RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-15_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.46 25.3273 0.912380
2 to 25 15.81 20.8506 0.766957
3 to 26 15.49 24.3735 0.890364
4 to 27 15.77 15.9261 0.470919
5 to 28 15.75 30.6391 0.977912
6 to 29 15.75 18.1191 0.618633
7 to 30 15.60 17.4084 0.572956
8 to 31 15.65 10.3850 0.113307
9 to 32 15.83 11.2970 0.159285
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.408551
Tough bday spacings test for dh-ranFile-2018-04-15_17:31: 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 5 33 84 103 90 79 54 27 16 5 4
(O-E)^2/E 1.9 0.4 1.6 0.3 0.6 0.0 0.1 0.3 0.1 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.531, p= 0.147
RESULTS OF GCD FOR dh-ranFile-2018-04-15_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.875444
p-value, dist. of gcd's: 0.811908
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-15_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.939 0.303 0.349 0.462 0.925 0.577 0.635 0.653
Bits 8 to 15---> 0.001 0.474 0.489 0.975 0.164 0.297 0.469 0.784
Bits 16 to 23---> 0.854 0.626 0.628 0.200 0.868 0.200 0.200 0.638
Bits 24 to 31---> 0.118 0.610 0.882 0.513 0.577 0.700 0.141 0.912
KS test for the above 32 p values: 0.384
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-15_17:31,
p-values for 5 runs: 0.7531, 0.7392, 0.8877, 0.2881, 0.4412
Rank test for binary matrices (31x31) for dh-ranFile-2018-04-15_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5043 5134.0 1.613 1.885
r= 30 23249 23103.0 0.922 2.807
r= 31 11489 11551.5 0.338 3.146
chi-square = 3.146 with df = 3; p-value = 0.630
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-04-15_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 201 211.4 0.513 0.513
r= 30 5196 5134.0 0.748 1.262
r= 31 22889 23103.0 1.983 3.245
r= 32 11714 11551.5 2.285 5.530
chi-square = 5.530 with df = 3; p-value = 0.863
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-04-15_17:31
b-rank test for bits 1 to 8, p=0.19689
b-rank test for bits 2 to 9, p=0.42888
b-rank test for bits 3 to 10, p=0.14943
b-rank test for bits 4 to 11, p=0.48245
b-rank test for bits 5 to 12, p=0.30887
b-rank test for bits 6 to 13, p=0.97762
b-rank test for bits 7 to 14, p=0.53143
b-rank test for bits 8 to 15, p=0.29493
b-rank test for bits 9 to 16, p=0.11112
b-rank test for bits 10 to 17, p=0.40010
b-rank test for bits 11 to 18, p=0.75743
b-rank test for bits 12 to 19, p=0.05698
b-rank test for bits 13 to 20, p=0.54976
b-rank test for bits 14 to 21, p=0.67380
b-rank test for bits 15 to 22, p=0.99253
b-rank test for bits 16 to 23, p=0.78379
b-rank test for bits 17 to 24, p=0.87804
b-rank test for bits 18 to 25, p=0.67458
b-rank test for bits 19 to 26, p=0.79626
b-rank test for bits 20 to 27, p=0.65440
b-rank test for bits 21 to 28, p=0.57275
b-rank test for bits 22 to 29, p=0.38570
b-rank test for bits 23 to 30, p=0.53690
b-rank test for bits 24 to 31, p=0.11713
b-rank test for bits 25 to 32, p=0.73901
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 = 0.889369
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-15_17:31
(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 141695 -0.50 0.308266
2 142274 0.85 0.802902
3 141655 -0.59 0.276180
4 141819 -0.21 0.416424
5 141772 -0.32 0.374157
6 143267 3.17 0.999243
7 141904 -0.01 0.495032
8 141864 -0.11 0.457826
9 142114 0.48 0.683746
10 142704 1.86 0.968323
11 142353 1.04 0.850042
12 142263 0.83 0.795692
13 142301 0.92 0.819935
14 141414 -1.16 0.123572
15 141933 0.06 0.522052
16 141843 -0.15 0.438420
17 142411 1.17 0.879427
18 142805 2.09 0.981811
19 141824 -0.20 0.420987
20 141809 -0.23 0.407331
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-04-15_17:31
Bits used No. missing words z-score p-value
23 to 32 142034 0.4299 0.666365
22 to 31 142375 1.6058 0.945837
21 to 30 141942 0.1127 0.544848
20 to 29 141036 -3.0115 0.001300
19 to 28 141886 -0.0804 0.467940
18 to 27 142458 1.8920 0.970752
17 to 26 141801 -0.3736 0.354369
16 to 25 141823 -0.2977 0.382970
15 to 24 141907 -0.0080 0.496795
14 to 23 141419 -1.6908 0.045438
13 to 22 142107 0.6816 0.752261
12 to 21 141767 -0.4908 0.311786
11 to 20 142146 0.8161 0.792780
10 to 19 141735 -0.6011 0.273874
9 to 18 141609 -1.0356 0.150190
8 to 17 142027 0.4058 0.657540
7 to 16 141755 -0.5322 0.297303
6 to 15 141321 -2.0287 0.021243
5 to 14 141893 -0.0563 0.477547
4 to 13 141483 -1.4701 0.070767
3 to 12 141914 0.0161 0.506424
2 to 11 141461 -1.5460 0.061056
1 to 10 141527 -1.3184 0.093688
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-04-15_17:31
Bits used No. missing words z-score p-value
28 to 32 141823 -0.2926 0.384897
27 to 31 141712 -0.6689 0.251775
26 to 30 142385 1.6124 0.946567
25 to 29 141982 0.2463 0.597290
24 to 28 141912 0.0091 0.503611
23 to 27 141803 -0.3604 0.359259
22 to 26 141793 -0.3943 0.346665
21 to 25 142356 1.5141 0.935004
20 to 24 142428 1.7582 0.960644
19 to 23 141629 -0.9503 0.170987
18 to 22 141876 -0.1130 0.455022
17 to 21 141276 -2.1469 0.015901
16 to 20 142396 1.6497 0.950501
15 to 19 141637 -0.9232 0.177964
14 to 18 141908 -0.0045 0.498201
13 to 17 142326 1.4124 0.921090
12 to 16 141876 -0.1130 0.455022
11 to 15 141753 -0.5299 0.298080
10 to 14 141563 -1.1740 0.120198
9 to 13 141988 0.2667 0.605141
8 to 12 142408 1.6904 0.954525
7 to 11 142527 2.0938 0.981861
6 to 10 141707 -0.6859 0.246399
5 to 9 141389 -1.7638 0.038880
4 to 8 141630 -0.9469 0.171850
3 to 7 141429 -1.6282 0.051737
2 to 6 142189 0.9480 0.828444
1 to 5 141809 -0.3401 0.366890
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-04-15_17:31
Bits used No. missing words z-score p-value
31 to 32 141997 0.2586 0.602033
30 to 31 142059 0.4415 0.670576
29 to 30 142111 0.5949 0.724044
28 to 29 141458 -1.3314 0.091536
27 to 28 142328 1.2350 0.891588
26 to 27 141250 -1.9449 0.025892
25 to 26 141727 -0.5378 0.295342
24 to 25 142199 0.8545 0.803582
23 to 24 142172 0.7748 0.780782
22 to 23 142104 0.5742 0.717100
21 to 22 142332 1.2468 0.893767
20 to 21 141795 -0.3373 0.367962
19 to 20 142199 0.8545 0.803582
18 to 19 141429 -1.4169 0.078256
17 to 18 141930 0.0610 0.524310
16 to 17 142049 0.4120 0.659832
15 to 16 141877 -0.0954 0.462011
14 to 15 141235 -1.9892 0.023341
13 to 14 141527 -1.1278 0.129699
12 to 13 142128 0.6450 0.740551
11 to 12 141718 -0.5644 0.286243
10 to 11 142033 0.3648 0.642373
9 to 10 141689 -0.6499 0.257865
8 to 9 141997 0.2586 0.602033
7 to 8 141601 -0.9095 0.181536
6 to 7 141757 -0.4494 0.326589
5 to 6 142173 0.7778 0.781653
4 to 5 141600 -0.9125 0.180759
3 to 4 141055 -2.5201 0.005865
2 to 3 142004 0.2793 0.609978
1 to 2 141439 -1.3874 0.082659
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-15_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2598.51 1.393 0.918219
Test results for specific bytes for dh-ranFile-2018-04-15_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2481.31 -0.264 0.395741
2 to 9 2308.32 -2.711 0.003357
3 to 10 2498.95 -0.015 0.494064
4 to 11 2462.44 -0.531 0.297660
5 to 12 2570.94 1.003 0.842130
6 to 13 2510.14 0.143 0.557016
7 to 14 2559.37 0.840 0.799428
8 to 15 2500.10 0.001 0.500581
9 to 16 2478.47 -0.305 0.380369
10 to 17 2508.28 0.117 0.546597
11 to 18 2476.84 -0.327 0.371656
12 to 19 2421.39 -1.112 0.133128
13 to 20 2502.60 0.037 0.514650
14 to 21 2506.64 0.094 0.537428
15 to 22 2497.84 -0.031 0.487813
16 to 23 2459.05 -0.579 0.281248
17 to 24 2377.70 -1.730 0.041849
18 to 25 2608.08 1.528 0.936797
19 to 26 2479.06 -0.296 0.383541
20 to 27 2556.89 0.805 0.789462
21 to 28 2621.07 1.712 0.956574
22 to 29 2519.06 0.270 0.606240
23 to 30 2459.31 -0.575 0.282510
24 to 31 2639.87 1.978 0.976037
25 to 32 2417.81 -1.162 0.122546
CDPARK for dh-ranFile-2018-04-15_17:31: 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
3513 -0.4566 0.323972
3502 -0.9589 0.168804
3546 1.0502 0.853193
3520 -0.1370 0.445521
3506 -0.7763 0.218799
3506 -0.7763 0.218799
3522 -0.0457 0.481790
3532 0.4110 0.659449
3509 -0.6393 0.261324
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3517.00 sample std.=12.87
p-value of the KSTEST for those 10 p-values: 0.237098
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-15_17:31
0.2462,0.8798,0.9832,0.9011,0.8135,0.2226,0.0460,0.8237,0.1869,0.0529,
The KS test for those 10 p-values: 0.252380
The 3DSPHERES test for dh-ranFile-2018-04-15_17:31
sample no r^3 equiv. uni.
1 24.250 0.554394
2 55.854 0.844608
3 10.177 0.287694
4 27.270 0.597069
5 29.275 0.623117
6 22.273 0.524044
7 39.568 0.732582
8 29.209 0.622294
9 30.628 0.639744
10 5.319 0.162458
11 38.324 0.721261
12 23.735 0.546691
13 7.798 0.228901
14 20.873 0.501314
15 30.605 0.639465
16 58.510 0.857773
17 6.179 0.186143
18 38.616 0.723959
19 17.482 0.441629
20 5.647 0.171578
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.234322
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-15_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 -0.8 -0.3 0.7 0.1
-1.7 1.0 -2.3 -0.1 0.8 0.1
-2.4 0.1 0.8 -1.3 1.6 0.2
0.8 1.0 -0.0 -1.0 -0.7 -0.6
-0.8 0.2 0.5 1.9 -0.1 1.1
0.7 0.8 -0.8 0.3 0.8 0.4
-0.5 -0.1 -1.2 -1.3 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:40.597453
z-score=-0.153030, p-value=0.467425
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-04-15_17:31
Test no p-value
1 0.610980
2 0.098599
3 0.601983
4 0.032482
5 0.764323
6 0.052475
7 0.120504
8 0.305987
9 0.327498
10 0.930507
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.265238
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-15_17:31:
(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 66737 0.07 66439 0.78
3 25000.00 24975 0.03 25261 2.72
4 6666.67 6668 0.00 6656 0.02
5 1388.89 1362 0.52 1381 0.04
6 238.10 216 2.05 225 0.72
7 34.72 35 0.00 37 0.15
8 4.96 6 0.22 0 4.96
p=0.17758 p=0.84741
Number of rngs required: 687777, p-value: 0.235
RESULTS OF CRAPS TEST for dh-ranFile-2018-04-15_17:31
No. of wins: Observed Expected
98734 98585.9
z-score= 0.663, pvalue=0.74620
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66445 66666.7 0.737 0.737
2 37715 37654.3 0.098 0.835
3 27191 26954.7 2.071 2.906
4 19165 19313.5 1.141 4.047
5 13954 13851.4 0.760 4.807
6 9925 9943.5 0.035 4.841
7 7161 7145.0 0.036 4.877
8 5083 5139.1 0.612 5.489
9 3695 3699.9 0.006 5.495
10 2672 2666.3 0.012 5.507
11 1978 1923.3 1.554 7.061
12 1323 1388.7 3.112 10.173
13 1015 1003.7 0.127 10.300
14 780 726.1 3.995 14.295
15 532 525.8 0.072 14.367
16 370 381.2 0.326 14.694
17 261 276.5 0.873 15.567
18 213 200.8 0.737 16.304
19 151 146.0 0.172 16.477
20 90 106.2 2.475 18.952
21 281 287.1 0.130 19.082
Chisq= 19.08 for 20 degrees of freedom, p= 0.48352
SUMMARY of craptest
p-value for no. of wins: 0.746199
p-value for throws/game: 0.483521
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-15_17:31
No. of wins: Observed Expected
98149 98585.9
z-score=-1.954, pvalue=0.02536
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66686 66666.7 0.006 0.006
2 37729 37654.3 0.148 0.154
3 27194 26954.7 2.124 2.278
4 19114 19313.5 2.060 4.338
5 13844 13851.4 0.004 4.342
6 9937 9943.5 0.004 4.346
7 7129 7145.0 0.036 4.382
8 5143 5139.1 0.003 4.385
9 3648 3699.9 0.727 5.112
10 2663 2666.3 0.004 5.116
11 1913 1923.3 0.055 5.171
12 1406 1388.7 0.215 5.386
13 996 1003.7 0.059 5.445
14 691 726.1 1.701 7.146
15 539 525.8 0.330 7.475
16 384 381.2 0.021 7.497
17 260 276.5 0.989 8.486
18 204 200.8 0.050 8.536
19 145 146.0 0.007 8.543
20 108 106.2 0.030 8.573
21 267 287.1 1.409 9.982
Chisq= 9.98 for 20 degrees of freedom, p= 0.03150
SUMMARY of craptest
p-value for no. of wins: 0.025357
p-value for throws/game: 0.031496
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0013,0.0034,0.0059,0.0159,0.0212,0.0233,0.0254,0.0259,0.0315,
0.0325,0.0389,0.0418,0.0454,0.0460,0.0517,0.0525,0.0529,0.0570,0.0611,
0.0708,0.0783,0.0827,0.0915,0.0937,0.0986,0.1111,0.1133,0.1171,0.1178,
0.1202,0.1205,0.1225,0.1236,0.1297,0.1331,0.1411,0.1470,0.1494,0.1502,
0.1593,0.1625,0.1636,0.1688,0.1710,0.1716,0.1718,0.1776,0.1780,0.1808,
0.1815,0.1861,0.1869,0.1969,0.1996,0.1997,0.2000,0.2188,0.2188,0.2226,
0.2289,0.2343,0.2349,0.2371,0.2462,0.2464,0.2518,0.2524,0.2579,0.2613,
0.2652,0.2739,0.2762,0.2812,0.2825,0.2862,0.2877,0.2881,0.2949,0.2953,
0.2969,0.2973,0.2977,0.2981,0.3030,0.3060,0.3083,0.3089,0.3118,0.3240,
0.3266,0.3275,0.3406,0.3467,0.3492,0.3544,0.3593,0.3669,0.3680,0.3717,
0.3742,0.3804,0.3830,0.3835,0.3840,0.3849,0.3857,0.3957,0.4001,0.4073,
0.4086,0.4164,0.4210,0.4289,0.4384,0.4412,0.4416,0.4455,0.4550,0.4550,
0.4578,0.4617,0.4620,0.4674,0.4679,0.4690,0.4709,0.4736,0.4775,0.4818,
0.4824,0.4835,0.4878,0.4891,0.4941,0.4950,0.4968,0.4982,0.5006,0.5013,
0.5036,0.5064,0.5127,0.5147,0.5221,0.5240,0.5243,0.5314,0.5369,0.5374,
0.5448,0.5466,0.5467,0.5498,0.5544,0.5570,0.5727,0.5730,0.5770,0.5774,
0.5971,0.5973,0.6020,0.6020,0.6020,0.6051,0.6062,0.6100,0.6100,0.6110,
0.6186,0.6223,0.6231,0.6259,0.6280,0.6303,0.6348,0.6385,0.6395,0.6397,
0.6424,0.6531,0.6544,0.6575,0.6594,0.6598,0.6664,0.6706,0.6738,0.6746,
0.6837,0.6997,0.7171,0.7213,0.7240,0.7240,0.7326,0.7390,0.7392,0.7406,
0.7462,0.7523,0.7531,0.7574,0.7643,0.7670,0.7808,0.7817,0.7838,0.7844,
0.7895,0.7928,0.7957,0.7963,0.7994,0.8029,0.8036,0.8036,0.8119,0.8135,
0.8199,0.8237,0.8284,0.8421,0.8446,0.8474,0.8500,0.8532,0.8542,0.8578,
0.8632,0.8682,0.8754,0.8780,0.8794,0.8798,0.8819,0.8877,0.8894,0.8904,
0.8916,0.8938,0.9011,0.9116,0.9124,0.9182,0.9211,0.9249,0.9305,0.9350,
0.9368,0.9386,0.9458,0.9466,0.9505,0.9545,0.9566,0.9606,0.9683,0.9708,
0.9753,0.9760,0.9776,0.9779,0.9818,0.9819,0.9832,0.9925,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.993012
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.