RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.83 24.4357 0.891927
2 to 25 15.71 23.2210 0.857808
3 to 26 15.59 29.0243 0.965697
4 to 27 15.61 22.3769 0.829344
5 to 28 15.65 32.2905 0.986155
6 to 29 15.45 27.4579 0.948315
7 to 30 15.66 23.5955 0.869152
8 to 31 15.79 14.6947 0.382542
9 to 32 15.91 30.2820 0.975618
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000042
Tough bday spacings test for dh-ranFile-2018-07-04_11:31: 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 10 39 77 96 89 85 53 27 13 7 4
(O-E)^2/E 0.1 0.2 0.2 0.0 0.8 0.6 0.0 0.3 0.2 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 2.359, p= 0.007
RESULTS OF GCD FOR dh-ranFile-2018-07-04_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.433898
p-value, dist. of gcd's: 0.390909
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.294 0.413 0.663 0.507 0.744 0.399 0.325 0.611
Bits 8 to 15---> 0.133 0.325 0.398 0.162 0.163 0.429 0.455 0.795
Bits 16 to 23---> 0.351 0.779 0.281 0.435 0.951 0.295 0.346 0.000
Bits 24 to 31---> 0.383 0.739 0.733 0.369 0.598 0.517 0.581 0.659
KS test for the above 32 p values: 0.888
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_11:31,
p-values for 5 runs: 0.0932, 0.9444, 0.4429, 0.3172, 0.7602
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5032 5134.0 2.027 2.540
r= 30 23250 23103.0 0.935 3.475
r= 31 11517 11551.5 0.103 3.578
chi-square = 3.578 with df = 3; p-value = 0.689
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 230 211.4 1.633 1.633
r= 30 5233 5134.0 1.909 3.542
r= 31 22944 23103.0 1.095 4.637
r= 32 11593 11551.5 0.149 4.786
chi-square = 4.786 with df = 3; p-value = 0.812
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_11:31
b-rank test for bits 1 to 8, p=0.99684
b-rank test for bits 2 to 9, p=0.56328
b-rank test for bits 3 to 10, p=0.47440
b-rank test for bits 4 to 11, p=0.77027
b-rank test for bits 5 to 12, p=0.28591
b-rank test for bits 6 to 13, p=0.83480
b-rank test for bits 7 to 14, p=0.64382
b-rank test for bits 8 to 15, p=0.90079
b-rank test for bits 9 to 16, p=0.78018
b-rank test for bits 10 to 17, p=0.30912
b-rank test for bits 11 to 18, p=0.45613
b-rank test for bits 12 to 19, p=0.35390
b-rank test for bits 13 to 20, p=0.61952
b-rank test for bits 14 to 21, p=0.51951
b-rank test for bits 15 to 22, p=0.47476
b-rank test for bits 16 to 23, p=0.43146
b-rank test for bits 17 to 24, p=0.90324
b-rank test for bits 18 to 25, p=0.53359
b-rank test for bits 19 to 26, p=0.72041
b-rank test for bits 20 to 27, p=0.29781
b-rank test for bits 21 to 28, p=0.53286
b-rank test for bits 22 to 29, p=0.06392
b-rank test for bits 23 to 30, p=0.47766
b-rank test for bits 24 to 31, p=0.03516
b-rank test for bits 25 to 32, p=0.94157
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 = 0.357641
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_11:31
(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 142186 0.65 0.740998
2 142002 0.22 0.585708
3 142023 0.27 0.604720
4 141518 -0.91 0.180274
5 142731 1.92 0.972558
6 142221 0.73 0.766755
7 141629 -0.65 0.256241
8 142004 0.22 0.587528
9 142937 2.40 0.991827
10 141705 -0.48 0.316536
11 141415 -1.15 0.124050
12 141695 -0.50 0.308266
13 142170 0.61 0.728752
14 142767 2.00 0.977460
15 141683 -0.53 0.298469
16 141203 -1.65 0.049440
17 142349 1.03 0.847852
18 141611 -0.70 0.242891
19 141751 -0.37 0.355717
20 141908 -0.00 0.498760
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_11:31
Bits used No. missing words z-score p-value
23 to 32 141530 -1.3080 0.095431
22 to 31 141756 -0.5287 0.298498
21 to 30 142351 1.5230 0.936121
20 to 29 141687 -0.7667 0.221643
19 to 28 141820 -0.3080 0.379028
18 to 27 142031 0.4196 0.662594
17 to 26 142330 1.4506 0.926552
16 to 25 141882 -0.0942 0.462459
15 to 24 142189 0.9644 0.832572
14 to 23 142121 0.7299 0.767273
13 to 22 141584 -1.1218 0.130968
12 to 21 142361 1.5575 0.940322
11 to 20 141942 0.1127 0.544848
10 to 19 141894 -0.0529 0.478921
9 to 18 141628 -0.9701 0.165998
8 to 17 141827 -0.2839 0.388245
7 to 16 141845 -0.2218 0.412224
6 to 15 142052 0.4920 0.688628
5 to 14 141926 0.0575 0.522920
4 to 13 141359 -1.8977 0.028868
3 to 12 142159 0.8609 0.805362
2 to 11 141682 -0.7839 0.216550
1 to 10 141738 -0.5908 0.277330
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_11:31
Bits used No. missing words z-score p-value
28 to 32 142440 1.7989 0.963981
27 to 31 141981 0.2429 0.595978
26 to 30 141911 0.0057 0.502258
25 to 29 142094 0.6260 0.734343
24 to 28 142317 1.3819 0.916504
23 to 27 142264 1.2023 0.885371
22 to 26 142400 1.6633 0.951873
21 to 25 141858 -0.1740 0.430933
20 to 24 142435 1.7819 0.962620
19 to 23 142043 0.4531 0.674768
18 to 22 142167 0.8735 0.808793
17 to 21 141957 0.1616 0.564187
16 to 20 141684 -0.7638 0.222484
15 to 19 141888 -0.0723 0.471180
14 to 18 141289 -2.1028 0.017741
13 to 17 141706 -0.6893 0.245332
12 to 16 141618 -0.9876 0.161684
11 to 15 141632 -0.9401 0.173583
10 to 14 142302 1.3311 0.908419
9 to 13 142333 1.4362 0.924523
8 to 12 141822 -0.2960 0.383602
7 to 11 141865 -0.1503 0.440275
6 to 10 142094 0.6260 0.734343
5 to 9 142657 2.5345 0.994369
4 to 8 141598 -1.0554 0.145631
3 to 7 141746 -0.5537 0.289905
2 to 6 142070 0.5446 0.707001
1 to 5 141942 0.1107 0.544091
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_11:31
Bits used No. missing words z-score p-value
31 to 32 141976 0.1967 0.577956
30 to 31 141835 -0.2193 0.413223
29 to 30 141976 0.1967 0.577956
28 to 29 141916 0.0197 0.507849
27 to 28 141604 -0.9007 0.183880
26 to 27 141989 0.2350 0.592901
25 to 26 141831 -0.2311 0.408633
24 to 25 141597 -0.9213 0.178440
23 to 24 142258 1.0285 0.848149
22 to 23 141727 -0.5378 0.295342
21 to 22 141823 -0.2547 0.399493
20 to 21 141700 -0.6175 0.268455
19 to 20 142078 0.4976 0.690600
18 to 19 142101 0.5654 0.714099
17 to 18 142172 0.7748 0.780782
16 to 17 142005 0.2822 0.611110
15 to 16 142495 1.7276 0.957974
14 to 15 141732 -0.5231 0.300453
13 to 14 141678 -0.6824 0.247496
12 to 13 141953 0.1288 0.551250
11 to 12 141774 -0.3992 0.344872
10 to 11 141986 0.2262 0.589464
9 to 10 141836 -0.2163 0.414372
8 to 9 141378 -1.5673 0.058517
7 to 8 141816 -0.2753 0.391539
6 to 7 141455 -1.3402 0.090089
5 to 6 142458 1.6185 0.947222
4 to 5 141472 -1.2901 0.098515
3 to 4 142172 0.7748 0.780782
2 to 3 141705 -0.6027 0.273340
1 to 2 141295 -1.8122 0.034979
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2415.71 -1.192 0.116618
Test results for specific bytes for dh-ranFile-2018-07-04_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2545.71 0.646 0.740981
2 to 9 2547.07 0.666 0.747189
3 to 10 2493.91 -0.086 0.465674
4 to 11 2497.44 -0.036 0.485588
5 to 12 2572.19 1.021 0.846348
6 to 13 2328.34 -2.428 0.007600
7 to 14 2521.27 0.301 0.618234
8 to 15 2452.08 -0.678 0.249002
9 to 16 2471.08 -0.409 0.341258
10 to 17 2512.58 0.178 0.570581
11 to 18 2624.79 1.765 0.961203
12 to 19 2575.19 1.063 0.856192
13 to 20 2568.71 0.972 0.834406
14 to 21 2573.30 1.037 0.850034
15 to 22 2479.26 -0.293 0.384643
16 to 23 2517.88 0.253 0.599795
17 to 24 2602.97 1.456 0.927331
18 to 25 2463.85 -0.511 0.304579
19 to 26 2483.87 -0.228 0.409781
20 to 27 2522.46 0.318 0.624615
21 to 28 2472.15 -0.394 0.346848
22 to 29 2491.75 -0.117 0.453546
23 to 30 2505.71 0.081 0.532193
24 to 31 2323.51 -2.496 0.006280
25 to 32 2389.89 -1.557 0.059715
CDPARK for dh-ranFile-2018-07-04_11:31: 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
3556 1.5068 0.934075
3542 0.8676 0.807188
3483 -1.8265 0.033889
3546 1.0502 0.853193
3546 1.0502 0.853193
3517 -0.2740 0.392053
3566 1.9635 0.975204
3510 -0.5936 0.276387
3503 -0.9132 0.180558
3512 -0.5023 0.307734
Square side=100, avg. no. parked=3528.10 sample std.=25.34
p-value of the KSTEST for those 10 p-values: 0.420012
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_11:31
0.2803,0.2133,0.3525,0.2133,0.2492,0.4114,0.0718,0.1115,0.1956,0.6238,
The KS test for those 10 p-values: 0.014195
The 3DSPHERES test for dh-ranFile-2018-07-04_11:31
sample no r^3 equiv. uni.
1 37.177 0.710390
2 10.082 0.285436
3 18.194 0.454728
4 62.532 0.875618
5 16.508 0.423204
6 24.231 0.554115
7 18.214 0.455091
8 24.915 0.564171
9 2.322 0.074486
10 4.187 0.130263
11 42.088 0.754122
12 11.767 0.324454
13 28.162 0.608873
14 51.912 0.822788
15 11.432 0.316858
16 57.008 0.850472
17 21.858 0.517412
18 21.367 0.509452
19 25.406 0.571246
20 12.539 0.341625
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.419394
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.2 -0.6 1.2 -0.5 0.3
-0.6 0.1 -0.7 0.2 -0.7 0.9
-0.8 1.5 1.4 -0.4 0.6 0.4
-1.3 -0.3 1.3 -0.7 -0.5 1.6
-0.5 -1.5 -1.0 -0.2 -1.1 -1.2
-0.3 -0.5 -0.2 0.7 1.0 -1.2
-1.2 1.5 -0.8 -0.7 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:35.109800
z-score=-0.751782, p-value=0.234694
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_11:31
Test no p-value
1 0.765803
2 0.914515
3 0.797451
4 0.100543
5 0.001771
6 0.205247
7 0.767524
8 0.716619
9 0.003096
10 0.077617
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.051462
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_11:31:
(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 66721 0.04 66805 0.29
3 25000.00 24874 0.64 24863 0.75
4 6666.67 6695 0.12 6663 0.00
5 1388.89 1430 1.22 1372 0.21
6 238.10 238 0.00 249 0.50
7 34.72 38 0.31 40 0.80
8 4.96 3 0.77 7 0.84
p=0.20392 p=0.24101
Number of rngs required: 687820, p-value: 0.251
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_11:31
No. of wins: Observed Expected
98451 98585.9
z-score=-0.603, pvalue=0.27320
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66271 66666.7 2.348 2.348
2 37348 37654.3 2.492 4.840
3 27019 26954.7 0.153 4.993
4 19451 19313.5 0.979 5.973
5 14133 13851.4 5.724 11.697
6 9881 9943.5 0.393 12.090
7 7283 7145.0 2.664 14.755
8 5111 5139.1 0.153 14.908
9 3804 3699.9 2.931 17.839
10 2729 2666.3 1.475 19.314
11 1925 1923.3 0.001 19.315
12 1400 1388.7 0.091 19.406
13 969 1003.7 1.201 20.607
14 760 726.1 1.579 22.186
15 537 525.8 0.237 22.423
16 347 381.2 3.060 25.483
17 290 276.5 0.655 26.138
18 200 200.8 0.003 26.141
19 140 146.0 0.245 26.387
20 117 106.2 1.095 27.482
21 285 287.1 0.016 27.497
Chisq= 27.50 for 20 degrees of freedom, p= 0.87816
SUMMARY of craptest
p-value for no. of wins: 0.273199
p-value for throws/game: 0.878157
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_11:31
No. of wins: Observed Expected
98703 98585.9
z-score= 0.524, pvalue=0.69983
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66624 66666.7 0.027 0.027
2 37546 37654.3 0.312 0.339
3 26790 26954.7 1.007 1.346
4 19302 19313.5 0.007 1.352
5 14027 13851.4 2.226 3.578
6 10032 9943.5 0.787 4.365
7 7343 7145.0 5.485 9.850
8 5185 5139.1 0.410 10.261
9 3673 3699.9 0.195 10.456
10 2611 2666.3 1.147 11.603
11 1820 1923.3 5.551 17.154
12 1403 1388.7 0.146 17.301
13 1024 1003.7 0.410 17.710
14 741 726.1 0.304 18.015
15 521 525.8 0.044 18.059
16 366 381.2 0.602 18.661
17 271 276.5 0.111 18.772
18 204 200.8 0.050 18.822
19 147 146.0 0.007 18.829
20 103 106.2 0.097 18.927
21 267 287.1 1.409 20.336
Chisq= 20.34 for 20 degrees of freedom, p= 0.56289
SUMMARY of craptest
p-value for no. of wins: 0.699835
p-value for throws/game: 0.562890
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0002,0.0018,0.0031,0.0063,0.0072,0.0076,0.0142,0.0177,0.0289,
0.0339,0.0350,0.0352,0.0494,0.0515,0.0585,0.0597,0.0639,0.0718,0.0745,
0.0776,0.0901,0.0932,0.0954,0.0985,0.1005,0.1115,0.1166,0.1241,0.1303,
0.1310,0.1330,0.1456,0.1617,0.1619,0.1632,0.1660,0.1736,0.1784,0.1803,
0.1806,0.1839,0.1956,0.2039,0.2052,0.2133,0.2133,0.2166,0.2216,0.2225,
0.2347,0.2410,0.2429,0.2453,0.2475,0.2490,0.2492,0.2505,0.2562,0.2685,
0.2732,0.2733,0.2764,0.2773,0.2803,0.2812,0.2854,0.2859,0.2899,0.2935,
0.2953,0.2954,0.2978,0.2985,0.2985,0.3005,0.3046,0.3077,0.3083,0.3091,
0.3165,0.3169,0.3172,0.3245,0.3249,0.3251,0.3413,0.3416,0.3449,0.3458,
0.3468,0.3511,0.3525,0.3539,0.3557,0.3576,0.3688,0.3790,0.3825,0.3825,
0.3836,0.3846,0.3882,0.3909,0.3915,0.3921,0.3984,0.3989,0.3995,0.4086,
0.4098,0.4114,0.4122,0.4132,0.4134,0.4144,0.4194,0.4200,0.4232,0.4288,
0.4309,0.4315,0.4339,0.4346,0.4403,0.4429,0.4535,0.4547,0.4547,0.4551,
0.4561,0.4625,0.4657,0.4712,0.4744,0.4748,0.4777,0.4789,0.4856,0.4988,
0.5023,0.5066,0.5078,0.5095,0.5173,0.5174,0.5195,0.5229,0.5322,0.5329,
0.5336,0.5441,0.5448,0.5513,0.5541,0.5629,0.5633,0.5642,0.5642,0.5706,
0.5712,0.5780,0.5780,0.5813,0.5857,0.5875,0.5895,0.5929,0.5960,0.5981,
0.5998,0.6047,0.6089,0.6106,0.6111,0.6182,0.6195,0.6238,0.6246,0.6438,
0.6592,0.6626,0.6631,0.6748,0.6886,0.6892,0.6906,0.6998,0.7070,0.7104,
0.7141,0.7166,0.7204,0.7288,0.7330,0.7343,0.7343,0.7387,0.7410,0.7410,
0.7443,0.7472,0.7541,0.7602,0.7658,0.7668,0.7673,0.7675,0.7703,0.7788,
0.7802,0.7808,0.7808,0.7948,0.7975,0.8054,0.8072,0.8088,0.8118,0.8228,
0.8293,0.8326,0.8344,0.8348,0.8463,0.8479,0.8481,0.8500,0.8505,0.8532,
0.8532,0.8562,0.8578,0.8692,0.8756,0.8782,0.8854,0.8881,0.8919,0.9008,
0.9032,0.9084,0.9145,0.9165,0.9245,0.9266,0.9273,0.9341,0.9361,0.9403,
0.9416,0.9444,0.9472,0.9483,0.9508,0.9519,0.9580,0.9612,0.9626,0.9640,
0.9657,0.9726,0.9752,0.9756,0.9775,0.9862,0.9918,0.9944,0.9968,
Overall p-value after applying KStest on 269 p-values = 0.485520
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.