RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_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 15.92 7.6547 0.026616
2 to 25 15.54 22.9773 0.850010
3 to 26 15.53 18.3825 0.634899
4 to 27 15.89 17.3410 0.568494
5 to 28 15.61 20.7774 0.763594
6 to 29 15.48 24.9082 0.903217
7 to 30 15.84 22.5439 0.835303
8 to 31 15.86 14.5069 0.369047
9 to 32 15.88 13.5142 0.298860
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.589649
Tough bday spacings test for dh-ranFile-2018-07-10_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 45 75 104 100 68 50 27 9 4 9
(O-E)^2/E 0.0 1.9 0.0 0.4 0.1 1.3 0.1 0.3 2.3 1.0 6.0
Birthday Spacings: Sum(O-E)^2/E= 13.427, p= 0.799
RESULTS OF GCD FOR dh-ranFile-2018-07-10_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.104123
p-value, dist. of gcd's: 0.952240
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.450 0.835 0.041 0.483 0.343 0.536 0.050 0.319
Bits 8 to 15---> 0.100 0.731 0.319 0.195 0.378 0.530 0.573 0.611
Bits 16 to 23---> 0.589 0.497 0.099 0.089 0.155 0.439 0.784 0.472
Bits 24 to 31---> 0.134 0.957 0.843 0.565 0.698 0.129 0.537 0.444
KS test for the above 32 p values: 0.789
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_10:31,
p-values for 5 runs: 0.9533, 0.0160, 0.8233, 0.8865, 0.3340
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 217 211.4 0.147 0.147
r= 29 5076 5134.0 0.655 0.803
r= 30 23202 23103.0 0.424 1.227
r= 31 11505 11551.5 0.187 1.414
chi-square = 1.414 with df = 3; p-value = 0.298
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 195 211.4 1.275 1.275
r= 30 5017 5134.0 2.667 3.942
r= 31 23268 23103.0 1.178 5.120
r= 32 11520 11551.5 0.086 5.206
chi-square = 5.206 with df = 3; p-value = 0.843
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_10:31
b-rank test for bits 1 to 8, p=0.92330
b-rank test for bits 2 to 9, p=0.97725
b-rank test for bits 3 to 10, p=0.00035
b-rank test for bits 4 to 11, p=0.78353
b-rank test for bits 5 to 12, p=0.76581
b-rank test for bits 6 to 13, p=0.27899
b-rank test for bits 7 to 14, p=0.15962
b-rank test for bits 8 to 15, p=0.19961
b-rank test for bits 9 to 16, p=0.69052
b-rank test for bits 10 to 17, p=0.05273
b-rank test for bits 11 to 18, p=0.69718
b-rank test for bits 12 to 19, p=0.77902
b-rank test for bits 13 to 20, p=0.11412
b-rank test for bits 14 to 21, p=0.79972
b-rank test for bits 15 to 22, p=0.15711
b-rank test for bits 16 to 23, p=0.33226
b-rank test for bits 17 to 24, p=0.11523
b-rank test for bits 18 to 25, p=0.53950
b-rank test for bits 19 to 26, p=0.42995
b-rank test for bits 20 to 27, p=0.08555
b-rank test for bits 21 to 28, p=0.66167
b-rank test for bits 22 to 29, p=0.29133
b-rank test for bits 23 to 30, p=0.68477
b-rank test for bits 24 to 31, p=0.71075
b-rank test for bits 25 to 32, p=0.79497
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 = 0.549268
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_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 141883 -0.06 0.475473
2 142282 0.87 0.808048
3 142058 0.35 0.635840
4 141276 -1.48 0.069471
5 140793 -2.61 0.004550
6 142466 1.30 0.903308
7 142048 0.32 0.627029
8 142158 0.58 0.719381
9 141720 -0.44 0.329114
10 143177 2.96 0.998471
11 142355 1.04 0.851128
12 141800 -0.26 0.399190
13 141689 -0.51 0.303350
14 141639 -0.63 0.263820
15 141474 -1.02 0.154547
16 142200 0.68 0.751474
17 141794 -0.27 0.393787
18 142496 1.37 0.914770
19 141431 -1.12 0.131870
20 141812 -0.23 0.410054
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_10:31
Bits used No. missing words z-score p-value
23 to 32 142107 0.6816 0.752261
22 to 31 142204 1.0161 0.845210
21 to 30 141506 -1.3908 0.082144
20 to 29 141600 -1.0667 0.143064
19 to 28 141815 -0.3253 0.372486
18 to 27 141784 -0.4322 0.332808
17 to 26 142369 1.5851 0.943525
16 to 25 141673 -0.8149 0.207556
15 to 24 142005 0.3299 0.629261
14 to 23 142353 1.5299 0.936979
13 to 22 142073 0.5644 0.713752
12 to 21 142428 1.7885 0.963154
11 to 20 141764 -0.5011 0.308137
10 to 19 142048 0.4782 0.683736
9 to 18 141770 -0.4804 0.315454
8 to 17 142020 0.3816 0.648629
7 to 16 142305 1.3644 0.913776
6 to 15 142137 0.7851 0.783793
5 to 14 142247 1.1644 0.877865
4 to 13 142244 1.1540 0.875757
3 to 12 142191 0.9713 0.834295
2 to 11 142512 2.0782 0.981153
1 to 10 142186 0.9540 0.829967
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_10:31
Bits used No. missing words z-score p-value
28 to 32 142104 0.6599 0.745341
27 to 31 142194 0.9650 0.832723
26 to 30 141909 -0.0011 0.499554
25 to 29 142484 1.9480 0.974295
24 to 28 142213 1.0294 0.848352
23 to 27 142111 0.6836 0.752895
22 to 26 142113 0.6904 0.755031
21 to 25 142302 1.3311 0.908419
20 to 24 141776 -0.4520 0.325647
19 to 23 142394 1.6429 0.949803
18 to 22 142141 0.7853 0.783868
17 to 21 142413 1.7074 0.956122
16 to 20 142220 1.0531 0.853857
15 to 19 141789 -0.4079 0.341674
14 to 18 141769 -0.4757 0.317146
13 to 17 142009 0.3379 0.632267
12 to 16 141842 -0.2282 0.409731
11 to 15 141956 0.1582 0.562852
10 to 14 141688 -0.7503 0.226546
9 to 13 141966 0.1921 0.576169
8 to 12 142079 0.5752 0.717406
7 to 11 141389 -1.7638 0.038880
6 to 10 141599 -1.0520 0.146408
5 to 9 142109 0.6768 0.750749
4 to 8 141689 -0.7469 0.227568
3 to 7 141588 -1.0893 0.138021
2 to 6 141833 -0.2587 0.397916
1 to 5 141748 -0.5469 0.292230
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_10:31
Bits used No. missing words z-score p-value
31 to 32 142211 0.8899 0.813235
30 to 31 141572 -0.9951 0.159850
29 to 30 141641 -0.7915 0.214316
28 to 29 141637 -0.8033 0.210891
27 to 28 141630 -0.8240 0.204975
26 to 27 141410 -1.4729 0.070382
25 to 26 142487 1.7040 0.955813
24 to 25 141333 -1.7001 0.044557
23 to 24 142337 1.2616 0.896447
22 to 23 142042 0.3914 0.652233
21 to 22 142145 0.6952 0.756532
20 to 21 141954 0.1318 0.552417
19 to 20 141659 -0.7384 0.230125
18 to 19 141691 -0.6440 0.259774
17 to 18 141970 0.1790 0.571018
16 to 17 141861 -0.1426 0.443316
15 to 16 141885 -0.0718 0.471393
14 to 15 142405 1.4622 0.928150
13 to 14 141481 -1.2635 0.103203
12 to 13 141780 -0.3815 0.351415
11 to 12 141692 -0.6411 0.260732
10 to 11 142155 0.7247 0.765679
9 to 10 142240 0.9754 0.835326
8 to 9 141372 -1.5850 0.056478
7 to 8 142647 2.1760 0.985223
6 to 7 141846 -0.1868 0.425903
5 to 6 141931 0.0639 0.525484
4 to 5 141704 -0.6057 0.272359
3 to 4 142052 0.4209 0.663070
2 to 3 142553 1.8987 0.971200
1 to 2 141882 -0.0806 0.467872
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2462.08 -0.536 0.295872
Test results for specific bytes for dh-ranFile-2018-07-10_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2353.49 -2.072 0.019131
2 to 9 2530.08 0.425 0.664726
3 to 10 2570.74 1.000 0.841461
4 to 11 2433.24 -0.944 0.172563
5 to 12 2490.46 -0.135 0.446364
6 to 13 2402.99 -1.372 0.085051
7 to 14 2609.54 1.549 0.939323
8 to 15 2436.62 -0.896 0.185040
9 to 16 2473.81 -0.370 0.355570
10 to 17 2535.50 0.502 0.692180
11 to 18 2539.95 0.565 0.713965
12 to 19 2442.33 -0.816 0.207365
13 to 20 2434.37 -0.928 0.176664
14 to 21 2529.93 0.423 0.663961
15 to 22 2517.42 0.246 0.597273
16 to 23 2517.77 0.251 0.599200
17 to 24 2454.30 -0.646 0.259022
18 to 25 2546.72 0.661 0.745602
19 to 26 2488.77 -0.159 0.436908
20 to 27 2503.38 0.048 0.519045
21 to 28 2570.79 1.001 0.841613
22 to 29 2419.54 -1.138 0.127599
23 to 30 2555.76 0.789 0.784835
24 to 31 2560.19 0.851 0.802683
25 to 32 2497.17 -0.040 0.484053
CDPARK for dh-ranFile-2018-07-10_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
3495 -1.2785 0.100530
3475 -2.1918 0.014198
3518 -0.2283 0.409702
3526 0.1370 0.554479
3510 -0.5936 0.276387
3508 -0.6849 0.246694
3504 -0.8676 0.192812
3536 0.5936 0.723613
3526 0.1370 0.554479
3533 0.4566 0.676028
Square side=100, avg. no. parked=3513.10 sample std.=17.82
p-value of the KSTEST for those 10 p-values: 0.286506
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_10:31
0.7112,0.6898,0.3261,0.9131,0.6287,0.1714,0.4204,0.3103,0.2826,0.7261,
The KS test for those 10 p-values: 0.763964
The 3DSPHERES test for dh-ranFile-2018-07-10_10:31
sample no r^3 equiv. uni.
1 27.812 0.604284
2 37.344 0.712005
3 66.844 0.892270
4 20.257 0.490969
5 52.956 0.828849
6 7.766 0.228063
7 36.752 0.706266
8 55.674 0.843674
9 3.025 0.095924
10 33.186 0.669188
11 32.157 0.657641
12 61.846 0.872741
13 1.616 0.052445
14 38.844 0.726050
15 43.301 0.763866
16 19.595 0.479606
17 67.977 0.896262
18 7.539 0.222206
19 10.071 0.285155
20 0.413 0.013669
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.442084
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 -0.4 0.0 -0.9 -0.1
-0.9 1.6 1.4 0.6 -0.6 0.1
1.9 -1.6 2.0 0.3 -1.6 -1.7
-0.5 -0.8 1.0 0.9 0.2 -0.9
0.1 0.8 -0.5 -0.2 1.5 -0.9
1.6 -2.0 0.4 -0.6 -0.1 1.3
-0.2 0.5 -0.4 -0.1 -0.6 -1.0
0.8
Chi-square with 42 degrees of freedom:44.890339
z-score=0.315362, p-value=0.648331
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_10:31
Test no p-value
1 0.794865
2 0.204965
3 0.105808
4 0.372839
5 0.271571
6 0.201887
7 0.161474
8 0.095098
9 0.124708
10 0.236528
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.006505
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_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 66745 0.09 66507 0.38
3 25000.00 24961 0.06 25218 1.90
4 6666.67 6679 0.02 6606 0.55
5 1388.89 1337 1.94 1421 0.74
6 238.10 238 0.00 213 2.65
7 34.72 36 0.05 32 0.21
8 4.96 3 0.77 2 1.77
p=0.18317 p=0.77636
Number of rngs required: 688473, p-value: 0.532
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_10:31
No. of wins: Observed Expected
98332 98585.9
z-score=-1.135, pvalue=0.12810
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66993 66666.7 1.597 1.597
2 37646 37654.3 0.002 1.599
3 26979 26954.7 0.022 1.621
4 19125 19313.5 1.839 3.460
5 13809 13851.4 0.130 3.590
6 9837 9943.5 1.142 4.732
7 7227 7145.0 0.940 5.672
8 5055 5139.1 1.375 7.047
9 3728 3699.9 0.214 7.261
10 2659 2666.3 0.020 7.281
11 1898 1923.3 0.334 7.615
12 1409 1388.7 0.296 7.911
13 971 1003.7 1.066 8.977
14 733 726.1 0.065 9.042
15 523 525.8 0.015 9.057
16 394 381.2 0.433 9.490
17 257 276.5 1.381 10.871
18 195 200.8 0.169 11.040
19 159 146.0 1.160 12.200
20 125 106.2 3.322 15.523
21 278 287.1 0.289 15.812
Chisq= 15.81 for 20 degrees of freedom, p= 0.27178
SUMMARY of craptest
p-value for no. of wins: 0.128103
p-value for throws/game: 0.271776
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_10:31
No. of wins: Observed Expected
98136 98585.9
z-score=-2.012, pvalue=0.02211
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66493 66666.7 0.452 0.452
2 37742 37654.3 0.204 0.657
3 27095 26954.7 0.730 1.386
4 19349 19313.5 0.065 1.452
5 13821 13851.4 0.067 1.519
6 9971 9943.5 0.076 1.595
7 7215 7145.0 0.685 2.280
8 5150 5139.1 0.023 2.303
9 3603 3699.9 2.536 4.839
10 2600 2666.3 1.648 6.488
11 1851 1923.3 2.720 9.208
12 1400 1388.7 0.091 9.299
13 1075 1003.7 5.063 14.362
14 729 726.1 0.011 14.373
15 522 525.8 0.028 14.401
16 402 381.2 1.140 15.541
17 278 276.5 0.008 15.549
18 175 200.8 3.322 18.871
19 135 146.0 0.827 19.698
20 114 106.2 0.571 20.268
21 280 287.1 0.176 20.444
Chisq= 20.44 for 20 degrees of freedom, p= 0.56955
SUMMARY of craptest
p-value for no. of wins: 0.022108
p-value for throws/game: 0.569547
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0046,0.0065,0.0137,0.0142,0.0160,0.0191,0.0221,0.0266,0.0389,
0.0410,0.0446,0.0499,0.0524,0.0527,0.0565,0.0695,0.0704,0.0821,0.0851,
0.0855,0.0894,0.0951,0.0959,0.0994,0.0998,0.1005,0.1032,0.1041,0.1058,
0.1141,0.1152,0.1247,0.1276,0.1281,0.1293,0.1319,0.1337,0.1380,0.1431,
0.1464,0.1545,0.1554,0.1571,0.1596,0.1599,0.1615,0.1714,0.1726,0.1767,
0.1832,0.1850,0.1928,0.1952,0.1996,0.2019,0.2050,0.2050,0.2074,0.2076,
0.2109,0.2143,0.2222,0.2265,0.2276,0.2281,0.2301,0.2365,0.2467,0.2590,
0.2598,0.2607,0.2638,0.2716,0.2718,0.2724,0.2764,0.2790,0.2826,0.2852,
0.2865,0.2913,0.2922,0.2959,0.2978,0.2989,0.3034,0.3081,0.3103,0.3155,
0.3171,0.3190,0.3190,0.3256,0.3261,0.3291,0.3323,0.3328,0.3340,0.3417,
0.3427,0.3514,0.3556,0.3690,0.3725,0.3728,0.3784,0.3938,0.3979,0.3992,
0.4097,0.4097,0.4101,0.4204,0.4259,0.4300,0.4369,0.4395,0.4421,0.4433,
0.4439,0.4464,0.4505,0.4679,0.4714,0.4725,0.4755,0.4796,0.4831,0.4841,
0.4910,0.4970,0.4996,0.5190,0.5255,0.5305,0.5321,0.5362,0.5366,0.5395,
0.5493,0.5524,0.5545,0.5545,0.5629,0.5650,0.5685,0.5695,0.5710,0.5726,
0.5762,0.5889,0.5896,0.5973,0.5992,0.6043,0.6110,0.6270,0.6287,0.6293,
0.6323,0.6349,0.6358,0.6483,0.6486,0.6522,0.6576,0.6617,0.6631,0.6640,
0.6647,0.6692,0.6760,0.6837,0.6848,0.6898,0.6905,0.6922,0.6972,0.6980,
0.7063,0.7108,0.7112,0.7120,0.7138,0.7140,0.7174,0.7194,0.7236,0.7260,
0.7261,0.7307,0.7453,0.7456,0.7507,0.7515,0.7523,0.7529,0.7550,0.7565,
0.7636,0.7639,0.7640,0.7657,0.7658,0.7764,0.7790,0.7835,0.7838,0.7839,
0.7839,0.7848,0.7888,0.7949,0.7950,0.7992,0.7997,0.8027,0.8080,0.8132,
0.8233,0.8288,0.8300,0.8327,0.8343,0.8346,0.8353,0.8353,0.8415,0.8416,
0.8427,0.8433,0.8437,0.8452,0.8484,0.8500,0.8511,0.8539,0.8727,0.8758,
0.8779,0.8865,0.8923,0.8963,0.8964,0.9032,0.9033,0.9084,0.9131,0.9138,
0.9148,0.9233,0.9282,0.9370,0.9393,0.9435,0.9498,0.9522,0.9533,0.9558,
0.9561,0.9568,0.9632,0.9712,0.9743,0.9772,0.9812,0.9852,0.9985,
Overall p-value after applying KStest on 269 p-values = 0.770426
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.