RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.90 18.0071 0.611607
2 to 25 16.11 13.3029 0.284318
3 to 26 15.60 16.9129 0.539715
4 to 27 15.62 22.5419 0.835234
5 to 28 15.61 18.3281 0.631570
6 to 29 15.98 14.3087 0.354854
7 to 30 15.92 13.7912 0.318177
8 to 31 15.62 16.3563 0.501265
9 to 32 15.87 17.2789 0.564369
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.356883
Tough bday spacings test for dh-ranFile-2018-07-07_08:31: 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 10 27 79 101 105 63 60 30 11 6 8
(O-E)^2/E 0.1 2.5 0.4 0.1 0.5 2.9 1.2 0.0 1.0 0.1 3.8
Birthday Spacings: Sum(O-E)^2/E= 12.733, p= 0.761
RESULTS OF GCD FOR dh-ranFile-2018-07-07_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.094864
p-value, dist. of gcd's: 0.906802
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.155 0.328 0.463 0.766 0.867 0.142 0.566 0.583
Bits 8 to 15---> 0.804 0.523 0.628 0.385 0.649 0.996 0.849 0.337
Bits 16 to 23---> 0.885 0.367 0.254 0.062 0.005 0.813 0.193 0.833
Bits 24 to 31---> 0.986 0.201 0.858 0.021 0.391 0.504 0.474 0.960
KS test for the above 32 p values: 0.187
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_08:31,
p-values for 5 runs: 0.7854, 0.1653, 0.4956, 0.4846, 0.7607
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5207 5134.0 1.038 1.069
r= 30 23086 23103.0 0.013 1.082
r= 31 11493 11551.5 0.297 1.378
chi-square = 1.378 with df = 3; p-value = 0.289
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 240 211.4 3.864 3.864
r= 30 5161 5134.0 0.142 4.006
r= 31 23059 23103.0 0.084 4.090
r= 32 11540 11551.5 0.011 4.101
chi-square = 4.101 with df = 3; p-value = 0.749
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_08:31
b-rank test for bits 1 to 8, p=0.46340
b-rank test for bits 2 to 9, p=0.95552
b-rank test for bits 3 to 10, p=0.81394
b-rank test for bits 4 to 11, p=0.35501
b-rank test for bits 5 to 12, p=0.01624
b-rank test for bits 6 to 13, p=0.01392
b-rank test for bits 7 to 14, p=0.42091
b-rank test for bits 8 to 15, p=0.73365
b-rank test for bits 9 to 16, p=0.09168
b-rank test for bits 10 to 17, p=0.45573
b-rank test for bits 11 to 18, p=0.58485
b-rank test for bits 12 to 19, p=0.11025
b-rank test for bits 13 to 20, p=0.51831
b-rank test for bits 14 to 21, p=0.66320
b-rank test for bits 15 to 22, p=0.54324
b-rank test for bits 16 to 23, p=0.59376
b-rank test for bits 17 to 24, p=0.10217
b-rank test for bits 18 to 25, p=0.15996
b-rank test for bits 19 to 26, p=0.22741
b-rank test for bits 20 to 27, p=0.48393
b-rank test for bits 21 to 28, p=0.95548
b-rank test for bits 22 to 29, p=0.91091
b-rank test for bits 23 to 30, p=0.44928
b-rank test for bits 24 to 31, p=0.34593
b-rank test for bits 25 to 32, p=0.26527
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 = 0.583419
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_08:31
(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 140942 -2.26 0.011907
2 142195 0.67 0.747759
3 142149 0.56 0.712252
4 142274 0.85 0.802902
5 141859 -0.12 0.453195
6 141592 -0.74 0.229218
7 141677 -0.54 0.293624
8 141824 -0.20 0.420987
9 142013 0.24 0.595695
10 142994 2.53 0.994366
11 141581 -0.77 0.221503
12 141194 -1.67 0.047328
13 141934 0.06 0.522982
14 141693 -0.51 0.306624
15 142201 0.68 0.752214
16 142249 0.79 0.786292
17 141332 -1.35 0.088684
18 141608 -0.70 0.240703
19 142212 0.71 0.760271
20 142242 0.78 0.781499
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_08:31
Bits used No. missing words z-score p-value
23 to 32 141609 -1.0356 0.150190
22 to 31 141371 -1.8563 0.031705
21 to 30 141518 -1.3494 0.088602
20 to 29 142083 0.5989 0.725368
19 to 28 142480 1.9678 0.975456
18 to 27 141726 -0.6322 0.263637
17 to 26 141978 0.2368 0.593591
16 to 25 142160 0.8644 0.806310
15 to 24 142259 1.2058 0.886045
14 to 23 141677 -0.8011 0.211526
13 to 22 141558 -1.2115 0.112855
12 to 21 142175 0.9161 0.820194
11 to 20 141644 -0.9149 0.180114
10 to 19 141172 -2.5425 0.005503
9 to 18 141968 0.2023 0.580163
8 to 17 142478 1.9609 0.975056
7 to 16 141544 -1.2598 0.103878
6 to 15 142014 0.3609 0.640925
5 to 14 142099 0.6540 0.743455
4 to 13 142277 1.2678 0.897570
3 to 12 141571 -1.1667 0.121675
2 to 11 142189 0.9644 0.832572
1 to 10 141988 0.2713 0.606911
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_08:31
Bits used No. missing words z-score p-value
28 to 32 142234 1.1006 0.864459
27 to 31 141529 -1.2893 0.098655
26 to 30 141395 -1.7435 0.040624
25 to 29 142379 1.5921 0.944319
24 to 28 142068 0.5379 0.704665
23 to 27 141556 -1.1977 0.115511
22 to 26 141992 0.2802 0.610352
21 to 25 141792 -0.3977 0.345415
20 to 24 142208 1.0124 0.844336
19 to 23 141729 -0.6113 0.270504
18 to 22 141976 0.2260 0.589399
17 to 21 141794 -0.3909 0.347917
16 to 20 141977 0.2294 0.590717
15 to 19 141721 -0.6384 0.261605
14 to 18 141814 -0.3232 0.373290
13 to 17 142155 0.8328 0.797516
12 to 16 141985 0.2565 0.601221
11 to 15 141568 -1.1571 0.123626
10 to 14 141750 -0.5401 0.294564
9 to 13 142156 0.8362 0.798470
8 to 12 142316 1.3785 0.915982
7 to 11 141815 -0.3198 0.374574
6 to 10 141729 -0.6113 0.270504
5 to 9 142521 2.0735 0.980935
4 to 8 142117 0.7040 0.759273
3 to 7 142109 0.6768 0.750749
2 to 6 141738 -0.5808 0.280695
1 to 5 141853 -0.1909 0.424283
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_08:31
Bits used No. missing words z-score p-value
31 to 32 141420 -1.4435 0.074447
30 to 31 141767 -0.4199 0.337297
29 to 30 141411 -1.4700 0.070781
28 to 29 141800 -0.3225 0.373534
27 to 28 141177 -2.1603 0.015376
26 to 27 141432 -1.4081 0.079558
25 to 26 142455 1.6096 0.946262
24 to 25 142303 1.1613 0.877234
23 to 24 141813 -0.2842 0.388144
22 to 23 141956 0.1377 0.554749
21 to 22 142047 0.4061 0.657668
20 to 21 141893 -0.0482 0.480790
19 to 20 141580 -0.9715 0.165656
18 to 19 141998 0.2616 0.603171
17 to 18 141627 -0.8328 0.202470
16 to 17 142074 0.4858 0.686429
15 to 16 141787 -0.3609 0.359104
14 to 15 141832 -0.2281 0.409780
13 to 14 142090 0.5329 0.702966
12 to 13 142107 0.5831 0.720086
11 to 12 141955 0.1347 0.553583
10 to 11 141652 -0.7591 0.223901
9 to 10 141945 0.1052 0.541900
8 to 9 141647 -0.7738 0.219514
7 to 8 141840 -0.2045 0.418976
6 to 7 141993 0.2468 0.597474
5 to 6 141571 -0.9980 0.159134
4 to 5 141872 -0.1101 0.456158
3 to 4 142001 0.2704 0.606579
2 to 3 141934 0.0728 0.529007
1 to 2 141760 -0.4405 0.329787
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2494.55 -0.077 0.469299
Test results for specific bytes for dh-ranFile-2018-07-07_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2505.88 0.083 0.533159
2 to 9 2603.53 1.464 0.928427
3 to 10 2484.55 -0.218 0.413540
4 to 11 2523.57 0.333 0.630578
5 to 12 2499.35 -0.009 0.496317
6 to 13 2571.56 1.012 0.844249
7 to 14 2541.10 0.581 0.719461
8 to 15 2526.75 0.378 0.647374
9 to 16 2514.87 0.210 0.583301
10 to 17 2528.59 0.404 0.657016
11 to 18 2485.01 -0.212 0.416039
12 to 19 2561.97 0.876 0.809595
13 to 20 2520.95 0.296 0.616506
14 to 21 2535.21 0.498 0.690726
15 to 22 2462.84 -0.525 0.299624
16 to 23 2434.49 -0.926 0.177123
17 to 24 2459.11 -0.578 0.281519
18 to 25 2483.64 -0.231 0.408525
19 to 26 2462.09 -0.536 0.295940
20 to 27 2599.70 1.410 0.920717
21 to 28 2569.86 0.988 0.838422
22 to 29 2425.43 -1.055 0.145805
23 to 30 2512.06 0.171 0.567705
24 to 31 2570.53 0.997 0.840723
25 to 32 2562.89 0.889 0.813092
CDPARK for dh-ranFile-2018-07-07_08:31: 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
3519 -0.1826 0.427537
3562 1.7808 0.962529
3517 -0.2740 0.392053
3515 -0.3653 0.357445
3523 0.0000 0.500000
3570 2.1461 0.984068
3524 0.0457 0.518210
3498 -1.1416 0.126820
3539 0.7306 0.767486
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3528.00 sample std.=21.40
p-value of the KSTEST for those 10 p-values: 0.559157
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_08:31
0.4777,0.9133,0.6701,0.5586,0.2126,0.7565,0.1563,0.8579,0.0380,0.6545,
The KS test for those 10 p-values: 0.958010
The 3DSPHERES test for dh-ranFile-2018-07-07_08:31
sample no r^3 equiv. uni.
1 0.361 0.011974
2 10.742 0.300962
3 16.116 0.415616
4 13.983 0.372566
5 31.743 0.652888
6 13.593 0.364353
7 1.231 0.040199
8 82.144 0.935310
9 27.889 0.605304
10 2.358 0.075598
11 110.333 0.974721
12 1.696 0.054954
13 16.093 0.415160
14 31.471 0.649726
15 5.065 0.155340
16 5.931 0.179389
17 30.722 0.640872
18 9.731 0.277019
19 11.673 0.322339
20 7.834 0.229834
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.105419
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 -1.1 -1.0 0.0 1.3
-1.3 -0.9 -1.8 -1.7 0.1 0.5
1.3 0.0 -1.8 -1.3 1.9 0.0
1.9 -0.4 2.2 -0.8 0.8 -0.9
-0.3 0.4 -0.7 -0.6 -1.5 -0.2
-0.2 -1.2 -0.1 2.2 -0.1 -0.3
0.3 -1.3 -2.0 -0.7 -1.3 1.0
-0.1
Chi-square with 42 degrees of freedom:55.984206
z-score=1.525802, p-value=0.927062
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_08:31
Test no p-value
1 0.044545
2 0.384638
3 0.144009
4 0.693470
5 0.179837
6 0.052981
7 0.577698
8 0.056458
9 0.353357
10 0.022177
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.005627
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_08:31:
(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 66553 0.19 66886 0.72
3 25000.00 25119 0.57 24758 2.34
4 6666.67 6677 0.02 6664 0.00
5 1388.89 1391 0.00 1392 0.01
6 238.10 222 1.09 250 0.60
7 34.72 34 0.01 42 1.53
8 4.96 3 0.77 7 0.84
p=0.14949 p=0.58049
Number of rngs required: 688615, p-value: 0.596
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_08:31
No. of wins: Observed Expected
98368 98585.9
z-score=-0.974, pvalue=0.16493
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66522 66666.7 0.314 0.314
2 37710 37654.3 0.082 0.396
3 26896 26954.7 0.128 0.524
4 19488 19313.5 1.577 2.102
5 13728 13851.4 1.100 3.201
6 10010 9943.5 0.444 3.645
7 7130 7145.0 0.032 3.677
8 5143 5139.1 0.003 3.680
9 3671 3699.9 0.225 3.905
10 2634 2666.3 0.391 4.296
11 1956 1923.3 0.555 4.851
12 1375 1388.7 0.136 4.987
13 1030 1003.7 0.688 5.676
14 753 726.1 0.994 6.669
15 563 525.8 2.627 9.296
16 373 381.2 0.174 9.470
17 282 276.5 0.108 9.578
18 193 200.8 0.305 9.883
19 125 146.0 3.016 12.900
20 121 106.2 2.058 14.958
21 297 287.1 0.340 15.298
Chisq= 15.30 for 20 degrees of freedom, p= 0.24089
SUMMARY of craptest
p-value for no. of wins: 0.164931
p-value for throws/game: 0.240889
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_08:31
No. of wins: Observed Expected
98618 98585.9
z-score= 0.144, pvalue=0.55715
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66702 66666.7 0.019 0.019
2 37889 37654.3 1.463 1.481
3 26857 26954.7 0.354 1.836
4 19527 19313.5 2.361 4.197
5 13630 13851.4 3.539 7.736
6 9795 9943.5 2.219 9.955
7 7229 7145.0 0.987 10.942
8 5272 5139.1 3.438 14.380
9 3651 3699.9 0.645 15.026
10 2615 2666.3 0.987 16.013
11 1857 1923.3 2.287 18.300
12 1364 1388.7 0.441 18.741
13 988 1003.7 0.246 18.987
14 703 726.1 0.737 19.724
15 504 525.8 0.907 20.631
16 354 381.2 1.934 22.565
17 258 276.5 1.243 23.808
18 182 200.8 1.765 25.574
19 166 146.0 2.744 28.318
20 125 106.2 3.322 31.640
21 332 287.1 7.017 38.657
Chisq= 38.66 for 20 degrees of freedom, p= 0.99265
SUMMARY of craptest
p-value for no. of wins: 0.557153
p-value for throws/game: 0.992648
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0053,0.0055,0.0056,0.0119,0.0120,0.0139,0.0154,0.0162,0.0209,0.0222,
0.0317,0.0380,0.0402,0.0406,0.0445,0.0473,0.0530,0.0550,0.0565,0.0619,
0.0708,0.0744,0.0756,0.0796,0.0886,0.0887,0.0917,0.0949,0.0987,0.1022,
0.1039,0.1054,0.1103,0.1129,0.1155,0.1217,0.1236,0.1268,0.1422,0.1440,
0.1458,0.1495,0.1502,0.1548,0.1553,0.1563,0.1591,0.1600,0.1649,0.1653,
0.1657,0.1771,0.1794,0.1798,0.1801,0.1867,0.1929,0.2007,0.2025,0.2115,
0.2126,0.2195,0.2215,0.2239,0.2274,0.2292,0.2298,0.2407,0.2409,0.2537,
0.2616,0.2636,0.2653,0.2705,0.2705,0.2770,0.2807,0.2815,0.2843,0.2894,
0.2936,0.2946,0.2959,0.2996,0.3010,0.3066,0.3182,0.3223,0.3240,0.3281,
0.3298,0.3373,0.3374,0.3454,0.3459,0.3479,0.3534,0.3549,0.3550,0.3569,
0.3574,0.3591,0.3644,0.3674,0.3726,0.3733,0.3735,0.3746,0.3846,0.3854,
0.3881,0.3906,0.3921,0.4085,0.4098,0.4135,0.4152,0.4156,0.4160,0.4190,
0.4209,0.4210,0.4243,0.4275,0.4493,0.4532,0.4557,0.4562,0.4630,0.4634,
0.4693,0.4738,0.4777,0.4808,0.4839,0.4846,0.4956,0.4963,0.5000,0.5013,
0.5035,0.5182,0.5183,0.5230,0.5234,0.5290,0.5332,0.5397,0.5419,0.5432,
0.5536,0.5547,0.5572,0.5586,0.5592,0.5644,0.5657,0.5677,0.5777,0.5802,
0.5805,0.5833,0.5833,0.5834,0.5848,0.5894,0.5907,0.5936,0.5938,0.5957,
0.5964,0.5975,0.6012,0.6032,0.6053,0.6066,0.6069,0.6104,0.6116,0.6165,
0.6282,0.6306,0.6316,0.6409,0.6409,0.6474,0.6488,0.6497,0.6529,0.6545,
0.6570,0.6577,0.6632,0.6701,0.6864,0.6907,0.6935,0.7030,0.7047,0.7123,
0.7195,0.7201,0.7254,0.7336,0.7435,0.7478,0.7493,0.7507,0.7522,0.7565,
0.7593,0.7603,0.7607,0.7610,0.7660,0.7675,0.7815,0.7854,0.7863,0.7975,
0.7985,0.8029,0.8038,0.8063,0.8096,0.8131,0.8134,0.8139,0.8202,0.8326,
0.8328,0.8352,0.8384,0.8407,0.8442,0.8443,0.8490,0.8579,0.8582,0.8645,
0.8671,0.8772,0.8854,0.8860,0.8976,0.9068,0.9109,0.9133,0.9160,0.9207,
0.9271,0.9284,0.9353,0.9443,0.9463,0.9555,0.9555,0.9580,0.9600,0.9625,
0.9747,0.9751,0.9755,0.9809,0.9841,0.9861,0.9926,0.9944,0.9961,
Overall p-value after applying KStest on 269 p-values = 0.572568
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.