RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.72 22.8301 0.845137
2 to 25 15.81 19.6056 0.705102
3 to 26 15.93 18.9596 0.669142
4 to 27 16.01 18.1884 0.622950
5 to 28 15.62 27.0233 0.942272
6 to 29 16.03 10.7474 0.130610
7 to 30 15.88 19.8150 0.716198
8 to 31 16.11 13.7097 0.312469
9 to 32 16.00 15.8126 0.462844
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.490802
Tough bday spacings test for dh-ranFile-2018-07-02_01:31: 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 34 69 109 105 69 47 31 16 6 7
(O-E)^2/E 0.5 0.2 0.2 1.3 0.5 1.1 0.5 0.1 0.1 0.1 2.1
Birthday Spacings: Sum(O-E)^2/E= 6.682, p= 0.245
RESULTS OF GCD FOR dh-ranFile-2018-07-02_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.494939
p-value, dist. of gcd's: 0.590418
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.278 0.381 0.555 0.258 0.432 0.637 0.388 0.477
Bits 8 to 15---> 0.886 0.285 0.102 0.682 0.905 0.821 0.461 0.312
Bits 16 to 23---> 0.298 0.766 0.400 0.692 0.125 0.740 0.177 0.942
Bits 24 to 31---> 0.661 0.006 0.646 0.713 0.357 0.256 0.514 0.914
KS test for the above 32 p values: 0.240
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_01:31,
p-values for 5 runs: 0.3667, 0.1402, 0.5759, 0.7796, 0.7665
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5208 5134.0 1.066 1.580
r= 30 23175 23103.0 0.224 1.804
r= 31 11416 11551.5 1.590 3.394
chi-square = 3.394 with df = 3; p-value = 0.665
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5076 5134.0 0.655 0.794
r= 31 23213 23103.0 0.523 1.318
r= 32 11505 11551.5 0.187 1.505
chi-square = 1.505 with df = 3; p-value = 0.319
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_01:31
b-rank test for bits 1 to 8, p=0.17059
b-rank test for bits 2 to 9, p=0.12198
b-rank test for bits 3 to 10, p=0.59130
b-rank test for bits 4 to 11, p=0.88352
b-rank test for bits 5 to 12, p=0.47957
b-rank test for bits 6 to 13, p=0.13304
b-rank test for bits 7 to 14, p=0.24222
b-rank test for bits 8 to 15, p=0.90618
b-rank test for bits 9 to 16, p=0.41254
b-rank test for bits 10 to 17, p=0.31270
b-rank test for bits 11 to 18, p=0.47364
b-rank test for bits 12 to 19, p=0.82700
b-rank test for bits 13 to 20, p=0.18765
b-rank test for bits 14 to 21, p=0.84949
b-rank test for bits 15 to 22, p=0.39570
b-rank test for bits 16 to 23, p=0.99296
b-rank test for bits 17 to 24, p=0.98660
b-rank test for bits 18 to 25, p=0.14822
b-rank test for bits 19 to 26, p=0.85826
b-rank test for bits 20 to 27, p=0.94123
b-rank test for bits 21 to 28, p=0.95600
b-rank test for bits 22 to 29, p=0.44447
b-rank test for bits 23 to 30, p=0.00150
b-rank test for bits 24 to 31, p=0.10049
b-rank test for bits 25 to 32, p=0.14275
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 = 0.245904
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_01:31
(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 142329 0.98 0.836590
2 141343 -1.32 0.092884
3 142023 0.27 0.604720
4 140988 -2.15 0.015673
5 141359 -1.29 0.099253
6 141969 0.14 0.555439
7 141745 -0.38 0.350508
8 142476 1.32 0.907248
9 142326 0.97 0.834855
10 141995 0.20 0.579324
11 141958 0.11 0.545268
12 141854 -0.13 0.448570
13 142549 1.49 0.932485
14 141851 -0.14 0.445798
15 141430 -1.12 0.131372
16 141190 -1.68 0.046413
17 141572 -0.79 0.215303
18 142063 0.36 0.640218
19 142203 0.69 0.753689
20 142382 1.10 0.865284
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_01:31
Bits used No. missing words z-score p-value
23 to 32 141575 -1.1529 0.124484
22 to 31 142083 0.5989 0.725368
21 to 30 142425 1.7782 0.962312
20 to 29 141680 -0.7908 0.214532
19 to 28 141938 0.0989 0.539376
18 to 27 141529 -1.3115 0.094847
17 to 26 142021 0.3851 0.649907
16 to 25 142105 0.6747 0.750075
15 to 24 142068 0.5471 0.707858
14 to 23 142799 3.0678 0.998922
13 to 22 142226 1.0920 0.862576
12 to 21 141999 0.3092 0.621418
11 to 20 141384 -1.8115 0.035033
10 to 19 142144 0.8092 0.790802
9 to 18 141955 0.1575 0.562568
8 to 17 142251 1.1782 0.880636
7 to 16 141370 -1.8598 0.031460
6 to 15 142376 1.6092 0.946214
5 to 14 142026 0.4023 0.656272
4 to 13 141953 0.1506 0.559849
3 to 12 141968 0.2023 0.580163
2 to 11 142009 0.3437 0.634460
1 to 10 141475 -1.4977 0.067107
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_01:31
Bits used No. missing words z-score p-value
28 to 32 141783 -0.4282 0.334239
27 to 31 141717 -0.6520 0.257212
26 to 30 142410 1.6972 0.955169
25 to 29 142207 1.0091 0.843525
24 to 28 142086 0.5989 0.725374
23 to 27 142322 1.3989 0.919076
22 to 26 141627 -0.9571 0.169271
21 to 25 142160 0.8497 0.802262
20 to 24 142242 1.1277 0.870276
19 to 23 141710 -0.6757 0.249617
18 to 22 141605 -1.0316 0.151123
17 to 21 141722 -0.6350 0.262709
16 to 20 141349 -1.8994 0.028754
15 to 19 141815 -0.3198 0.374574
14 to 18 141753 -0.5299 0.298080
13 to 17 141624 -0.9672 0.166717
12 to 16 142234 1.1006 0.864459
11 to 15 141624 -0.9672 0.166717
10 to 14 141846 -0.2147 0.415009
9 to 13 141781 -0.4350 0.331775
8 to 12 142232 1.0938 0.862978
7 to 11 141836 -0.2486 0.401844
6 to 10 142096 0.6328 0.736561
5 to 9 141912 0.0091 0.503611
4 to 8 141753 -0.5299 0.298080
3 to 7 141887 -0.0757 0.469831
2 to 6 141416 -1.6723 0.047232
1 to 5 141760 -0.5062 0.306357
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_01:31
Bits used No. missing words z-score p-value
31 to 32 141513 -1.1691 0.121179
30 to 31 142257 1.0256 0.847454
29 to 30 141731 -0.5260 0.299428
28 to 29 141781 -0.3786 0.352509
27 to 28 141433 -1.4051 0.079995
26 to 27 142254 1.0167 0.845358
25 to 26 141643 -0.7856 0.216041
24 to 25 142342 1.2763 0.899078
23 to 24 141823 -0.2547 0.399493
22 to 23 142461 1.6273 0.948168
21 to 22 142429 1.5329 0.937356
20 to 21 142581 1.9813 0.976223
19 to 20 142038 0.3796 0.647863
18 to 19 142080 0.5035 0.692677
17 to 18 142123 0.6303 0.735749
16 to 17 141685 -0.6617 0.254069
15 to 16 141762 -0.4346 0.331926
14 to 15 142083 0.5123 0.695780
13 to 14 141931 0.0639 0.525484
12 to 13 142148 0.7040 0.759297
11 to 12 141577 -0.9803 0.163463
10 to 11 141986 0.2262 0.589464
9 to 10 141560 -1.0305 0.151394
8 to 9 142143 0.6893 0.754680
7 to 8 141860 -0.1455 0.442152
6 to 7 142072 0.4799 0.684334
5 to 6 141628 -0.8299 0.203303
4 to 5 141424 -1.4317 0.076122
3 to 4 142455 1.6096 0.946262
2 to 3 142152 0.7158 0.762955
1 to 2 142149 0.7070 0.760214
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2437.63 -0.882 0.188872
Test results for specific bytes for dh-ranFile-2018-07-02_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2548.63 0.688 0.754207
2 to 9 2576.32 1.079 0.859765
3 to 10 2443.49 -0.799 0.212108
4 to 11 2562.76 0.888 0.812603
5 to 12 2581.27 1.149 0.874795
6 to 13 2333.06 -2.361 0.009114
7 to 14 2567.27 0.951 0.829296
8 to 15 2398.35 -1.438 0.075277
9 to 16 2562.11 0.878 0.810145
10 to 17 2529.48 0.417 0.661629
11 to 18 2519.02 0.269 0.606029
12 to 19 2592.55 1.309 0.904705
13 to 20 2555.31 0.782 0.782972
14 to 21 2471.39 -0.405 0.342900
15 to 22 2539.64 0.561 0.712485
16 to 23 2472.55 -0.388 0.348925
17 to 24 2441.11 -0.833 0.202477
18 to 25 2500.48 0.007 0.502722
19 to 26 2510.89 0.154 0.561217
20 to 27 2403.94 -1.358 0.087161
21 to 28 2670.98 2.418 0.992198
22 to 29 2606.19 1.502 0.933425
23 to 30 2377.89 -1.727 0.042096
24 to 31 2290.55 -2.962 0.001528
25 to 32 2474.12 -0.366 0.357158
CDPARK for dh-ranFile-2018-07-02_01:31: 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
3516 -0.3196 0.374623
3522 -0.0457 0.481790
3558 1.5982 0.944998
3509 -0.6393 0.261324
3536 0.5936 0.723613
3522 -0.0457 0.481790
3513 -0.4566 0.323972
3499 -1.0959 0.136563
3521 -0.0913 0.463617
3491 -1.4612 0.071982
Square side=100, avg. no. parked=3518.70 sample std.=17.78
p-value of the KSTEST for those 10 p-values: 0.603528
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_01:31
0.9895,0.2911,0.7224,0.5378,0.7835,0.4163,0.1911,0.9619,0.0976,0.7998,
The KS test for those 10 p-values: 0.559305
The 3DSPHERES test for dh-ranFile-2018-07-02_01:31
sample no r^3 equiv. uni.
1 52.950 0.828813
2 28.258 0.610129
3 10.500 0.295317
4 41.205 0.746781
5 23.897 0.549120
6 0.628 0.020713
7 9.231 0.264869
8 11.771 0.324543
9 29.432 0.625086
10 5.921 0.179111
11 2.313 0.074204
12 34.601 0.684432
13 47.529 0.794910
14 55.423 0.842359
15 0.893 0.029331
16 50.747 0.815767
17 4.366 0.135444
18 52.891 0.828476
19 16.920 0.431063
20 31.348 0.648290
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.716573
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 3.4 1.8 -0.4 -0.1 -2.1
1.8 1.0 -0.3 -0.8 0.6 -0.7
-0.4 -0.9 -0.1 -0.7 1.9 -0.2
0.1 0.8 -0.4 0.6 0.3 0.6
-0.5 -0.6 -0.3 -1.2 0.0 0.1
-1.8 -0.5 1.1 1.2 0.2 1.3
0.3 0.5 -0.8 -0.1 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:46.603094
z-score=0.502239, p-value=0.711292
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_01:31
Test no p-value
1 0.559201
2 0.033932
3 0.111473
4 0.007276
5 0.462558
6 0.423872
7 0.428680
8 0.321522
9 0.151557
10 0.389708
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.025720
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_01:31:
(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 66624 0.03 66643 0.01
3 25000.00 25068 0.18 25065 0.17
4 6666.67 6661 0.00 6593 0.81
5 1388.89 1355 0.83 1409 0.29
6 238.10 253 0.93 247 0.33
7 34.72 32 0.21 34 0.01
8 4.96 6 0.22 8 1.86
p=0.12141 p=0.25521
Number of rngs required: 687880, p-value: 0.273
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_01:31
No. of wins: Observed Expected
98801 98585.9
z-score= 0.962, pvalue=0.83203
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66728 66666.7 0.056 0.056
2 37650 37654.3 0.000 0.057
3 26765 26954.7 1.336 1.392
4 19392 19313.5 0.319 1.712
5 13672 13851.4 2.324 4.036
6 10073 9943.5 1.685 5.721
7 7215 7145.0 0.685 6.407
8 5143 5139.1 0.003 6.410
9 3801 3699.9 2.765 9.174
10 2672 2666.3 0.012 9.186
11 1963 1923.3 0.818 10.005
12 1335 1388.7 2.080 12.084
13 1027 1003.7 0.540 12.624
14 758 726.1 1.398 14.022
15 507 525.8 0.675 14.697
16 372 381.2 0.220 14.917
17 266 276.5 0.402 15.318
18 185 200.8 1.248 16.566
19 139 146.0 0.334 16.900
20 86 106.2 3.847 20.748
21 251 287.1 4.543 25.290
Chisq= 25.29 for 20 degrees of freedom, p= 0.80944
SUMMARY of craptest
p-value for no. of wins: 0.832035
p-value for throws/game: 0.809443
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_01:31
No. of wins: Observed Expected
98441 98585.9
z-score=-0.648, pvalue=0.25853
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66661 66666.7 0.000 0.000
2 37693 37654.3 0.040 0.040
3 27014 26954.7 0.130 0.171
4 19403 19313.5 0.415 0.586
5 13735 13851.4 0.979 1.564
6 9920 9943.5 0.056 1.620
7 7039 7145.0 1.573 3.193
8 5172 5139.1 0.211 3.404
9 3828 3699.9 4.438 7.842
10 2640 2666.3 0.259 8.101
11 1865 1923.3 1.769 9.870
12 1371 1388.7 0.227 10.097
13 1046 1003.7 1.781 11.878
14 725 726.1 0.002 11.880
15 515 525.8 0.223 12.103
16 320 381.2 9.811 21.914
17 291 276.5 0.756 22.670
18 210 200.8 0.419 23.089
19 175 146.0 5.767 28.856
20 97 106.2 0.800 29.656
21 280 287.1 0.176 29.832
Chisq= 29.83 for 20 degrees of freedom, p= 0.92737
SUMMARY of craptest
p-value for no. of wins: 0.258527
p-value for throws/game: 0.927374
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0015,0.0015,0.0063,0.0073,0.0091,0.0157,0.0207,0.0257,0.0288,0.0293,
0.0315,0.0339,0.0350,0.0421,0.0464,0.0472,0.0671,0.0720,0.0742,0.0753,
0.0761,0.0800,0.0872,0.0929,0.0948,0.0976,0.0993,0.1005,0.1022,0.1115,
0.1212,0.1214,0.1220,0.1245,0.1246,0.1306,0.1314,0.1330,0.1354,0.1366,
0.1402,0.1428,0.1482,0.1511,0.1514,0.1516,0.1635,0.1667,0.1667,0.1693,
0.1706,0.1771,0.1791,0.1877,0.1889,0.1911,0.2025,0.2033,0.2121,0.2145,
0.2153,0.2160,0.2397,0.2422,0.2450,0.2459,0.2496,0.2541,0.2552,0.2557,
0.2572,0.2576,0.2585,0.2613,0.2627,0.2649,0.2732,0.2775,0.2849,0.2911,
0.2953,0.2981,0.2981,0.2984,0.2994,0.3064,0.3119,0.3125,0.3127,0.3189,
0.3215,0.3240,0.3245,0.3318,0.3319,0.3342,0.3429,0.3489,0.3505,0.3525,
0.3572,0.3572,0.3667,0.3746,0.3746,0.3815,0.3877,0.3897,0.3957,0.3995,
0.3999,0.4018,0.4125,0.4150,0.4163,0.4239,0.4287,0.4311,0.4320,0.4422,
0.4445,0.4458,0.4486,0.4611,0.4626,0.4628,0.4636,0.4698,0.4736,0.4767,
0.4796,0.4818,0.4818,0.4908,0.4949,0.5027,0.5036,0.5140,0.5255,0.5378,
0.5394,0.5453,0.5491,0.5548,0.5554,0.5592,0.5593,0.5598,0.5612,0.5626,
0.5759,0.5793,0.5802,0.5895,0.5904,0.5913,0.6035,0.6047,0.6060,0.6101,
0.6214,0.6229,0.6251,0.6345,0.6374,0.6402,0.6463,0.6479,0.6483,0.6499,
0.6563,0.6605,0.6616,0.6652,0.6691,0.6815,0.6843,0.6844,0.6924,0.6927,
0.6958,0.7051,0.7079,0.7113,0.7125,0.7130,0.7162,0.7166,0.7224,0.7236,
0.7254,0.7254,0.7357,0.7366,0.7404,0.7468,0.7501,0.7537,0.7542,0.7547,
0.7593,0.7602,0.7630,0.7655,0.7665,0.7796,0.7830,0.7835,0.7908,0.7949,
0.7998,0.8023,0.8094,0.8101,0.8126,0.8158,0.8211,0.8270,0.8285,0.8288,
0.8293,0.8320,0.8349,0.8366,0.8424,0.8435,0.8451,0.8454,0.8475,0.8495,
0.8583,0.8598,0.8626,0.8630,0.8645,0.8653,0.8703,0.8748,0.8806,0.8835,
0.8861,0.8991,0.9047,0.9048,0.9062,0.9072,0.9143,0.9191,0.9274,0.9325,
0.9334,0.9374,0.9412,0.9417,0.9423,0.9450,0.9462,0.9463,0.9482,0.9552,
0.9560,0.9619,0.9623,0.9762,0.9866,0.9895,0.9922,0.9930,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.947522
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.