RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-09-04_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 15.58 11.4939 0.170231
2 to 25 15.44 20.7222 0.761035
3 to 26 15.40 33.9753 0.991542
4 to 27 15.90 22.6076 0.837535
5 to 28 15.64 20.0636 0.729013
6 to 29 16.14 21.4624 0.793712
7 to 30 15.79 22.9905 0.850440
8 to 31 15.72 21.5720 0.798257
9 to 32 15.66 25.4218 0.914340
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.005457
Tough bday spacings test for dh-ranFile-2018-09-04_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 6 41 61 100 94 69 60 37 15 14 3
(O-E)^2/E 1.1 0.5 2.1 0.1 0.1 1.1 1.2 1.8 0.0 8.2 0.3
Birthday Spacings: Sum(O-E)^2/E= 16.404, p= 0.911
RESULTS OF GCD FOR dh-ranFile-2018-09-04_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.418318
p-value, dist. of gcd's: 0.906613
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-09-04_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.653 0.445 0.572 0.754 0.910 0.340 0.272 0.435
Bits 8 to 15---> 0.677 0.206 0.264 0.282 0.816 0.859 0.921 0.035
Bits 16 to 23---> 0.363 0.618 0.722 0.404 0.590 0.113 0.324 0.580
Bits 24 to 31---> 0.723 0.209 0.938 0.669 0.285 0.853 0.656 0.879
KS test for the above 32 p values: 0.512
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-09-04_11:31,
p-values for 5 runs: 0.6998, 0.0501, 0.6989, 0.5681, 0.3247
Rank test for binary matrices (31x31) for dh-ranFile-2018-09-04_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 189 211.4 2.377 2.377
r= 29 5157 5134.0 0.103 2.480
r= 30 23191 23103.0 0.335 2.815
r= 31 11463 11551.5 0.678 3.493
chi-square = 3.493 with df = 3; p-value = 0.678
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-09-04_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5105 5134.0 0.164 0.225
r= 31 22964 23103.0 0.837 1.061
r= 32 11716 11551.5 2.342 3.403
chi-square = 3.403 with df = 3; p-value = 0.666
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-09-04_11:31
b-rank test for bits 1 to 8, p=0.67894
b-rank test for bits 2 to 9, p=0.36588
b-rank test for bits 3 to 10, p=0.71199
b-rank test for bits 4 to 11, p=0.27714
b-rank test for bits 5 to 12, p=0.98984
b-rank test for bits 6 to 13, p=0.25244
b-rank test for bits 7 to 14, p=0.92434
b-rank test for bits 8 to 15, p=0.70458
b-rank test for bits 9 to 16, p=0.28532
b-rank test for bits 10 to 17, p=0.50279
b-rank test for bits 11 to 18, p=0.67227
b-rank test for bits 12 to 19, p=0.57156
b-rank test for bits 13 to 20, p=0.01308
b-rank test for bits 14 to 21, p=0.31105
b-rank test for bits 15 to 22, p=0.31026
b-rank test for bits 16 to 23, p=0.02809
b-rank test for bits 17 to 24, p=0.70547
b-rank test for bits 18 to 25, p=0.91267
b-rank test for bits 19 to 26, p=0.76531
b-rank test for bits 20 to 27, p=0.18137
b-rank test for bits 21 to 28, p=0.60241
b-rank test for bits 22 to 29, p=0.28489
b-rank test for bits 23 to 30, p=0.97310
b-rank test for bits 24 to 31, p=0.50284
b-rank test for bits 25 to 32, p=0.04965
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 = 0.884754
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-09-04_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 141791 -0.28 0.391093
2 142212 0.71 0.760271
3 141604 -0.71 0.237803
4 141368 -1.26 0.102973
5 141773 -0.32 0.375042
6 141924 0.03 0.513671
7 142026 0.27 0.607417
8 141638 -0.63 0.263057
9 141496 -0.97 0.167091
10 141313 -1.39 0.081765
11 141990 0.19 0.574750
12 141472 -1.02 0.153438
13 142375 1.09 0.861706
14 141852 -0.13 0.446722
15 140941 -2.26 0.011835
16 141285 -1.46 0.072322
17 142275 0.85 0.803550
18 142273 0.85 0.802253
19 142258 0.81 0.792364
20 141540 -0.86 0.194091
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-09-04_11:31
Bits used No. missing words z-score p-value
23 to 32 142116 0.7127 0.761970
22 to 31 142357 1.5437 0.938668
21 to 30 142087 0.6127 0.729948
20 to 29 141761 -0.5115 0.304507
19 to 28 142178 0.9264 0.822894
18 to 27 142110 0.6920 0.755521
17 to 26 142231 1.1092 0.866330
16 to 25 142088 0.6161 0.731087
15 to 24 141638 -0.9356 0.174734
14 to 23 141943 0.1161 0.546215
13 to 22 141744 -0.5701 0.284304
12 to 21 141988 0.2713 0.606911
11 to 20 142006 0.3333 0.630563
10 to 19 141690 -0.7563 0.224732
9 to 18 141913 0.0127 0.505049
8 to 17 142107 0.6816 0.752261
7 to 16 141861 -0.1667 0.433821
6 to 15 142083 0.5989 0.725368
5 to 14 142166 0.8851 0.811940
4 to 13 141750 -0.5494 0.291361
3 to 12 141559 -1.2080 0.113517
2 to 11 142476 1.9540 0.974651
1 to 10 141575 -1.1529 0.124484
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-09-04_11:31
Bits used No. missing words z-score p-value
28 to 32 141684 -0.7638 0.222484
27 to 31 142326 1.4124 0.921090
26 to 30 142131 0.7514 0.773801
25 to 29 141452 -1.5503 0.060538
24 to 28 141679 -0.7808 0.217466
23 to 27 141990 0.2735 0.607749
22 to 26 142263 1.1989 0.884713
21 to 25 142141 0.7853 0.783868
20 to 24 142322 1.3989 0.919076
19 to 23 141897 -0.0418 0.483330
18 to 22 141550 -1.2181 0.111599
17 to 21 142043 0.4531 0.674768
16 to 20 141465 -1.5062 0.066008
15 to 19 141452 -1.5503 0.060538
14 to 18 142131 0.7514 0.773801
13 to 17 141430 -1.6248 0.052098
12 to 16 141924 0.0497 0.519831
11 to 15 141945 0.1209 0.548121
10 to 14 141809 -0.3401 0.366890
9 to 13 141995 0.2904 0.614248
8 to 12 142231 1.0904 0.862233
7 to 11 141669 -0.8147 0.207628
6 to 10 142572 2.2463 0.987659
5 to 9 142195 0.9684 0.833571
4 to 8 141912 0.0091 0.503611
3 to 7 142014 0.3548 0.638635
2 to 6 141712 -0.6689 0.251775
1 to 5 141762 -0.4994 0.308741
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-09-04_11:31
Bits used No. missing words z-score p-value
31 to 32 141623 -0.8446 0.199158
30 to 31 142076 0.4917 0.688517
29 to 30 141331 -1.7060 0.044005
28 to 29 142111 0.5949 0.724044
27 to 28 141847 -0.1839 0.427060
26 to 27 141852 -0.1691 0.432853
25 to 26 141668 -0.7119 0.238267
24 to 25 142092 0.5388 0.705005
23 to 24 141711 -0.5850 0.279259
22 to 23 142093 0.5418 0.706022
21 to 22 141796 -0.3343 0.369074
20 to 21 141946 0.1082 0.543070
19 to 20 141496 -1.2193 0.111372
18 to 19 142071 0.4769 0.683284
17 to 18 141894 -0.0452 0.481966
16 to 17 142327 1.2321 0.891038
15 to 16 141784 -0.3697 0.355801
14 to 15 141593 -0.9331 0.175377
13 to 14 142175 0.7837 0.783388
12 to 13 141689 -0.6499 0.257865
11 to 12 142139 0.6775 0.750953
10 to 11 142235 0.9607 0.831643
9 to 10 142348 1.2940 0.902169
8 to 9 142377 1.3796 0.916139
7 to 8 142401 1.4504 0.926520
6 to 7 141580 -0.9715 0.165656
5 to 6 141993 0.2468 0.597474
4 to 5 142495 1.7276 0.957974
3 to 4 141735 -0.5142 0.303539
2 to 3 141799 -0.3255 0.372418
1 to 2 142008 0.2911 0.614498
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-09-04_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2387.78 -1.587 0.056254
Test results for specific bytes for dh-ranFile-2018-09-04_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2478.76 -0.300 0.381959
2 to 9 2586.53 1.224 0.889473
3 to 10 2335.96 -2.320 0.010175
4 to 11 2500.33 0.005 0.501854
5 to 12 2544.10 0.624 0.733572
6 to 13 2523.78 0.336 0.631702
7 to 14 2587.97 1.244 0.893254
8 to 15 2548.21 0.682 0.752323
9 to 16 2419.25 -1.142 0.126724
10 to 17 2383.37 -1.649 0.049527
11 to 18 2438.08 -0.876 0.190619
12 to 19 2455.42 -0.631 0.264176
13 to 20 2447.88 -0.737 0.230547
14 to 21 2401.51 -1.393 0.081824
15 to 22 2554.30 0.768 0.778714
16 to 23 2640.47 1.987 0.976511
17 to 24 2572.03 1.019 0.845811
18 to 25 2521.65 0.306 0.620290
19 to 26 2574.46 1.053 0.853848
20 to 27 2502.55 0.036 0.514382
21 to 28 2423.50 -1.082 0.139643
22 to 29 2552.11 0.737 0.769437
23 to 30 2489.73 -0.145 0.442248
24 to 31 2554.07 0.765 0.777775
25 to 32 2459.15 -0.578 0.281735
CDPARK for dh-ranFile-2018-09-04_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
3521 -0.0913 0.463617
3515 -0.3653 0.357445
3496 -1.2329 0.108811
3509 -0.6393 0.261324
3512 -0.5023 0.307734
3527 0.1826 0.572463
3517 -0.2740 0.392053
3572 2.2374 0.987371
3488 -1.5982 0.055002
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3517.10 sample std.=21.27
p-value of the KSTEST for those 10 p-values: 0.219948
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-09-04_11:31
0.3433,0.4356,0.1160,0.5704,0.0096,0.7550,0.5428,0.8082,0.3319,0.9762,
The KS test for those 10 p-values: 0.960726
The 3DSPHERES test for dh-ranFile-2018-09-04_11:31
sample no r^3 equiv. uni.
1 24.326 0.555530
2 33.535 0.673008
3 13.207 0.356124
4 11.345 0.314880
5 12.642 0.343877
6 16.251 0.418238
7 20.207 0.490112
8 11.466 0.317631
9 18.168 0.454256
10 50.256 0.812729
11 102.535 0.967217
12 8.784 0.253828
13 42.607 0.758343
14 5.663 0.172014
15 10.334 0.291407
16 14.232 0.377742
17 23.566 0.544128
18 13.448 0.361267
19 18.423 0.458864
20 1.819 0.058846
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.190658
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-09-04_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 -0.1 -1.7 0.7 -0.1
0.3 1.4 -1.6 2.3 0.1 -0.7
-0.2 -3.1 0.3 -0.2 0.1 1.8
-1.4 -1.7 1.8 0.8 0.7 1.2
-1.2 -0.9 0.4 0.9 -0.1 1.6
-0.3 -0.5 1.0 0.7 -0.4 -0.8
0.0 1.1 -0.8 -0.7 -0.6 1.0
0.8
Chi-square with 42 degrees of freedom:50.002984
z-score=0.873197, p-value=0.814585
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-09-04_11:31
Test no p-value
1 0.010268
2 0.143043
3 0.136256
4 0.235277
5 0.452803
6 0.407573
7 0.860613
8 0.315257
9 0.986370
10 0.792403
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.564611
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-09-04_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 66695 0.01 66621 0.03
3 25000.00 25048 0.09 25145 0.84
4 6666.67 6591 0.86 6636 0.14
5 1388.89 1384 0.02 1298 5.95
6 238.10 247 0.33 262 2.40
7 34.72 32 0.21 34 0.01
8 4.96 2 1.77 3 0.77
p=0.22871 p=0.88156
Number of rngs required: 687368, p-value: 0.115
RESULTS OF CRAPS TEST for dh-ranFile-2018-09-04_11:31
No. of wins: Observed Expected
98804 98585.9
z-score= 0.976, pvalue=0.83538
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66855 66666.7 0.532 0.532
2 37531 37654.3 0.404 0.936
3 26975 26954.7 0.015 0.951
4 19229 19313.5 0.369 1.321
5 13956 13851.4 0.790 2.110
6 9828 9943.5 1.343 3.453
7 7180 7145.0 0.171 3.624
8 5081 5139.1 0.656 4.280
9 3697 3699.9 0.002 4.282
10 2743 2666.3 2.207 6.489
11 1980 1923.3 1.670 8.159
12 1351 1388.7 1.026 9.184
13 993 1003.7 0.114 9.299
14 719 726.1 0.070 9.369
15 502 525.8 1.080 10.449
16 390 381.2 0.205 10.655
17 244 276.5 3.829 14.484
18 182 200.8 1.765 16.249
19 126 146.0 2.736 18.985
20 137 106.2 8.922 27.907
21 301 287.1 0.672 28.579
Chisq= 28.58 for 20 degrees of freedom, p= 0.90361
SUMMARY of craptest
p-value for no. of wins: 0.835382
p-value for throws/game: 0.903614
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-09-04_11:31
No. of wins: Observed Expected
98493 98585.9
z-score=-0.415, pvalue=0.33895
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66775 66666.7 0.176 0.176
2 37493 37654.3 0.691 0.867
3 27052 26954.7 0.351 1.218
4 19065 19313.5 3.196 4.415
5 13808 13851.4 0.136 4.551
6 10096 9943.5 2.338 6.888
7 7197 7145.0 0.378 7.266
8 4999 5139.1 3.818 11.084
9 3711 3699.9 0.034 11.118
10 2797 2666.3 6.407 17.525
11 1895 1923.3 0.417 17.942
12 1398 1388.7 0.062 18.004
13 1077 1003.7 5.351 23.355
14 729 726.1 0.011 23.366
15 515 525.8 0.223 23.589
16 385 381.2 0.039 23.628
17 268 276.5 0.264 23.892
18 188 200.8 0.820 24.711
19 167 146.0 3.025 27.737
20 108 106.2 0.030 27.767
21 277 287.1 0.356 28.123
Chisq= 28.12 for 20 degrees of freedom, p= 0.89348
SUMMARY of craptest
p-value for no. of wins: 0.338955
p-value for throws/game: 0.893478
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0055,0.0096,0.0102,0.0103,0.0118,0.0131,0.0281,0.0354,0.0440,0.0495,
0.0497,0.0501,0.0521,0.0550,0.0563,0.0588,0.0605,0.0605,0.0660,0.0723,
0.0818,0.0818,0.1030,0.1088,0.1114,0.1116,0.1128,0.1135,0.1145,0.1160,
0.1245,0.1267,0.1363,0.1396,0.1430,0.1534,0.1657,0.1671,0.1702,0.1720,
0.1747,0.1754,0.1814,0.1906,0.1907,0.1941,0.1992,0.2065,0.2076,0.2093,
0.2175,0.2199,0.2225,0.2247,0.2287,0.2305,0.2353,0.2378,0.2383,0.2518,
0.2524,0.2538,0.2579,0.2613,0.2631,0.2641,0.2642,0.2716,0.2771,0.2793,
0.2817,0.2817,0.2843,0.2849,0.2849,0.2853,0.2914,0.2914,0.3035,0.3045,
0.3077,0.3087,0.3103,0.3110,0.3149,0.3153,0.3176,0.3236,0.3247,0.3319,
0.3390,0.3398,0.3406,0.3433,0.3439,0.3558,0.3561,0.3574,0.3613,0.3633,
0.3659,0.3669,0.3691,0.3724,0.3750,0.3777,0.3820,0.3911,0.3921,0.4036,
0.4076,0.4182,0.4183,0.4271,0.4329,0.4338,0.4346,0.4356,0.4422,0.4447,
0.4467,0.4528,0.4543,0.4589,0.4636,0.4820,0.4833,0.4901,0.5019,0.5028,
0.5028,0.5036,0.5050,0.5118,0.5137,0.5144,0.5198,0.5428,0.5431,0.5441,
0.5462,0.5481,0.5555,0.5646,0.5681,0.5704,0.5716,0.5722,0.5725,0.5748,
0.5796,0.5904,0.5975,0.6024,0.6069,0.6074,0.6077,0.6142,0.6145,0.6178,
0.6203,0.6306,0.6317,0.6386,0.6535,0.6565,0.6665,0.6693,0.6723,0.6730,
0.6748,0.6774,0.6784,0.6789,0.6833,0.6885,0.6989,0.6998,0.7046,0.7050,
0.7055,0.7060,0.7120,0.7221,0.7228,0.7240,0.7254,0.7290,0.7299,0.7311,
0.7336,0.7510,0.7523,0.7523,0.7540,0.7550,0.7555,0.7583,0.7603,0.7610,
0.7620,0.7653,0.7694,0.7738,0.7738,0.7778,0.7787,0.7834,0.7839,0.7924,
0.7924,0.7937,0.7983,0.8023,0.8035,0.8082,0.8119,0.8127,0.8146,0.8160,
0.8229,0.8316,0.8336,0.8354,0.8375,0.8458,0.8504,0.8535,0.8538,0.8591,
0.8606,0.8617,0.8622,0.8663,0.8795,0.8816,0.8847,0.8848,0.8895,0.8910,
0.8933,0.8935,0.9022,0.9036,0.9066,0.9101,0.9114,0.9127,0.9143,0.9161,
0.9191,0.9206,0.9211,0.9243,0.9265,0.9383,0.9387,0.9580,0.9607,0.9672,
0.9731,0.9747,0.9762,0.9765,0.9864,0.9874,0.9877,0.9898,0.9915,
Overall p-value after applying KStest on 269 p-values = 0.655473
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.