RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.42 26.2785 0.930466
2 to 25 15.67 42.0413 0.999338
3 to 26 15.39 21.9264 0.812435
4 to 27 15.56 24.5786 0.895453
5 to 28 15.68 21.1261 0.779299
6 to 29 15.95 24.0972 0.883182
7 to 30 15.87 15.5600 0.444789
8 to 31 15.76 24.3884 0.890739
9 to 32 15.78 26.7648 0.938392
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000154
Tough bday spacings test for dh-ranFile-2018-06-17_17:31: 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 41 86 99 98 77 41 27 15 5 1
(O-E)^2/E 0.1 0.5 2.2 0.0 0.0 0.0 2.4 0.3 0.0 0.4 2.3
Birthday Spacings: Sum(O-E)^2/E= 8.178, p= 0.389
RESULTS OF GCD FOR dh-ranFile-2018-06-17_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.091935
p-value, dist. of gcd's: 0.927935
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.938 0.417 0.557 0.828 0.195 0.192 0.168 0.926
Bits 8 to 15---> 0.486 0.009 0.478 0.804 0.066 0.601 0.638 0.804
Bits 16 to 23---> 0.184 0.340 0.123 0.889 0.377 0.572 0.954 0.238
Bits 24 to 31---> 0.017 0.749 0.100 0.646 0.986 0.800 0.768 0.613
KS test for the above 32 p values: 0.083
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_17:31,
p-values for 5 runs: 0.0219, 0.3287, 0.4957, 0.9675, 0.8986
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5117 5134.0 0.056 0.805
r= 30 22973 23103.0 0.732 1.537
r= 31 11686 11551.5 1.565 3.103
chi-square = 3.103 with df = 3; p-value = 0.624
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 224 211.4 0.749 0.749
r= 30 5126 5134.0 0.012 0.761
r= 31 22988 23103.0 0.573 1.334
r= 32 11662 11551.5 1.057 2.391
chi-square = 2.391 with df = 3; p-value = 0.505
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_17:31
b-rank test for bits 1 to 8, p=0.79734
b-rank test for bits 2 to 9, p=0.93602
b-rank test for bits 3 to 10, p=0.34232
b-rank test for bits 4 to 11, p=0.67854
b-rank test for bits 5 to 12, p=0.42414
b-rank test for bits 6 to 13, p=0.56734
b-rank test for bits 7 to 14, p=0.94185
b-rank test for bits 8 to 15, p=0.52644
b-rank test for bits 9 to 16, p=0.88587
b-rank test for bits 10 to 17, p=0.99847
b-rank test for bits 11 to 18, p=0.83242
b-rank test for bits 12 to 19, p=0.77776
b-rank test for bits 13 to 20, p=0.96719
b-rank test for bits 14 to 21, p=0.52927
b-rank test for bits 15 to 22, p=0.74392
b-rank test for bits 16 to 23, p=0.97638
b-rank test for bits 17 to 24, p=0.32028
b-rank test for bits 18 to 25, p=0.27061
b-rank test for bits 19 to 26, p=0.60180
b-rank test for bits 20 to 27, p=0.01392
b-rank test for bits 21 to 28, p=0.74635
b-rank test for bits 22 to 29, p=0.41686
b-rank test for bits 23 to 30, p=0.27414
b-rank test for bits 24 to 31, p=0.27308
b-rank test for bits 25 to 32, p=0.98883
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 = 0.019728
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_17:31
(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 141768 -0.33 0.370621
2 142478 1.33 0.908021
3 141947 0.09 0.535067
4 141356 -1.29 0.098035
5 142062 0.36 0.639344
6 141872 -0.09 0.465249
7 142698 1.84 0.967313
8 141901 -0.02 0.492236
9 141640 -0.63 0.264584
10 141895 -0.03 0.486645
11 141663 -0.58 0.282464
12 141562 -0.81 0.208534
13 142339 1.00 0.842287
14 142298 0.91 0.818089
15 141679 -0.54 0.295235
16 141340 -1.33 0.091725
17 142480 1.33 0.908790
18 142413 1.18 0.880362
19 142494 1.37 0.914039
20 142203 0.69 0.753689
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_17:31
Bits used No. missing words z-score p-value
23 to 32 142116 0.7127 0.761970
22 to 31 142203 1.0127 0.844388
21 to 30 141998 0.3058 0.620106
20 to 29 141951 0.1437 0.557127
19 to 28 141660 -0.8598 0.194961
18 to 27 141282 -2.1632 0.015263
17 to 26 142580 2.3127 0.989629
16 to 25 142129 0.7575 0.775620
15 to 24 141782 -0.4391 0.330306
14 to 23 141894 -0.0529 0.478921
13 to 22 141680 -0.7908 0.214532
12 to 21 141975 0.2264 0.589574
11 to 20 142467 1.9230 0.972760
10 to 19 141516 -1.3563 0.087500
9 to 18 142004 0.3264 0.627957
8 to 17 141785 -0.4287 0.334062
7 to 16 141634 -0.9494 0.171205
6 to 15 141937 0.0954 0.538007
5 to 14 142133 0.7713 0.779728
4 to 13 141783 -0.4356 0.331556
3 to 12 141749 -0.5529 0.290179
2 to 11 141745 -0.5667 0.285474
1 to 10 142254 1.1885 0.882685
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_17:31
Bits used No. missing words z-score p-value
28 to 32 141982 0.2463 0.597290
27 to 31 141635 -0.9299 0.176203
26 to 30 141808 -0.3435 0.365614
25 to 29 141993 0.2836 0.611652
24 to 28 141809 -0.3401 0.366890
23 to 27 141620 -0.9808 0.163351
22 to 26 142122 0.7209 0.764519
21 to 25 141972 0.2124 0.584118
20 to 24 142338 1.4531 0.926905
19 to 23 142045 0.4599 0.677205
18 to 22 141874 -0.1198 0.452336
17 to 21 141733 -0.5977 0.275010
16 to 20 142019 0.3718 0.644965
15 to 19 141919 0.0328 0.513075
14 to 18 141676 -0.7909 0.214487
13 to 17 141644 -0.8994 0.184214
12 to 16 141760 -0.5062 0.306357
11 to 15 141741 -0.5706 0.284132
10 to 14 141200 -2.4045 0.008097
9 to 13 141761 -0.5028 0.307548
8 to 12 142227 1.0768 0.859226
7 to 11 142012 0.3480 0.636093
6 to 10 141851 -0.1977 0.421629
5 to 9 141959 0.1684 0.566855
4 to 8 142426 1.7514 0.960064
3 to 7 141805 -0.3537 0.361797
2 to 6 141914 0.0158 0.506315
1 to 5 142563 2.2158 0.986648
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_17:31
Bits used No. missing words z-score p-value
31 to 32 142274 1.0757 0.858974
30 to 31 141710 -0.5880 0.278268
29 to 30 141829 -0.2370 0.406343
28 to 29 142598 2.0315 0.978897
27 to 28 141972 0.1849 0.573333
26 to 27 142051 0.4179 0.661992
25 to 26 142350 1.2999 0.903184
24 to 25 141858 -0.1514 0.439824
23 to 24 141634 -0.8122 0.208343
22 to 23 142061 0.4474 0.672708
21 to 22 141633 -0.8151 0.207498
20 to 21 141951 0.1229 0.548915
19 to 20 142187 0.8191 0.793631
18 to 19 142239 0.9725 0.834594
17 to 18 142007 0.2881 0.613370
16 to 17 141930 0.0610 0.524310
15 to 16 141955 0.1347 0.553583
14 to 15 142710 2.3619 0.990908
13 to 14 142540 1.8604 0.968584
12 to 13 141163 -2.2016 0.013848
11 to 12 141779 -0.3845 0.350321
10 to 11 141827 -0.2429 0.404056
9 to 10 141507 -1.1868 0.117650
8 to 9 141698 -0.6234 0.266513
7 to 8 142161 0.7424 0.771074
6 to 7 142315 1.1967 0.884282
5 to 6 141862 -0.1396 0.444482
4 to 5 142227 0.9371 0.825641
3 to 4 141768 -0.4169 0.338375
2 to 3 141776 -0.3933 0.347048
1 to 2 141960 0.1495 0.559408
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2454.98 -0.637 0.262181
Test results for specific bytes for dh-ranFile-2018-06-17_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2380.06 -1.696 0.044920
2 to 9 2565.57 0.927 0.823131
3 to 10 2498.99 -0.014 0.494300
4 to 11 2654.30 2.182 0.985451
5 to 12 2528.95 0.409 0.658859
6 to 13 2488.08 -0.169 0.433061
7 to 14 2665.28 2.337 0.990291
8 to 15 2523.19 0.328 0.628517
9 to 16 2523.70 0.335 0.631243
10 to 17 2477.11 -0.324 0.373069
11 to 18 2489.22 -0.152 0.439428
12 to 19 2438.15 -0.875 0.190879
13 to 20 2464.71 -0.499 0.308854
14 to 21 2515.29 0.216 0.585570
15 to 22 2594.68 1.339 0.909710
16 to 23 2566.78 0.944 0.827535
17 to 24 2447.70 -0.740 0.229779
18 to 25 2349.32 -2.131 0.016546
19 to 26 2626.29 1.786 0.962949
20 to 27 2501.98 0.028 0.511184
21 to 28 2421.67 -1.108 0.133974
22 to 29 2531.98 0.452 0.674467
23 to 30 2416.81 -1.177 0.119693
24 to 31 2449.17 -0.719 0.236123
25 to 32 2459.07 -0.579 0.281363
CDPARK for dh-ranFile-2018-06-17_17:31: 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
3530 0.3196 0.625377
3544 0.9589 0.831196
3539 0.7306 0.767486
3505 -0.8219 0.205562
3492 -1.4155 0.078457
3533 0.4566 0.676028
3523 0.0000 0.500000
3552 1.3242 0.907282
3527 0.1826 0.572463
3509 -0.6393 0.261324
Square side=100, avg. no. parked=3525.40 sample std.=17.68
p-value of the KSTEST for those 10 p-values: 0.923286
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_17:31
0.2655,0.5561,0.1103,0.2076,0.3426,0.2797,0.6957,0.6893,0.7164,0.8838,
The KS test for those 10 p-values: 0.856681
The 3DSPHERES test for dh-ranFile-2018-06-17_17:31
sample no r^3 equiv. uni.
1 8.225 0.239784
2 51.417 0.819837
3 69.186 0.900362
4 134.131 0.988564
5 14.893 0.391300
6 8.581 0.248762
7 57.038 0.850620
8 40.312 0.739132
9 57.687 0.853816
10 32.147 0.657532
11 15.855 0.410517
12 0.904 0.029694
13 13.074 0.353248
14 22.495 0.527553
15 7.941 0.232562
16 29.370 0.624310
17 48.543 0.801727
18 12.980 0.351222
19 7.651 0.225122
20 64.920 0.885136
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.562388
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 1.3 0.3 0.0 0.4 1.6
0.4 -0.3 0.4 0.5 -0.4 -0.2
0.3 2.2 -0.6 0.2 -0.9 -0.9
0.1 -0.9 0.4 0.2 -1.1 -0.6
-0.5 2.6 0.5 0.9 -0.4 -0.1
-0.1 -0.6 -1.3 -0.3 -0.6 -0.8
0.3 -0.7 -1.6 1.0 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:33.005871
z-score=-0.981340, p-value=0.161700
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_17:31
Test no p-value
1 0.369090
2 0.910938
3 0.044918
4 0.937642
5 0.251502
6 0.087192
7 0.043687
8 0.413523
9 0.457157
10 0.754172
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.469827
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_17:31:
(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 66717 0.04 66712 0.03
3 25000.00 25054 0.12 25011 0.00
4 6666.67 6557 1.80 6629 0.21
5 1388.89 1399 0.07 1352 0.98
6 238.10 219 1.53 249 0.50
7 34.72 49 5.87 40 0.80
8 4.96 4 0.19 6 0.22
p=0.85854 p=0.16035
Number of rngs required: 688340, p-value: 0.471
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_17:31
No. of wins: Observed Expected
98473 98585.9
z-score=-0.505, pvalue=0.30686
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66439 66666.7 0.777 0.777
2 38028 37654.3 3.708 4.486
3 27028 26954.7 0.199 4.685
4 19193 19313.5 0.751 5.436
5 13902 13851.4 0.185 5.621
6 9791 9943.5 2.340 7.961
7 7156 7145.0 0.017 7.978
8 5206 5139.1 0.872 8.850
9 3801 3699.9 2.765 11.614
10 2532 2666.3 6.764 18.379
11 1946 1923.3 0.267 18.646
12 1411 1388.7 0.357 19.003
13 956 1003.7 2.268 21.271
14 709 726.1 0.405 21.675
15 523 525.8 0.015 21.691
16 396 381.2 0.579 22.269
17 259 276.5 1.112 23.382
18 215 200.8 1.000 24.382
19 142 146.0 0.109 24.490
20 103 106.2 0.097 24.588
21 264 287.1 1.861 26.448
Chisq= 26.45 for 20 degrees of freedom, p= 0.84849
SUMMARY of craptest
p-value for no. of wins: 0.306860
p-value for throws/game: 0.848492
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_17:31
No. of wins: Observed Expected
98444 98585.9
z-score=-0.634, pvalue=0.26289
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66451 66666.7 0.698 0.698
2 37687 37654.3 0.028 0.726
3 27022 26954.7 0.168 0.894
4 19426 19313.5 0.656 1.550
5 13823 13851.4 0.058 1.608
6 9916 9943.5 0.076 1.684
7 7089 7145.0 0.439 2.124
8 5155 5139.1 0.049 2.173
9 3733 3699.9 0.297 2.470
10 2685 2666.3 0.131 2.601
11 1987 1923.3 2.108 4.709
12 1371 1388.7 0.227 4.935
13 1053 1003.7 2.420 7.355
14 674 726.1 3.744 11.099
15 562 525.8 2.487 13.586
16 386 381.2 0.062 13.648
17 275 276.5 0.009 13.657
18 192 200.8 0.388 14.045
19 137 146.0 0.553 14.598
20 95 106.2 1.184 15.782
21 281 287.1 0.130 15.912
Chisq= 15.91 for 20 degrees of freedom, p= 0.27795
SUMMARY of craptest
p-value for no. of wins: 0.262886
p-value for throws/game: 0.277949
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0081,0.0088,0.0138,0.0139,0.0153,0.0165,0.0175,0.0197,0.0219,
0.0297,0.0437,0.0449,0.0449,0.0657,0.0785,0.0833,0.0872,0.0875,0.0917,
0.0919,0.0980,0.1003,0.1103,0.1177,0.1197,0.1235,0.1340,0.1604,0.1617,
0.1634,0.1684,0.1712,0.1762,0.1838,0.1842,0.1909,0.1923,0.1950,0.1954,
0.2056,0.2075,0.2076,0.2083,0.2085,0.2145,0.2145,0.2251,0.2298,0.2326,
0.2361,0.2375,0.2398,0.2488,0.2515,0.2613,0.2622,0.2629,0.2646,0.2655,
0.2665,0.2706,0.2731,0.2741,0.2750,0.2779,0.2783,0.2797,0.2814,0.2825,
0.2841,0.2855,0.2902,0.2952,0.3064,0.3069,0.3075,0.3089,0.3203,0.3287,
0.3303,0.3316,0.3341,0.3384,0.3402,0.3423,0.3426,0.3470,0.3503,0.3512,
0.3532,0.3618,0.3656,0.3669,0.3691,0.3706,0.3731,0.3771,0.3885,0.3913,
0.4041,0.4063,0.4105,0.4135,0.4168,0.4169,0.4216,0.4241,0.4331,0.4394,
0.4398,0.4445,0.4448,0.4523,0.4572,0.4652,0.4698,0.4711,0.4779,0.4789,
0.4856,0.4866,0.4922,0.4943,0.4957,0.5000,0.5046,0.5063,0.5112,0.5131,
0.5243,0.5264,0.5276,0.5293,0.5351,0.5380,0.5489,0.5536,0.5561,0.5571,
0.5571,0.5594,0.5624,0.5669,0.5673,0.5722,0.5725,0.5733,0.5841,0.5856,
0.5896,0.5973,0.6006,0.6018,0.6117,0.6128,0.6134,0.6201,0.6239,0.6243,
0.6254,0.6280,0.6285,0.6312,0.6361,0.6379,0.6393,0.6450,0.6464,0.6575,
0.6589,0.6620,0.6727,0.6745,0.6760,0.6772,0.6785,0.6893,0.6957,0.7164,
0.7391,0.7439,0.7463,0.7487,0.7537,0.7542,0.7620,0.7645,0.7675,0.7676,
0.7711,0.7756,0.7778,0.7793,0.7797,0.7936,0.7973,0.7996,0.8017,0.8036,
0.8038,0.8124,0.8181,0.8198,0.8231,0.8256,0.8275,0.8284,0.8312,0.8324,
0.8346,0.8423,0.8444,0.8485,0.8506,0.8538,0.8567,0.8585,0.8590,0.8592,
0.8804,0.8827,0.8832,0.8838,0.8843,0.8851,0.8859,0.8894,0.8907,0.8955,
0.8986,0.9004,0.9032,0.9073,0.9080,0.9088,0.9097,0.9109,0.9140,0.9233,
0.9257,0.9269,0.9279,0.9305,0.9360,0.9376,0.9379,0.9384,0.9419,0.9538,
0.9601,0.9629,0.9672,0.9673,0.9675,0.9686,0.9728,0.9764,0.9789,0.9855,
0.9865,0.9866,0.9886,0.9888,0.9896,0.9903,0.9909,0.9985,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.041442
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.