RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.59 22.2413 0.824384
2 to 25 15.60 15.2618 0.423371
3 to 26 15.94 11.9136 0.194661
4 to 27 15.92 13.6852 0.310753
5 to 28 15.75 25.5743 0.917426
6 to 29 15.91 13.4602 0.295127
7 to 30 16.00 24.7113 0.898640
8 to 31 15.75 16.2400 0.493108
9 to 32 15.78 19.0376 0.673622
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.772046
Tough bday spacings test for dh-ranFile-2018-06-20_14:31: 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 35 64 101 84 80 64 36 19 7 4
(O-E)^2/E 1.1 0.1 1.2 0.1 1.9 0.0 2.7 1.3 1.1 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 9.590, p= 0.523
RESULTS OF GCD FOR dh-ranFile-2018-06-20_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.934069
p-value, dist. of gcd's: 0.284449
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.542 0.467 0.653 0.330 0.839 0.050 0.117 0.800
Bits 8 to 15---> 0.834 0.843 0.827 0.203 0.667 0.925 0.760 0.939
Bits 16 to 23---> 0.047 0.409 0.407 0.202 0.716 0.656 0.405 0.111
Bits 24 to 31---> 0.297 0.741 0.497 0.145 0.769 0.817 0.641 0.387
KS test for the above 32 p values: 0.355
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_14:31,
p-values for 5 runs: 0.7811, 0.7535, 0.7586, 0.6138, 0.5361
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 5091 5134.0 0.360 0.780
r= 30 23129 23103.0 0.029 0.809
r= 31 11578 11551.5 0.061 0.870
chi-square = 0.870 with df = 3; p-value = 0.167
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5242 5134.0 2.271 2.419
r= 31 22908 23103.0 1.647 4.066
r= 32 11633 11551.5 0.575 4.640
chi-square = 4.640 with df = 3; p-value = 0.800
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_14:31
b-rank test for bits 1 to 8, p=0.18043
b-rank test for bits 2 to 9, p=0.55165
b-rank test for bits 3 to 10, p=0.27557
b-rank test for bits 4 to 11, p=0.68480
b-rank test for bits 5 to 12, p=0.12673
b-rank test for bits 6 to 13, p=0.46501
b-rank test for bits 7 to 14, p=0.86661
b-rank test for bits 8 to 15, p=0.04802
b-rank test for bits 9 to 16, p=0.39612
b-rank test for bits 10 to 17, p=0.96342
b-rank test for bits 11 to 18, p=0.72920
b-rank test for bits 12 to 19, p=0.23087
b-rank test for bits 13 to 20, p=0.32474
b-rank test for bits 14 to 21, p=0.74270
b-rank test for bits 15 to 22, p=0.70839
b-rank test for bits 16 to 23, p=0.26724
b-rank test for bits 17 to 24, p=0.11215
b-rank test for bits 18 to 25, p=0.87252
b-rank test for bits 19 to 26, p=0.99765
b-rank test for bits 20 to 27, p=0.81494
b-rank test for bits 21 to 28, p=0.72500
b-rank test for bits 22 to 29, p=0.75386
b-rank test for bits 23 to 30, p=0.67633
b-rank test for bits 24 to 31, p=0.02862
b-rank test for bits 25 to 32, p=0.34694
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 = 0.911351
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_14:31
(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 141693 -0.51 0.306624
2 141905 -0.01 0.495964
3 142089 0.42 0.662681
4 141713 -0.46 0.323219
5 141822 -0.20 0.419160
6 140807 -2.58 0.005004
7 141460 -1.05 0.146897
8 142395 1.13 0.871759
9 141500 -0.96 0.169441
10 141939 0.07 0.527634
11 142100 0.45 0.672017
12 141451 -1.07 0.142115
13 142125 0.50 0.692835
14 141694 -0.50 0.307444
15 141994 0.20 0.578410
16 142343 1.01 0.844529
17 141836 -0.17 0.431981
18 142366 1.07 0.857011
19 141757 -0.36 0.360954
20 141411 -1.16 0.122147
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_14:31
Bits used No. missing words z-score p-value
23 to 32 142132 0.7678 0.778705
22 to 31 142269 1.2402 0.892557
21 to 30 141809 -0.3460 0.364684
20 to 29 141640 -0.9287 0.176516
19 to 28 141808 -0.3494 0.363389
18 to 27 141684 -0.7770 0.218579
17 to 26 142064 0.5333 0.703103
16 to 25 141860 -0.1701 0.432464
15 to 24 141541 -1.2701 0.102024
14 to 23 141593 -1.0908 0.137682
13 to 22 141969 0.2058 0.581510
12 to 21 142069 0.5506 0.709041
11 to 20 142082 0.5954 0.724217
10 to 19 141899 -0.0356 0.485792
9 to 18 142304 1.3609 0.913232
8 to 17 141567 -1.1804 0.118911
7 to 16 141498 -1.4184 0.078040
6 to 15 141827 -0.2839 0.388245
5 to 14 141854 -0.1908 0.424344
4 to 13 141733 -0.6080 0.271582
3 to 12 141661 -0.8563 0.195913
2 to 11 141890 -0.0667 0.473428
1 to 10 141631 -0.9598 0.168588
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_14:31
Bits used No. missing words z-score p-value
28 to 32 142025 0.3921 0.652509
27 to 31 142093 0.6226 0.733230
26 to 30 142560 2.2057 0.986296
25 to 29 141809 -0.3401 0.366890
24 to 28 142385 1.6124 0.946567
23 to 27 142038 0.4362 0.668643
22 to 26 141988 0.2667 0.605141
21 to 25 141719 -0.6452 0.259403
20 to 24 142298 1.3175 0.906169
19 to 23 142160 0.8497 0.802262
18 to 22 142166 0.8701 0.807868
17 to 21 142393 1.6396 0.949452
16 to 20 141843 -0.2248 0.411049
15 to 19 142078 0.5718 0.716259
14 to 18 141835 -0.2520 0.400534
13 to 17 141866 -0.1469 0.441613
12 to 16 141717 -0.6520 0.257212
11 to 15 142177 0.9074 0.817891
10 to 14 142192 0.9582 0.831020
9 to 13 142179 0.9141 0.819677
8 to 12 141488 -1.4282 0.076612
7 to 11 142439 1.7955 0.963712
6 to 10 141357 -1.8723 0.030582
5 to 9 141925 0.0531 0.521181
4 to 8 141807 -0.3469 0.364340
3 to 7 141386 -1.7740 0.038032
2 to 6 141730 -0.6079 0.271628
1 to 5 141938 0.0972 0.538711
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_14:31
Bits used No. missing words z-score p-value
31 to 32 141692 -0.6411 0.260732
30 to 31 141900 -0.0275 0.489022
29 to 30 142407 1.4681 0.928955
28 to 29 141674 -0.6942 0.243782
27 to 28 142468 1.6480 0.950323
26 to 27 142098 0.5565 0.711082
25 to 26 141606 -0.8948 0.185453
24 to 25 141265 -1.9007 0.028672
23 to 24 142154 0.7217 0.764773
22 to 23 141937 0.0816 0.532527
21 to 22 141189 -2.1249 0.016799
20 to 21 141944 0.1023 0.540729
19 to 20 141572 -0.9951 0.159850
18 to 19 141981 0.2114 0.583719
17 to 18 141929 0.0580 0.523135
16 to 17 141834 -0.2222 0.412074
15 to 16 141896 -0.0393 0.484317
14 to 15 142200 0.8574 0.804397
13 to 14 141523 -1.1396 0.127223
12 to 13 141941 0.0934 0.537216
11 to 12 142340 1.2704 0.898031
10 to 11 141974 0.1908 0.575646
9 to 10 142016 0.3147 0.623490
8 to 9 142111 0.5949 0.724044
7 to 8 142237 0.9666 0.833123
6 to 7 141794 -0.3402 0.366851
5 to 6 142046 0.4032 0.656583
4 to 5 141292 -1.8210 0.034301
3 to 4 141784 -0.3697 0.355801
2 to 3 142397 1.4386 0.924862
1 to 2 141807 -0.3019 0.381380
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2536.67 0.519 0.697960
Test results for specific bytes for dh-ranFile-2018-06-20_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2544.88 0.635 0.737180
2 to 9 2336.14 -2.317 0.010242
3 to 10 2486.73 -0.188 0.425542
4 to 11 2485.65 -0.203 0.419567
5 to 12 2445.95 -0.764 0.222319
6 to 13 2470.44 -0.418 0.337957
7 to 14 2434.30 -0.929 0.176409
8 to 15 2592.80 1.312 0.905303
9 to 16 2401.42 -1.394 0.081647
10 to 17 2576.17 1.077 0.859294
11 to 18 2464.63 -0.500 0.308480
12 to 19 2570.65 0.999 0.841146
13 to 20 2454.24 -0.647 0.258771
14 to 21 2550.44 0.713 0.762190
15 to 22 2564.49 0.912 0.819130
16 to 23 2575.82 1.072 0.858192
17 to 24 2466.40 -0.475 0.317308
18 to 25 2497.96 -0.029 0.488514
19 to 26 2476.01 -0.339 0.367195
20 to 27 2534.70 0.491 0.688212
21 to 28 2475.56 -0.346 0.364823
22 to 29 2465.94 -0.482 0.315003
23 to 30 2503.17 0.045 0.517864
24 to 31 2361.59 -1.957 0.025149
25 to 32 2472.23 -0.393 0.347276
CDPARK for dh-ranFile-2018-06-20_14:31: 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
3517 -0.2740 0.392053
3518 -0.2283 0.409702
3513 -0.4566 0.323972
3539 0.7306 0.767486
3503 -0.9132 0.180558
3518 -0.2283 0.409702
3538 0.6849 0.753306
3508 -0.6849 0.246694
3503 -0.9132 0.180558
3524 0.0457 0.518210
Square side=100, avg. no. parked=3518.10 sample std.=12.05
p-value of the KSTEST for those 10 p-values: 0.308404
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_14:31
0.1407,0.2422,0.1920,0.5586,0.9068,0.6305,0.8561,0.6218,0.0310,0.3520,
The KS test for those 10 p-values: 0.936833
The 3DSPHERES test for dh-ranFile-2018-06-20_14:31
sample no r^3 equiv. uni.
1 8.514 0.247086
2 11.946 0.328472
3 61.235 0.870122
4 26.768 0.590278
5 5.810 0.176071
6 16.079 0.414903
7 22.948 0.534628
8 16.078 0.414877
9 7.415 0.218997
10 20.814 0.500320
11 3.195 0.101022
12 16.961 0.431843
13 41.800 0.751755
14 25.834 0.577321
15 107.305 0.972035
16 2.135 0.068688
17 13.817 0.369068
18 9.153 0.262951
19 77.048 0.923331
20 16.829 0.429346
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.573362
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.8 -0.4 -1.4 0.5 -1.3
-0.1 0.7 -0.5 0.2 0.0 -0.3
0.2 0.3 -0.2 -1.0 -0.1 -0.0
1.9 1.5 -1.2 -0.7 -0.7 0.0
0.2 0.2 -0.2 0.2 -0.6 0.8
-0.1 -0.5 -0.1 -1.4 -0.5 1.0
-0.2 0.2 0.9 -0.1 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:25.503517
z-score=-1.799914, p-value=0.020914
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_14:31
Test no p-value
1 0.404747
2 0.055811
3 0.056117
4 0.126793
5 0.192791
6 0.160700
7 0.611907
8 0.523522
9 0.026735
10 0.050898
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001759
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_14:31:
(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 66727 0.05 66718 0.04
3 25000.00 24917 0.28 24955 0.08
4 6666.67 6640 0.11 6617 0.37
5 1388.89 1409 0.29 1437 1.67
6 238.10 257 1.50 235 0.04
7 34.72 41 1.14 34 0.01
8 4.96 8 1.86 3 0.77
p=0.48510 p=0.18949
Number of rngs required: 687636, p-value: 0.187
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_14:31
No. of wins: Observed Expected
98416 98585.9
z-score=-0.760, pvalue=0.22371
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66279 66666.7 2.254 2.254
2 38065 37654.3 4.479 6.733
3 26929 26954.7 0.025 6.758
4 19252 19313.5 0.196 6.954
5 13839 13851.4 0.011 6.965
6 10022 9943.5 0.619 7.584
7 7278 7145.0 2.475 10.058
8 5191 5139.1 0.525 10.583
9 3678 3699.9 0.129 10.712
10 2647 2666.3 0.140 10.852
11 1899 1923.3 0.308 11.160
12 1358 1388.7 0.680 11.840
13 972 1003.7 1.002 12.842
14 673 726.1 3.889 16.731
15 528 525.8 0.009 16.740
16 362 381.2 0.962 17.702
17 262 276.5 0.764 18.467
18 232 200.8 4.838 23.305
19 158 146.0 0.989 24.294
20 88 106.2 3.124 27.417
21 288 287.1 0.003 27.420
Chisq= 27.42 for 20 degrees of freedom, p= 0.87615
SUMMARY of craptest
p-value for no. of wins: 0.223715
p-value for throws/game: 0.876149
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_14:31
No. of wins: Observed Expected
98602 98585.9
z-score= 0.072, pvalue=0.52878
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66489 66666.7 0.473 0.473
2 37892 37654.3 1.500 1.974
3 26789 26954.7 1.019 2.993
4 19332 19313.5 0.018 3.011
5 13736 13851.4 0.962 3.972
6 10021 9943.5 0.603 4.576
7 7024 7145.0 2.050 6.626
8 5195 5139.1 0.609 7.234
9 3767 3699.9 1.218 8.453
10 2742 2666.3 2.149 10.602
11 1913 1923.3 0.055 10.657
12 1408 1388.7 0.267 10.924
13 1008 1003.7 0.018 10.943
14 731 726.1 0.033 10.975
15 530 525.8 0.033 11.008
16 395 381.2 0.503 11.511
17 281 276.5 0.072 11.583
18 199 200.8 0.017 11.600
19 137 146.0 0.553 12.153
20 120 106.2 1.789 13.942
21 291 287.1 0.053 13.995
Chisq= 13.99 for 20 degrees of freedom, p= 0.16923
SUMMARY of craptest
p-value for no. of wins: 0.528776
p-value for throws/game: 0.169232
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0050,0.0102,0.0168,0.0209,0.0251,0.0267,0.0286,0.0287,0.0306,
0.0310,0.0343,0.0380,0.0472,0.0480,0.0499,0.0509,0.0558,0.0561,0.0687,
0.0766,0.0780,0.0816,0.1010,0.1020,0.1106,0.1121,0.1167,0.1189,0.1221,
0.1267,0.1268,0.1272,0.1377,0.1407,0.1421,0.1454,0.1469,0.1599,0.1607,
0.1673,0.1686,0.1692,0.1694,0.1761,0.1764,0.1765,0.1804,0.1806,0.1806,
0.1855,0.1874,0.1895,0.1920,0.1928,0.1947,0.1959,0.2022,0.2028,0.2186,
0.2190,0.2223,0.2237,0.2309,0.2422,0.2438,0.2467,0.2471,0.2572,0.2588,
0.2594,0.2607,0.2630,0.2672,0.2716,0.2716,0.2756,0.2844,0.2951,0.2974,
0.3066,0.3074,0.3084,0.3085,0.3108,0.3150,0.3173,0.3232,0.3240,0.3247,
0.3285,0.3296,0.3380,0.3469,0.3473,0.3520,0.3552,0.3558,0.3610,0.3634,
0.3643,0.3647,0.3648,0.3669,0.3669,0.3672,0.3691,0.3814,0.3869,0.3882,
0.3921,0.3961,0.4005,0.4046,0.4047,0.4066,0.4091,0.4097,0.4097,0.4110,
0.4121,0.4149,0.4149,0.4192,0.4196,0.4234,0.4243,0.4255,0.4293,0.4318,
0.4320,0.4325,0.4416,0.4650,0.4665,0.4734,0.4843,0.4851,0.4858,0.4885,
0.4890,0.4931,0.4960,0.4973,0.5003,0.5179,0.5182,0.5212,0.5228,0.5231,
0.5235,0.5276,0.5288,0.5325,0.5346,0.5361,0.5372,0.5387,0.5407,0.5423,
0.5517,0.5586,0.5734,0.5756,0.5773,0.5784,0.5815,0.5837,0.5903,0.6051,
0.6119,0.6138,0.6218,0.6235,0.6305,0.6414,0.6525,0.6532,0.6561,0.6566,
0.6627,0.6673,0.6686,0.6720,0.6736,0.6763,0.6848,0.6882,0.6928,0.6980,
0.7031,0.7084,0.7090,0.7111,0.7157,0.7163,0.7240,0.7242,0.7250,0.7292,
0.7332,0.7372,0.7411,0.7427,0.7518,0.7533,0.7535,0.7539,0.7586,0.7597,
0.7622,0.7648,0.7675,0.7689,0.7720,0.7787,0.7811,0.7999,0.8005,0.8023,
0.8044,0.8079,0.8149,0.8174,0.8179,0.8191,0.8197,0.8244,0.8269,0.8310,
0.8331,0.8343,0.8390,0.8411,0.8433,0.8445,0.8561,0.8570,0.8582,0.8593,
0.8666,0.8701,0.8718,0.8725,0.8761,0.8926,0.8980,0.8986,0.9053,0.9062,
0.9068,0.9114,0.9132,0.9174,0.9233,0.9249,0.9254,0.9290,0.9341,0.9368,
0.9386,0.9466,0.9495,0.9503,0.9634,0.9637,0.9720,0.9863,0.9976,
Overall p-value after applying KStest on 269 p-values = 0.444971
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.