RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.43 19.0559 0.674669
2 to 25 15.57 24.4166 0.891449
3 to 26 15.68 19.3618 0.691834
4 to 27 15.71 23.2136 0.857575
5 to 28 15.79 15.5302 0.442654
6 to 29 15.79 22.6133 0.837733
7 to 30 15.41 26.1529 0.928280
8 to 31 15.52 21.0669 0.776687
9 to 32 15.66 18.8090 0.660397
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.011543
Tough bday spacings test for dh-ranFile-2018-06-23_01:31: 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 12 39 74 111 102 68 43 29 12 6 4
(O-E)^2/E 0.9 0.2 0.0 1.8 0.2 1.3 1.6 0.0 0.6 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 6.593, p= 0.237
RESULTS OF GCD FOR dh-ranFile-2018-06-23_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.522852
p-value, dist. of gcd's: 0.879460
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.871 0.208 0.033 0.590 0.273 0.767 0.799 0.219
Bits 8 to 15---> 0.798 0.023 0.935 0.500 0.751 0.841 0.999 0.686
Bits 16 to 23---> 0.913 0.133 0.747 0.273 0.714 0.163 0.795 0.727
Bits 24 to 31---> 0.025 0.935 0.123 0.170 0.532 0.237 0.511 0.451
KS test for the above 32 p values: 0.465
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_01:31,
p-values for 5 runs: 0.2883, 0.9284, 0.7189, 0.7955, 0.9328
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5065 5134.0 0.928 2.228
r= 30 23290 23103.0 1.513 3.741
r= 31 11417 11551.5 1.567 5.308
chi-square = 5.308 with df = 3; p-value = 0.849
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5097 5134.0 0.267 2.239
r= 31 23208 23103.0 0.477 2.715
r= 32 11504 11551.5 0.196 2.911
chi-square = 2.911 with df = 3; p-value = 0.594
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_01:31
b-rank test for bits 1 to 8, p=0.82765
b-rank test for bits 2 to 9, p=0.63026
b-rank test for bits 3 to 10, p=0.99283
b-rank test for bits 4 to 11, p=0.91206
b-rank test for bits 5 to 12, p=0.86345
b-rank test for bits 6 to 13, p=0.55368
b-rank test for bits 7 to 14, p=0.16853
b-rank test for bits 8 to 15, p=0.07751
b-rank test for bits 9 to 16, p=0.05877
b-rank test for bits 10 to 17, p=0.40351
b-rank test for bits 11 to 18, p=0.30324
b-rank test for bits 12 to 19, p=0.87715
b-rank test for bits 13 to 20, p=0.18769
b-rank test for bits 14 to 21, p=0.51732
b-rank test for bits 15 to 22, p=0.15070
b-rank test for bits 16 to 23, p=0.35960
b-rank test for bits 17 to 24, p=0.92083
b-rank test for bits 18 to 25, p=0.56018
b-rank test for bits 19 to 26, p=0.49046
b-rank test for bits 20 to 27, p=0.28836
b-rank test for bits 21 to 28, p=0.68572
b-rank test for bits 22 to 29, p=0.75790
b-rank test for bits 23 to 30, p=0.88645
b-rank test for bits 24 to 31, p=0.21714
b-rank test for bits 25 to 32, p=0.50355
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 = 0.920759
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_01:31
(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 142674 1.79 0.963000
2 141308 -1.40 0.080014
3 143054 2.67 0.996258
4 142229 0.75 0.772436
5 141628 -0.66 0.255490
6 141990 0.19 0.574750
7 142047 0.32 0.626144
8 141606 -0.71 0.239251
9 141828 -0.19 0.424645
10 141537 -0.87 0.192169
11 141746 -0.38 0.351375
12 141863 -0.11 0.456900
13 142024 0.27 0.605620
14 141214 -1.62 0.052124
15 142481 1.34 0.909173
16 141703 -0.48 0.314875
17 141764 -0.34 0.367095
18 141743 -0.39 0.348778
19 141839 -0.16 0.434739
20 142211 0.70 0.759544
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_01:31
Bits used No. missing words z-score p-value
23 to 32 142099 0.6540 0.743455
22 to 31 141372 -1.8529 0.031951
21 to 30 141936 0.0920 0.536637
20 to 29 142104 0.6713 0.748978
19 to 28 141857 -0.1804 0.428400
18 to 27 141395 -1.7736 0.038069
17 to 26 142175 0.9161 0.820194
16 to 25 142199 0.9989 0.841069
15 to 24 141826 -0.2873 0.386924
14 to 23 141531 -1.3046 0.096017
13 to 22 142157 0.8540 0.803457
12 to 21 141733 -0.6080 0.271582
11 to 20 142224 1.0851 0.861054
10 to 19 141550 -1.2391 0.107660
9 to 18 141888 -0.0736 0.470684
8 to 17 141920 0.0368 0.514675
7 to 16 141572 -1.1632 0.122373
6 to 15 141452 -1.5770 0.057398
5 to 14 142124 0.7402 0.770423
4 to 13 141701 -0.7184 0.236262
3 to 12 142397 1.6816 0.953679
2 to 11 142099 0.6540 0.743455
1 to 10 141671 -0.8218 0.205588
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_01:31
Bits used No. missing words z-score p-value
28 to 32 141623 -0.9706 0.165871
27 to 31 142323 1.4023 0.919583
26 to 30 142217 1.0429 0.851514
25 to 29 141312 -2.0248 0.021442
24 to 28 141840 -0.2350 0.407098
23 to 27 141885 -0.0825 0.467135
22 to 26 141834 -0.2554 0.399224
21 to 25 141969 0.2023 0.580148
20 to 24 142119 0.7107 0.761379
19 to 23 141761 -0.5028 0.307548
18 to 22 141244 -2.2554 0.012056
17 to 21 141602 -1.0418 0.148753
16 to 20 141827 -0.2791 0.390090
15 to 19 141814 -0.3232 0.373290
14 to 18 142006 0.3277 0.628429
13 to 17 141946 0.1243 0.549463
12 to 16 142335 1.4429 0.925483
11 to 15 142444 1.8124 0.965041
10 to 14 141753 -0.5299 0.298080
9 to 13 142147 0.8057 0.789781
8 to 12 141914 0.0158 0.506315
7 to 11 141591 -1.0791 0.140275
6 to 10 142253 1.1650 0.877987
5 to 9 142248 1.1480 0.874523
4 to 8 142383 1.6057 0.945826
3 to 7 141735 -0.5909 0.277277
2 to 6 141549 -1.2215 0.110956
1 to 5 142009 0.3379 0.632267
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_01:31
Bits used No. missing words z-score p-value
31 to 32 142380 1.3884 0.917493
30 to 31 141954 0.1318 0.552417
29 to 30 141968 0.1731 0.568701
28 to 29 142210 0.8869 0.812442
27 to 28 141833 -0.2252 0.410927
26 to 27 142032 0.3619 0.641271
25 to 26 142232 0.9518 0.829408
24 to 25 142079 0.5005 0.691639
23 to 24 141524 -1.1367 0.127839
22 to 23 141684 -0.6647 0.253124
21 to 22 142308 1.1760 0.880206
20 to 21 141984 0.2203 0.587168
19 to 20 142414 1.4887 0.931717
18 to 19 141514 -1.1662 0.121774
17 to 18 141853 -0.1662 0.434014
16 to 17 141396 -1.5142 0.064982
15 to 16 141660 -0.7355 0.231022
14 to 15 141440 -1.3845 0.083110
13 to 14 141718 -0.5644 0.286243
12 to 13 141470 -1.2960 0.097495
11 to 12 142129 0.6480 0.741506
10 to 11 142239 0.9725 0.834594
9 to 10 141585 -0.9567 0.169353
8 to 9 141956 0.1377 0.554749
7 to 8 142028 0.3501 0.636853
6 to 7 142521 1.8043 0.964411
5 to 6 141621 -0.8505 0.197515
4 to 5 141771 -0.4081 0.341617
3 to 4 142241 0.9784 0.836056
2 to 3 141771 -0.4081 0.341617
1 to 2 141353 -1.6411 0.050389
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2502.50 0.035 0.514122
Test results for specific bytes for dh-ranFile-2018-06-23_01:31
(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 0.823284
2 to 9 2543.50 0.615 0.730780
3 to 10 2543.16 0.610 0.729193
4 to 11 2576.32 1.079 0.859781
5 to 12 2452.57 -0.671 0.251191
6 to 13 2505.77 0.082 0.532515
7 to 14 2368.60 -1.858 0.031563
8 to 15 2535.86 0.507 0.693963
9 to 16 2483.97 -0.227 0.410336
10 to 17 2639.51 1.973 0.975752
11 to 18 2482.05 -0.254 0.399795
12 to 19 2465.49 -0.488 0.312743
13 to 20 2493.05 -0.098 0.460831
14 to 21 2541.56 0.588 0.721660
15 to 22 2564.35 0.910 0.818596
16 to 23 2520.96 0.296 0.616549
17 to 24 2483.96 -0.227 0.410290
18 to 25 2548.59 0.687 0.754006
19 to 26 2548.37 0.684 0.753020
20 to 27 2594.69 1.339 0.909733
21 to 28 2577.95 1.102 0.864846
22 to 29 2354.97 -2.051 0.020129
23 to 30 2552.63 0.744 0.771637
24 to 31 2609.80 1.553 0.939765
25 to 32 2437.76 -0.880 0.189377
CDPARK for dh-ranFile-2018-06-23_01:31: 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
3545 1.0046 0.842447
3485 -1.7352 0.041356
3481 -1.9178 0.027568
3515 -0.3653 0.357445
3496 -1.2329 0.108811
3527 0.1826 0.572463
3469 -2.4658 0.006836
3484 -1.7808 0.037471
3507 -0.7306 0.232514
3527 0.1826 0.572463
Square side=100, avg. no. parked=3503.60 sample std.=23.34
p-value of the KSTEST for those 10 p-values: 0.006901
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_01:31
0.3082,0.3855,0.2206,0.2553,0.5080,0.8633,0.2186,0.4802,0.3167,0.7748,
The KS test for those 10 p-values: 0.353233
The 3DSPHERES test for dh-ranFile-2018-06-23_01:31
sample no r^3 equiv. uni.
1 24.014 0.550877
2 4.208 0.130860
3 1.762 0.057043
4 20.449 0.494209
5 0.938 0.030786
6 10.049 0.284639
7 16.553 0.424073
8 24.396 0.556562
9 44.469 0.772889
10 44.971 0.776650
11 6.860 0.204401
12 10.587 0.297362
13 1.672 0.054198
14 6.879 0.204900
15 39.733 0.734049
16 66.058 0.889410
17 12.395 0.338457
18 5.305 0.162070
19 19.225 0.473143
20 8.304 0.241786
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.124273
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.6 -1.3 -0.1 -0.4 0.7
0.3 0.6 1.3 -1.6 -0.4 -0.0
0.1 -2.4 -0.8 -1.1 -0.4 0.7
1.3 0.8 -0.4 1.2 -1.2 1.4
0.6 1.3 1.4 -0.5 -0.4 -0.0
2.0 -0.2 0.2 -1.9 -0.2 -1.4
-0.5 -0.4 -0.4 0.4 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:43.194843
z-score=0.130368, p-value=0.579965
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_01:31
Test no p-value
1 0.150083
2 0.303516
3 0.175735
4 0.058989
5 0.049052
6 0.510289
7 0.845092
8 0.603117
9 0.384781
10 0.371151
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.158397
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_01:31:
(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 66142 4.13 66806 0.29
3 25000.00 25424 7.19 24912 0.31
4 6666.67 6741 0.83 6616 0.39
5 1388.89 1445 2.27 1378 0.09
6 238.10 217 1.87 249 0.50
7 34.72 24 3.31 37 0.15
8 4.96 6 0.22 1 3.16
p=0.99701 p=0.44100
Number of rngs required: 688066, p-value: 0.349
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_01:31
No. of wins: Observed Expected
98925 98585.9
z-score= 1.517, pvalue=0.93535
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67096 66666.7 2.765 2.765
2 37513 37654.3 0.530 3.295
3 26857 26954.7 0.354 3.650
4 19394 19313.5 0.336 3.986
5 13743 13851.4 0.849 4.834
6 10027 9943.5 0.700 5.535
7 7013 7145.0 2.440 7.974
8 5133 5139.1 0.007 7.981
9 3707 3699.9 0.014 7.995
10 2608 2666.3 1.275 9.270
11 1908 1923.3 0.122 9.392
12 1382 1388.7 0.033 9.425
13 1004 1003.7 0.000 9.425
14 725 726.1 0.002 9.427
15 509 525.8 0.539 9.966
16 425 381.2 5.045 15.010
17 267 276.5 0.329 15.339
18 185 200.8 1.248 16.587
19 132 146.0 1.340 17.927
20 102 106.2 0.167 18.094
21 270 287.1 1.020 19.114
Chisq= 19.11 for 20 degrees of freedom, p= 0.48558
SUMMARY of craptest
p-value for no. of wins: 0.935346
p-value for throws/game: 0.485575
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_01:31
No. of wins: Observed Expected
98344 98585.9
z-score=-1.082, pvalue=0.13969
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66558 66666.7 0.177 0.177
2 37631 37654.3 0.014 0.192
3 27091 26954.7 0.689 0.880
4 19313 19313.5 0.000 0.880
5 13811 13851.4 0.118 0.998
6 9895 9943.5 0.237 1.235
7 7184 7145.0 0.213 1.448
8 5213 5139.1 1.063 2.511
9 3639 3699.9 1.001 3.513
10 2681 2666.3 0.081 3.594
11 1954 1923.3 0.489 4.083
12 1394 1388.7 0.020 4.103
13 1023 1003.7 0.371 4.473
14 666 726.1 4.981 9.454
15 557 525.8 1.847 11.301
16 341 381.2 4.229 15.531
17 279 276.5 0.022 15.553
18 224 200.8 2.673 18.226
19 170 146.0 3.951 22.177
20 105 106.2 0.014 22.191
21 271 287.1 0.904 23.095
Chisq= 23.09 for 20 degrees of freedom, p= 0.71584
SUMMARY of craptest
p-value for no. of wins: 0.139686
p-value for throws/game: 0.715843
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0068,0.0069,0.0115,0.0121,0.0201,0.0214,0.0232,0.0251,0.0276,0.0308,
0.0316,0.0320,0.0328,0.0375,0.0381,0.0414,0.0491,0.0504,0.0521,0.0542,
0.0570,0.0574,0.0588,0.0590,0.0650,0.0775,0.0800,0.0831,0.0960,0.0975,
0.1077,0.1088,0.1110,0.1218,0.1224,0.1225,0.1243,0.1278,0.1309,0.1330,
0.1397,0.1403,0.1488,0.1501,0.1507,0.1584,0.1621,0.1630,0.1659,0.1685,
0.1694,0.1703,0.1757,0.1877,0.1894,0.1922,0.1975,0.2044,0.2049,0.2056,
0.2079,0.2171,0.2186,0.2187,0.2206,0.2310,0.2325,0.2363,0.2367,0.2368,
0.2393,0.2418,0.2512,0.2531,0.2553,0.2555,0.2716,0.2726,0.2731,0.2773,
0.2846,0.2862,0.2883,0.2884,0.2974,0.2981,0.3032,0.3035,0.3075,0.3082,
0.3127,0.3149,0.3167,0.3385,0.3416,0.3416,0.3488,0.3490,0.3514,0.3532,
0.3574,0.3596,0.3671,0.3712,0.3733,0.3848,0.3855,0.3869,0.3901,0.3992,
0.3998,0.4035,0.4071,0.4103,0.4103,0.4109,0.4241,0.4246,0.4284,0.4340,
0.4347,0.4410,0.4427,0.4510,0.4569,0.4608,0.4655,0.4671,0.4707,0.4731,
0.4802,0.4856,0.4905,0.4942,0.4998,0.5035,0.5063,0.5080,0.5103,0.5114,
0.5141,0.5147,0.5173,0.5229,0.5318,0.5325,0.5366,0.5495,0.5509,0.5524,
0.5537,0.5547,0.5566,0.5602,0.5687,0.5725,0.5725,0.5748,0.5800,0.5801,
0.5872,0.5897,0.5944,0.6031,0.6056,0.6165,0.6261,0.6284,0.6303,0.6323,
0.6369,0.6413,0.6604,0.6747,0.6855,0.6857,0.6916,0.6918,0.6940,0.7139,
0.7158,0.7189,0.7217,0.7274,0.7292,0.7308,0.7340,0.7415,0.7435,0.7435,
0.7467,0.7490,0.7513,0.7530,0.7540,0.7579,0.7595,0.7614,0.7671,0.7704,
0.7716,0.7724,0.7729,0.7748,0.7767,0.7767,0.7898,0.7948,0.7955,0.7979,
0.7992,0.8035,0.8124,0.8186,0.8202,0.8233,0.8276,0.8294,0.8346,0.8361,
0.8377,0.8406,0.8411,0.8424,0.8451,0.8494,0.8515,0.8576,0.8598,0.8611,
0.8633,0.8635,0.8648,0.8706,0.8745,0.8771,0.8780,0.8795,0.8802,0.8864,
0.8894,0.8914,0.9092,0.9097,0.9121,0.9130,0.9175,0.9196,0.9208,0.9208,
0.9255,0.9283,0.9284,0.9317,0.9328,0.9345,0.9353,0.9353,0.9398,0.9458,
0.9537,0.9630,0.9644,0.9650,0.9758,0.9928,0.9963,0.9970,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.661002
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.