RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_22:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.66 24.8951 0.902918
2 to 25 16.06 15.4314 0.435564
3 to 26 15.88 15.1041 0.412019
4 to 27 15.69 20.3373 0.742657
5 to 28 15.76 24.1073 0.883451
6 to 29 15.61 11.5026 0.170721
7 to 30 15.52 15.4825 0.439230
8 to 31 15.41 26.7548 0.938237
9 to 32 15.99 18.5164 0.643016
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.353561
Tough bday spacings test for dh-ranFile-2018-07-07_22:31: 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 3 35 83 100 101 66 52 32 21 4 3
(O-E)^2/E 4.1 0.1 1.3 0.1 0.1 1.9 0.0 0.2 2.5 1.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 11.556, p= 0.684
RESULTS OF GCD FOR dh-ranFile-2018-07-07_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.938086
p-value, dist. of gcd's: 0.782230
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.975 0.468 0.256 0.824 0.940 0.380 0.184 0.674
Bits 8 to 15---> 0.598 0.948 0.619 0.631 0.576 0.564 0.425 0.055
Bits 16 to 23---> 0.260 0.264 0.204 0.008 0.322 0.947 0.289 0.806
Bits 24 to 31---> 0.269 0.596 0.602 0.792 0.479 0.925 0.792 0.229
KS test for the above 32 p values: 0.266
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_22:31,
p-values for 5 runs: 0.7366, 0.4967, 0.6189, 0.4100, 0.3251
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 231 211.4 1.814 1.814
r= 29 5146 5134.0 0.028 1.842
r= 30 23091 23103.0 0.006 1.848
r= 31 11532 11551.5 0.033 1.881
chi-square = 1.881 with df = 3; p-value = 0.403
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 198 211.4 0.852 0.852
r= 30 5218 5134.0 1.374 2.226
r= 31 22885 23103.0 2.058 4.284
r= 32 11699 11551.5 1.883 6.166
chi-square = 6.166 with df = 3; p-value = 0.896
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_22:31
b-rank test for bits 1 to 8, p=0.30786
b-rank test for bits 2 to 9, p=0.51805
b-rank test for bits 3 to 10, p=0.23349
b-rank test for bits 4 to 11, p=0.31469
b-rank test for bits 5 to 12, p=0.51183
b-rank test for bits 6 to 13, p=0.36828
b-rank test for bits 7 to 14, p=0.21424
b-rank test for bits 8 to 15, p=0.07561
b-rank test for bits 9 to 16, p=0.67642
b-rank test for bits 10 to 17, p=0.41877
b-rank test for bits 11 to 18, p=0.18409
b-rank test for bits 12 to 19, p=0.64291
b-rank test for bits 13 to 20, p=0.69335
b-rank test for bits 14 to 21, p=0.39375
b-rank test for bits 15 to 22, p=0.07618
b-rank test for bits 16 to 23, p=0.12627
b-rank test for bits 17 to 24, p=0.39051
b-rank test for bits 18 to 25, p=0.57970
b-rank test for bits 19 to 26, p=0.02566
b-rank test for bits 20 to 27, p=0.69707
b-rank test for bits 21 to 28, p=0.92271
b-rank test for bits 22 to 29, p=0.70042
b-rank test for bits 23 to 30, p=0.05132
b-rank test for bits 24 to 31, p=0.86695
b-rank test for bits 25 to 32, p=0.74618
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 = 0.372135
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_22:31
(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 141877 -0.08 0.469894
2 141372 -1.26 0.104659
3 142043 0.31 0.622599
4 141927 0.04 0.516466
5 141949 0.09 0.536924
6 142256 0.81 0.791023
7 142153 0.57 0.715431
8 142194 0.67 0.747012
9 141672 -0.55 0.289615
10 141660 -0.58 0.280099
11 142480 1.33 0.908790
12 141701 -0.49 0.313217
13 141767 -0.33 0.369738
14 142066 0.37 0.642837
15 141361 -1.28 0.100071
16 141098 -1.90 0.029004
17 142091 0.42 0.664386
18 142131 0.52 0.697743
19 141572 -0.79 0.215303
20 141666 -0.57 0.284838
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_22:31
Bits used No. missing words z-score p-value
23 to 32 142047 0.4747 0.682508
22 to 31 141381 -1.8218 0.034241
21 to 30 141360 -1.8942 0.029096
20 to 29 142143 0.8058 0.789809
19 to 28 141887 -0.0770 0.469312
18 to 27 141824 -0.2942 0.384287
17 to 26 142064 0.5333 0.703103
16 to 25 141975 0.2264 0.589574
15 to 24 142298 1.3402 0.909917
14 to 23 142014 0.3609 0.640925
13 to 22 142296 1.3333 0.908791
12 to 21 141739 -0.5873 0.278486
11 to 20 141976 0.2299 0.590914
10 to 19 142012 0.3540 0.638344
9 to 18 141459 -1.5529 0.060228
8 to 17 142153 0.8402 0.799614
7 to 16 142144 0.8092 0.790802
6 to 15 141462 -1.5425 0.061474
5 to 14 141718 -0.6598 0.254704
4 to 13 141833 -0.2632 0.396196
3 to 12 142710 2.7609 0.997118
2 to 11 141661 -0.8563 0.195913
1 to 10 141724 -0.6391 0.261389
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_22:31
Bits used No. missing words z-score p-value
28 to 32 142416 1.7175 0.957058
27 to 31 142308 1.3514 0.911720
26 to 30 142516 2.0565 0.980133
25 to 29 141944 0.1175 0.546778
24 to 28 142441 1.8023 0.964249
23 to 27 142440 1.7989 0.963981
22 to 26 141816 -0.3164 0.375860
21 to 25 141926 0.0565 0.522532
20 to 24 141939 0.1006 0.540057
19 to 23 141752 -0.5333 0.296905
18 to 22 141781 -0.4350 0.331775
17 to 21 141925 0.0531 0.521181
16 to 20 141861 -0.1638 0.434932
15 to 19 141909 -0.0011 0.499554
14 to 18 141346 -1.9096 0.028093
13 to 17 141967 0.1955 0.577496
12 to 16 141965 0.1887 0.574841
11 to 15 142167 0.8735 0.808793
10 to 14 141881 -0.0960 0.461747
9 to 13 142653 2.5209 0.994148
8 to 12 141725 -0.6248 0.266036
7 to 11 141909 -0.0011 0.499554
6 to 10 142008 0.3345 0.630989
5 to 9 141867 -0.1435 0.442951
4 to 8 141696 -0.7232 0.234793
3 to 7 142323 1.4023 0.919583
2 to 6 141873 -0.1232 0.450993
1 to 5 142046 0.4633 0.678421
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_22:31
Bits used No. missing words z-score p-value
31 to 32 141841 -0.2016 0.420129
30 to 31 142015 0.3117 0.622370
29 to 30 141841 -0.2016 0.420129
28 to 29 142136 0.6686 0.748138
27 to 28 141071 -2.4729 0.006700
26 to 27 142146 0.6981 0.757456
25 to 26 141647 -0.7738 0.219514
24 to 25 141456 -1.3373 0.090569
23 to 24 141946 0.1082 0.543070
22 to 23 141939 0.0875 0.534872
21 to 22 141728 -0.5349 0.296361
20 to 21 141834 -0.2222 0.412074
19 to 20 142521 1.8043 0.964411
18 to 19 141624 -0.8417 0.199983
17 to 18 142544 1.8722 0.969409
16 to 17 141727 -0.5378 0.295342
15 to 16 141788 -0.3579 0.360207
14 to 15 141351 -1.6470 0.049780
13 to 14 141601 -0.9095 0.181536
12 to 13 141336 -1.6912 0.045396
11 to 12 141619 -0.8564 0.195880
10 to 11 141802 -0.3166 0.375771
9 to 10 141659 -0.7384 0.230125
8 to 9 142151 0.7129 0.762043
7 to 8 141989 0.2350 0.592901
6 to 7 142080 0.5035 0.692677
5 to 6 142260 1.0344 0.849531
4 to 5 142123 0.6303 0.735749
3 to 4 141727 -0.5378 0.295342
2 to 3 141981 0.2114 0.583719
1 to 2 142239 0.9725 0.834594
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2400.89 -1.402 0.080507
Test results for specific bytes for dh-ranFile-2018-07-07_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2484.57 -0.218 0.413619
2 to 9 2555.69 0.788 0.784529
3 to 10 2480.44 -0.277 0.391019
4 to 11 2445.54 -0.770 0.220611
5 to 12 2529.83 0.422 0.663440
6 to 13 2655.60 2.200 0.986114
7 to 14 2608.86 1.539 0.938156
8 to 15 2447.46 -0.743 0.228731
9 to 16 2532.04 0.453 0.674747
10 to 17 2473.38 -0.377 0.353263
11 to 18 2538.88 0.550 0.708775
12 to 19 2393.51 -1.506 0.066037
13 to 20 2562.01 0.877 0.809727
14 to 21 2412.20 -1.242 0.107183
15 to 22 2460.99 -0.552 0.290589
16 to 23 2491.78 -0.116 0.453732
17 to 24 2515.58 0.220 0.587214
18 to 25 2398.51 -1.435 0.075606
19 to 26 2426.52 -1.039 0.149375
20 to 27 2474.78 -0.357 0.360678
21 to 28 2556.01 0.792 0.785846
22 to 29 2563.05 0.892 0.813698
23 to 30 2643.88 2.035 0.979064
24 to 31 2537.34 0.528 0.701264
25 to 32 2424.58 -1.067 0.143082
CDPARK for dh-ranFile-2018-07-07_22:31: 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
3543 0.9132 0.819442
3544 0.9589 0.831196
3561 1.7352 0.958644
3501 -1.0046 0.157553
3531 0.3653 0.642555
3558 1.5982 0.944998
3506 -0.7763 0.218799
3508 -0.6849 0.246694
3493 -1.3699 0.085365
3527 0.1826 0.572463
Square side=100, avg. no. parked=3527.20 sample std.=23.05
p-value of the KSTEST for those 10 p-values: 0.669184
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_22:31
0.5160,0.7993,0.3320,0.1488,0.2467,0.0827,0.2455,0.2118,0.7703,0.6235,
The KS test for those 10 p-values: 0.399379
The 3DSPHERES test for dh-ranFile-2018-07-07_22:31
sample no r^3 equiv. uni.
1 130.294 0.987004
2 78.035 0.925814
3 18.785 0.465357
4 24.517 0.558346
5 1.066 0.034897
6 35.698 0.695760
7 19.101 0.470973
8 56.800 0.849432
9 23.738 0.546736
10 15.151 0.396524
11 83.174 0.937491
12 53.285 0.830714
13 10.694 0.299848
14 99.992 0.964316
15 74.616 0.916859
16 15.407 0.401636
17 42.739 0.759402
18 6.128 0.184742
19 74.055 0.915287
20 2.487 0.079565
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.092734
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.7 -0.8 0.0 -1.0 0.1
0.6 2.2 -1.3 0.1 0.1 0.5
-0.4 0.4 -1.2 0.4 1.0 0.4
-0.4 -0.1 -0.5 -1.3 -0.2 -0.5
0.1 1.6 0.6 1.2 -1.3 -0.1
1.3 0.4 -1.1 -0.1 -1.9 -0.3
-0.7 -0.7 -0.8 1.0 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:34.065639
z-score=-0.865710, p-value=0.196796
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_22:31
Test no p-value
1 0.154898
2 0.257025
3 0.039339
4 0.390629
5 0.780329
6 0.043089
7 0.700131
8 0.094302
9 0.438768
10 0.009760
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.020484
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_22:31:
(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 66785 0.21 66470 0.58
3 25000.00 24952 0.09 25158 1.00
4 6666.67 6648 0.05 6725 0.51
5 1388.89 1340 1.72 1393 0.01
6 238.10 241 0.04 207 4.06
7 34.72 31 0.40 42 1.53
8 4.96 2 1.77 4 0.19
p=0.36061 p=0.75256
Number of rngs required: 688510, p-value: 0.549
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_22:31
No. of wins: Observed Expected
98936 98585.9
z-score= 1.566, pvalue=0.94133
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66898 66666.7 0.803 0.803
2 37524 37654.3 0.451 1.254
3 26925 26954.7 0.033 1.287
4 19240 19313.5 0.279 1.566
5 14003 13851.4 1.659 3.225
6 9952 9943.5 0.007 3.232
7 7067 7145.0 0.852 4.084
8 5211 5139.1 1.007 5.091
9 3655 3699.9 0.544 5.635
10 2631 2666.3 0.467 6.102
11 1957 1923.3 0.589 6.692
12 1372 1388.7 0.202 6.893
13 996 1003.7 0.059 6.953
14 718 726.1 0.091 7.044
15 496 525.8 1.693 8.737
16 363 381.2 0.864 9.601
17 275 276.5 0.009 9.610
18 189 200.8 0.697 10.307
19 128 146.0 2.216 12.522
20 122 106.2 2.346 14.868
21 278 287.1 0.289 15.157
Chisq= 15.16 for 20 degrees of freedom, p= 0.23266
SUMMARY of craptest
p-value for no. of wins: 0.941330
p-value for throws/game: 0.232656
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_22:31
No. of wins: Observed Expected
98539 98585.9
z-score=-0.210, pvalue=0.41700
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66729 66666.7 0.058 0.058
2 38103 37654.3 5.346 5.405
3 26656 26954.7 3.311 8.715
4 19221 19313.5 0.443 9.158
5 13848 13851.4 0.001 9.159
6 9926 9943.5 0.031 9.190
7 7101 7145.0 0.271 9.461
8 5150 5139.1 0.023 9.484
9 3695 3699.9 0.006 9.491
10 2609 2666.3 1.231 10.722
11 1883 1923.3 0.846 11.568
12 1460 1388.7 3.657 15.224
13 1004 1003.7 0.000 15.224
14 751 726.1 0.851 16.075
15 488 525.8 2.722 18.798
16 377 381.2 0.045 18.843
17 261 276.5 0.873 19.716
18 187 200.8 0.952 20.669
19 143 146.0 0.061 20.730
20 107 106.2 0.006 20.735
21 301 287.1 0.672 21.407
Chisq= 21.41 for 20 degrees of freedom, p= 0.62646
SUMMARY of craptest
p-value for no. of wins: 0.416998
p-value for throws/game: 0.626462
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0067,0.0077,0.0098,0.0205,0.0257,0.0281,0.0290,0.0291,0.0342,0.0349,
0.0393,0.0431,0.0454,0.0498,0.0513,0.0550,0.0602,0.0615,0.0660,0.0756,
0.0756,0.0762,0.0796,0.0805,0.0827,0.0854,0.0906,0.0927,0.0943,0.1001,
0.1047,0.1072,0.1263,0.1431,0.1488,0.1494,0.1549,0.1576,0.1707,0.1815,
0.1839,0.1841,0.1847,0.1959,0.1959,0.1968,0.2000,0.2035,0.2118,0.2142,
0.2153,0.2188,0.2195,0.2206,0.2287,0.2291,0.2301,0.2327,0.2335,0.2348,
0.2455,0.2467,0.2467,0.2547,0.2557,0.2570,0.2597,0.2614,0.2637,0.2660,
0.2662,0.2693,0.2785,0.2801,0.2848,0.2886,0.2896,0.2906,0.2953,0.2953,
0.2964,0.2969,0.2998,0.3079,0.3132,0.3147,0.3223,0.3251,0.3318,0.3320,
0.3533,0.3536,0.3602,0.3606,0.3607,0.3683,0.3697,0.3721,0.3758,0.3759,
0.3798,0.3843,0.3905,0.3906,0.3910,0.3938,0.3962,0.3965,0.3994,0.4016,
0.4025,0.4100,0.4120,0.4121,0.4136,0.4170,0.4188,0.4201,0.4201,0.4247,
0.4349,0.4356,0.4388,0.4392,0.4430,0.4510,0.4537,0.4617,0.4654,0.4685,
0.4693,0.4699,0.4710,0.4793,0.4967,0.4996,0.4996,0.5118,0.5160,0.5165,
0.5180,0.5212,0.5225,0.5349,0.5369,0.5401,0.5431,0.5467,0.5468,0.5490,
0.5583,0.5637,0.5725,0.5748,0.5763,0.5775,0.5797,0.5837,0.5872,0.5896,
0.5909,0.5929,0.5960,0.5980,0.6024,0.6185,0.6189,0.6224,0.6226,0.6235,
0.6265,0.6310,0.6314,0.6383,0.6409,0.6426,0.6428,0.6429,0.6430,0.6634,
0.6644,0.6692,0.6741,0.6747,0.6764,0.6784,0.6825,0.6841,0.6927,0.6933,
0.6958,0.6971,0.6977,0.7001,0.7004,0.7013,0.7031,0.7088,0.7154,0.7357,
0.7366,0.7427,0.7462,0.7470,0.7481,0.7526,0.7575,0.7594,0.7620,0.7703,
0.7803,0.7822,0.7845,0.7858,0.7898,0.7908,0.7910,0.7919,0.7921,0.7993,
0.7996,0.8061,0.8088,0.8097,0.8137,0.8194,0.8238,0.8307,0.8312,0.8346,
0.8494,0.8495,0.8669,0.8835,0.8962,0.9029,0.9088,0.9088,0.9099,0.9117,
0.9153,0.9169,0.9196,0.9227,0.9248,0.9258,0.9375,0.9381,0.9382,0.9382,
0.9399,0.9413,0.9450,0.9467,0.9479,0.9571,0.9586,0.9640,0.9642,0.9643,
0.9644,0.9694,0.9748,0.9791,0.9801,0.9861,0.9870,0.9941,0.9971,
Overall p-value after applying KStest on 269 p-values = 0.886273
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.