RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.60 10.3850 0.113304
2 to 25 15.62 15.2405 0.421837
3 to 26 16.09 12.8522 0.253980
4 to 27 15.93 19.5411 0.701628
5 to 28 15.50 41.4887 0.999205
6 to 29 15.62 13.7007 0.311838
7 to 30 15.70 29.7870 0.972077
8 to 31 15.73 25.4858 0.915648
9 to 32 15.60 38.5138 0.997912
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.016807
Tough bday spacings test for dh-ranFile-2018-06-29_17:31: 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 7 42 74 93 108 81 42 29 16 6 2
(O-E)^2/E 0.5 0.8 0.0 0.2 1.1 0.1 2.0 0.0 0.1 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 5.889, p= 0.175
RESULTS OF GCD FOR dh-ranFile-2018-06-29_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.103793
p-value, dist. of gcd's: 0.663333
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.291 0.769 0.030 0.336 0.401 0.573 0.335 0.145
Bits 8 to 15---> 0.537 0.267 0.331 0.520 0.094 0.859 0.365 0.417
Bits 16 to 23---> 0.763 0.247 0.819 0.318 0.875 0.105 0.393 0.876
Bits 24 to 31---> 0.564 0.093 0.567 0.164 0.120 0.889 0.835 0.550
KS test for the above 32 p values: 0.580
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_17:31,
p-values for 5 runs: 0.8601, 0.7784, 0.3500, 0.3493, 0.6117
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 196 211.4 1.124 1.124
r= 29 5016 5134.0 2.713 3.837
r= 30 23040 23103.0 0.172 4.009
r= 31 11748 11551.5 3.342 7.351
chi-square = 7.351 with df = 3; p-value = 0.938
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 194 211.4 1.435 1.435
r= 30 5121 5134.0 0.033 1.468
r= 31 23064 23103.0 0.066 1.534
r= 32 11621 11551.5 0.418 1.952
chi-square = 1.952 with df = 3; p-value = 0.418
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_17:31
b-rank test for bits 1 to 8, p=0.22832
b-rank test for bits 2 to 9, p=0.02405
b-rank test for bits 3 to 10, p=0.52975
b-rank test for bits 4 to 11, p=0.97956
b-rank test for bits 5 to 12, p=0.49073
b-rank test for bits 6 to 13, p=0.96561
b-rank test for bits 7 to 14, p=0.65101
b-rank test for bits 8 to 15, p=0.93284
b-rank test for bits 9 to 16, p=0.99581
b-rank test for bits 10 to 17, p=0.68832
b-rank test for bits 11 to 18, p=0.67238
b-rank test for bits 12 to 19, p=0.27565
b-rank test for bits 13 to 20, p=0.10420
b-rank test for bits 14 to 21, p=0.76132
b-rank test for bits 15 to 22, p=0.88865
b-rank test for bits 16 to 23, p=0.23360
b-rank test for bits 17 to 24, p=0.67117
b-rank test for bits 18 to 25, p=0.18933
b-rank test for bits 19 to 26, p=0.71175
b-rank test for bits 20 to 27, p=0.42060
b-rank test for bits 21 to 28, p=0.10289
b-rank test for bits 22 to 29, p=0.74038
b-rank test for bits 23 to 30, p=0.80859
b-rank test for bits 24 to 31, p=0.12532
b-rank test for bits 25 to 32, p=0.23353
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 = 0.567321
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_17:31
(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 141843 -0.15 0.438420
2 141326 -1.36 0.086454
3 142109 0.47 0.679578
4 142474 1.32 0.906469
5 141818 -0.21 0.415512
6 142860 2.22 0.986831
7 141785 -0.29 0.385720
8 142247 0.79 0.784929
9 142116 0.48 0.685407
10 141599 -0.73 0.234205
11 141604 -0.71 0.237803
12 142050 0.33 0.628797
13 141332 -1.35 0.088684
14 142460 1.29 0.900885
15 142070 0.38 0.646317
16 141784 -0.29 0.384827
17 142701 1.85 0.967821
18 142524 1.44 0.924519
19 141393 -1.21 0.113836
20 142458 1.28 0.900068
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_17:31
Bits used No. missing words z-score p-value
23 to 32 141803 -0.3667 0.356938
22 to 31 142366 1.5747 0.942340
21 to 30 141685 -0.7736 0.219598
20 to 29 141718 -0.6598 0.254704
19 to 28 142032 0.4230 0.663852
18 to 27 141912 0.0092 0.503673
17 to 26 141278 -2.1770 0.014740
16 to 25 141518 -1.3494 0.088602
15 to 24 141822 -0.3011 0.381655
14 to 23 141886 -0.0804 0.467940
13 to 22 142378 1.6161 0.946964
12 to 21 142100 0.6575 0.744565
11 to 20 141928 0.0644 0.525666
10 to 19 141844 -0.2253 0.410882
9 to 18 141382 -1.8184 0.034503
8 to 17 141856 -0.1839 0.427047
7 to 16 141237 -2.3184 0.010214
6 to 15 141672 -0.8184 0.206570
5 to 14 141811 -0.3391 0.367279
4 to 13 141636 -0.9425 0.172964
3 to 12 141662 -0.8529 0.196868
2 to 11 142085 0.6058 0.727663
1 to 10 142157 0.8540 0.803457
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_17:31
Bits used No. missing words z-score p-value
28 to 32 141868 -0.1401 0.444290
27 to 31 141577 -1.1265 0.129968
26 to 30 141906 -0.0113 0.495497
25 to 29 141512 -1.3469 0.089009
24 to 28 141796 -0.3842 0.350426
23 to 27 142185 0.9345 0.824970
22 to 26 141996 0.2938 0.615543
21 to 25 141621 -0.9774 0.164188
20 to 24 142213 1.0294 0.848352
19 to 23 141755 -0.5232 0.300434
18 to 22 141342 -1.9232 0.027230
17 to 21 142157 0.8396 0.799422
16 to 20 141890 -0.0655 0.473878
15 to 19 142100 0.6463 0.740970
14 to 18 141799 -0.3740 0.354202
13 to 17 141710 -0.6757 0.249617
12 to 16 141974 0.2192 0.586761
11 to 15 141354 -1.8825 0.029886
10 to 14 142264 1.2023 0.885371
9 to 13 141898 -0.0384 0.484682
8 to 12 141905 -0.0147 0.494145
7 to 11 142304 1.3379 0.909530
6 to 10 141742 -0.5672 0.285282
5 to 9 141411 -1.6893 0.045585
4 to 8 141610 -1.0147 0.155130
3 to 7 142211 1.0226 0.846754
2 to 6 141805 -0.3537 0.361797
1 to 5 141718 -0.6486 0.258306
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_17:31
Bits used No. missing words z-score p-value
31 to 32 142357 1.3206 0.906676
30 to 31 141954 0.1318 0.552417
29 to 30 141922 0.0374 0.514907
28 to 29 141933 0.0698 0.527833
27 to 28 141662 -0.7296 0.232821
26 to 27 141744 -0.4877 0.312882
25 to 26 141860 -0.1455 0.442152
24 to 25 142081 0.5064 0.693713
23 to 24 141660 -0.7355 0.231022
22 to 23 142635 2.1406 0.983848
21 to 22 141499 -1.2104 0.113060
20 to 21 141697 -0.6263 0.265545
19 to 20 141547 -1.0688 0.142575
18 to 19 141788 -0.3579 0.360207
17 to 18 141811 -0.2901 0.385886
16 to 17 141614 -0.8712 0.191828
15 to 16 141948 0.1141 0.545409
14 to 15 142531 1.8338 0.966661
13 to 14 141617 -0.8623 0.194253
12 to 13 141756 -0.4523 0.325526
11 to 12 142142 0.6863 0.753751
10 to 11 141898 -0.0334 0.486669
9 to 10 142181 0.8014 0.788546
8 to 9 142127 0.6421 0.739594
7 to 8 142083 0.5123 0.695780
6 to 7 141771 -0.4081 0.341617
5 to 6 142031 0.3589 0.640168
4 to 5 142205 0.8722 0.808446
3 to 4 141914 0.0138 0.505496
2 to 3 142524 1.8132 0.965098
1 to 2 141849 -0.1780 0.429375
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2369.87 -1.840 0.032861
Test results for specific bytes for dh-ranFile-2018-06-29_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2502.35 0.033 0.513266
2 to 9 2584.68 1.198 0.884468
3 to 10 2617.90 1.667 0.952283
4 to 11 2371.83 -1.813 0.034946
5 to 12 2661.66 2.286 0.988877
6 to 13 2629.78 1.835 0.966779
7 to 14 2577.94 1.102 0.864806
8 to 15 2510.69 0.151 0.560110
9 to 16 2531.46 0.445 0.671798
10 to 17 2368.72 -1.857 0.031682
11 to 18 2339.63 -2.268 0.011666
12 to 19 2596.81 1.369 0.914507
13 to 20 2513.80 0.195 0.577390
14 to 21 2680.14 2.548 0.994577
15 to 22 2411.96 -1.245 0.106556
16 to 23 2492.29 -0.109 0.456578
17 to 24 2537.83 0.535 0.703660
18 to 25 2605.30 1.489 0.931780
19 to 26 2516.78 0.237 0.593790
20 to 27 2557.54 0.814 0.792087
21 to 28 2420.76 -1.121 0.131229
22 to 29 2415.21 -1.199 0.115233
23 to 30 2588.61 1.253 0.894921
24 to 31 2553.17 0.752 0.773961
25 to 32 2550.79 0.718 0.763694
CDPARK for dh-ranFile-2018-06-29_17:31: 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
3487 -1.6438 0.050105
3550 1.2329 0.891189
3516 -0.3196 0.374623
3568 2.0548 0.980051
3570 2.1461 0.984068
3525 0.0913 0.536383
3540 0.7763 0.781201
3567 2.0091 0.977738
3508 -0.6849 0.246694
3534 0.5023 0.692266
Square side=100, avg. no. parked=3536.50 sample std.=26.57
p-value of the KSTEST for those 10 p-values: 0.050319
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_17:31
0.4058,0.7607,0.0715,0.2041,0.3606,0.0707,0.0252,0.9440,0.2688,0.6167,
The KS test for those 10 p-values: 0.245594
The 3DSPHERES test for dh-ranFile-2018-06-29_17:31
sample no r^3 equiv. uni.
1 20.447 0.494168
2 24.220 0.553961
3 123.431 0.983664
4 27.588 0.601325
5 31.605 0.651286
6 4.527 0.140055
7 33.006 0.667195
8 11.264 0.313027
9 11.058 0.308289
10 13.626 0.365034
11 11.363 0.315286
12 106.980 0.971732
13 66.075 0.889474
14 10.473 0.294668
15 117.500 0.980093
16 60.325 0.866123
17 16.880 0.430304
18 14.940 0.392264
19 63.468 0.879438
20 15.211 0.397730
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.192326
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.1 0.1 -2.2 0.5 0.1
-1.0 -0.5 -0.4 -1.0 -0.2 1.1
0.1 0.1 0.8 0.1 0.8 -1.1
-0.0 -1.0 0.7 -0.5 0.2 0.0
0.5 1.2 -1.6 0.7 -0.2 0.1
0.3 0.4 -1.2 -0.4 -0.5 1.0
0.5 -0.4 -1.6 -0.7 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:27.728219
z-score=-1.557179, p-value=0.044135
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_17:31
Test no p-value
1 0.019028
2 0.517305
3 0.406258
4 0.025594
5 0.543587
6 0.185685
7 0.521455
8 0.081711
9 0.139459
10 0.867416
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.072600
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_17:31:
(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 66678 0.00 66707 0.02
3 25000.00 25116 0.54 24894 0.45
4 6666.67 6544 2.26 6703 0.20
5 1388.89 1373 0.18 1412 0.38
6 238.10 249 0.50 243 0.10
7 34.72 31 0.40 39 0.53
8 4.96 8 1.86 1 3.16
p=0.54711 p=0.43637
Number of rngs required: 688287, p-value: 0.447
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_17:31
No. of wins: Observed Expected
98610 98585.9
z-score= 0.108, pvalue=0.54299
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66579 66666.7 0.115 0.115
2 37725 37654.3 0.133 0.248
3 26976 26954.7 0.017 0.265
4 19468 19313.5 1.237 1.501
5 13816 13851.4 0.091 1.592
6 9713 9943.5 5.345 6.937
7 7100 7145.0 0.284 7.221
8 5263 5139.1 2.988 10.209
9 3736 3699.9 0.353 10.562
10 2695 2666.3 0.309 10.871
11 1921 1923.3 0.003 10.874
12 1379 1388.7 0.068 10.942
13 982 1003.7 0.470 11.412
14 742 726.1 0.346 11.758
15 548 525.8 0.934 12.693
16 340 381.2 4.443 17.136
17 227 276.5 8.875 26.010
18 214 200.8 0.864 26.874
19 176 146.0 6.171 33.045
20 131 106.2 5.783 38.829
21 269 287.1 1.143 39.971
Chisq= 39.97 for 20 degrees of freedom, p= 0.99496
SUMMARY of craptest
p-value for no. of wins: 0.542992
p-value for throws/game: 0.994963
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_17:31
No. of wins: Observed Expected
98966 98585.9
z-score= 1.700, pvalue=0.95545
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66953 66666.7 1.230 1.230
2 37791 37654.3 0.496 1.726
3 26769 26954.7 1.280 3.006
4 19220 19313.5 0.452 3.458
5 13797 13851.4 0.214 3.672
6 9938 9943.5 0.003 3.675
7 7121 7145.0 0.081 3.756
8 5125 5139.1 0.039 3.794
9 3678 3699.9 0.129 3.923
10 2621 2666.3 0.770 4.693
11 1888 1923.3 0.649 5.342
12 1364 1388.7 0.441 5.783
13 1032 1003.7 0.797 6.580
14 727 726.1 0.001 6.581
15 517 525.8 0.148 6.729
16 385 381.2 0.039 6.768
17 277 276.5 0.001 6.769
18 219 200.8 1.644 8.413
19 145 146.0 0.007 8.419
20 120 106.2 1.789 10.208
21 313 287.1 2.334 12.542
Chisq= 12.54 for 20 degrees of freedom, p= 0.10385
SUMMARY of craptest
p-value for no. of wins: 0.955455
p-value for throws/game: 0.103854
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0102,0.0117,0.0147,0.0168,0.0190,0.0240,0.0252,0.0256,0.0272,0.0297,
0.0299,0.0317,0.0329,0.0345,0.0349,0.0441,0.0456,0.0501,0.0503,0.0707,
0.0715,0.0726,0.0817,0.0865,0.0886,0.0887,0.0890,0.0930,0.0941,0.1029,
0.1038,0.1039,0.1042,0.1052,0.1066,0.1131,0.1133,0.1138,0.1152,0.1204,
0.1253,0.1300,0.1312,0.1395,0.1401,0.1426,0.1450,0.1551,0.1639,0.1642,
0.1730,0.1755,0.1857,0.1893,0.1918,0.1923,0.1943,0.1969,0.2041,0.2066,
0.2196,0.2283,0.2310,0.2328,0.2335,0.2336,0.2342,0.2378,0.2456,0.2467,
0.2469,0.2496,0.2540,0.2547,0.2583,0.2655,0.2666,0.2688,0.2756,0.2853,
0.2913,0.2947,0.3004,0.3083,0.3118,0.3129,0.3130,0.3153,0.3182,0.3255,
0.3314,0.3353,0.3358,0.3416,0.3493,0.3500,0.3504,0.3542,0.3569,0.3602,
0.3606,0.3618,0.3648,0.3650,0.3673,0.3746,0.3817,0.3848,0.3857,0.3859,
0.3923,0.3934,0.3977,0.4007,0.4058,0.4063,0.4109,0.4155,0.4168,0.4175,
0.4206,0.4218,0.4270,0.4294,0.4303,0.4364,0.4384,0.4422,0.4443,0.4469,
0.4566,0.4679,0.4739,0.4847,0.4867,0.4907,0.4941,0.4942,0.4955,0.5037,
0.5055,0.5133,0.5149,0.5173,0.5199,0.5215,0.5257,0.5278,0.5297,0.5364,
0.5374,0.5430,0.5436,0.5454,0.5471,0.5504,0.5524,0.5540,0.5601,0.5642,
0.5671,0.5673,0.5727,0.5774,0.5797,0.5868,0.5938,0.6013,0.6117,0.6155,
0.6167,0.6288,0.6402,0.6463,0.6510,0.6513,0.6633,0.6639,0.6672,0.6712,
0.6718,0.6724,0.6796,0.6854,0.6883,0.6923,0.6937,0.6958,0.7016,0.7037,
0.7118,0.7277,0.7396,0.7404,0.7410,0.7446,0.7538,0.7607,0.7613,0.7629,
0.7637,0.7688,0.7740,0.7784,0.7812,0.7849,0.7885,0.7921,0.7994,0.8035,
0.8084,0.8086,0.8185,0.8250,0.8354,0.8468,0.8484,0.8595,0.8601,0.8648,
0.8661,0.8674,0.8755,0.8758,0.8794,0.8845,0.8854,0.8887,0.8889,0.8895,
0.8912,0.8949,0.9001,0.9009,0.9065,0.9067,0.9095,0.9145,0.9156,0.9245,
0.9318,0.9328,0.9385,0.9423,0.9440,0.9470,0.9523,0.9555,0.9651,0.9656,
0.9667,0.9668,0.9678,0.9717,0.9721,0.9777,0.9796,0.9801,0.9801,0.9837,
0.9838,0.9841,0.9868,0.9889,0.9946,0.9950,0.9958,0.9979,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.223026
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.