RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_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 15.86 16.7375 0.527716
2 to 25 15.68 22.5946 0.837080
3 to 26 15.91 19.9487 0.723139
4 to 27 15.57 18.5347 0.644114
5 to 28 15.95 28.8390 0.963960
6 to 29 15.71 21.2673 0.785437
7 to 30 15.72 20.7641 0.762978
8 to 31 15.92 7.1290 0.018184
9 to 32 15.63 20.8014 0.764699
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.070738
Tough bday spacings test for dh-ranFile-2018-06-19_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 4 36 84 92 104 72 57 23 18 3 7
(O-E)^2/E 2.9 0.0 1.6 0.3 0.4 0.5 0.5 1.5 0.7 2.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 12.458, p= 0.744
RESULTS OF GCD FOR dh-ranFile-2018-06-19_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.986593
p-value, dist. of gcd's: 0.577579
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.578 0.255 0.520 0.140 0.454 0.739 0.351 0.918
Bits 8 to 15---> 0.688 0.086 0.618 0.074 0.322 0.861 0.933 0.937
Bits 16 to 23---> 0.972 0.810 0.512 0.291 0.570 0.420 0.851 0.875
Bits 24 to 31---> 0.658 0.415 0.012 0.591 0.365 0.818 0.375 0.426
KS test for the above 32 p values: 0.371
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_18:31,
p-values for 5 runs: 0.6741, 0.5215, 0.5938, 0.0970, 0.6514
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5119 5134.0 0.044 0.249
r= 30 23072 23103.0 0.042 0.291
r= 31 11591 11551.5 0.135 0.425
chi-square = 0.425 with df = 3; p-value = 0.065
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5302 5134.0 5.497 5.506
r= 31 22978 23103.0 0.677 6.183
r= 32 11510 11551.5 0.149 6.332
chi-square = 6.332 with df = 3; p-value = 0.903
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_18:31
b-rank test for bits 1 to 8, p=0.19702
b-rank test for bits 2 to 9, p=0.54214
b-rank test for bits 3 to 10, p=0.51138
b-rank test for bits 4 to 11, p=0.36482
b-rank test for bits 5 to 12, p=0.10363
b-rank test for bits 6 to 13, p=0.83579
b-rank test for bits 7 to 14, p=0.57423
b-rank test for bits 8 to 15, p=0.03477
b-rank test for bits 9 to 16, p=0.54999
b-rank test for bits 10 to 17, p=0.41479
b-rank test for bits 11 to 18, p=0.14348
b-rank test for bits 12 to 19, p=0.85842
b-rank test for bits 13 to 20, p=0.01562
b-rank test for bits 14 to 21, p=0.69289
b-rank test for bits 15 to 22, p=0.44214
b-rank test for bits 16 to 23, p=0.22931
b-rank test for bits 17 to 24, p=0.55959
b-rank test for bits 18 to 25, p=0.55188
b-rank test for bits 19 to 26, p=0.63744
b-rank test for bits 20 to 27, p=0.98836
b-rank test for bits 21 to 28, p=0.49304
b-rank test for bits 22 to 29, p=0.93595
b-rank test for bits 23 to 30, p=0.13389
b-rank test for bits 24 to 31, p=0.47702
b-rank test for bits 25 to 32, p=0.09169
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 = 0.583435
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_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 142311 0.94 0.826001
2 141816 -0.22 0.413691
3 141269 -1.50 0.067314
4 142368 1.07 0.858063
5 142059 0.35 0.636717
6 142792 2.06 0.980411
7 141791 -0.28 0.391093
8 141743 -0.39 0.348778
9 142336 1.00 0.840592
10 141569 -0.80 0.213259
11 141972 0.15 0.558207
12 141589 -0.75 0.227099
13 141575 -0.78 0.217359
14 141395 -1.20 0.114739
15 142624 1.67 0.952520
16 142054 0.34 0.632324
17 142688 1.82 0.965569
18 142286 0.88 0.810589
19 141221 -1.61 0.053890
20 141113 -1.86 0.031401
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_18:31
Bits used No. missing words z-score p-value
23 to 32 141856 -0.1839 0.427047
22 to 31 141702 -0.7149 0.237326
21 to 30 141584 -1.1218 0.130968
20 to 29 142438 1.8230 0.965848
19 to 28 142461 1.9023 0.971435
18 to 27 142205 1.0196 0.846029
17 to 26 142007 0.3368 0.631864
16 to 25 141777 -0.4563 0.324083
15 to 24 142067 0.5437 0.706673
14 to 23 142106 0.6782 0.751169
13 to 22 142274 1.2575 0.895711
12 to 21 142397 1.6816 0.953679
11 to 20 142110 0.6920 0.755521
10 to 19 141692 -0.7494 0.226804
9 to 18 141624 -0.9839 0.162583
8 to 17 142081 0.5920 0.723063
7 to 16 141507 -1.3873 0.082668
6 to 15 141606 -1.0460 0.147789
5 to 14 142072 0.5609 0.712578
4 to 13 142004 0.3264 0.627957
3 to 12 142204 1.0161 0.845210
2 to 11 141604 -1.0529 0.146202
1 to 10 142115 0.7092 0.760902
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_18:31
Bits used No. missing words z-score p-value
28 to 32 141678 -0.7842 0.216470
27 to 31 141815 -0.3198 0.374574
26 to 30 142057 0.5006 0.691665
25 to 29 141834 -0.2554 0.399224
24 to 28 142029 0.4057 0.657504
23 to 27 141749 -0.5435 0.293396
22 to 26 141222 -2.3299 0.009905
21 to 25 141627 -0.9571 0.169271
20 to 24 141945 0.1209 0.548121
19 to 23 142052 0.4836 0.685675
18 to 22 141689 -0.7469 0.227568
17 to 21 141842 -0.2282 0.409731
16 to 20 141706 -0.6893 0.245332
15 to 19 141588 -1.0893 0.138021
14 to 18 141781 -0.4350 0.331775
13 to 17 141863 -0.1571 0.437602
12 to 16 142162 0.8565 0.804142
11 to 15 141638 -0.9198 0.178848
10 to 14 141764 -0.4926 0.311132
9 to 13 141919 0.0328 0.513075
8 to 12 142892 3.3311 0.999567
7 to 11 141907 -0.0079 0.496849
6 to 10 142080 0.5785 0.718551
5 to 9 142065 0.5277 0.701145
4 to 8 141953 0.1480 0.558842
3 to 7 141723 -0.6316 0.263815
2 to 6 142076 0.5650 0.713957
1 to 5 141634 -0.9333 0.175327
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_18:31
Bits used No. missing words z-score p-value
31 to 32 141753 -0.4612 0.322345
30 to 31 142350 1.2999 0.903184
29 to 30 141693 -0.6381 0.261691
28 to 29 141351 -1.6470 0.049780
27 to 28 141517 -1.1573 0.123572
26 to 27 141824 -0.2517 0.400632
25 to 26 140928 -2.8948 0.001897
24 to 25 141761 -0.4376 0.330856
23 to 24 141972 0.1849 0.573333
22 to 23 142115 0.6067 0.727974
21 to 22 141874 -0.1042 0.458498
20 to 21 141965 0.1642 0.565220
19 to 20 141815 -0.2783 0.390407
18 to 19 141833 -0.2252 0.410927
17 to 18 141930 0.0610 0.524310
16 to 17 141510 -1.1780 0.119405
15 to 16 141940 0.0905 0.536044
14 to 15 141929 0.0580 0.523135
13 to 14 141638 -0.8004 0.211744
12 to 13 141433 -1.4051 0.079995
11 to 12 142407 1.4681 0.928955
10 to 11 142047 0.4061 0.657668
9 to 10 141628 -0.8299 0.203303
8 to 9 142559 1.9164 0.972345
7 to 8 141909 -0.0010 0.499612
6 to 7 142459 1.6214 0.947539
5 to 6 141639 -0.7974 0.212600
4 to 5 142404 1.4592 0.927745
3 to 4 141683 -0.6676 0.252182
2 to 3 141902 -0.0216 0.491375
1 to 2 142297 1.1436 0.873599
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2419.52 -1.138 0.127516
Test results for specific bytes for dh-ranFile-2018-06-19_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2547.99 0.679 0.751319
2 to 9 2495.99 -0.057 0.477366
3 to 10 2506.32 0.089 0.535600
4 to 11 2486.15 -0.196 0.422342
5 to 12 2532.79 0.464 0.678563
6 to 13 2406.12 -1.328 0.092150
7 to 14 2554.59 0.772 0.779953
8 to 15 2433.55 -0.940 0.173663
9 to 16 2399.37 -1.423 0.077358
10 to 17 2413.87 -1.218 0.111589
11 to 18 2565.40 0.925 0.822472
12 to 19 2479.12 -0.295 0.383867
13 to 20 2499.15 -0.012 0.495225
14 to 21 2458.98 -0.580 0.280901
15 to 22 2557.22 0.809 0.790799
16 to 23 2539.76 0.562 0.713035
17 to 24 2497.58 -0.034 0.486337
18 to 25 2568.29 0.966 0.832928
19 to 26 2421.91 -1.104 0.134708
20 to 27 2450.53 -0.700 0.242070
21 to 28 2474.91 -0.355 0.361385
22 to 29 2469.13 -0.437 0.331223
23 to 30 2584.70 1.198 0.884505
24 to 31 2438.10 -0.875 0.190661
25 to 32 2678.44 2.524 0.994190
CDPARK for dh-ranFile-2018-06-19_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
3518 -0.2283 0.409702
3502 -0.9589 0.168804
3506 -0.7763 0.218799
3509 -0.6393 0.261324
3526 0.1370 0.554479
3557 1.5525 0.939730
3539 0.7306 0.767486
3502 -0.9589 0.168804
3554 1.4155 0.921543
3531 0.3653 0.642555
Square side=100, avg. no. parked=3524.40 sample std.=19.54
p-value of the KSTEST for those 10 p-values: 0.920089
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_18:31
0.9804,0.8050,0.3469,0.5620,0.5283,0.0301,0.0709,0.4447,0.5752,0.9246,
The KS test for those 10 p-values: 0.842771
The 3DSPHERES test for dh-ranFile-2018-06-19_18:31
sample no r^3 equiv. uni.
1 35.110 0.689739
2 23.888 0.548994
3 6.079 0.183428
4 7.259 0.214915
5 28.835 0.617560
6 32.941 0.666478
7 66.229 0.890038
8 5.634 0.171206
9 48.246 0.799752
10 20.733 0.498976
11 32.534 0.661923
12 0.040 0.001342
13 25.112 0.567019
14 16.542 0.423850
15 58.059 0.855620
16 54.834 0.839233
17 17.993 0.451056
18 51.363 0.819516
19 26.276 0.583497
20 0.720 0.023705
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.517899
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 2.6 -1.3 -0.1 -0.8 -0.6
-0.9 0.8 0.6 0.2 -0.0 0.4
-0.1 0.3 0.0 1.7 0.6 -0.8
-0.9 -0.6 -0.3 -0.2 -0.0 1.2
-0.9 1.6 0.1 -2.2 -0.7 -1.0
0.0 -1.2 1.1 -0.4 1.0 -0.1
2.4 0.5 -0.8 0.4 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:40.120088
z-score=-0.205115, p-value=0.446241
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_18:31
Test no p-value
1 0.130176
2 0.228131
3 0.000213
4 0.633445
5 0.096462
6 0.859134
7 0.063559
8 0.477418
9 0.513623
10 0.062176
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.021246
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_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 66652 0.00 66699 0.02
3 25000.00 25070 0.20 24981 0.01
4 6666.67 6572 1.34 6635 0.15
5 1388.89 1415 0.49 1392 0.01
6 238.10 236 0.02 256 1.35
7 34.72 46 3.66 29 0.94
8 4.96 8 1.86 7 0.84
p=0.72955 p=0.23165
Number of rngs required: 688200, p-value: 0.408
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_18:31
No. of wins: Observed Expected
98509 98585.9
z-score=-0.344, pvalue=0.36551
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66626 66666.7 0.025 0.025
2 37708 37654.3 0.077 0.101
3 26748 26954.7 1.586 1.687
4 19510 19313.5 2.000 3.687
5 13688 13851.4 1.928 5.615
6 9833 9943.5 1.229 6.844
7 7106 7145.0 0.213 7.057
8 5239 5139.1 1.943 9.000
9 3800 3699.9 2.710 11.710
10 2685 2666.3 0.131 11.841
11 1930 1923.3 0.023 11.865
12 1393 1388.7 0.013 11.878
13 1032 1003.7 0.797 12.675
14 762 726.1 1.771 14.446
15 529 525.8 0.019 14.465
16 401 381.2 1.034 15.498
17 274 276.5 0.023 15.522
18 187 200.8 0.952 16.474
19 117 146.0 5.755 22.229
20 111 106.2 0.216 22.444
21 321 287.1 3.999 26.444
Chisq= 26.44 for 20 degrees of freedom, p= 0.84834
SUMMARY of craptest
p-value for no. of wins: 0.365515
p-value for throws/game: 0.848341
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_18:31
No. of wins: Observed Expected
98783 98585.9
z-score= 0.882, pvalue=0.81104
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66939 66666.7 1.112 1.112
2 37796 37654.3 0.533 1.646
3 26819 26954.7 0.683 2.329
4 19231 19313.5 0.352 2.681
5 13759 13851.4 0.617 3.298
6 9874 9943.5 0.486 3.784
7 7166 7145.0 0.062 3.846
8 5133 5139.1 0.007 3.853
9 3679 3699.9 0.118 3.971
10 2658 2666.3 0.026 3.996
11 1949 1923.3 0.343 4.339
12 1436 1388.7 1.608 5.947
13 999 1003.7 0.022 5.969
14 685 726.1 2.331 8.300
15 522 525.8 0.028 8.328
16 361 381.2 1.065 9.394
17 278 276.5 0.008 9.401
18 196 200.8 0.116 9.518
19 150 146.0 0.110 9.628
20 100 106.2 0.364 9.992
21 270 287.1 1.020 11.012
Chisq= 11.01 for 20 degrees of freedom, p= 0.05408
SUMMARY of craptest
p-value for no. of wins: 0.811039
p-value for throws/game: 0.054083
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0013,0.0019,0.0099,0.0122,0.0156,0.0182,0.0212,0.0237,0.0301,
0.0314,0.0348,0.0498,0.0539,0.0541,0.0622,0.0636,0.0651,0.0673,0.0707,
0.0709,0.0736,0.0774,0.0800,0.0827,0.0860,0.0917,0.0921,0.0965,0.0970,
0.1036,0.1116,0.1147,0.1194,0.1236,0.1275,0.1302,0.1310,0.1339,0.1347,
0.1380,0.1401,0.1435,0.1462,0.1478,0.1626,0.1688,0.1688,0.1693,0.1712,
0.1737,0.1753,0.1788,0.1834,0.1907,0.1970,0.2033,0.2117,0.2126,0.2133,
0.2149,0.2165,0.2174,0.2188,0.2268,0.2271,0.2276,0.2281,0.2293,0.2316,
0.2373,0.2421,0.2453,0.2522,0.2549,0.2613,0.2617,0.2638,0.2809,0.2909,
0.2934,0.3111,0.3223,0.3223,0.3241,0.3309,0.3312,0.3318,0.3469,0.3488,
0.3512,0.3614,0.3648,0.3653,0.3655,0.3712,0.3746,0.3747,0.3839,0.3904,
0.3911,0.3992,0.4006,0.4076,0.4097,0.4097,0.4109,0.4137,0.4148,0.4150,
0.4197,0.4223,0.4238,0.4256,0.4270,0.4376,0.4421,0.4447,0.4462,0.4511,
0.4541,0.4585,0.4770,0.4774,0.4774,0.4863,0.4914,0.4930,0.4952,0.4968,
0.4990,0.4996,0.5114,0.5119,0.5131,0.5136,0.5179,0.5199,0.5215,0.5231,
0.5243,0.5277,0.5283,0.5356,0.5360,0.5421,0.5481,0.5490,0.5500,0.5519,
0.5545,0.5582,0.5588,0.5596,0.5620,0.5652,0.5670,0.5701,0.5733,0.5742,
0.5752,0.5776,0.5779,0.5834,0.5835,0.5910,0.5938,0.6176,0.6180,0.6280,
0.6319,0.6323,0.6334,0.6367,0.6374,0.6426,0.6441,0.6514,0.6575,0.6577,
0.6585,0.6619,0.6665,0.6741,0.6786,0.6857,0.6882,0.6897,0.6917,0.6929,
0.7011,0.7067,0.7126,0.7130,0.7140,0.7186,0.7231,0.7231,0.7280,0.7295,
0.7393,0.7444,0.7512,0.7513,0.7555,0.7609,0.7630,0.7647,0.7675,0.7800,
0.7854,0.7908,0.7998,0.8041,0.8050,0.8103,0.8106,0.8110,0.8185,0.8195,
0.8225,0.8260,0.8329,0.8358,0.8371,0.8392,0.8406,0.8428,0.8452,0.8460,
0.8483,0.8508,0.8556,0.8581,0.8584,0.8591,0.8611,0.8736,0.8746,0.8845,
0.8900,0.8957,0.9032,0.9035,0.9176,0.9201,0.9215,0.9246,0.9277,0.9290,
0.9329,0.9359,0.9366,0.9397,0.9475,0.9525,0.9537,0.9640,0.9656,0.9658,
0.9714,0.9723,0.9724,0.9804,0.9804,0.9866,0.9884,0.9942,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.976613
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.