RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.76 17.5664 0.583327
2 to 25 15.47 22.1038 0.819239
3 to 26 15.77 22.2065 0.823091
4 to 27 15.65 13.7124 0.312654
5 to 28 15.74 11.8737 0.192274
6 to 29 15.46 18.8545 0.663053
7 to 30 16.01 15.5779 0.446068
8 to 31 16.07 16.7411 0.527967
9 to 32 15.61 21.7236 0.804416
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.509652
Tough bday spacings test for dh-ranFile-2018-06-30_13:31: 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 42 67 93 88 88 58 22 18 11 3
(O-E)^2/E 0.1 0.8 0.5 0.2 1.0 1.2 0.7 2.0 0.7 2.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.360, p= 0.591
RESULTS OF GCD FOR dh-ranFile-2018-06-30_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.199751
p-value, dist. of gcd's: 0.415910
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.457 0.561 0.517 0.522 0.432 0.717 0.672 0.086
Bits 8 to 15---> 0.718 0.936 0.219 0.601 0.102 0.257 0.273 0.550
Bits 16 to 23---> 0.980 0.620 0.306 0.953 0.813 0.988 0.108 0.700
Bits 24 to 31---> 0.775 0.376 0.588 0.410 0.385 0.077 0.559 0.901
KS test for the above 32 p values: 0.370
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_13:31,
p-values for 5 runs: 0.5659, 0.2380, 0.9026, 0.1316, 0.5623
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5170 5134.0 0.252 0.766
r= 30 23162 23103.0 0.150 0.916
r= 31 11467 11551.5 0.618 1.535
chi-square = 1.535 with df = 3; p-value = 0.326
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 226 211.4 1.006 1.006
r= 30 5160 5134.0 0.132 1.137
r= 31 23036 23103.0 0.195 1.332
r= 32 11578 11551.5 0.061 1.393
chi-square = 1.393 with df = 3; p-value = 0.293
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_13:31
b-rank test for bits 1 to 8, p=0.38639
b-rank test for bits 2 to 9, p=0.48741
b-rank test for bits 3 to 10, p=0.92888
b-rank test for bits 4 to 11, p=0.98452
b-rank test for bits 5 to 12, p=0.58405
b-rank test for bits 6 to 13, p=0.87512
b-rank test for bits 7 to 14, p=0.77144
b-rank test for bits 8 to 15, p=0.53860
b-rank test for bits 9 to 16, p=0.74973
b-rank test for bits 10 to 17, p=0.84611
b-rank test for bits 11 to 18, p=0.89570
b-rank test for bits 12 to 19, p=0.71149
b-rank test for bits 13 to 20, p=0.61633
b-rank test for bits 14 to 21, p=0.92564
b-rank test for bits 15 to 22, p=0.35342
b-rank test for bits 16 to 23, p=0.50713
b-rank test for bits 17 to 24, p=0.93383
b-rank test for bits 18 to 25, p=0.81044
b-rank test for bits 19 to 26, p=0.95041
b-rank test for bits 20 to 27, p=0.93747
b-rank test for bits 21 to 28, p=0.48000
b-rank test for bits 22 to 29, p=0.30583
b-rank test for bits 23 to 30, p=0.54801
b-rank test for bits 24 to 31, p=0.87326
b-rank test for bits 25 to 32, p=0.09333
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 = 0.001920
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_13:31
(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 142086 0.41 0.660116
2 141900 -0.02 0.491304
3 141725 -0.43 0.333351
4 141729 -0.42 0.336756
5 141843 -0.15 0.438420
6 141324 -1.37 0.085720
7 141073 -1.95 0.025348
8 141529 -0.89 0.187103
9 142231 0.75 0.773844
10 141945 0.08 0.533210
11 142493 1.36 0.913671
12 142662 1.76 0.960675
13 142046 0.32 0.625259
14 141737 -0.40 0.343607
15 142175 0.62 0.732610
16 141987 0.18 0.572001
17 141959 0.12 0.546194
18 141543 -0.86 0.196023
19 140904 -2.35 0.009414
20 142351 1.03 0.848950
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_13:31
Bits used No. missing words z-score p-value
23 to 32 141998 0.3058 0.620106
22 to 31 141862 -0.1632 0.435178
21 to 30 141612 -1.0253 0.152617
20 to 29 141950 0.1402 0.555765
19 to 28 141963 0.1851 0.573413
18 to 27 142109 0.6885 0.754436
17 to 26 141825 -0.2908 0.385605
16 to 25 141604 -1.0529 0.146202
15 to 24 142032 0.4230 0.663852
14 to 23 141796 -0.3908 0.347975
13 to 22 142037 0.4402 0.670119
12 to 21 141490 -1.4460 0.074093
11 to 20 141389 -1.7942 0.036387
10 to 19 141937 0.0954 0.538007
9 to 18 141694 -0.7425 0.228887
8 to 17 141496 -1.4253 0.077039
7 to 16 141807 -0.3529 0.362096
6 to 15 142129 0.7575 0.775620
5 to 14 141676 -0.8046 0.210529
4 to 13 141465 -1.5322 0.062740
3 to 12 141820 -0.3080 0.379028
2 to 11 141741 -0.5804 0.280806
1 to 10 141863 -0.1598 0.436536
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_13:31
Bits used No. missing words z-score p-value
28 to 32 141932 0.0768 0.530628
27 to 31 141526 -1.2994 0.096899
26 to 30 141986 0.2599 0.602529
25 to 29 142758 2.8768 0.997992
24 to 28 141870 -0.1333 0.446969
23 to 27 142263 1.1989 0.884713
22 to 26 142055 0.4938 0.689275
21 to 25 141900 -0.0316 0.487385
20 to 24 142242 1.1277 0.870276
19 to 23 141807 -0.3469 0.364340
18 to 22 141684 -0.7638 0.222484
17 to 21 142057 0.5006 0.691665
16 to 20 141950 0.1379 0.554826
15 to 19 141817 -0.3130 0.377147
14 to 18 141854 -0.1876 0.425611
13 to 17 141949 0.1345 0.553486
12 to 16 141843 -0.2248 0.411049
11 to 15 142056 0.4972 0.690471
10 to 14 142132 0.7548 0.774820
9 to 13 141704 -0.6960 0.243204
8 to 12 141794 -0.3909 0.347917
7 to 11 141704 -0.6960 0.243204
6 to 10 141964 0.1853 0.573512
5 to 9 142243 1.1311 0.870990
4 to 8 142133 0.7582 0.775835
3 to 7 142026 0.3955 0.653760
2 to 6 141714 -0.6621 0.253942
1 to 5 142063 0.5209 0.698787
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_13:31
Bits used No. missing words z-score p-value
31 to 32 142012 0.3029 0.619002
30 to 31 141706 -0.5998 0.274322
29 to 30 142231 0.9489 0.828659
28 to 29 141564 -1.0187 0.154179
27 to 28 141925 0.0462 0.518434
26 to 27 141860 -0.1455 0.442152
25 to 26 141866 -0.1278 0.449147
24 to 25 142119 0.6185 0.731876
23 to 24 141664 -0.7237 0.234629
22 to 23 141524 -1.1367 0.127839
21 to 22 142026 0.3442 0.634637
20 to 21 142023 0.3353 0.631304
19 to 20 142031 0.3589 0.640168
18 to 19 141631 -0.8210 0.205814
17 to 18 141495 -1.2222 0.110814
16 to 17 142167 0.7601 0.776399
15 to 16 141976 0.1967 0.577956
14 to 15 142367 1.3501 0.911501
13 to 14 141892 -0.0511 0.479615
12 to 13 141838 -0.2104 0.416673
11 to 12 141509 -1.1809 0.118818
10 to 11 141757 -0.4494 0.326589
9 to 10 141831 -0.2311 0.408633
8 to 9 141931 0.0639 0.525484
7 to 8 141913 0.0108 0.504319
6 to 7 142410 1.4769 0.930149
5 to 6 141761 -0.4376 0.330856
4 to 5 142098 0.5565 0.711082
3 to 4 141794 -0.3402 0.366851
2 to 3 142220 0.9164 0.820280
1 to 2 142059 0.4415 0.670576
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2634.25 1.899 0.971186
Test results for specific bytes for dh-ranFile-2018-06-30_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2440.64 -0.839 0.200618
2 to 9 2474.71 -0.358 0.360300
3 to 10 2527.29 0.386 0.650220
4 to 11 2483.90 -0.228 0.409928
5 to 12 2410.64 -1.264 0.103163
6 to 13 2520.88 0.295 0.616098
7 to 14 2641.04 1.995 0.976960
8 to 15 2527.19 0.385 0.649705
9 to 16 2362.34 -1.947 0.025780
10 to 17 2481.83 -0.257 0.398602
11 to 18 2458.95 -0.581 0.280753
12 to 19 2422.95 -1.090 0.137925
13 to 20 2499.75 -0.004 0.498599
14 to 21 2519.14 0.271 0.606686
15 to 22 2405.54 -1.336 0.090792
16 to 23 2457.15 -0.606 0.272243
17 to 24 2467.87 -0.454 0.324755
18 to 25 2556.63 0.801 0.788391
19 to 26 2442.43 -0.814 0.207766
20 to 27 2437.64 -0.882 0.188931
21 to 28 2497.63 -0.034 0.486620
22 to 29 2661.61 2.285 0.988857
23 to 30 2442.04 -0.820 0.206199
24 to 31 2531.85 0.450 0.673794
25 to 32 2553.75 0.760 0.776421
CDPARK for dh-ranFile-2018-06-30_13:31: 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
3482 -1.8721 0.030593
3482 -1.8721 0.030593
3496 -1.2329 0.108811
3548 1.1416 0.873180
3523 0.0000 0.500000
3505 -0.8219 0.205562
3549 1.1872 0.882429
3557 1.5525 0.939730
3504 -0.8676 0.192812
3553 1.3699 0.914635
Square side=100, avg. no. parked=3519.90 sample std.=28.35
p-value of the KSTEST for those 10 p-values: 0.188480
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_13:31
0.0451,0.0419,0.6060,0.4593,0.3326,0.9790,0.8832,0.4901,0.5045,0.6261,
The KS test for those 10 p-values: 0.793645
The 3DSPHERES test for dh-ranFile-2018-06-30_13:31
sample no r^3 equiv. uni.
1 36.491 0.703695
2 24.402 0.556655
3 10.690 0.299752
4 23.442 0.542230
5 22.201 0.522904
6 32.940 0.666464
7 24.213 0.553855
8 70.786 0.905535
9 29.986 0.631952
10 56.217 0.846475
11 48.999 0.804719
12 4.974 0.152792
13 36.366 0.702454
14 6.907 0.205639
15 4.498 0.139227
16 10.800 0.302316
17 38.618 0.723976
18 14.614 0.385623
19 10.747 0.301089
20 6.200 0.186704
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.610675
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.3 0.8 0.5 -0.6 -0.9
0.6 -0.5 0.5 -0.5 1.8 -1.7
1.5 -0.7 -1.3 0.6 0.6 1.2
-1.1 -1.8 -1.0 -0.1 0.6 0.4
1.9 -0.0 -0.3 0.1 1.4 -1.0
0.2 -0.2 0.3 0.2 0.6 -0.7
1.2 -0.7 0.5 2.6 3.1 0.0
-0.1
Chi-square with 42 degrees of freedom:52.381325
z-score=1.132695, p-value=0.869135
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_13:31
Test no p-value
1 0.052125
2 0.003936
3 0.877962
4 0.064467
5 0.871600
6 0.270612
7 0.017762
8 0.089670
9 0.174159
10 0.012682
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000272
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_13:31:
(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 66759 0.13 66410 0.99
3 25000.00 24953 0.09 25098 0.38
4 6666.67 6629 0.21 6874 6.45
5 1388.89 1379 0.07 1331 2.41
6 238.10 253 0.93 238 0.00
7 34.72 22 4.66 44 2.48
8 4.96 4 0.19 4 0.19
p=0.60727 p=0.95534
Number of rngs required: 689834, p-value: 0.953
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_13:31
No. of wins: Observed Expected
98742 98585.9
z-score= 0.698, pvalue=0.75752
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66836 66666.7 0.430 0.430
2 37454 37654.3 1.066 1.496
3 26956 26954.7 0.000 1.496
4 19165 19313.5 1.141 2.637
5 13931 13851.4 0.457 3.094
6 10010 9943.5 0.444 3.538
7 7104 7145.0 0.236 3.774
8 5231 5139.1 1.644 5.418
9 3625 3699.9 1.515 6.933
10 2750 2666.3 2.628 9.561
11 1899 1923.3 0.308 9.869
12 1390 1388.7 0.001 9.870
13 984 1003.7 0.387 10.257
14 713 726.1 0.238 10.495
15 511 525.8 0.419 10.913
16 405 381.2 1.492 12.406
17 288 276.5 0.475 12.881
18 209 200.8 0.332 13.213
19 140 146.0 0.245 13.458
20 110 106.2 0.135 13.593
21 289 287.1 0.012 13.606
Chisq= 13.61 for 20 degrees of freedom, p= 0.15009
SUMMARY of craptest
p-value for no. of wins: 0.757523
p-value for throws/game: 0.150087
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_13:31
No. of wins: Observed Expected
98594 98585.9
z-score= 0.036, pvalue=0.51452
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66864 66666.7 0.584 0.584
2 37710 37654.3 0.082 0.666
3 26849 26954.7 0.415 1.081
4 19203 19313.5 0.632 1.713
5 13684 13851.4 2.024 3.737
6 10056 9943.5 1.272 5.008
7 7063 7145.0 0.942 5.950
8 5217 5139.1 1.182 7.132
9 3788 3699.9 2.099 9.231
10 2744 2666.3 2.264 11.496
11 1833 1923.3 4.242 15.738
12 1363 1388.7 0.477 16.215
13 985 1003.7 0.349 16.564
14 693 726.1 1.513 18.077
15 561 525.8 2.352 20.428
16 372 381.2 0.220 20.648
17 248 276.5 2.945 23.593
18 214 200.8 0.864 24.457
19 170 146.0 3.951 28.408
20 102 106.2 0.167 28.575
21 281 287.1 0.130 28.705
Chisq= 28.71 for 20 degrees of freedom, p= 0.90627
SUMMARY of craptest
p-value for no. of wins: 0.514524
p-value for throws/game: 0.906267
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0019,0.0039,0.0094,0.0127,0.0178,0.0253,0.0258,0.0306,0.0306,
0.0364,0.0419,0.0451,0.0521,0.0627,0.0645,0.0741,0.0770,0.0773,0.0857,
0.0863,0.0897,0.0908,0.0933,0.0969,0.1023,0.1032,0.1085,0.1088,0.1108,
0.1188,0.1278,0.1316,0.1379,0.1392,0.1462,0.1501,0.1526,0.1528,0.1542,
0.1742,0.1867,0.1871,0.1885,0.1889,0.1923,0.1928,0.1960,0.1998,0.2006,
0.2056,0.2056,0.2058,0.2062,0.2078,0.2105,0.2185,0.2225,0.2289,0.2346,
0.2380,0.2432,0.2432,0.2539,0.2574,0.2706,0.2722,0.2725,0.2743,0.2808,
0.2808,0.2927,0.2998,0.3011,0.3023,0.3058,0.3059,0.3127,0.3248,0.3257,
0.3266,0.3309,0.3326,0.3334,0.3368,0.3436,0.3479,0.3480,0.3534,0.3603,
0.3621,0.3643,0.3669,0.3702,0.3755,0.3771,0.3790,0.3850,0.3856,0.3856,
0.3864,0.3986,0.4086,0.4099,0.4102,0.4110,0.4159,0.4167,0.4256,0.4315,
0.4352,0.4365,0.4384,0.4422,0.4461,0.4470,0.4491,0.4568,0.4593,0.4796,
0.4800,0.4866,0.4874,0.4874,0.4901,0.4913,0.4986,0.5000,0.5043,0.5045,
0.5071,0.5097,0.5145,0.5172,0.5184,0.5217,0.5229,0.5255,0.5280,0.5306,
0.5332,0.5380,0.5386,0.5422,0.5462,0.5480,0.5502,0.5535,0.5539,0.5548,
0.5558,0.5567,0.5591,0.5615,0.5623,0.5659,0.5720,0.5734,0.5735,0.5780,
0.5833,0.5841,0.5884,0.5905,0.6007,0.6025,0.6060,0.6067,0.6073,0.6107,
0.6161,0.6163,0.6190,0.6197,0.6201,0.6253,0.6261,0.6313,0.6320,0.6346,
0.6402,0.6497,0.6502,0.6538,0.6601,0.6631,0.6639,0.6665,0.6701,0.6706,
0.6724,0.6738,0.6893,0.6905,0.6917,0.6988,0.7002,0.7025,0.7037,0.7111,
0.7115,0.7171,0.7179,0.7240,0.7319,0.7326,0.7497,0.7544,0.7575,0.7714,
0.7738,0.7748,0.7748,0.7756,0.7758,0.7764,0.7764,0.7884,0.7936,0.8044,
0.8047,0.8104,0.8127,0.8192,0.8203,0.8231,0.8287,0.8461,0.8465,0.8489,
0.8691,0.8703,0.8710,0.8716,0.8732,0.8733,0.8751,0.8780,0.8824,0.8832,
0.8847,0.8957,0.9006,0.9026,0.9055,0.9063,0.9115,0.9137,0.9146,0.9256,
0.9289,0.9301,0.9338,0.9359,0.9375,0.9397,0.9504,0.9530,0.9533,0.9553,
0.9607,0.9712,0.9770,0.9790,0.9798,0.9845,0.9875,0.9889,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.735999
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.