RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.84 11.3924 0.164548
2 to 25 15.59 24.4964 0.893438
3 to 26 15.91 14.5897 0.374990
4 to 27 16.33 12.0377 0.202154
5 to 28 15.80 26.4729 0.933735
6 to 29 15.70 11.8983 0.193745
7 to 30 15.65 14.3410 0.357169
8 to 31 15.59 16.6730 0.523272
9 to 32 15.73 17.7553 0.595570
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.811756
Tough bday spacings test for dh-ranFile-2018-06-21_09:31: 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 6 34 56 114 103 83 40 36 15 11 2
(O-E)^2/E 1.1 0.2 4.1 2.7 0.3 0.3 2.8 1.3 0.0 2.9 1.0
Birthday Spacings: Sum(O-E)^2/E= 16.731, p= 0.919
RESULTS OF GCD FOR dh-ranFile-2018-06-21_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.917755
p-value, dist. of gcd's: 0.887689
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.061 0.254 0.598 0.857 0.807 0.591 0.306 0.231
Bits 8 to 15---> 0.870 0.422 0.404 0.136 0.391 0.640 0.515 0.379
Bits 16 to 23---> 0.592 0.088 0.870 0.777 0.786 0.003 0.256 0.817
Bits 24 to 31---> 0.775 0.581 0.500 0.829 0.756 0.189 0.861 0.313
KS test for the above 32 p values: 0.323
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_09:31,
p-values for 5 runs: 0.8956, 0.8710, 0.8208, 0.6861, 0.5261
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5204 5134.0 0.954 3.812
r= 30 23134 23103.0 0.041 3.854
r= 31 11426 11551.5 1.364 5.218
chi-square = 5.218 with df = 3; p-value = 0.843
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5056 5134.0 1.185 1.457
r= 31 23143 23103.0 0.069 1.526
r= 32 11582 11551.5 0.080 1.607
chi-square = 1.607 with df = 3; p-value = 0.342
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_09:31
b-rank test for bits 1 to 8, p=0.45802
b-rank test for bits 2 to 9, p=0.20192
b-rank test for bits 3 to 10, p=0.69234
b-rank test for bits 4 to 11, p=0.37674
b-rank test for bits 5 to 12, p=0.49137
b-rank test for bits 6 to 13, p=0.92538
b-rank test for bits 7 to 14, p=0.15116
b-rank test for bits 8 to 15, p=0.56742
b-rank test for bits 9 to 16, p=0.06843
b-rank test for bits 10 to 17, p=0.89382
b-rank test for bits 11 to 18, p=0.67629
b-rank test for bits 12 to 19, p=0.82212
b-rank test for bits 13 to 20, p=0.18805
b-rank test for bits 14 to 21, p=0.61084
b-rank test for bits 15 to 22, p=0.30765
b-rank test for bits 16 to 23, p=0.51457
b-rank test for bits 17 to 24, p=0.25972
b-rank test for bits 18 to 25, p=0.65716
b-rank test for bits 19 to 26, p=0.07543
b-rank test for bits 20 to 27, p=0.81894
b-rank test for bits 21 to 28, p=0.70247
b-rank test for bits 22 to 29, p=0.43305
b-rank test for bits 23 to 30, p=0.60271
b-rank test for bits 24 to 31, p=0.12249
b-rank test for bits 25 to 32, p=0.52137
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 = 0.823072
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_09:31
(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 142260 0.82 0.793699
2 142084 0.41 0.658403
3 141548 -0.84 0.199271
4 141350 -1.31 0.095633
5 141002 -2.12 0.017006
6 142350 1.03 0.848402
7 141451 -1.07 0.142115
8 142003 0.22 0.586619
9 141596 -0.73 0.232060
10 141119 -1.85 0.032405
11 141472 -1.02 0.153438
12 142100 0.45 0.672017
13 141706 -0.48 0.317369
14 141715 -0.45 0.324899
15 141832 -0.18 0.428310
16 142455 1.27 0.898833
17 141658 -0.59 0.278528
18 142477 1.33 0.907635
19 142316 0.95 0.828985
20 141442 -1.09 0.137440
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_09:31
Bits used No. missing words z-score p-value
23 to 32 141961 0.1782 0.570706
22 to 31 141453 -1.5736 0.057796
21 to 30 141880 -0.1011 0.459721
20 to 29 141100 -2.7908 0.002629
19 to 28 141532 -1.3011 0.096606
18 to 27 141783 -0.4356 0.331556
17 to 26 141542 -1.2667 0.102639
16 to 25 141910 0.0023 0.500922
15 to 24 142142 0.8023 0.788813
14 to 23 142049 0.4816 0.684962
13 to 22 141937 0.0954 0.538007
12 to 21 142218 1.0644 0.856422
11 to 20 142205 1.0196 0.846029
10 to 19 142342 1.4920 0.932146
9 to 18 142246 1.1609 0.877165
8 to 17 141798 -0.3839 0.350528
7 to 16 141745 -0.5667 0.285474
6 to 15 141882 -0.0942 0.462459
5 to 14 142295 1.3299 0.908224
4 to 13 142209 1.0333 0.849279
3 to 12 142243 1.1506 0.875049
2 to 11 141135 -2.6701 0.003791
1 to 10 141660 -0.8598 0.194961
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_09:31
Bits used No. missing words z-score p-value
28 to 32 141702 -0.7028 0.241086
27 to 31 142195 0.9684 0.833571
26 to 30 141668 -0.8181 0.206659
25 to 29 141638 -0.9198 0.178848
24 to 28 141491 -1.4181 0.078086
23 to 27 141649 -0.8825 0.188760
22 to 26 142192 0.9582 0.831020
21 to 25 142037 0.4328 0.667413
20 to 24 142194 0.9650 0.832723
19 to 23 141952 0.1446 0.557504
18 to 22 142528 2.0972 0.982011
17 to 21 142639 2.4735 0.993309
16 to 20 141974 0.2192 0.586761
15 to 19 141856 -0.1808 0.428270
14 to 18 141741 -0.5706 0.284132
13 to 17 142109 0.6768 0.750749
12 to 16 142357 1.5175 0.935433
11 to 15 142263 1.1989 0.884713
10 to 14 142008 0.3345 0.630989
9 to 13 142446 1.8192 0.965561
8 to 12 142258 1.1819 0.881384
7 to 11 142029 0.4057 0.657504
6 to 10 141983 0.2497 0.598602
5 to 9 141903 -0.0215 0.491440
4 to 8 142338 1.4531 0.926905
3 to 7 141867 -0.1435 0.442951
2 to 6 141562 -1.1774 0.119520
1 to 5 141841 -0.2316 0.408414
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_09:31
Bits used No. missing words z-score p-value
31 to 32 141468 -1.3019 0.096482
30 to 31 141276 -1.8682 0.030865
29 to 30 141630 -0.8240 0.204975
28 to 29 142385 1.4032 0.919715
27 to 28 141690 -0.6470 0.258819
26 to 27 140647 -3.7237 0.000098
25 to 26 142005 0.2822 0.611110
24 to 25 142248 0.9990 0.841109
23 to 24 142011 0.2999 0.617878
22 to 23 141657 -0.7443 0.228337
21 to 22 142158 0.7335 0.768385
20 to 21 141956 0.1377 0.554749
19 to 20 142444 1.5772 0.942625
18 to 19 142391 1.4209 0.922321
17 to 18 141337 -1.6883 0.045678
16 to 17 142032 0.3619 0.641271
15 to 16 141562 -1.0246 0.152783
14 to 15 142547 1.8810 0.970016
13 to 14 142492 1.7188 0.957174
12 to 13 142576 1.9666 0.975384
11 to 12 142326 1.2291 0.890486
10 to 11 141961 0.1524 0.560572
9 to 10 141611 -0.8800 0.189422
8 to 9 141962 0.1554 0.561735
7 to 8 141406 -1.4847 0.068805
6 to 7 141876 -0.0983 0.460840
5 to 6 142173 0.7778 0.781653
4 to 5 142541 1.8633 0.968792
3 to 4 141912 0.0079 0.503142
2 to 3 142084 0.5153 0.696811
1 to 2 141088 -2.4228 0.007701
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2353.38 -2.074 0.019061
Test results for specific bytes for dh-ranFile-2018-06-21_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2360.82 -1.968 0.024518
2 to 9 2629.85 1.836 0.966850
3 to 10 2487.40 -0.178 0.429292
4 to 11 2553.74 0.760 0.776376
5 to 12 2517.35 0.245 0.596934
6 to 13 2508.69 0.123 0.548892
7 to 14 2384.03 -1.640 0.050492
8 to 15 2512.23 0.173 0.568682
9 to 16 2511.14 0.158 0.562581
10 to 17 2393.65 -1.504 0.066285
11 to 18 2471.49 -0.403 0.343427
12 to 19 2532.24 0.456 0.675769
13 to 20 2600.57 1.422 0.922525
14 to 21 2434.12 -0.932 0.175753
15 to 22 2487.74 -0.173 0.431175
16 to 23 2521.00 0.297 0.616754
17 to 24 2537.22 0.526 0.700709
18 to 25 2546.30 0.655 0.743677
19 to 26 2359.97 -1.980 0.023837
20 to 27 2588.87 1.257 0.895597
21 to 28 2470.12 -0.423 0.336293
22 to 29 2488.07 -0.169 0.433037
23 to 30 2592.12 1.303 0.903671
24 to 31 2456.40 -0.617 0.268738
25 to 32 2355.09 -2.049 0.020218
CDPARK for dh-ranFile-2018-06-21_09:31: 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
3509 -0.6393 0.261324
3526 0.1370 0.554479
3499 -1.0959 0.136563
3528 0.2283 0.590298
3527 0.1826 0.572463
3534 0.5023 0.692266
3534 0.5023 0.692266
3517 -0.2740 0.392053
3515 -0.3653 0.357445
3524 0.0457 0.518210
Square side=100, avg. no. parked=3521.30 sample std.=10.66
p-value of the KSTEST for those 10 p-values: 0.357521
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_09:31
0.8125,0.6334,0.3262,0.0464,0.6250,0.3462,0.2644,0.7354,0.1303,0.4639,
The KS test for those 10 p-values: 0.782810
The 3DSPHERES test for dh-ranFile-2018-06-21_09:31
sample no r^3 equiv. uni.
1 20.874 0.501320
2 23.445 0.542282
3 5.848 0.177111
4 7.253 0.214765
5 74.989 0.917884
6 0.811 0.026664
7 0.082 0.002720
8 2.366 0.075822
9 3.960 0.123660
10 37.880 0.717098
11 15.072 0.394926
12 13.925 0.371346
13 21.592 0.513115
14 12.784 0.346962
15 21.051 0.504251
16 35.855 0.697350
17 17.310 0.438421
18 23.057 0.536320
19 24.172 0.553239
20 56.906 0.849960
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.301192
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 1.1 -1.1 -0.4 2.5
0.1 -0.1 0.2 -1.8 1.4 -0.2
-1.0 -0.6 0.3 0.0 1.6 -0.6
0.5 0.7 -1.3 0.0 0.0 -1.0
-0.6 -0.6 0.2 1.8 0.4 0.3
1.1 0.4 -1.1 0.0 0.1 0.1
0.0 -1.0 0.5 -0.1 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:31.879398
z-score=-1.104248, p-value=0.128485
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_09:31
Test no p-value
1 0.001116
2 0.669997
3 0.039537
4 0.009462
5 0.013428
6 0.852756
7 0.178964
8 0.179614
9 0.057367
10 0.830268
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000813
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_09:31:
(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 66732 0.06 66648 0.01
3 25000.00 25071 0.20 24932 0.18
4 6666.67 6541 2.37 6706 0.23
5 1388.89 1374 0.16 1430 1.22
6 238.10 229 0.35 230 0.28
7 34.72 42 1.53 45 3.04
8 4.96 10 5.12 8 1.86
p=0.86619 p=0.66230
Number of rngs required: 688620, p-value: 0.599
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_09:31
No. of wins: Observed Expected
98282 98585.9
z-score=-1.359, pvalue=0.08707
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66360 66666.7 1.411 1.411
2 37852 37654.3 1.038 2.448
3 26801 26954.7 0.877 3.325
4 19246 19313.5 0.236 3.561
5 14059 13851.4 3.111 6.672
6 9946 9943.5 0.001 6.672
7 7264 7145.0 1.981 8.653
8 5087 5139.1 0.528 9.181
9 3774 3699.9 1.485 10.667
10 2622 2666.3 0.736 11.402
11 1937 1923.3 0.097 11.500
12 1425 1388.7 0.947 12.446
13 963 1003.7 1.652 14.098
14 706 726.1 0.559 14.657
15 499 525.8 1.370 16.026
16 397 381.2 0.659 16.685
17 301 276.5 2.164 18.849
18 198 200.8 0.040 18.889
19 152 146.0 0.248 19.137
20 112 106.2 0.315 19.452
21 299 287.1 0.492 19.944
Chisq= 19.94 for 20 degrees of freedom, p= 0.53854
SUMMARY of craptest
p-value for no. of wins: 0.087068
p-value for throws/game: 0.538541
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_09:31
No. of wins: Observed Expected
98540 98585.9
z-score=-0.205, pvalue=0.41874
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66656 66666.7 0.002 0.002
2 37537 37654.3 0.366 0.367
3 26835 26954.7 0.532 0.899
4 19303 19313.5 0.006 0.905
5 13732 13851.4 1.030 1.934
6 10121 9943.5 3.167 5.101
7 7136 7145.0 0.011 5.113
8 5176 5139.1 0.265 5.378
9 3760 3699.9 0.977 6.355
10 2722 2666.3 1.164 7.519
11 1948 1923.3 0.316 7.836
12 1359 1388.7 0.637 8.473
13 1035 1003.7 0.975 9.448
14 754 726.1 1.069 10.517
15 490 525.8 2.442 12.959
16 406 381.2 1.620 14.579
17 282 276.5 0.108 14.687
18 217 200.8 1.302 15.989
19 151 146.0 0.172 16.161
20 112 106.2 0.315 16.476
21 268 287.1 1.272 17.748
Chisq= 17.75 for 20 degrees of freedom, p= 0.39603
SUMMARY of craptest
p-value for no. of wins: 0.418745
p-value for throws/game: 0.396025
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0008,0.0011,0.0026,0.0027,0.0034,0.0038,0.0077,0.0095,0.0134,
0.0170,0.0191,0.0202,0.0238,0.0245,0.0267,0.0309,0.0324,0.0395,0.0457,
0.0464,0.0505,0.0574,0.0578,0.0612,0.0663,0.0684,0.0688,0.0754,0.0758,
0.0781,0.0871,0.0880,0.0956,0.0965,0.0966,0.1026,0.1195,0.1225,0.1237,
0.1285,0.1303,0.1356,0.1366,0.1374,0.1421,0.1512,0.1528,0.1534,0.1645,
0.1758,0.1771,0.1788,0.1790,0.1796,0.1881,0.1888,0.1889,0.1894,0.1937,
0.1950,0.1993,0.2019,0.2022,0.2050,0.2067,0.2148,0.2283,0.2310,0.2321,
0.2411,0.2536,0.2564,0.2588,0.2597,0.2613,0.2644,0.2687,0.2785,0.2841,
0.2855,0.3012,0.3055,0.3077,0.3135,0.3174,0.3234,0.3249,0.3262,0.3316,
0.3363,0.3421,0.3434,0.3462,0.3470,0.3505,0.3572,0.3574,0.3575,0.3713,
0.3750,0.3767,0.3791,0.3908,0.3921,0.3949,0.3960,0.4039,0.4084,0.4187,
0.4223,0.4283,0.4283,0.4293,0.4312,0.4330,0.4331,0.4384,0.4430,0.4580,
0.4597,0.4608,0.4625,0.4639,0.4914,0.4914,0.4998,0.5009,0.5013,0.5031,
0.5043,0.5131,0.5146,0.5149,0.5182,0.5214,0.5233,0.5261,0.5363,0.5380,
0.5385,0.5423,0.5489,0.5532,0.5545,0.5547,0.5575,0.5606,0.5617,0.5626,
0.5674,0.5687,0.5707,0.5725,0.5809,0.5866,0.5868,0.5903,0.5909,0.5917,
0.5956,0.5969,0.5977,0.5986,0.5986,0.6027,0.6108,0.6111,0.6168,0.6179,
0.6250,0.6310,0.6334,0.6397,0.6413,0.6572,0.6575,0.6584,0.6623,0.6674,
0.6700,0.6720,0.6758,0.6763,0.6850,0.6861,0.6923,0.6923,0.6923,0.6968,
0.6974,0.7007,0.7025,0.7171,0.7354,0.7437,0.7507,0.7562,0.7684,0.7748,
0.7764,0.7771,0.7817,0.7828,0.7862,0.7888,0.7937,0.8065,0.8118,0.8125,
0.8166,0.8189,0.8208,0.8221,0.8231,0.8286,0.8290,0.8303,0.8310,0.8327,
0.8336,0.8411,0.8435,0.8460,0.8484,0.8493,0.8500,0.8528,0.8564,0.8569,
0.8608,0.8662,0.8699,0.8702,0.8710,0.8750,0.8772,0.8814,0.8847,0.8877,
0.8905,0.8934,0.8938,0.8956,0.8956,0.8988,0.9037,0.9076,0.9082,0.9178,
0.9179,0.9195,0.9197,0.9223,0.9225,0.9254,0.9269,0.9321,0.9337,0.9354,
0.9426,0.9572,0.9656,0.9668,0.9688,0.9700,0.9754,0.9820,0.9933,
Overall p-value after applying KStest on 269 p-values = 0.247800
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.