RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_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 15.83 14.2127 0.348006
2 to 25 15.66 30.0339 0.973898
3 to 26 15.85 15.0342 0.406980
4 to 27 15.48 25.2145 0.909989
5 to 28 15.55 32.6959 0.987686
6 to 29 15.88 14.2120 0.347955
7 to 30 15.76 13.2626 0.281564
8 to 31 15.68 19.8938 0.720302
9 to 32 15.67 19.7367 0.712082
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.155417
Tough bday spacings test for dh-ranFile-2018-07-12_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 11 42 62 99 100 81 47 22 19 12 5
(O-E)^2/E 0.4 0.8 1.7 0.0 0.1 0.1 0.5 2.0 1.1 4.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 11.327, p= 0.667
RESULTS OF GCD FOR dh-ranFile-2018-07-12_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.675484
p-value, dist. of gcd's: 0.848936
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.408 0.990 0.723 0.599 0.203 0.735 0.849 0.865
Bits 8 to 15---> 0.485 0.623 0.092 0.882 0.506 0.753 0.187 0.791
Bits 16 to 23---> 0.185 0.604 0.899 0.586 0.986 0.191 0.606 0.668
Bits 24 to 31---> 0.603 0.423 0.627 0.847 0.899 0.061 0.200 0.407
KS test for the above 32 p values: 0.820
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_17:31,
p-values for 5 runs: 0.0318, 0.9500, 0.9935, 0.2327, 0.6752
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 193 211.4 1.605 1.605
r= 29 5182 5134.0 0.449 2.053
r= 30 23170 23103.0 0.194 2.247
r= 31 11455 11551.5 0.807 3.054
chi-square = 3.054 with df = 3; p-value = 0.617
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 5165 5134.0 0.187 0.382
r= 31 23033 23103.0 0.212 0.594
r= 32 11597 11551.5 0.179 0.773
chi-square = 0.773 with df = 3; p-value = 0.144
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_17:31
b-rank test for bits 1 to 8, p=0.18369
b-rank test for bits 2 to 9, p=0.95293
b-rank test for bits 3 to 10, p=0.10578
b-rank test for bits 4 to 11, p=0.35198
b-rank test for bits 5 to 12, p=0.09061
b-rank test for bits 6 to 13, p=0.36234
b-rank test for bits 7 to 14, p=0.07823
b-rank test for bits 8 to 15, p=0.90195
b-rank test for bits 9 to 16, p=0.80389
b-rank test for bits 10 to 17, p=0.94824
b-rank test for bits 11 to 18, p=0.32835
b-rank test for bits 12 to 19, p=0.80186
b-rank test for bits 13 to 20, p=0.65864
b-rank test for bits 14 to 21, p=0.00890
b-rank test for bits 15 to 22, p=0.23785
b-rank test for bits 16 to 23, p=0.16691
b-rank test for bits 17 to 24, p=0.17521
b-rank test for bits 18 to 25, p=0.72041
b-rank test for bits 19 to 26, p=0.29828
b-rank test for bits 20 to 27, p=0.09756
b-rank test for bits 21 to 28, p=0.40791
b-rank test for bits 22 to 29, p=0.13812
b-rank test for bits 23 to 30, p=0.33428
b-rank test for bits 24 to 31, p=0.07958
b-rank test for bits 25 to 32, p=0.39921
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 = 0.042783
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_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 141756 -0.36 0.360079
2 141672 -0.55 0.289615
3 142135 0.53 0.700996
4 141898 -0.03 0.489440
5 141330 -1.35 0.087936
6 142134 0.52 0.700184
7 143075 2.72 0.996771
8 141396 -1.20 0.115192
9 142065 0.36 0.641965
10 142118 0.49 0.687065
11 142068 0.37 0.644579
12 141875 -0.08 0.468035
13 141709 -0.47 0.319871
14 141486 -0.99 0.161310
15 142496 1.37 0.914770
16 141854 -0.13 0.448570
17 142347 1.02 0.846750
18 141953 0.10 0.540635
19 142028 0.28 0.609212
20 142629 1.68 0.953664
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_17:31
Bits used No. missing words z-score p-value
23 to 32 142134 0.7747 0.780749
22 to 31 141826 -0.2873 0.386924
21 to 30 141493 -1.4356 0.075555
20 to 29 142192 0.9747 0.835151
19 to 28 142253 1.1851 0.882005
18 to 27 142863 3.2885 0.999496
17 to 26 142186 0.9540 0.829967
16 to 25 142240 1.1402 0.872907
15 to 24 141872 -0.1287 0.448788
14 to 23 142293 1.3230 0.907082
13 to 22 141663 -0.8494 0.197826
12 to 21 141720 -0.6529 0.256923
11 to 20 142205 1.0196 0.846029
10 to 19 141758 -0.5218 0.300895
9 to 18 141706 -0.7011 0.241609
8 to 17 141884 -0.0873 0.465199
7 to 16 142072 0.5609 0.712578
6 to 15 141676 -0.8046 0.210529
5 to 14 141937 0.0954 0.538007
4 to 13 142163 0.8747 0.809138
3 to 12 141738 -0.5908 0.277330
2 to 11 142174 0.9127 0.819288
1 to 10 141888 -0.0736 0.470684
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_17:31
Bits used No. missing words z-score p-value
28 to 32 141612 -1.0079 0.156752
27 to 31 142012 0.3480 0.636093
26 to 30 141869 -0.1367 0.445629
25 to 29 142014 0.3548 0.638635
24 to 28 141856 -0.1808 0.428270
23 to 27 142283 1.2667 0.897365
22 to 26 141640 -0.9130 0.180626
21 to 25 141965 0.1887 0.574841
20 to 24 142004 0.3209 0.625863
19 to 23 141856 -0.1808 0.428270
18 to 22 142118 0.7074 0.760327
17 to 21 141605 -1.0316 0.151123
16 to 20 142239 1.1175 0.868115
15 to 19 141776 -0.4520 0.325647
14 to 18 140929 -3.3232 0.000445
13 to 17 141996 0.2938 0.615543
12 to 16 141656 -0.8587 0.195240
11 to 15 141471 -1.4859 0.068658
10 to 14 141808 -0.3435 0.365614
9 to 13 141546 -1.2316 0.109044
8 to 12 142152 0.8226 0.794635
7 to 11 141444 -1.5774 0.057353
6 to 10 141745 -0.5571 0.288746
5 to 9 142302 1.3311 0.908419
4 to 8 141928 0.0633 0.525232
3 to 7 142024 0.3887 0.651255
2 to 6 141839 -0.2384 0.405783
1 to 5 141588 -1.0893 0.138021
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_17:31
Bits used No. missing words z-score p-value
31 to 32 141851 -0.1721 0.431693
30 to 31 141425 -1.4287 0.076545
29 to 30 141512 -1.1721 0.120586
28 to 29 142056 0.4327 0.667367
27 to 28 141987 0.2291 0.590610
26 to 27 142091 0.5359 0.703986
25 to 26 141760 -0.4405 0.329787
24 to 25 142002 0.2734 0.607713
23 to 24 141952 0.1259 0.550083
22 to 23 141668 -0.7119 0.238267
21 to 22 142472 1.6598 0.951522
20 to 21 142087 0.5241 0.699896
19 to 20 141854 -0.1632 0.435174
18 to 19 142237 0.9666 0.833123
17 to 18 141801 -0.3196 0.374652
16 to 17 142629 2.1229 0.983120
15 to 16 142102 0.5683 0.715101
14 to 15 141398 -1.5083 0.065733
13 to 14 142154 0.7217 0.764773
12 to 13 142004 0.2793 0.609978
11 to 12 142018 0.3206 0.625728
10 to 11 141719 -0.5614 0.287247
9 to 10 142084 0.5153 0.696811
8 to 9 142053 0.4238 0.664146
7 to 8 142098 0.5565 0.711082
6 to 7 141812 -0.2871 0.387014
5 to 6 141974 0.1908 0.575646
4 to 5 142209 0.8840 0.811647
3 to 4 141708 -0.5939 0.276292
2 to 3 141774 -0.3992 0.344872
1 to 2 141621 -0.8505 0.197515
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2444.96 -0.778 0.218192
Test results for specific bytes for dh-ranFile-2018-07-12_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2565.62 0.928 0.823297
2 to 9 2387.03 -1.598 0.055069
3 to 10 2570.40 0.996 0.840267
4 to 11 2495.14 -0.069 0.472600
5 to 12 2451.19 -0.690 0.244994
6 to 13 2405.33 -1.339 0.090306
7 to 14 2461.46 -0.545 0.292875
8 to 15 2575.00 1.061 0.855571
9 to 16 2525.36 0.359 0.640081
10 to 17 2553.71 0.760 0.776228
11 to 18 2397.27 -1.453 0.073137
12 to 19 2493.00 -0.099 0.460581
13 to 20 2439.31 -0.858 0.195359
14 to 21 2523.10 0.327 0.628020
15 to 22 2561.56 0.871 0.808016
16 to 23 2522.29 0.315 0.623724
17 to 24 2470.52 -0.417 0.338392
18 to 25 2522.73 0.321 0.626070
19 to 26 2585.21 1.205 0.885911
20 to 27 2480.07 -0.282 0.389012
21 to 28 2531.89 0.451 0.673999
22 to 29 2499.13 -0.012 0.495103
23 to 30 2369.78 -1.842 0.032767
24 to 31 2665.14 2.335 0.990239
25 to 32 2463.88 -0.511 0.304743
CDPARK for dh-ranFile-2018-07-12_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
3574 2.3288 0.990064
3511 -0.5479 0.291865
3558 1.5982 0.944998
3564 1.8721 0.969407
3523 0.0000 0.500000
3499 -1.0959 0.136563
3506 -0.7763 0.218799
3527 0.1826 0.572463
3551 1.2785 0.899470
3521 -0.0913 0.463617
Square side=100, avg. no. parked=3533.40 sample std.=24.98
p-value of the KSTEST for those 10 p-values: 0.186320
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_17:31
0.6091,0.3742,0.6206,0.9671,0.5892,0.7233,0.5480,0.2554,0.1192,0.2741,
The KS test for those 10 p-values: 0.818088
The 3DSPHERES test for dh-ranFile-2018-07-12_17:31
sample no r^3 equiv. uni.
1 0.983 0.032226
2 81.580 0.934082
3 18.894 0.467309
4 30.004 0.632167
5 36.105 0.699856
6 55.696 0.843785
7 14.358 0.380346
8 6.763 0.201824
9 42.268 0.755594
10 80.410 0.931460
11 52.062 0.823669
12 49.762 0.809623
13 37.716 0.715550
14 24.691 0.560902
15 12.155 0.333129
16 3.857 0.120650
17 31.734 0.652778
18 37.590 0.714354
19 4.494 0.139114
20 16.662 0.426149
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.581081
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 0.3 0.9 0.1 -0.2
-0.7 -0.6 0.7 -1.0 -1.1 -1.5
1.5 -1.1 0.2 1.9 1.6 -0.4
-1.1 1.4 1.3 1.2 -2.1 -0.5
-1.0 -1.3 -0.4 0.4 1.2 -1.6
-0.8 -2.0 0.0 2.9 -0.9 -1.4
-0.9 -2.0 -1.2 -0.7 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:60.604657
z-score=2.029934, p-value=0.968571
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_17:31
Test no p-value
1 0.864461
2 0.021401
3 0.000017
4 0.663263
5 0.741836
6 0.118324
7 0.015470
8 0.084814
9 0.062388
10 0.473276
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002559
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_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 66644 0.01 66780 0.19
3 25000.00 25144 0.83 24906 0.35
4 6666.67 6571 1.37 6619 0.34
5 1388.89 1329 2.58 1425 0.94
6 238.10 274 5.41 225 0.72
7 34.72 31 0.40 39 0.53
8 4.96 6 0.22 5 0.00
p=0.90602 p=0.20049
Number of rngs required: 689584, p-value: 0.916
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_17:31
No. of wins: Observed Expected
98538 98585.9
z-score=-0.214, pvalue=0.41525
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66093 66666.7 4.936 4.936
2 37882 37654.3 1.377 6.313
3 26926 26954.7 0.031 6.344
4 19579 19313.5 3.651 9.995
5 13781 13851.4 0.358 10.353
6 10068 9943.5 1.558 11.910
7 7185 7145.0 0.224 12.134
8 5152 5139.1 0.033 12.166
9 3689 3699.9 0.032 12.198
10 2612 2666.3 1.106 13.304
11 1945 1923.3 0.244 13.548
12 1425 1388.7 0.947 14.495
13 969 1003.7 1.201 15.696
14 769 726.1 2.530 18.225
15 516 525.8 0.184 18.409
16 373 381.2 0.174 18.584
17 279 276.5 0.022 18.606
18 195 200.8 0.169 18.775
19 145 146.0 0.007 18.781
20 104 106.2 0.046 18.828
21 313 287.1 2.334 21.162
Chisq= 21.16 for 20 degrees of freedom, p= 0.61232
SUMMARY of craptest
p-value for no. of wins: 0.415253
p-value for throws/game: 0.612318
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_17:31
No. of wins: Observed Expected
98235 98585.9
z-score=-1.569, pvalue=0.05830
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66627 66666.7 0.024 0.024
2 37432 37654.3 1.313 1.336
3 26759 26954.7 1.421 2.758
4 19627 19313.5 5.090 7.848
5 14069 13851.4 3.418 11.265
6 9994 9943.5 0.256 11.521
7 6976 7145.0 3.999 15.520
8 5085 5139.1 0.569 16.089
9 3692 3699.9 0.017 16.106
10 2706 2666.3 0.591 16.697
11 1953 1923.3 0.458 17.155
12 1387 1388.7 0.002 17.157
13 977 1003.7 0.711 17.868
14 759 726.1 1.487 19.355
15 519 525.8 0.089 19.444
16 363 381.2 0.864 20.308
17 278 276.5 0.008 20.316
18 221 200.8 2.026 22.341
19 159 146.0 1.160 23.502
20 107 106.2 0.006 23.508
21 310 287.1 1.824 25.332
Chisq= 25.33 for 20 degrees of freedom, p= 0.81097
SUMMARY of craptest
p-value for no. of wins: 0.058296
p-value for throws/game: 0.810972
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0004,0.0026,0.0089,0.0155,0.0214,0.0318,0.0322,0.0328,0.0428,
0.0551,0.0574,0.0583,0.0612,0.0624,0.0657,0.0687,0.0731,0.0756,0.0765,
0.0782,0.0796,0.0848,0.0879,0.0903,0.0906,0.0916,0.0976,0.1058,0.1090,
0.1152,0.1183,0.1192,0.1206,0.1207,0.1366,0.1380,0.1381,0.1391,0.1442,
0.1511,0.1554,0.1568,0.1613,0.1669,0.1752,0.1806,0.1837,0.1850,0.1863,
0.1866,0.1909,0.1952,0.1954,0.1975,0.1978,0.2004,0.2005,0.2018,0.2034,
0.2105,0.2182,0.2188,0.2327,0.2378,0.2383,0.2416,0.2450,0.2554,0.2569,
0.2741,0.2763,0.2773,0.2816,0.2872,0.2887,0.2896,0.2919,0.2929,0.2983,
0.3009,0.3047,0.3199,0.3256,0.3284,0.3298,0.3331,0.3343,0.3384,0.3449,
0.3480,0.3480,0.3520,0.3601,0.3623,0.3656,0.3742,0.3747,0.3803,0.3869,
0.3870,0.3890,0.3992,0.4058,0.4067,0.4070,0.4079,0.4080,0.4153,0.4231,
0.4261,0.4283,0.4283,0.4317,0.4352,0.4456,0.4486,0.4488,0.4606,0.4636,
0.4652,0.4673,0.4680,0.4707,0.4726,0.4733,0.4850,0.4894,0.4951,0.5000,
0.5062,0.5252,0.5380,0.5406,0.5480,0.5501,0.5609,0.5725,0.5748,0.5756,
0.5811,0.5864,0.5892,0.5906,0.5992,0.6032,0.6045,0.6059,0.6077,0.6091,
0.6092,0.6100,0.6123,0.6155,0.6166,0.6206,0.6226,0.6237,0.6257,0.6259,
0.6261,0.6267,0.6280,0.6322,0.6361,0.6386,0.6401,0.6420,0.6446,0.6513,
0.6528,0.6586,0.6633,0.6641,0.6674,0.6674,0.6685,0.6740,0.6752,0.6755,
0.6871,0.6968,0.6999,0.6999,0.7002,0.7010,0.7040,0.7111,0.7121,0.7126,
0.7144,0.7151,0.7155,0.7203,0.7204,0.7233,0.7235,0.7353,0.7418,0.7529,
0.7556,0.7603,0.7648,0.7762,0.7807,0.7910,0.7946,0.8019,0.8039,0.8080,
0.8091,0.8096,0.8110,0.8116,0.8181,0.8193,0.8200,0.8233,0.8237,0.8300,
0.8331,0.8352,0.8403,0.8438,0.8460,0.8467,0.8470,0.8488,0.8489,0.8556,
0.8645,0.8646,0.8681,0.8729,0.8820,0.8821,0.8859,0.8974,0.8989,0.8994,
0.8995,0.9019,0.9060,0.9071,0.9084,0.9100,0.9148,0.9157,0.9315,0.9341,
0.9450,0.9482,0.9500,0.9515,0.9529,0.9537,0.9671,0.9686,0.9694,0.9739,
0.9831,0.9862,0.9877,0.9901,0.9902,0.9904,0.9935,0.9968,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.616244
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.