0.1
0.5 -0.3 -2.1 -0.4 0.5 -1.0
0.4 -0.1 -0.3 0.1 0.2 1.2
1.8 -0.5 0.1 -0.5 0.2 -0.1
1.2 -0.1 0.9 -0.1 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:35.541403
z-score=-0.704691, p-value=0.251222
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_10:31
Test no p-value
1 0.063905
2 0.574303
3 0.489562
4 0.139669
5 0.098786
6 0.067520
7 0.119660
8 0.966026
9 0.969604
10 0.308736
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.092143
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_10:31:
(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 67063 2.36 66956 1.26
3 25000.00 24631 5.45 24757 2.36
4 6666.67 6594 0.79 6574 1.29
5 1388.89 1404 0.16 1427 1.05
6 238.10 247 0.33 246 0.26
7 34.72 48 5.08 33 0.09
8 4.96 12 9.99 6 0.22
p=0.99951 p=0.63219
Number of rngs required: 687288, p-value: 0.097
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_10:31
No. of wins: Observed Expected
98446 98585.9
z-score=-0.626, pvalue=0.26581
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66823 66666.7 0.367 0.367
2 37872 37654.3 1.258 1.625
3 27024 26954.7 0.178 1.803
4 19192 19313.5 0.764 2.567
5 13743 13851.4 0.849 3.416
6 9901 9943.5 0.182 3.598
7 7122 7145.0 0.074 3.672
8 5113 5139.1 0.132 3.804
9 3541 3699.9 6.821 10.625
10 2757 2666.3 3.086 13.711
11 1924 1923.3 0.000 13.711
12 1370 1388.7 0.253 13.964
13 1025 1003.7 0.451 14.415
14 722 726.1 0.024 14.439
15 506 525.8 0.748 15.187
16 362 381.2 0.962 16.149
17 269 276.5 0.206 16.355
18 200 200.8 0.003 16.358
19 149 146.0 0.062 16.421
20 107 106.2 0.006 16.427
21 278 287.1 0.289 16.716
Chisq= 16.72 for 20 degrees of freedom, p= 0.32866
SUMMARY of craptest
p-value for no. of wins: 0.265812
p-value for throws/game: 0.328660
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_10:31
No. of wins: Observed Expected
98649 98585.9
z-score= 0.282, pvalue=0.61118
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66573 66666.7 0.132 0.132
2 37569 37654.3 0.193 0.325
3 27205 26954.7 2.324 2.649
4 19217 19313.5 0.482 3.130
5 13806 13851.4 0.149 3.279
6 9957 9943.5 0.018 3.298
7 7160 7145.0 0.031 3.329
8 5238 5139.1 1.904 5.233
9 3631 3699.9 1.282 6.515
10 2628 2666.3 0.550 7.065
11 1936 1923.3 0.083 7.149
12 1414 1388.7 0.459 7.608
13 1014 1003.7 0.105 7.713
14 724 726.1 0.006 7.720
15 538 525.8 0.281 8.001
16 379 381.2 0.012 8.013
17 280 276.5 0.043 8.057
18 199 200.8 0.017 8.073
19 155 146.0 0.557 8.630
20 94 106.2 1.405 10.035
21 283 287.1 0.059 10.094
Chisq= 10.09 for 20 degrees of freedom, p= 0.03356
SUMMARY of craptest
p-value for no. of wins: 0.611184
p-value for throws/game: 0.033561
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0069,0.0177,0.0210,0.0252,0.0322,0.0336,0.0355,0.0356,0.0413,0.0419,
0.0587,0.0590,0.0606,0.0639,0.0660,0.0670,0.0675,0.0811,0.0883,0.0920,
0.0921,0.0961,0.0972,0.0981,0.0985,0.0988,0.1011,0.1032,0.1053,0.1070,
0.1197,0.1220,0.1250,0.1257,0.1269,0.1397,0.1426,0.1453,0.1456,0.1469,
0.1471,0.1543,0.1565,0.1586,0.1671,0.1671,0.1678,0.1688,0.1742,0.1819,
0.1828,0.1839,0.1962,0.2000,0.2019,0.2076,0.2117,0.2139,0.2225,0.2274,
0.2303,0.2341,0.2356,0.2469,0.2480,0.2494,0.2505,0.2512,0.2658,0.2660,
0.2668,0.2715,0.2726,0.2827,0.2829,0.2842,0.2861,0.2884,0.2886,0.2933,
0.2957,0.2964,0.3035,0.3064,0.3087,0.3087,0.3107,0.3189,0.3195,0.3234,
0.3238,0.3266,0.3287,0.3291,0.3343,0.3404,0.3406,0.3492,0.3502,0.3547,
0.3602,0.3604,0.3733,0.3751,0.3803,0.3836,0.3896,0.3920,0.3921,0.4009,
0.4021,0.4054,0.4095,0.4114,0.4155,0.4189,0.4285,0.4316,0.4317,0.4403,
0.4420,0.4480,0.4534,0.4556,0.4569,0.4643,0.4658,0.4658,0.4666,0.4690,
0.4714,0.4763,0.4793,0.4853,0.4858,0.4891,0.4896,0.4897,0.4928,0.4996,
0.5000,0.5076,0.5089,0.5146,0.5204,0.5243,0.5344,0.5380,0.5383,0.5427,
0.5436,0.5582,0.5601,0.5611,0.5647,0.5688,0.5725,0.5743,0.5762,0.5833,
0.5851,0.5903,0.5962,0.5973,0.6038,0.6064,0.6112,0.6170,0.6179,0.6205,
0.6218,0.6254,0.6322,0.6324,0.6332,0.6508,0.6631,0.6667,0.6699,0.6722,
0.6736,0.6739,0.6760,0.6775,0.6924,0.6927,0.6974,0.7002,0.7031,0.7083,
0.7124,0.7181,0.7181,0.7184,0.7195,0.7214,0.7254,0.7294,0.7348,0.7425,
0.7540,0.7543,0.7544,0.7568,0.7593,0.7648,0.7689,0.7701,0.7745,0.7780,
0.7801,0.7878,0.7885,0.7898,0.7907,0.7944,0.7986,0.8016,0.8089,0.8108,
0.8134,0.8138,0.8176,0.8250,0.8375,0.8376,0.8419,0.8424,0.8602,0.8654,
0.8667,0.8668,0.8736,0.8743,0.8820,0.8832,0.8867,0.8875,0.8906,0.8995,
0.9072,0.9111,0.9149,0.9149,0.9188,0.9203,0.9230,0.9297,0.9309,0.9309,
0.9384,0.9446,0.9478,0.9541,0.9583,0.9625,0.9660,0.9676,0.9684,0.9696,
0.9723,0.9740,0.9753,0.9755,0.9774,0.9794,0.9861,0.9867,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.974470
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.