RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.67 19.8436 0.717691
2 to 25 15.96 14.5342 0.371005
3 to 26 15.84 19.3236 0.689720
4 to 27 15.62 27.4869 0.948698
5 to 28 15.74 18.5433 0.644634
6 to 29 15.59 23.9818 0.880071
7 to 30 15.86 11.2586 0.157193
8 to 31 15.86 11.1735 0.152594
9 to 32 15.98 15.7122 0.455682
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.880032
Tough bday spacings test for dh-ranFile-2018-06-19_00:31: 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 8 32 68 90 112 83 43 25 19 13 7
(O-E)^2/E 0.1 0.6 0.4 0.6 2.1 0.3 1.6 0.8 1.1 6.2 2.1
Birthday Spacings: Sum(O-E)^2/E= 15.883, p= 0.897
RESULTS OF GCD FOR dh-ranFile-2018-06-19_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.633737
p-value, dist. of gcd's: 0.748358
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.458 0.934 0.759 0.280 0.714 0.204 0.297 0.281
Bits 8 to 15---> 0.319 0.138 0.313 0.143 0.266 0.723 0.795 0.621
Bits 16 to 23---> 0.993 0.838 0.736 0.560 0.407 0.922 0.344 0.920
Bits 24 to 31---> 0.629 0.467 0.656 0.474 0.763 0.213 0.090 0.077
KS test for the above 32 p values: 0.095
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_00:31,
p-values for 5 runs: 0.9952, 0.0217, 0.1291, 0.5300, 0.1213
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5225 5134.0 1.613 1.640
r= 30 23140 23103.0 0.059 1.699
r= 31 11426 11551.5 1.364 3.063
chi-square = 3.063 with df = 3; p-value = 0.618
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 202 211.4 0.420 0.420
r= 30 5214 5134.0 1.246 1.666
r= 31 22970 23103.0 0.766 2.432
r= 32 11614 11551.5 0.338 2.770
chi-square = 2.770 with df = 3; p-value = 0.572
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_00:31
b-rank test for bits 1 to 8, p=0.05587
b-rank test for bits 2 to 9, p=0.55012
b-rank test for bits 3 to 10, p=0.26186
b-rank test for bits 4 to 11, p=0.42854
b-rank test for bits 5 to 12, p=0.64061
b-rank test for bits 6 to 13, p=0.27486
b-rank test for bits 7 to 14, p=0.65257
b-rank test for bits 8 to 15, p=0.80764
b-rank test for bits 9 to 16, p=0.41575
b-rank test for bits 10 to 17, p=0.68992
b-rank test for bits 11 to 18, p=0.76268
b-rank test for bits 12 to 19, p=0.50575
b-rank test for bits 13 to 20, p=0.74262
b-rank test for bits 14 to 21, p=0.68241
b-rank test for bits 15 to 22, p=0.05561
b-rank test for bits 16 to 23, p=0.16419
b-rank test for bits 17 to 24, p=0.39610
b-rank test for bits 18 to 25, p=0.01601
b-rank test for bits 19 to 26, p=0.30575
b-rank test for bits 20 to 27, p=0.79700
b-rank test for bits 21 to 28, p=0.94390
b-rank test for bits 22 to 29, p=0.28490
b-rank test for bits 23 to 30, p=0.37139
b-rank test for bits 24 to 31, p=0.03516
b-rank test for bits 25 to 32, p=0.10062
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 = 0.436412
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_00:31
(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 141832 -0.18 0.428310
2 141779 -0.30 0.380370
3 142773 2.02 0.978200
4 142237 0.77 0.778038
5 142180 0.63 0.736439
6 142520 1.43 0.923181
7 142343 1.01 0.844529
8 142550 1.50 0.932789
9 142081 0.40 0.655826
10 141908 -0.00 0.498760
11 141688 -0.52 0.302534
12 142143 0.55 0.707453
13 141712 -0.46 0.322381
14 142231 0.75 0.773844
15 141823 -0.20 0.420073
16 142122 0.50 0.690368
17 142450 1.26 0.896750
18 142010 0.24 0.592977
19 141949 0.09 0.536924
20 141884 -0.06 0.476404
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_00:31
Bits used No. missing words z-score p-value
23 to 32 142023 0.3920 0.652458
22 to 31 141974 0.2230 0.588232
21 to 30 141835 -0.2563 0.398856
20 to 29 142529 2.1368 0.983693
19 to 28 142083 0.5989 0.725368
18 to 27 141646 -0.9080 0.181930
17 to 26 141804 -0.3632 0.358225
16 to 25 141572 -1.1632 0.122373
15 to 24 142094 0.6368 0.737870
14 to 23 142322 1.4230 0.922632
13 to 22 142569 2.2747 0.988539
12 to 21 142010 0.3471 0.635756
11 to 20 142211 1.0402 0.850886
10 to 19 142339 1.4816 0.930779
9 to 18 142462 1.9058 0.971659
8 to 17 142229 1.1023 0.864837
7 to 16 141945 0.1230 0.548947
6 to 15 141619 -1.0011 0.158380
5 to 14 142315 1.3989 0.919073
4 to 13 141826 -0.2873 0.386924
3 to 12 142041 0.4540 0.675098
2 to 11 142102 0.6644 0.746776
1 to 10 141684 -0.7770 0.218579
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_00:31
Bits used No. missing words z-score p-value
28 to 32 142015 0.3582 0.639905
27 to 31 141883 -0.0893 0.464440
26 to 30 142230 1.0870 0.861485
25 to 29 141786 -0.4181 0.337949
24 to 28 141839 -0.2384 0.405783
23 to 27 141969 0.2023 0.580148
22 to 26 141844 -0.2215 0.412368
21 to 25 141849 -0.2045 0.418978
20 to 24 141994 0.2870 0.612950
19 to 23 142209 1.0158 0.845145
18 to 22 142093 0.6226 0.733230
17 to 21 141716 -0.6554 0.256119
16 to 20 141800 -0.3706 0.355464
15 to 19 142525 2.0870 0.981557
14 to 18 141737 -0.5842 0.279553
13 to 17 141751 -0.5367 0.295733
12 to 16 142102 0.6531 0.743160
11 to 15 142272 1.2294 0.890537
10 to 14 141723 -0.6316 0.263815
9 to 13 142019 0.3718 0.644965
8 to 12 141591 -1.0791 0.140275
7 to 11 142232 1.0938 0.862978
6 to 10 141802 -0.3638 0.357992
5 to 9 142149 0.8124 0.791731
4 to 8 141498 -1.3943 0.081608
3 to 7 141991 0.2768 0.609051
2 to 6 141971 0.2091 0.582796
1 to 5 142354 1.5074 0.934140
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_00:31
Bits used No. missing words z-score p-value
31 to 32 141856 -0.1573 0.437498
30 to 31 141905 -0.0128 0.494905
29 to 30 141372 -1.5850 0.056478
28 to 29 142115 0.6067 0.727974
27 to 28 142491 1.7158 0.956904
26 to 27 141865 -0.1308 0.447980
25 to 26 141406 -1.4847 0.068805
24 to 25 142107 0.5831 0.720086
23 to 24 141446 -1.3668 0.085851
22 to 23 142052 0.4209 0.663070
21 to 22 142225 0.9312 0.824120
20 to 21 142296 1.1406 0.872986
19 to 20 141473 -1.2871 0.099028
18 to 19 142324 1.2232 0.889376
17 to 18 141820 -0.2635 0.396079
16 to 17 142424 1.5182 0.935518
15 to 16 142297 1.1436 0.873599
14 to 15 141652 -0.7591 0.223901
13 to 14 141388 -1.5378 0.062043
12 to 13 141890 -0.0570 0.477264
11 to 12 141785 -0.3668 0.356901
10 to 11 142299 1.1495 0.874819
9 to 10 141478 -1.2724 0.101623
8 to 9 141865 -0.1308 0.447980
7 to 8 141412 -1.4671 0.071181
6 to 7 142076 0.4917 0.688517
5 to 6 141499 -1.2104 0.113060
4 to 5 142428 1.5300 0.936992
3 to 4 142549 1.8869 0.970415
2 to 3 141675 -0.6912 0.244708
1 to 2 142274 1.0757 0.858974
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2531.42 0.444 0.671625
Test results for specific bytes for dh-ranFile-2018-06-19_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2436.06 -0.904 0.182919
2 to 9 2389.19 -1.567 0.058549
3 to 10 2430.51 -0.983 0.162882
4 to 11 2411.15 -1.256 0.104473
5 to 12 2594.86 1.342 0.910124
6 to 13 2432.29 -0.958 0.169127
7 to 14 2502.32 0.033 0.513099
8 to 15 2517.49 0.247 0.597687
9 to 16 2560.20 0.851 0.802727
10 to 17 2594.84 1.341 0.910073
11 to 18 2524.67 0.349 0.636438
12 to 19 2418.66 -1.150 0.125020
13 to 20 2499.58 -0.006 0.497606
14 to 21 2384.40 -1.635 0.051045
15 to 22 2612.38 1.589 0.943997
16 to 23 2501.32 0.019 0.507473
17 to 24 2481.58 -0.260 0.397253
18 to 25 2591.25 1.290 0.901556
19 to 26 2462.50 -0.530 0.297946
20 to 27 2557.09 0.807 0.790257
21 to 28 2527.71 0.392 0.652409
22 to 29 2518.16 0.257 0.601349
23 to 30 2456.45 -0.616 0.268986
24 to 31 2484.24 -0.223 0.411798
25 to 32 2446.89 -0.751 0.226280
CDPARK for dh-ranFile-2018-06-19_00:31: 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
3512 -0.5023 0.307734
3512 -0.5023 0.307734
3514 -0.4110 0.340551
3537 0.6393 0.738676
3517 -0.2740 0.392053
3539 0.7306 0.767486
3530 0.3196 0.625377
3533 0.4566 0.676028
3481 -1.9178 0.027568
3486 -1.6895 0.045562
Square side=100, avg. no. parked=3516.10 sample std.=19.02
p-value of the KSTEST for those 10 p-values: 0.494105
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_00:31
0.7503,0.7141,0.7940,0.8571,0.2579,0.8090,0.9228,0.6857,0.9012,0.0943,
The KS test for those 10 p-values: 0.049247
The 3DSPHERES test for dh-ranFile-2018-06-19_00:31
sample no r^3 equiv. uni.
1 38.946 0.726978
2 0.368 0.012184
3 60.266 0.865861
4 18.749 0.464720
5 66.111 0.889604
6 35.946 0.698262
7 95.065 0.957948
8 34.096 0.679070
9 74.007 0.915152
10 7.983 0.233636
11 24.058 0.551538
12 93.223 0.955285
13 43.080 0.762124
14 34.349 0.681769
15 20.791 0.499944
16 11.759 0.324270
17 1.628 0.052828
18 89.033 0.948582
19 35.539 0.694143
20 26.957 0.592853
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.064890
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.3 0.6 0.6 0.0 -0.9
-1.1 -1.2 -1.5 -0.9 -1.8 -0.5
0.6 1.9 0.3 -0.5 -0.0 -0.7
-1.8 0.5 2.0 1.6 -0.7 0.6
1.8 -1.3 -1.3 0.7 1.0 0.8
-0.4 -0.3 -0.7 0.4 -0.5 0.1
-0.9 2.7 0.1 -1.3 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:48.995473
z-score=0.763269, p-value=0.787115
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_00:31
Test no p-value
1 0.644738
2 0.272783
3 0.105001
4 0.058978
5 0.459513
6 0.000521
7 0.707702
8 0.400510
9 0.157977
10 0.179732
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.032462
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_00:31:
(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 66520 0.32 66700 0.02
3 25000.00 25216 1.87 25036 0.05
4 6666.67 6505 3.92 6594 0.79
5 1388.89 1444 2.19 1404 0.16
6 238.10 272 4.83 228 0.43
7 34.72 35 0.00 35 0.00
8 4.96 7 0.84 2 1.77
p=0.96998 p=0.21946
Number of rngs required: 688035, p-value: 0.336
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_00:31
No. of wins: Observed Expected
98601 98585.9
z-score= 0.068, pvalue=0.52700
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66575 66666.7 0.126 0.126
2 37930 37654.3 2.018 2.144
3 27176 26954.7 1.816 3.961
4 19215 19313.5 0.502 4.463
5 13843 13851.4 0.005 4.468
6 9818 9943.5 1.585 6.053
7 7040 7145.0 1.544 7.597
8 5117 5139.1 0.095 7.691
9 3619 3699.9 1.767 9.459
10 2678 2666.3 0.051 9.510
11 1921 1923.3 0.003 9.513
12 1356 1388.7 0.772 10.285
13 999 1003.7 0.022 10.307
14 760 726.1 1.579 11.886
15 531 525.8 0.051 11.937
16 362 381.2 0.962 12.899
17 299 276.5 1.824 14.723
18 206 200.8 0.133 14.856
19 140 146.0 0.245 15.101
20 126 106.2 3.685 18.787
21 289 287.1 0.012 18.799
Chisq= 18.80 for 20 degrees of freedom, p= 0.46509
SUMMARY of craptest
p-value for no. of wins: 0.526996
p-value for throws/game: 0.465089
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_00:31
No. of wins: Observed Expected
98596 98585.9
z-score= 0.045, pvalue=0.51809
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66777 66666.7 0.183 0.183
2 37529 37654.3 0.417 0.600
3 26833 26954.7 0.550 1.149
4 19202 19313.5 0.643 1.793
5 13843 13851.4 0.005 1.798
6 10114 9943.5 2.922 4.720
7 7247 7145.0 1.455 6.175
8 5160 5139.1 0.085 6.261
9 3656 3699.9 0.520 6.781
10 2646 2666.3 0.155 6.935
11 1963 1923.3 0.818 7.753
12 1369 1388.7 0.281 8.034
13 973 1003.7 0.940 8.974
14 721 726.1 0.036 9.010
15 544 525.8 0.627 9.638
16 417 381.2 3.372 13.010
17 281 276.5 0.072 13.081
18 199 200.8 0.017 13.098
19 154 146.0 0.440 13.538
20 104 106.2 0.046 13.584
21 268 287.1 1.272 14.857
Chisq= 14.86 for 20 degrees of freedom, p= 0.21547
SUMMARY of craptest
p-value for no. of wins: 0.518089
p-value for throws/game: 0.215467
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0122,0.0160,0.0217,0.0276,0.0325,0.0352,0.0456,0.0492,0.0510,
0.0528,0.0556,0.0559,0.0565,0.0585,0.0590,0.0620,0.0649,0.0688,0.0712,
0.0770,0.0816,0.0859,0.0899,0.0943,0.0953,0.0990,0.1006,0.1016,0.1045,
0.1050,0.1131,0.1213,0.1224,0.1250,0.1291,0.1384,0.1403,0.1435,0.1526,
0.1572,0.1580,0.1584,0.1629,0.1642,0.1691,0.1797,0.1819,0.1829,0.2039,
0.2128,0.2155,0.2186,0.2195,0.2239,0.2263,0.2336,0.2447,0.2561,0.2579,
0.2619,0.2638,0.2659,0.2690,0.2728,0.2749,0.2796,0.2797,0.2813,0.2849,
0.2957,0.2971,0.2979,0.3025,0.3058,0.3077,0.3077,0.3127,0.3186,0.3224,
0.3243,0.3358,0.3379,0.3406,0.3445,0.3555,0.3569,0.3580,0.3582,0.3710,
0.3714,0.3804,0.3869,0.3921,0.3961,0.3961,0.3973,0.3989,0.4005,0.4058,
0.4066,0.4118,0.4124,0.4158,0.4190,0.4201,0.4283,0.4285,0.4364,0.4375,
0.4480,0.4480,0.4557,0.4583,0.4595,0.4644,0.4647,0.4651,0.4673,0.4743,
0.4764,0.4773,0.4941,0.4949,0.4976,0.4988,0.4999,0.5058,0.5075,0.5131,
0.5181,0.5270,0.5300,0.5369,0.5489,0.5501,0.5515,0.5603,0.5715,0.5801,
0.5828,0.5882,0.5929,0.5930,0.5977,0.6013,0.6091,0.6130,0.6180,0.6211,
0.6254,0.6294,0.6337,0.6358,0.6364,0.6399,0.6406,0.6446,0.6447,0.6450,
0.6524,0.6525,0.6526,0.6558,0.6558,0.6631,0.6716,0.6751,0.6760,0.6791,
0.6818,0.6824,0.6857,0.6885,0.6897,0.6899,0.6904,0.6941,0.6983,0.7075,
0.7077,0.7141,0.7143,0.7177,0.7201,0.7226,0.7254,0.7270,0.7280,0.7332,
0.7359,0.7364,0.7379,0.7387,0.7426,0.7432,0.7468,0.7484,0.7503,0.7594,
0.7621,0.7627,0.7629,0.7675,0.7738,0.7780,0.7871,0.7903,0.7917,0.7940,
0.7953,0.7970,0.8027,0.8076,0.8090,0.8241,0.8382,0.8445,0.8451,0.8509,
0.8571,0.8590,0.8615,0.8630,0.8648,0.8659,0.8730,0.8736,0.8748,0.8800,
0.8801,0.8894,0.8896,0.8905,0.8967,0.8970,0.9012,0.9016,0.9101,0.9101,
0.9152,0.9191,0.9204,0.9216,0.9226,0.9228,0.9232,0.9308,0.9328,0.9341,
0.9341,0.9355,0.9370,0.9439,0.9440,0.9486,0.9487,0.9553,0.9569,0.9579,
0.9700,0.9704,0.9717,0.9782,0.9816,0.9837,0.9885,0.9925,0.9952,
Overall p-value after applying KStest on 269 p-values = 0.221019
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.