RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.94 13.2407 0.280070
2 to 25 15.92 11.3221 0.160660
3 to 26 15.84 11.7961 0.187674
4 to 27 15.87 9.7188 0.085015
5 to 28 16.04 7.6836 0.027148
6 to 29 15.72 18.8673 0.663800
7 to 30 15.83 18.8235 0.661244
8 to 31 15.70 13.6554 0.308675
9 to 32 15.77 17.8837 0.603788
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.124771
Tough bday spacings test for dh-ranFile-2018-06-24_07:31: 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 11 35 72 96 87 91 47 32 14 13 2
(O-E)^2/E 0.4 0.1 0.0 0.0 1.2 2.1 0.5 0.2 0.1 6.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 11.706, p= 0.695
RESULTS OF GCD FOR dh-ranFile-2018-06-24_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.594744
p-value, dist. of gcd's: 0.444919
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.380 0.184 0.433 0.615 0.952 0.764 0.773 0.464
Bits 8 to 15---> 0.316 0.266 0.951 0.215 0.044 0.462 0.151 0.165
Bits 16 to 23---> 0.518 0.429 0.509 0.810 0.898 0.720 0.513 0.787
Bits 24 to 31---> 0.397 0.335 0.532 0.263 0.184 0.433 0.106 0.933
KS test for the above 32 p values: 0.303
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_07:31,
p-values for 5 runs: 0.9298, 0.6599, 0.1941, 0.2803, 0.8841
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5123 5134.0 0.024 0.296
r= 30 23229 23103.0 0.687 0.982
r= 31 11429 11551.5 1.300 2.282
chi-square = 2.282 with df = 3; p-value = 0.484
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 193 211.4 1.605 1.605
r= 30 5079 5134.0 0.589 2.194
r= 31 23008 23103.0 0.391 2.585
r= 32 11720 11551.5 2.457 5.042
chi-square = 5.042 with df = 3; p-value = 0.831
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_07:31
b-rank test for bits 1 to 8, p=0.05580
b-rank test for bits 2 to 9, p=0.17719
b-rank test for bits 3 to 10, p=0.27871
b-rank test for bits 4 to 11, p=0.03616
b-rank test for bits 5 to 12, p=0.31260
b-rank test for bits 6 to 13, p=0.68741
b-rank test for bits 7 to 14, p=0.25313
b-rank test for bits 8 to 15, p=0.03782
b-rank test for bits 9 to 16, p=0.24464
b-rank test for bits 10 to 17, p=0.26706
b-rank test for bits 11 to 18, p=0.07643
b-rank test for bits 12 to 19, p=0.42467
b-rank test for bits 13 to 20, p=0.30318
b-rank test for bits 14 to 21, p=0.83823
b-rank test for bits 15 to 22, p=0.99481
b-rank test for bits 16 to 23, p=0.77982
b-rank test for bits 17 to 24, p=0.65423
b-rank test for bits 18 to 25, p=0.79534
b-rank test for bits 19 to 26, p=0.82301
b-rank test for bits 20 to 27, p=0.52422
b-rank test for bits 21 to 28, p=0.02136
b-rank test for bits 22 to 29, p=0.19368
b-rank test for bits 23 to 30, p=0.09367
b-rank test for bits 24 to 31, p=0.17088
b-rank test for bits 25 to 32, p=0.63517
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 = 0.054619
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_07:31
(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 141737 -0.40 0.343607
2 141867 -0.10 0.460608
3 141649 -0.61 0.271512
4 142146 0.55 0.709857
5 141709 -0.47 0.319871
6 142201 0.68 0.752214
7 141506 -0.94 0.173004
8 141900 -0.02 0.491304
9 142197 0.67 0.749248
10 141980 0.17 0.565574
11 141927 0.04 0.516466
12 142472 1.31 0.905686
13 142374 1.09 0.861189
14 141770 -0.33 0.372387
15 142505 1.39 0.918001
16 142032 0.29 0.612795
17 141686 -0.52 0.300905
18 141543 -0.86 0.196023
19 141443 -1.09 0.137954
20 141290 -1.45 0.073944
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_07:31
Bits used No. missing words z-score p-value
23 to 32 141919 0.0333 0.513300
22 to 31 142343 1.4954 0.932597
21 to 30 141672 -0.8184 0.206570
20 to 29 142202 1.0092 0.843562
19 to 28 142117 0.7161 0.763036
18 to 27 141955 0.1575 0.562568
17 to 26 142192 0.9747 0.835151
16 to 25 141890 -0.0667 0.473428
15 to 24 142216 1.0575 0.854854
14 to 23 141969 0.2058 0.581510
13 to 22 141861 -0.1667 0.433821
12 to 21 141384 -1.8115 0.035033
11 to 20 141657 -0.8701 0.192122
10 to 19 141974 0.2230 0.588232
9 to 18 142131 0.7644 0.777679
8 to 17 141434 -1.6391 0.050599
7 to 16 141896 -0.0460 0.481669
6 to 15 142163 0.8747 0.809138
5 to 14 142056 0.5058 0.693487
4 to 13 141972 0.2161 0.585547
3 to 12 142446 1.8506 0.967885
2 to 11 142262 1.2161 0.888027
1 to 10 141883 -0.0908 0.463829
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_07:31
Bits used No. missing words z-score p-value
28 to 32 141369 -1.8316 0.033504
27 to 31 141427 -1.6350 0.051023
26 to 30 141748 -0.5469 0.292230
25 to 29 141555 -1.2011 0.114853
24 to 28 141910 0.0023 0.500906
23 to 27 141567 -1.1604 0.122935
22 to 26 141548 -1.2248 0.110316
21 to 25 141897 -0.0418 0.483330
20 to 24 141908 -0.0045 0.498201
19 to 23 141654 -0.8655 0.193375
18 to 22 141325 -1.9808 0.023808
17 to 21 141694 -0.7299 0.232716
16 to 20 142146 0.8023 0.788802
15 to 19 142485 1.9514 0.974497
14 to 18 141761 -0.5028 0.307548
13 to 17 141687 -0.7537 0.225526
12 to 16 141809 -0.3401 0.366890
11 to 15 141746 -0.5537 0.289905
10 to 14 142164 0.8633 0.806011
9 to 13 142021 0.3785 0.647486
8 to 12 142031 0.4124 0.659992
7 to 11 142092 0.6192 0.732114
6 to 10 141682 -0.7706 0.220469
5 to 9 141703 -0.6994 0.242144
4 to 8 141897 -0.0418 0.483330
3 to 7 142129 0.7446 0.771757
2 to 6 142015 0.3582 0.639905
1 to 5 142517 2.0599 0.980296
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_07:31
Bits used No. missing words z-score p-value
31 to 32 141899 -0.0305 0.487845
30 to 31 141683 -0.6676 0.252182
29 to 30 142476 1.6716 0.952698
28 to 29 142368 1.3530 0.911974
27 to 28 141861 -0.1426 0.443316
26 to 27 142112 0.5978 0.725029
25 to 26 141805 -0.3078 0.379133
24 to 25 142097 0.5536 0.710073
23 to 24 141962 0.1554 0.561735
22 to 23 142017 0.3176 0.624610
21 to 22 141612 -0.8771 0.190222
20 to 21 141960 0.1495 0.559408
19 to 20 142174 0.7807 0.782522
18 to 19 141776 -0.3933 0.347048
17 to 18 141637 -0.8033 0.210891
16 to 17 141362 -1.6145 0.053205
15 to 16 142205 0.8722 0.808446
14 to 15 142311 1.1849 0.881965
13 to 14 142242 0.9813 0.836784
12 to 13 141153 -2.2311 0.012839
11 to 12 141189 -2.1249 0.016799
10 to 11 141836 -0.2163 0.414372
9 to 10 142040 0.3855 0.650051
8 to 9 141342 -1.6735 0.047111
7 to 8 141844 -0.1927 0.423592
6 to 7 142213 0.8958 0.814815
5 to 6 141771 -0.4081 0.341617
4 to 5 142267 1.0551 0.854304
3 to 4 141824 -0.2517 0.400632
2 to 3 142101 0.5654 0.714099
1 to 2 142428 1.5300 0.936992
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2499.17 -0.012 0.495306
Test results for specific bytes for dh-ranFile-2018-06-24_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2411.76 -1.248 0.106029
2 to 9 2583.00 1.174 0.879762
3 to 10 2468.73 -0.442 0.329181
4 to 11 2501.20 0.017 0.506773
5 to 12 2568.42 0.968 0.833382
6 to 13 2571.27 1.008 0.843260
7 to 14 2494.13 -0.083 0.466909
8 to 15 2533.96 0.480 0.684477
9 to 16 2467.90 -0.454 0.324948
10 to 17 2551.47 0.728 0.766681
11 to 18 2462.71 -0.527 0.298966
12 to 19 2562.90 0.889 0.813129
13 to 20 2619.80 1.694 0.954888
14 to 21 2413.53 -1.223 0.110679
15 to 22 2539.29 0.556 0.710751
16 to 23 2466.88 -0.468 0.319754
17 to 24 2537.11 0.525 0.700123
18 to 25 2537.53 0.531 0.702227
19 to 26 2610.13 1.558 0.940325
20 to 27 2500.97 0.014 0.505482
21 to 28 2583.62 1.183 0.881505
22 to 29 2395.03 -1.485 0.068836
23 to 30 2541.54 0.587 0.721556
24 to 31 2574.03 1.047 0.852441
25 to 32 2453.32 -0.660 0.254575
CDPARK for dh-ranFile-2018-06-24_07:31: 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
3503 -0.9132 0.180558
3532 0.4110 0.659449
3528 0.2283 0.590298
3489 -1.5525 0.060270
3523 0.0000 0.500000
3577 2.4658 0.993164
3510 -0.5936 0.276387
3500 -1.0502 0.146807
3551 1.2785 0.899470
3552 1.3242 0.907282
Square side=100, avg. no. parked=3526.50 sample std.=26.04
p-value of the KSTEST for those 10 p-values: 0.764879
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_07:31
0.5741,0.5502,0.0032,0.5285,0.2196,0.2891,0.8145,0.1561,0.4061,0.1580,
The KS test for those 10 p-values: 0.216471
The 3DSPHERES test for dh-ranFile-2018-06-24_07:31
sample no r^3 equiv. uni.
1 22.966 0.534907
2 105.016 0.969818
3 8.604 0.249347
4 117.902 0.980358
5 41.372 0.748188
6 28.836 0.617566
7 11.203 0.311629
8 35.304 0.691732
9 7.130 0.211548
10 97.158 0.960781
11 72.674 0.911298
12 15.792 0.409263
13 60.712 0.867838
14 67.844 0.895801
15 30.667 0.640215
16 2.377 0.076172
17 29.760 0.629169
18 12.888 0.349231
19 26.943 0.592657
20 55.311 0.841771
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.083979
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 -0.4 -0.1 -1.3 -0.6
1.1 2.1 -0.8 -2.2 1.0 -1.5
1.5 2.3 0.4 -0.2 -0.2 0.2
-0.4 -2.0 -1.3 -0.0 1.1 -0.8
0.3 0.5 -0.5 -0.2 1.5 -0.0
1.8 -1.1 -0.6 0.2 0.9 1.3
0.3 -0.1 1.3 0.4 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:48.625510
z-score=0.722902, p-value=0.776360
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_07:31
Test no p-value
1 0.307447
2 0.081049
3 0.447713
4 0.194801
5 0.009774
6 0.001708
7 0.719251
8 0.301668
9 0.054231
10 0.839713
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.014406
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_07:31:
(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 66554 0.19 66518 0.33
3 25000.00 25054 0.12 25176 1.24
4 6666.67 6686 0.06 6675 0.01
5 1388.89 1423 0.84 1358 0.69
6 238.10 249 0.50 237 0.01
7 34.72 31 0.40 30 0.64
8 4.96 2 1.77 5 0.00
p=0.30510 p=0.18057
Number of rngs required: 688714, p-value: 0.640
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_07:31
No. of wins: Observed Expected
98798 98585.9
z-score= 0.949, pvalue=0.82864
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66429 66666.7 0.847 0.847
2 37593 37654.3 0.100 0.947
3 26655 26954.7 3.333 4.280
4 19516 19313.5 2.124 6.404
5 13809 13851.4 0.130 6.534
6 10119 9943.5 3.096 9.630
7 7134 7145.0 0.017 9.647
8 5179 5139.1 0.310 9.957
9 3670 3699.9 0.241 10.198
10 2764 2666.3 3.580 13.778
11 1955 1923.3 0.522 14.300
12 1463 1388.7 3.971 18.271
13 1030 1003.7 0.688 18.959
14 727 726.1 0.001 18.960
15 556 525.8 1.730 20.691
16 373 381.2 0.174 20.865
17 262 276.5 0.764 21.629
18 218 200.8 1.468 23.097
19 146 146.0 0.000 23.097
20 112 106.2 0.315 23.412
21 290 287.1 0.029 23.441
Chisq= 23.44 for 20 degrees of freedom, p= 0.73235
SUMMARY of craptest
p-value for no. of wins: 0.828644
p-value for throws/game: 0.732353
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_07:31
No. of wins: Observed Expected
98547 98585.9
z-score=-0.174, pvalue=0.43101
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66702 66666.7 0.019 0.019
2 37751 37654.3 0.248 0.267
3 27110 26954.7 0.894 1.161
4 19102 19313.5 2.315 3.477
5 13848 13851.4 0.001 3.477
6 9943 9943.5 0.000 3.478
7 7194 7145.0 0.336 3.813
8 5104 5139.1 0.239 4.053
9 3730 3699.9 0.245 4.298
10 2632 2666.3 0.441 4.739
11 1970 1923.3 1.133 5.872
12 1349 1388.7 1.137 7.009
13 998 1003.7 0.033 7.041
14 681 726.1 2.806 9.848
15 515 525.8 0.223 10.071
16 361 381.2 1.065 11.136
17 274 276.5 0.023 11.160
18 196 200.8 0.116 11.276
19 153 146.0 0.337 11.613
20 107 106.2 0.006 11.619
21 280 287.1 0.176 11.795
Chisq= 11.79 for 20 degrees of freedom, p= 0.07705
SUMMARY of craptest
p-value for no. of wins: 0.431012
p-value for throws/game: 0.077046
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0032,0.0098,0.0128,0.0144,0.0168,0.0214,0.0238,0.0271,0.0335,
0.0350,0.0362,0.0378,0.0445,0.0471,0.0506,0.0510,0.0532,0.0542,0.0546,
0.0558,0.0603,0.0688,0.0739,0.0762,0.0764,0.0770,0.0810,0.0840,0.0850,
0.0937,0.1060,0.1061,0.1103,0.1107,0.1149,0.1229,0.1248,0.1380,0.1468,
0.1508,0.1561,0.1580,0.1607,0.1646,0.1709,0.1730,0.1772,0.1806,0.1806,
0.1837,0.1840,0.1877,0.1902,0.1921,0.1934,0.1937,0.1941,0.1948,0.1960,
0.2066,0.2109,0.2115,0.2151,0.2165,0.2196,0.2205,0.2255,0.2327,0.2421,
0.2446,0.2493,0.2522,0.2531,0.2546,0.2631,0.2661,0.2671,0.2715,0.2764,
0.2787,0.2801,0.2803,0.2891,0.2899,0.2922,0.2990,0.3009,0.3017,0.3032,
0.3034,0.3051,0.3074,0.3075,0.3087,0.3116,0.3126,0.3156,0.3198,0.3199,
0.3249,0.3292,0.3346,0.3416,0.3436,0.3470,0.3492,0.3669,0.3724,0.3791,
0.3804,0.3965,0.4006,0.4061,0.4093,0.4144,0.4236,0.4247,0.4291,0.4310,
0.4327,0.4333,0.4338,0.4433,0.4449,0.4477,0.4606,0.4620,0.4638,0.4640,
0.4669,0.4734,0.4817,0.4833,0.4833,0.4840,0.4878,0.4913,0.4953,0.4982,
0.5000,0.5009,0.5055,0.5068,0.5090,0.5129,0.5133,0.5165,0.5180,0.5242,
0.5285,0.5315,0.5349,0.5502,0.5594,0.5617,0.5626,0.5656,0.5741,0.5815,
0.5855,0.5882,0.5903,0.5927,0.5947,0.6038,0.6128,0.6150,0.6176,0.6246,
0.6292,0.6352,0.6399,0.6399,0.6402,0.6475,0.6501,0.6542,0.6594,0.6599,
0.6600,0.6612,0.6638,0.6845,0.6874,0.6917,0.6935,0.6948,0.7001,0.7022,
0.7099,0.7101,0.7108,0.7141,0.7193,0.7203,0.7216,0.7250,0.7321,0.7324,
0.7482,0.7492,0.7522,0.7630,0.7638,0.7649,0.7667,0.7718,0.7735,0.7764,
0.7777,0.7798,0.7825,0.7871,0.7888,0.7953,0.8060,0.8084,0.8091,0.8104,
0.8131,0.8145,0.8148,0.8230,0.8286,0.8313,0.8334,0.8352,0.8368,0.8382,
0.8397,0.8418,0.8433,0.8436,0.8524,0.8543,0.8549,0.8612,0.8678,0.8798,
0.8815,0.8820,0.8841,0.8880,0.8958,0.8981,0.8995,0.9057,0.9073,0.9113,
0.9120,0.9180,0.9298,0.9326,0.9331,0.9370,0.9403,0.9506,0.9516,0.9527,
0.9549,0.9608,0.9679,0.9698,0.9745,0.9803,0.9804,0.9932,0.9948,
Overall p-value after applying KStest on 269 p-values = 0.671493
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.