RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.00 16.6195 0.519581
2 to 25 16.03 26.8070 0.939040
3 to 26 15.66 15.1359 0.414305
4 to 27 15.71 19.3328 0.690232
5 to 28 15.76 15.7601 0.459102
6 to 29 15.68 12.3282 0.220129
7 to 30 15.71 22.2253 0.823790
8 to 31 15.93 8.6699 0.049948
9 to 32 15.86 9.0523 0.061393
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.948236
Tough bday spacings test for dh-ranFile-2018-06-21_05:31: 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 5 36 87 81 89 82 67 32 13 6 2
(O-E)^2/E 1.9 0.0 2.6 2.8 0.8 0.2 4.3 0.2 0.2 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 14.061, p= 0.830
RESULTS OF GCD FOR dh-ranFile-2018-06-21_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.051548
p-value, dist. of gcd's: 0.383118
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.309 0.740 0.398 0.437 0.125 0.436 0.710 0.387
Bits 8 to 15---> 0.442 0.038 0.001 0.153 0.190 0.252 0.197 0.725
Bits 16 to 23---> 0.701 0.105 0.903 0.482 0.025 0.849 0.402 0.113
Bits 24 to 31---> 0.537 0.775 0.692 0.053 0.979 0.982 0.943 0.174
KS test for the above 32 p values: 0.652
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_05:31,
p-values for 5 runs: 0.6406, 0.6373, 0.3501, 0.5421, 0.1025
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 229 211.4 1.462 1.462
r= 29 5151 5134.0 0.056 1.518
r= 30 22964 23103.0 0.837 2.355
r= 31 11656 11551.5 0.945 3.300
chi-square = 3.300 with df = 3; p-value = 0.652
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 239 211.4 3.598 3.598
r= 30 5257 5134.0 2.946 6.545
r= 31 22905 23103.0 1.698 8.242
r= 32 11599 11551.5 0.195 8.438
chi-square = 8.438 with df = 3; p-value = 0.962
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_05:31
b-rank test for bits 1 to 8, p=0.06708
b-rank test for bits 2 to 9, p=0.11829
b-rank test for bits 3 to 10, p=0.36331
b-rank test for bits 4 to 11, p=0.28094
b-rank test for bits 5 to 12, p=0.68066
b-rank test for bits 6 to 13, p=0.68121
b-rank test for bits 7 to 14, p=0.04278
b-rank test for bits 8 to 15, p=0.41890
b-rank test for bits 9 to 16, p=0.81588
b-rank test for bits 10 to 17, p=0.52664
b-rank test for bits 11 to 18, p=0.61090
b-rank test for bits 12 to 19, p=0.61505
b-rank test for bits 13 to 20, p=0.43862
b-rank test for bits 14 to 21, p=0.37164
b-rank test for bits 15 to 22, p=0.18838
b-rank test for bits 16 to 23, p=0.33740
b-rank test for bits 17 to 24, p=0.78835
b-rank test for bits 18 to 25, p=0.88576
b-rank test for bits 19 to 26, p=0.75480
b-rank test for bits 20 to 27, p=0.03033
b-rank test for bits 21 to 28, p=0.97281
b-rank test for bits 22 to 29, p=0.83946
b-rank test for bits 23 to 30, p=0.46428
b-rank test for bits 24 to 31, p=0.27525
b-rank test for bits 25 to 32, p=0.63874
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 = 0.984874
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_05:31
(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 142486 1.35 0.911068
2 141726 -0.43 0.334201
3 141385 -1.23 0.110274
4 141244 -1.55 0.060031
5 142676 1.79 0.963376
6 142427 1.21 0.886766
7 142413 1.18 0.880362
8 142202 0.68 0.752952
9 142350 1.03 0.848402
10 142340 1.01 0.842850
11 141667 -0.57 0.285632
12 141983 0.17 0.568331
13 142117 0.49 0.686236
14 141246 -1.55 0.060590
15 141214 -1.62 0.052124
16 142016 0.25 0.598408
17 141562 -0.81 0.208534
18 141211 -1.63 0.051381
19 141981 0.17 0.566493
20 142097 0.44 0.669481
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_05:31
Bits used No. missing words z-score p-value
23 to 32 141926 0.0575 0.522920
22 to 31 141618 -1.0046 0.157548
21 to 30 141956 0.1609 0.563926
20 to 29 141890 -0.0667 0.473428
19 to 28 141420 -1.6873 0.045769
18 to 27 141889 -0.0701 0.472056
17 to 26 141836 -0.2529 0.400187
16 to 25 141765 -0.4977 0.309351
15 to 24 142084 0.6023 0.726516
14 to 23 142074 0.5678 0.714924
13 to 22 142322 1.4230 0.922632
12 to 21 142281 1.2816 0.900012
11 to 20 142093 0.6333 0.736746
10 to 19 142363 1.5644 0.941136
9 to 18 141796 -0.3908 0.347975
8 to 17 141597 -1.0770 0.140740
7 to 16 142372 1.5954 0.944690
6 to 15 142253 1.1851 0.882005
5 to 14 142087 0.6127 0.729948
4 to 13 141319 -2.0356 0.020894
3 to 12 141413 -1.7115 0.043496
2 to 11 142231 1.1092 0.866330
1 to 10 142480 1.9678 0.975456
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_05:31
Bits used No. missing words z-score p-value
28 to 32 142448 1.8260 0.966075
27 to 31 141772 -0.4655 0.320778
26 to 30 141701 -0.7062 0.240031
25 to 29 142229 1.0836 0.860735
24 to 28 141803 -0.3604 0.359259
23 to 27 141663 -0.8350 0.201854
22 to 26 141582 -1.1096 0.133587
21 to 25 141445 -1.5740 0.057744
20 to 24 142307 1.3480 0.911176
19 to 23 141906 -0.0113 0.495497
18 to 22 141307 -2.0418 0.020586
17 to 21 141556 -1.1977 0.115511
16 to 20 141604 -1.0350 0.150331
15 to 19 141681 -0.7740 0.219465
14 to 18 141668 -0.8181 0.206659
13 to 17 141929 0.0667 0.526581
12 to 16 141809 -0.3401 0.366890
11 to 15 141907 -0.0079 0.496849
10 to 14 142014 0.3548 0.638635
9 to 13 142069 0.5413 0.705834
8 to 12 142407 1.6870 0.954200
7 to 11 141546 -1.2316 0.109044
6 to 10 141300 -2.0655 0.019437
5 to 9 142397 1.6531 0.950847
4 to 8 141909 -0.0011 0.499554
3 to 7 141432 -1.6181 0.052824
2 to 6 142004 0.3209 0.625863
1 to 5 142211 1.0226 0.846754
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_05:31
Bits used No. missing words z-score p-value
31 to 32 141518 -1.1544 0.124175
30 to 31 142051 0.4179 0.661992
29 to 30 142108 0.5860 0.721078
28 to 29 141848 -0.1809 0.428217
27 to 28 141741 -0.4965 0.309754
26 to 27 141520 -1.1485 0.125388
25 to 26 141965 0.1642 0.565220
24 to 25 141713 -0.5791 0.281246
23 to 24 142084 0.5153 0.696811
22 to 23 141342 -1.6735 0.047111
21 to 22 142343 1.2793 0.899598
20 to 21 141565 -1.0157 0.154881
19 to 20 142318 1.2055 0.885998
18 to 19 141896 -0.0393 0.484317
17 to 18 141837 -0.2134 0.415522
16 to 17 142325 1.2262 0.889932
15 to 16 141542 -1.0836 0.139278
14 to 15 142346 1.2881 0.901147
13 to 14 141086 -2.4287 0.007576
12 to 13 141188 -2.1278 0.016676
11 to 12 141318 -1.7443 0.040550
10 to 11 142293 1.1318 0.871134
9 to 10 141845 -0.1898 0.424747
8 to 9 141839 -0.2075 0.417824
7 to 8 141886 -0.0688 0.472566
6 to 7 141779 -0.3845 0.350321
5 to 6 142325 1.2262 0.889932
4 to 5 142105 0.5772 0.718097
3 to 4 142413 1.4858 0.931328
2 to 3 142446 1.5831 0.943300
1 to 2 141316 -1.7502 0.040039
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2453.52 -0.657 0.255469
Test results for specific bytes for dh-ranFile-2018-06-21_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2507.49 0.106 0.542177
2 to 9 2576.53 1.082 0.860443
3 to 10 2373.80 -1.785 0.037157
4 to 11 2575.18 1.063 0.856155
5 to 12 2465.51 -0.488 0.312851
6 to 13 2620.23 1.700 0.955460
7 to 14 2634.98 1.909 0.971862
8 to 15 2544.58 0.630 0.735780
9 to 16 2402.07 -1.385 0.083039
10 to 17 2561.55 0.870 0.807963
11 to 18 2554.39 0.769 0.779100
12 to 19 2564.45 0.911 0.818972
13 to 20 2473.72 -0.372 0.355060
14 to 21 2542.71 0.604 0.727077
15 to 22 2409.67 -1.277 0.100715
16 to 23 2578.43 1.109 0.866333
17 to 24 2550.36 0.712 0.761835
18 to 25 2505.99 0.085 0.533734
19 to 26 2494.32 -0.080 0.467961
20 to 27 2540.99 0.580 0.718939
21 to 28 2500.26 0.004 0.501494
22 to 29 2435.96 -0.906 0.182571
23 to 30 2456.25 -0.619 0.268047
24 to 31 2536.40 0.515 0.696625
25 to 32 2445.97 -0.764 0.222385
CDPARK for dh-ranFile-2018-06-21_05:31: 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
3507 -0.7306 0.232514
3495 -1.2785 0.100530
3525 0.0913 0.536383
3537 0.6393 0.738676
3564 1.8721 0.969407
3525 0.0913 0.536383
3526 0.1370 0.554479
3536 0.5936 0.723613
3516 -0.3196 0.374623
3528 0.2283 0.590298
Square side=100, avg. no. parked=3525.90 sample std.=17.59
p-value of the KSTEST for those 10 p-values: 0.752060
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_05:31
0.0048,0.8483,0.0886,0.2630,0.2874,0.3247,0.8899,0.4756,0.3998,0.8603,
The KS test for those 10 p-values: 0.580598
The 3DSPHERES test for dh-ranFile-2018-06-21_05:31
sample no r^3 equiv. uni.
1 2.239 0.071902
2 5.392 0.164495
3 34.248 0.680696
4 3.006 0.095329
5 86.510 0.944071
6 15.497 0.403436
7 4.346 0.134854
8 22.388 0.525868
9 131.684 0.987593
10 66.344 0.890461
11 7.391 0.218375
12 58.022 0.855439
13 17.115 0.434752
14 5.875 0.177842
15 5.237 0.160188
16 6.450 0.193458
17 32.008 0.655934
18 5.030 0.154373
19 50.368 0.813426
20 41.756 0.751390
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.463588
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 -2.0 -1.3 -0.2 0.7
0.3 -1.0 -0.9 -0.8 0.1 1.7
0.2 0.4 -0.9 -0.7 -0.2 1.2
-1.1 0.4 0.2 1.5 0.1 -0.4
-0.7 1.9 -1.3 -0.3 1.0 -0.9
-1.8 0.7 -1.0 -0.1 -0.5 -0.1
-1.4 -1.0 -0.4 -0.1 0.1 -1.0
2.7
Chi-square with 42 degrees of freedom:43.138624
z-score=0.124234, p-value=0.577612
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_05:31
Test no p-value
1 0.367835
2 0.199355
3 0.344488
4 0.723997
5 0.760015
6 0.025823
7 0.152801
8 0.378410
9 0.032382
10 0.841396
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.277529
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_05:31:
(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 66774 0.17 66396 1.10
3 25000.00 25061 0.15 25234 2.19
4 6666.67 6537 2.52 6730 0.60
5 1388.89 1353 0.93 1371 0.23
6 238.10 238 0.00 239 0.00
7 34.72 27 1.72 28 1.30
8 4.96 9 3.29 1 3.16
p=0.81357 p=0.80182
Number of rngs required: 687291, p-value: 0.098
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_05:31
No. of wins: Observed Expected
98727 98585.9
z-score= 0.631, pvalue=0.73607
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66662 66666.7 0.000 0.000
2 37810 37654.3 0.644 0.644
3 26989 26954.7 0.044 0.688
4 19196 19313.5 0.714 1.402
5 13811 13851.4 0.118 1.520
6 9899 9943.5 0.200 1.719
7 7260 7145.0 1.850 3.570
8 5101 5139.1 0.282 3.852
9 3705 3699.9 0.007 3.859
10 2673 2666.3 0.017 3.876
11 1953 1923.3 0.458 4.333
12 1408 1388.7 0.267 4.600
13 945 1003.7 3.435 8.035
14 726 726.1 0.000 8.035
15 502 525.8 1.080 9.116
16 373 381.2 0.174 9.290
17 268 276.5 0.264 9.554
18 205 200.8 0.087 9.640
19 134 146.0 0.984 10.624
20 100 106.2 0.364 10.988
21 280 287.1 0.176 11.164
Chisq= 11.16 for 20 degrees of freedom, p= 0.05814
SUMMARY of craptest
p-value for no. of wins: 0.736067
p-value for throws/game: 0.058141
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_05:31
No. of wins: Observed Expected
98704 98585.9
z-score= 0.528, pvalue=0.70139
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66577 66666.7 0.121 0.121
2 37629 37654.3 0.017 0.138
3 26906 26954.7 0.088 0.226
4 19172 19313.5 1.036 1.262
5 13893 13851.4 0.125 1.387
6 10076 9943.5 1.764 3.151
7 7212 7145.0 0.628 3.779
8 5149 5139.1 0.019 3.798
9 3679 3699.9 0.118 3.916
10 2699 2666.3 0.401 4.317
11 1935 1923.3 0.071 4.388
12 1345 1388.7 1.378 5.765
13 1052 1003.7 2.323 8.088
14 794 726.1 6.342 14.430
15 529 525.8 0.019 14.449
16 389 381.2 0.162 14.610
17 273 276.5 0.045 14.656
18 171 200.8 4.431 19.086
19 140 146.0 0.245 19.332
20 90 106.2 2.475 21.807
21 290 287.1 0.029 21.836
Chisq= 21.84 for 20 degrees of freedom, p= 0.65054
SUMMARY of craptest
p-value for no. of wins: 0.701388
p-value for throws/game: 0.650541
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0048,0.0076,0.0167,0.0194,0.0206,0.0209,0.0247,0.0258,0.0303,
0.0324,0.0372,0.0376,0.0400,0.0406,0.0428,0.0435,0.0458,0.0471,0.0499,
0.0514,0.0515,0.0521,0.0528,0.0529,0.0577,0.0581,0.0600,0.0606,0.0614,
0.0671,0.0719,0.0830,0.0886,0.0953,0.0978,0.1005,0.1007,0.1025,0.1049,
0.1090,0.1103,0.1127,0.1155,0.1183,0.1242,0.1250,0.1254,0.1336,0.1349,
0.1393,0.1407,0.1503,0.1527,0.1528,0.1544,0.1549,0.1575,0.1602,0.1645,
0.1743,0.1778,0.1826,0.1884,0.1901,0.1935,0.1975,0.1994,0.2019,0.2067,
0.2085,0.2184,0.2195,0.2201,0.2224,0.2325,0.2400,0.2517,0.2555,0.2630,
0.2680,0.2752,0.2775,0.2809,0.2812,0.2856,0.2874,0.3091,0.3094,0.3098,
0.3129,0.3208,0.3247,0.3342,0.3374,0.3445,0.3480,0.3501,0.3503,0.3551,
0.3593,0.3633,0.3669,0.3678,0.3716,0.3746,0.3784,0.3831,0.3866,0.3981,
0.3998,0.4002,0.4015,0.4034,0.4143,0.4155,0.4178,0.4189,0.4247,0.4282,
0.4348,0.4365,0.4365,0.4386,0.4424,0.4591,0.4636,0.4643,0.4680,0.4721,
0.4726,0.4734,0.4756,0.4822,0.4843,0.4955,0.4968,0.4996,0.5015,0.5196,
0.5229,0.5259,0.5266,0.5266,0.5337,0.5364,0.5364,0.5374,0.5421,0.5422,
0.5545,0.5639,0.5652,0.5665,0.5683,0.5776,0.5806,0.5903,0.5984,0.6109,
0.6150,0.6259,0.6373,0.6386,0.6387,0.6406,0.6505,0.6524,0.6524,0.6559,
0.6620,0.6695,0.6807,0.6807,0.6812,0.6862,0.6902,0.6917,0.6966,0.6968,
0.7006,0.7014,0.7058,0.7099,0.7149,0.7181,0.7189,0.7211,0.7236,0.7240,
0.7255,0.7265,0.7271,0.7299,0.7358,0.7361,0.7367,0.7387,0.7404,0.7514,
0.7521,0.7530,0.7548,0.7600,0.7618,0.7747,0.7791,0.7883,0.8018,0.8080,
0.8134,0.8136,0.8159,0.8190,0.8238,0.8298,0.8395,0.8414,0.8428,0.8468,
0.8483,0.8484,0.8491,0.8554,0.8562,0.8603,0.8604,0.8607,0.8663,0.8663,
0.8711,0.8804,0.8820,0.8858,0.8860,0.8868,0.8899,0.8899,0.8899,0.8905,
0.8996,0.9000,0.9011,0.9034,0.9111,0.9112,0.9226,0.9313,0.9390,0.9411,
0.9432,0.9433,0.9441,0.9447,0.9482,0.9508,0.9542,0.9555,0.9622,0.9634,
0.9661,0.9694,0.9719,0.9728,0.9755,0.9789,0.9817,0.9849,0.9876,
Overall p-value after applying KStest on 269 p-values = 0.180359
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.