RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.75 21.4351 0.792571
2 to 25 15.59 18.3157 0.630809
3 to 26 16.00 18.4182 0.637072
4 to 27 15.91 22.9055 0.847647
5 to 28 15.65 20.5651 0.753648
6 to 29 15.66 11.6164 0.177214
7 to 30 15.86 27.6595 0.950922
8 to 31 15.89 24.2760 0.887871
9 to 32 15.86 16.1236 0.484910
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.088946
Tough bday spacings test for dh-ranFile-2018-07-10_18:31: 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 36 63 114 104 81 41 31 18 2 2
(O-E)^2/E 0.1 0.0 1.4 2.7 0.4 0.1 2.4 0.1 0.7 3.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 12.170, p= 0.726
RESULTS OF GCD FOR dh-ranFile-2018-07-10_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.733584
p-value, dist. of gcd's: 0.858077
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.103 0.845 0.163 0.133 0.017 0.121 0.010 0.384
Bits 8 to 15---> 0.284 0.313 0.717 0.085 0.872 0.541 0.909 0.456
Bits 16 to 23---> 0.622 0.941 0.986 0.553 0.771 0.859 0.376 0.761
Bits 24 to 31---> 0.629 0.543 0.536 0.584 0.166 0.779 0.110 0.584
KS test for the above 32 p values: 0.075
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_18:31,
p-values for 5 runs: 0.5135, 0.5995, 0.7369, 0.2635, 0.6984
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 191 211.4 1.972 1.972
r= 29 5068 5134.0 0.849 2.821
r= 30 23044 23103.0 0.151 2.972
r= 31 11697 11551.5 1.832 4.804
chi-square = 4.804 with df = 3; p-value = 0.813
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5149 5134.0 0.044 0.316
r= 31 23031 23103.0 0.225 0.540
r= 32 11601 11551.5 0.212 0.752
chi-square = 0.752 with df = 3; p-value = 0.139
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_18:31
b-rank test for bits 1 to 8, p=0.14323
b-rank test for bits 2 to 9, p=0.34993
b-rank test for bits 3 to 10, p=0.48339
b-rank test for bits 4 to 11, p=0.56708
b-rank test for bits 5 to 12, p=0.29945
b-rank test for bits 6 to 13, p=0.23046
b-rank test for bits 7 to 14, p=0.73614
b-rank test for bits 8 to 15, p=0.42654
b-rank test for bits 9 to 16, p=0.51315
b-rank test for bits 10 to 17, p=0.24143
b-rank test for bits 11 to 18, p=0.58999
b-rank test for bits 12 to 19, p=0.65619
b-rank test for bits 13 to 20, p=0.52028
b-rank test for bits 14 to 21, p=0.07134
b-rank test for bits 15 to 22, p=0.73940
b-rank test for bits 16 to 23, p=0.10204
b-rank test for bits 17 to 24, p=0.32984
b-rank test for bits 18 to 25, p=0.25799
b-rank test for bits 19 to 26, p=0.01805
b-rank test for bits 20 to 27, p=0.81957
b-rank test for bits 21 to 28, p=0.48423
b-rank test for bits 22 to 29, p=0.96674
b-rank test for bits 23 to 30, p=0.90417
b-rank test for bits 24 to 31, p=0.14492
b-rank test for bits 25 to 32, p=0.04560
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 = 0.394890
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_18:31
(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 142740 1.94 0.973860
2 141806 -0.24 0.404613
3 142555 1.51 0.934296
4 142191 0.66 0.744765
5 142464 1.30 0.902505
6 142461 1.29 0.901292
7 141591 -0.74 0.228510
8 142007 0.23 0.590255
9 141113 -1.86 0.031401
10 142207 0.70 0.756626
11 142209 0.70 0.758087
12 141997 0.20 0.581150
13 141928 0.04 0.517397
14 141504 -0.95 0.171811
15 142087 0.42 0.660972
16 142550 1.50 0.932789
17 141524 -0.90 0.183979
18 141722 -0.44 0.330807
19 141993 0.20 0.577496
20 141457 -1.06 0.145291
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_18:31
Bits used No. missing words z-score p-value
23 to 32 142177 0.9230 0.821996
22 to 31 142070 0.5540 0.710222
21 to 30 141803 -0.3667 0.356938
20 to 29 141636 -0.9425 0.172964
19 to 28 141803 -0.3667 0.356938
18 to 27 141688 -0.7632 0.222670
17 to 26 141271 -2.2011 0.013863
16 to 25 141893 -0.0563 0.477547
15 to 24 141857 -0.1804 0.428400
14 to 23 142290 1.3127 0.905350
13 to 22 141737 -0.5942 0.276175
12 to 21 141881 -0.0977 0.461089
11 to 20 141801 -0.3736 0.354369
10 to 19 141930 0.0713 0.528411
9 to 18 142536 2.1609 0.984650
8 to 17 141875 -0.1184 0.452884
7 to 16 142072 0.5609 0.712578
6 to 15 141819 -0.3115 0.377717
5 to 14 141690 -0.7563 0.224732
4 to 13 141991 0.2816 0.610883
3 to 12 141561 -1.2011 0.114849
2 to 11 142259 1.2058 0.886045
1 to 10 142109 0.6885 0.754436
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_18:31
Bits used No. missing words z-score p-value
28 to 32 141691 -0.7401 0.229619
27 to 31 141420 -1.6587 0.048584
26 to 30 141774 -0.4587 0.323208
25 to 29 141966 0.1921 0.576169
24 to 28 142281 1.2599 0.896147
23 to 27 141777 -0.4486 0.326869
22 to 26 141924 0.0497 0.519831
21 to 25 142048 0.4701 0.680847
20 to 24 142246 1.1413 0.873118
19 to 23 141701 -0.7062 0.240031
18 to 22 142278 1.2497 0.894301
17 to 21 141864 -0.1537 0.438939
16 to 20 142148 0.8091 0.790757
15 to 19 142384 1.6091 0.946197
14 to 18 141563 -1.1740 0.120198
13 to 17 141568 -1.1571 0.123626
12 to 16 141967 0.1955 0.577496
11 to 15 141920 0.0362 0.514426
10 to 14 141627 -0.9571 0.169271
9 to 13 142308 1.3514 0.911720
8 to 12 142157 0.8396 0.799422
7 to 11 141785 -0.4215 0.336711
6 to 10 142340 1.4599 0.927841
5 to 9 142257 1.1785 0.880710
4 to 8 142097 0.6362 0.737667
3 to 7 142246 1.1413 0.873118
2 to 6 142004 0.3209 0.625863
1 to 5 141954 0.1514 0.560179
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_18:31
Bits used No. missing words z-score p-value
31 to 32 141581 -0.9685 0.166391
30 to 31 142441 1.5683 0.941600
29 to 30 142141 0.6834 0.752821
28 to 29 141866 -0.1278 0.449147
27 to 28 141572 -0.9951 0.159850
26 to 27 142601 2.0403 0.979341
25 to 26 141950 0.1200 0.547747
24 to 25 142165 0.7542 0.774632
23 to 24 141400 -1.5024 0.066491
22 to 23 141957 0.1406 0.555915
21 to 22 142192 0.8338 0.797813
20 to 21 142186 0.8161 0.792789
19 to 20 141737 -0.5083 0.305605
18 to 19 141618 -0.8594 0.195065
17 to 18 142445 1.5801 0.942963
16 to 17 141667 -0.7148 0.237355
15 to 16 141983 0.2173 0.586019
14 to 15 141905 -0.0128 0.494905
13 to 14 141445 -1.3697 0.085390
12 to 13 142254 1.0167 0.845358
11 to 12 141797 -0.3314 0.370187
10 to 11 141767 -0.4199 0.337297
9 to 10 141765 -0.4258 0.335144
8 to 9 141805 -0.3078 0.379133
7 to 8 142202 0.8633 0.806023
6 to 7 141492 -1.2311 0.109150
5 to 6 142188 0.8220 0.794472
4 to 5 141693 -0.6381 0.261691
3 to 4 141863 -0.1367 0.445647
2 to 3 141295 -1.8122 0.034979
1 to 2 141951 0.1229 0.548915
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2447.66 -0.740 0.229582
Test results for specific bytes for dh-ranFile-2018-07-10_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2396.85 -1.459 0.072322
2 to 9 2593.10 1.317 0.906020
3 to 10 2554.41 0.769 0.779189
4 to 11 2476.07 -0.338 0.367518
5 to 12 2429.51 -0.997 0.159402
6 to 13 2544.12 0.624 0.733691
7 to 14 2557.31 0.810 0.791151
8 to 15 2544.51 0.629 0.735467
9 to 16 2488.69 -0.160 0.436487
10 to 17 2481.65 -0.259 0.397634
11 to 18 2465.95 -0.482 0.315043
12 to 19 2431.52 -0.968 0.166413
13 to 20 2508.54 0.121 0.548043
14 to 21 2442.31 -0.816 0.207307
15 to 22 2492.14 -0.111 0.455762
16 to 23 2399.94 -1.415 0.078531
17 to 24 2486.60 -0.190 0.424832
18 to 25 2453.91 -0.652 0.257244
19 to 26 2538.48 0.544 0.706839
20 to 27 2568.10 0.963 0.832235
21 to 28 2513.87 0.196 0.577774
22 to 29 2475.55 -0.346 0.364732
23 to 30 2716.56 3.063 0.998903
24 to 31 2502.48 0.035 0.513989
25 to 32 2496.79 -0.045 0.481919
CDPARK for dh-ranFile-2018-07-10_18:31: 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
3546 1.0502 0.853193
3557 1.5525 0.939730
3517 -0.2740 0.392053
3522 -0.0457 0.481790
3509 -0.6393 0.261324
3541 0.8219 0.794438
3543 0.9132 0.819442
3558 1.5982 0.944998
3562 1.7808 0.962529
3504 -0.8676 0.192812
Square side=100, avg. no. parked=3535.90 sample std.=20.21
p-value of the KSTEST for those 10 p-values: 0.072330
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_18:31
0.5324,0.9370,0.1120,0.9505,0.7713,0.4403,0.9536,0.4298,0.9983,0.1066,
The KS test for those 10 p-values: 0.076154
The 3DSPHERES test for dh-ranFile-2018-07-10_18:31
sample no r^3 equiv. uni.
1 3.322 0.104831
2 36.694 0.705694
3 0.347 0.011511
4 1.242 0.040539
5 76.955 0.923094
6 86.339 0.943751
7 75.015 0.917955
8 131.315 0.987439
9 41.691 0.750853
10 29.261 0.622949
11 11.006 0.307087
12 10.477 0.294764
13 37.971 0.717955
14 6.233 0.187615
15 33.595 0.673670
16 10.255 0.289543
17 58.934 0.859768
18 1.972 0.063633
19 21.506 0.511716
20 29.158 0.621651
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.612863
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.7 -0.1 -1.0 -2.0 1.8
-2.0 -1.2 1.0 1.3 -0.0 -1.4
-0.1 -0.4 -0.3 0.3 -0.2 1.2
-0.0 1.5 0.9 -0.9 0.6 -0.8
-0.9 0.2 -0.6 -0.5 -3.0 0.9
0.3 0.4 1.8 0.4 0.9 -0.3
-1.6 0.2 -1.2 -0.7 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:48.463296
z-score=0.705203, p-value=0.771531
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_18:31
Test no p-value
1 0.021441
2 0.667090
3 0.273229
4 0.021700
5 0.208846
6 0.839688
7 0.049160
8 0.029112
9 0.074782
10 0.287078
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001784
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_18:31:
(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 66674 0.00 66524 0.31
3 25000.00 24956 0.08 25029 0.03
4 6666.67 6728 0.56 6777 1.83
5 1388.89 1361 0.56 1423 0.84
6 238.10 239 0.00 211 3.08
7 34.72 39 0.53 28 1.30
8 4.96 2 1.77 7 0.84
p=0.25603 p=0.77797
Number of rngs required: 688724, p-value: 0.644
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_18:31
No. of wins: Observed Expected
98635 98585.9
z-score= 0.220, pvalue=0.58698
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66671 66666.7 0.000 0.000
2 37826 37654.3 0.783 0.783
3 26977 26954.7 0.018 0.801
4 19068 19313.5 3.120 3.921
5 13834 13851.4 0.022 3.943
6 9904 9943.5 0.157 4.100
7 7207 7145.0 0.538 4.638
8 5081 5139.1 0.656 5.294
9 3750 3699.9 0.679 5.973
10 2736 2666.3 1.822 7.796
11 1964 1923.3 0.860 8.656
12 1359 1388.7 0.637 9.292
13 1012 1003.7 0.068 9.361
14 709 726.1 0.405 9.765
15 551 525.8 1.204 10.970
16 334 381.2 5.833 16.803
17 285 276.5 0.259 17.061
18 207 200.8 0.190 17.251
19 133 146.0 1.155 18.406
20 96 106.2 0.982 19.388
21 296 287.1 0.275 19.663
Chisq= 19.66 for 20 degrees of freedom, p= 0.52084
SUMMARY of craptest
p-value for no. of wins: 0.586982
p-value for throws/game: 0.520838
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_18:31
No. of wins: Observed Expected
98383 98585.9
z-score=-0.907, pvalue=0.18212
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66780 66666.7 0.193 0.193
2 37757 37654.3 0.280 0.473
3 26962 26954.7 0.002 0.475
4 19379 19313.5 0.222 0.697
5 13825 13851.4 0.050 0.747
6 9907 9943.5 0.134 0.882
7 7171 7145.0 0.094 0.976
8 5096 5139.1 0.361 1.337
9 3670 3699.9 0.241 1.578
10 2664 2666.3 0.002 1.580
11 1935 1923.3 0.071 1.651
12 1303 1388.7 5.294 6.945
13 970 1003.7 1.132 8.077
14 718 726.1 0.091 8.168
15 492 525.8 2.177 10.346
16 341 381.2 4.229 14.575
17 283 276.5 0.151 14.726
18 208 200.8 0.256 14.982
19 165 146.0 2.477 17.459
20 106 106.2 0.000 17.459
21 268 287.1 1.272 18.732
Chisq= 18.73 for 20 degrees of freedom, p= 0.46069
SUMMARY of craptest
p-value for no. of wins: 0.182124
p-value for throws/game: 0.460686
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0096,0.0115,0.0139,0.0170,0.0180,0.0214,0.0217,0.0291,0.0314,
0.0350,0.0405,0.0456,0.0486,0.0492,0.0636,0.0665,0.0713,0.0723,0.0723,
0.0747,0.0748,0.0762,0.0785,0.0854,0.0854,0.0889,0.1020,0.1028,0.1048,
0.1066,0.1091,0.1095,0.1120,0.1148,0.1202,0.1206,0.1236,0.1335,0.1392,
0.1432,0.1449,0.1453,0.1594,0.1599,0.1633,0.1664,0.1664,0.1664,0.1693,
0.1718,0.1730,0.1772,0.1821,0.1840,0.1876,0.1928,0.1951,0.2073,0.2088,
0.2227,0.2247,0.2285,0.2296,0.2296,0.2305,0.2374,0.2400,0.2414,0.2560,
0.2572,0.2580,0.2613,0.2617,0.2635,0.2732,0.2762,0.2839,0.2871,0.2895,
0.2948,0.2995,0.3056,0.3071,0.3133,0.3150,0.3232,0.3269,0.3298,0.3308,
0.3351,0.3367,0.3373,0.3499,0.3544,0.3569,0.3569,0.3647,0.3675,0.3702,
0.3755,0.3777,0.3791,0.3842,0.3921,0.3949,0.3976,0.4046,0.4248,0.4265,
0.4284,0.4298,0.4365,0.4389,0.4403,0.4456,0.4491,0.4529,0.4558,0.4565,
0.4607,0.4611,0.4775,0.4818,0.4819,0.4834,0.4842,0.4849,0.4949,0.5117,
0.5131,0.5135,0.5140,0.5144,0.5174,0.5198,0.5203,0.5208,0.5284,0.5324,
0.5356,0.5409,0.5435,0.5477,0.5480,0.5489,0.5530,0.5559,0.5602,0.5671,
0.5762,0.5775,0.5775,0.5778,0.5812,0.5839,0.5839,0.5860,0.5870,0.5900,
0.5903,0.5995,0.6109,0.6129,0.6217,0.6221,0.6229,0.6259,0.6290,0.6308,
0.6371,0.6442,0.6562,0.6610,0.6671,0.6737,0.6808,0.6984,0.7057,0.7068,
0.7102,0.7126,0.7174,0.7180,0.7261,0.7336,0.7337,0.7355,0.7361,0.7369,
0.7377,0.7394,0.7448,0.7509,0.7528,0.7536,0.7544,0.7566,0.7581,0.7612,
0.7713,0.7713,0.7715,0.7746,0.7780,0.7789,0.7792,0.7908,0.7912,0.7926,
0.7928,0.7944,0.7945,0.7978,0.7994,0.8060,0.8132,0.8194,0.8196,0.8220,
0.8322,0.8397,0.8451,0.8454,0.8476,0.8532,0.8581,0.8594,0.8598,0.8724,
0.8731,0.8731,0.8807,0.8860,0.8879,0.8943,0.8961,0.9013,0.9025,0.9042,
0.9054,0.9060,0.9094,0.9117,0.9180,0.9231,0.9278,0.9328,0.9343,0.9370,
0.9397,0.9406,0.9416,0.9430,0.9438,0.9450,0.9462,0.9505,0.9509,0.9536,
0.9625,0.9667,0.9739,0.9793,0.9846,0.9858,0.9874,0.9983,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.892871
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.