RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.04 17.5577 0.582759
2 to 25 15.75 20.9301 0.770567
3 to 26 15.98 17.1174 0.553562
4 to 27 15.88 14.4529 0.365178
5 to 28 15.71 26.4656 0.933614
6 to 29 15.61 17.9020 0.604950
7 to 30 15.68 26.8241 0.939302
8 to 31 15.88 16.0079 0.476726
9 to 32 15.58 24.3062 0.888648
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.090527
Tough bday spacings test for dh-ranFile-2018-07-09_00:31: 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 8 49 72 87 92 82 58 27 12 9 4
(O-E)^2/E 0.1 4.2 0.0 1.2 0.3 0.2 0.7 0.3 0.6 0.9 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.380, p= 0.408
RESULTS OF GCD FOR dh-ranFile-2018-07-09_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.787985
p-value, dist. of gcd's: 0.963548
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.518 0.617 0.943 0.174 0.354 0.826 0.372 0.161
Bits 8 to 15---> 0.704 0.840 0.656 0.181 0.981 0.659 0.026 0.201
Bits 16 to 23---> 0.052 0.416 0.270 0.722 0.574 0.572 0.523 0.000
Bits 24 to 31---> 0.432 0.065 0.392 0.657 0.831 0.724 0.935 0.275
KS test for the above 32 p values: 0.053
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_00:31,
p-values for 5 runs: 0.5570, 0.9059, 0.2393, 0.7778, 0.9031
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5199 5134.0 0.823 1.674
r= 30 22907 23103.0 1.664 3.338
r= 31 11696 11551.5 1.807 5.145
chi-square = 5.145 with df = 3; p-value = 0.839
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 198 211.4 0.852 0.852
r= 30 5006 5134.0 3.192 4.043
r= 31 23154 23103.0 0.112 4.156
r= 32 11642 11551.5 0.709 4.864
chi-square = 4.864 with df = 3; p-value = 0.818
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_00:31
b-rank test for bits 1 to 8, p=0.28216
b-rank test for bits 2 to 9, p=0.43430
b-rank test for bits 3 to 10, p=0.02225
b-rank test for bits 4 to 11, p=0.18202
b-rank test for bits 5 to 12, p=0.03700
b-rank test for bits 6 to 13, p=0.02819
b-rank test for bits 7 to 14, p=0.12822
b-rank test for bits 8 to 15, p=0.91915
b-rank test for bits 9 to 16, p=0.64336
b-rank test for bits 10 to 17, p=0.08580
b-rank test for bits 11 to 18, p=0.25906
b-rank test for bits 12 to 19, p=0.42708
b-rank test for bits 13 to 20, p=0.90624
b-rank test for bits 14 to 21, p=0.19965
b-rank test for bits 15 to 22, p=0.64344
b-rank test for bits 16 to 23, p=0.89970
b-rank test for bits 17 to 24, p=0.49820
b-rank test for bits 18 to 25, p=0.37566
b-rank test for bits 19 to 26, p=0.01713
b-rank test for bits 20 to 27, p=0.78223
b-rank test for bits 21 to 28, p=0.43771
b-rank test for bits 22 to 29, p=0.91714
b-rank test for bits 23 to 30, p=0.15679
b-rank test for bits 24 to 31, p=0.13656
b-rank test for bits 25 to 32, p=0.79924
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 = 0.099411
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_00:31
(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 142202 0.68 0.752952
2 141880 -0.07 0.472683
3 142023 0.27 0.604720
4 141282 -1.47 0.071362
5 141427 -1.13 0.129884
6 141561 -0.81 0.207864
7 142384 1.11 0.866294
8 141805 -0.24 0.403708
9 141075 -1.95 0.025626
10 142152 0.57 0.714638
11 142377 1.09 0.862734
12 142418 1.19 0.882678
13 142317 0.95 0.829578
14 141741 -0.39 0.347051
15 141300 -1.42 0.077271
16 141948 0.09 0.535996
17 141260 -1.52 0.064617
18 141187 -1.69 0.045736
19 142253 0.80 0.789003
20 142021 0.26 0.602920
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_00:31
Bits used No. missing words z-score p-value
23 to 32 142122 0.7333 0.768326
22 to 31 142107 0.6816 0.752261
21 to 30 142577 2.3023 0.989341
20 to 29 142246 1.1609 0.877165
19 to 28 141643 -0.9184 0.179210
18 to 27 141271 -2.2011 0.013863
17 to 26 141899 -0.0356 0.485792
16 to 25 142100 0.6575 0.744565
15 to 24 142400 1.6920 0.954674
14 to 23 142295 1.3299 0.908224
13 to 22 141601 -1.0632 0.143844
12 to 21 141836 -0.2529 0.400187
11 to 20 141588 -1.1080 0.133923
10 to 19 142037 0.4402 0.670119
9 to 18 141703 -0.7115 0.238393
8 to 17 142050 0.4851 0.686186
7 to 16 141541 -1.2701 0.102024
6 to 15 141977 0.2333 0.592253
5 to 14 142196 0.9885 0.838550
4 to 13 141662 -0.8529 0.196868
3 to 12 141617 -1.0080 0.156719
2 to 11 142460 1.8989 0.971209
1 to 10 142045 0.4678 0.680046
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_00:31
Bits used No. missing words z-score p-value
28 to 32 142050 0.4768 0.683265
27 to 31 142428 1.7582 0.960644
26 to 30 142031 0.4124 0.659992
25 to 29 141437 -1.6011 0.054675
24 to 28 141906 -0.0113 0.495497
23 to 27 141867 -0.1435 0.442951
22 to 26 142037 0.4328 0.667413
21 to 25 142147 0.8057 0.789781
20 to 24 141926 0.0565 0.522532
19 to 23 142262 1.1955 0.884053
18 to 22 142160 0.8497 0.802262
17 to 21 141697 -0.7198 0.235836
16 to 20 142225 1.0701 0.857706
15 to 19 142414 1.7107 0.956436
14 to 18 141886 -0.0791 0.468483
13 to 17 141857 -0.1774 0.429601
12 to 16 141298 -2.0723 0.019119
11 to 15 142006 0.3277 0.628429
10 to 14 141757 -0.5164 0.302797
9 to 13 141311 -2.0282 0.021268
8 to 12 141586 -1.0960 0.136532
7 to 11 142502 2.0091 0.977734
6 to 10 142368 1.5548 0.940005
5 to 9 141642 -0.9062 0.182414
4 to 8 141678 -0.7842 0.216470
3 to 7 142293 1.3006 0.903298
2 to 6 142122 0.7209 0.764519
1 to 5 141526 -1.2994 0.096899
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_00:31
Bits used No. missing words z-score p-value
31 to 32 141512 -1.1721 0.120586
30 to 31 142279 1.0905 0.862247
29 to 30 141384 -1.5496 0.060613
28 to 29 142167 0.7601 0.776399
27 to 28 142168 0.7630 0.777280
26 to 27 141919 0.0285 0.511378
25 to 26 141683 -0.6676 0.252182
24 to 25 142043 0.3943 0.653323
23 to 24 142026 0.3442 0.634637
22 to 23 141309 -1.7709 0.038290
21 to 22 141444 -1.3727 0.084930
20 to 21 141915 0.0167 0.506672
19 to 20 142090 0.5329 0.702966
18 to 19 141372 -1.5850 0.056478
17 to 18 141958 0.1436 0.557080
16 to 17 142268 1.0580 0.854978
15 to 16 141893 -0.0482 0.480790
14 to 15 141816 -0.2753 0.391539
13 to 14 141688 -0.6529 0.256913
12 to 13 142166 0.7571 0.775517
11 to 12 142155 0.7247 0.765679
10 to 11 141981 0.2114 0.583719
9 to 10 141483 -1.2576 0.104266
8 to 9 142636 2.1436 0.983966
7 to 8 141970 0.1790 0.571018
6 to 7 141184 -2.1396 0.016193
5 to 6 141533 -1.1101 0.133474
4 to 5 142177 0.7896 0.785116
3 to 4 141879 -0.0895 0.464355
2 to 3 141915 0.0167 0.506672
1 to 2 141879 -0.0895 0.464355
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2408.85 -1.289 0.098691
Test results for specific bytes for dh-ranFile-2018-07-09_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2517.85 0.252 0.599629
2 to 9 2462.97 -0.524 0.300259
3 to 10 2622.00 1.725 0.957771
4 to 11 2567.62 0.956 0.830525
5 to 12 2526.36 0.373 0.645328
6 to 13 2606.41 1.505 0.933829
7 to 14 2506.28 0.089 0.535411
8 to 15 2581.20 1.148 0.874588
9 to 16 2516.97 0.240 0.594816
10 to 17 2519.15 0.271 0.606752
11 to 18 2461.24 -0.548 0.291785
12 to 19 2502.93 0.041 0.516547
13 to 20 2536.27 0.513 0.695992
14 to 21 2585.85 1.214 0.887637
15 to 22 2352.47 -2.086 0.018469
16 to 23 2545.11 0.638 0.738264
17 to 24 2540.43 0.572 0.716284
18 to 25 2502.39 0.034 0.513455
19 to 26 2566.86 0.946 0.827804
20 to 27 2539.74 0.562 0.712932
21 to 28 2657.77 2.231 0.987168
22 to 29 2481.53 -0.261 0.396975
23 to 30 2585.15 1.204 0.885753
24 to 31 2431.38 -0.970 0.165918
25 to 32 2488.54 -0.162 0.435643
CDPARK for dh-ranFile-2018-07-09_00:31: 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
3557 1.5525 0.939730
3507 -0.7306 0.232514
3513 -0.4566 0.323972
3513 -0.4566 0.323972
3530 0.3196 0.625377
3553 1.3699 0.914635
3508 -0.6849 0.246694
3539 0.7306 0.767486
3488 -1.5982 0.055002
3540 0.7763 0.781201
Square side=100, avg. no. parked=3524.80 sample std.=21.27
p-value of the KSTEST for those 10 p-values: 0.907911
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_00:31
0.6459,0.6815,0.4231,0.4497,0.0905,0.9280,0.1940,0.6518,0.5376,0.3261,
The KS test for those 10 p-values: 0.881337
The 3DSPHERES test for dh-ranFile-2018-07-09_00:31
sample no r^3 equiv. uni.
1 9.527 0.272087
2 15.943 0.412239
3 23.559 0.544011
4 63.350 0.878964
5 6.997 0.208032
6 32.450 0.660967
7 16.735 0.427548
8 19.072 0.470453
9 12.555 0.341974
10 6.983 0.207659
11 42.534 0.757753
12 28.951 0.619032
13 28.060 0.607542
14 31.347 0.648274
15 45.987 0.784093
16 44.856 0.775795
17 4.868 0.149797
18 49.382 0.807195
19 38.725 0.724957
20 36.744 0.706179
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.272682
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.6 -1.3 -0.4 1.4 -0.7
0.6 -0.3 0.2 0.2 -0.8 -0.4
1.4 0.6 0.5 -1.2 3.1 -1.3
-0.2 -0.7 -1.1 -0.5 -0.6 -0.9
0.8 -0.0 -1.3 -0.2 1.0 1.8
0.3 2.4 -1.1 1.4 1.7 -0.3
0.5 -0.7 -0.4 -0.1 -0.6 1.0
0.8
Chi-square with 42 degrees of freedom:50.396324
z-score=0.916114, p-value=0.824592
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_00:31
Test no p-value
1 0.733933
2 0.699045
3 0.160974
4 0.430119
5 0.087793
6 0.311096
7 0.790578
8 0.013110
9 0.759786
10 0.088665
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.343479
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_00:31:
(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 66599 0.07 66862 0.57
3 25000.00 25045 0.08 24931 0.19
4 6666.67 6731 0.62 6540 2.41
5 1388.89 1341 1.65 1371 0.23
6 238.10 241 0.04 240 0.02
7 34.72 40 0.80 48 5.08
8 4.96 2 1.77 7 0.84
p=0.45959 p=0.84434
Number of rngs required: 687097, p-value: 0.063
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_00:31
No. of wins: Observed Expected
98527 98585.9
z-score=-0.263, pvalue=0.39618
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66438 66666.7 0.784 0.784
2 37484 37654.3 0.770 1.555
3 26857 26954.7 0.354 1.909
4 19394 19313.5 0.336 2.245
5 14028 13851.4 2.251 4.496
6 9961 9943.5 0.031 4.527
7 7187 7145.0 0.247 4.773
8 5209 5139.1 0.952 5.725
9 3695 3699.9 0.006 5.731
10 2701 2666.3 0.452 6.183
11 1948 1923.3 0.316 6.499
12 1426 1388.7 1.000 7.499
13 1051 1003.7 2.228 9.727
14 758 726.1 1.398 11.124
15 502 525.8 1.080 12.205
16 371 381.2 0.270 12.475
17 244 276.5 3.829 16.304
18 230 200.8 4.237 20.541
19 155 146.0 0.557 21.098
20 110 106.2 0.135 21.233
21 251 287.1 4.543 25.775
Chisq= 25.78 for 20 degrees of freedom, p= 0.82663
SUMMARY of craptest
p-value for no. of wins: 0.396179
p-value for throws/game: 0.826629
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_00:31
No. of wins: Observed Expected
98792 98585.9
z-score= 0.922, pvalue=0.82173
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67091 66666.7 2.701 2.701
2 38309 37654.3 11.383 14.083
3 26751 26954.7 1.540 15.623
4 19204 19313.5 0.620 16.244
5 13730 13851.4 1.064 17.308
6 9949 9943.5 0.003 17.311
7 6896 7145.0 8.679 25.990
8 5028 5139.1 2.401 28.391
9 3586 3699.9 3.504 31.895
10 2554 2666.3 4.730 36.625
11 1947 1923.3 0.291 36.916
12 1333 1388.7 2.237 39.154
13 1012 1003.7 0.068 39.222
14 717 726.1 0.115 39.337
15 500 525.8 1.269 40.606
16 387 381.2 0.090 40.696
17 287 276.5 0.396 41.092
18 179 200.8 2.373 43.465
19 130 146.0 1.750 45.215
20 111 106.2 0.216 45.430
21 299 287.1 0.492 45.923
Chisq= 45.92 for 20 degrees of freedom, p= 0.99917
SUMMARY of craptest
p-value for no. of wins: 0.821732
p-value for throws/game: 0.999174
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0131,0.0139,0.0162,0.0171,0.0185,0.0191,0.0213,0.0222,0.0256,
0.0259,0.0282,0.0370,0.0383,0.0457,0.0521,0.0535,0.0547,0.0550,0.0565,
0.0606,0.0635,0.0646,0.0646,0.0714,0.0773,0.0849,0.0858,0.0878,0.0887,
0.0905,0.0905,0.0969,0.0987,0.0994,0.1020,0.1043,0.1206,0.1282,0.1299,
0.1335,0.1339,0.1365,0.1366,0.1438,0.1498,0.1567,0.1568,0.1608,0.1610,
0.1659,0.1738,0.1792,0.1810,0.1820,0.1824,0.1940,0.1969,0.1996,0.2013,
0.2077,0.2079,0.2080,0.2165,0.2325,0.2358,0.2384,0.2393,0.2467,0.2522,
0.2569,0.2591,0.2702,0.2721,0.2727,0.2754,0.2822,0.2918,0.3003,0.3028,
0.3111,0.3240,0.3240,0.3261,0.3420,0.3435,0.3471,0.3537,0.3652,0.3719,
0.3757,0.3915,0.3917,0.3962,0.3970,0.4002,0.4037,0.4082,0.4122,0.4161,
0.4231,0.4271,0.4275,0.4296,0.4301,0.4317,0.4343,0.4356,0.4377,0.4430,
0.4497,0.4596,0.4644,0.4644,0.4685,0.4705,0.4727,0.4767,0.4808,0.4858,
0.4955,0.4982,0.5067,0.5067,0.5114,0.5135,0.5165,0.5178,0.5225,0.5228,
0.5354,0.5360,0.5376,0.5440,0.5536,0.5570,0.5571,0.5710,0.5722,0.5735,
0.5828,0.5837,0.5923,0.5948,0.5996,0.6029,0.6047,0.6050,0.6068,0.6075,
0.6171,0.6190,0.6254,0.6284,0.6346,0.6434,0.6434,0.6453,0.6459,0.6483,
0.6518,0.6533,0.6558,0.6574,0.6595,0.6600,0.6610,0.6674,0.6701,0.6800,
0.6815,0.6833,0.6862,0.6960,0.6990,0.7030,0.7042,0.7062,0.7129,0.7146,
0.7163,0.7221,0.7236,0.7250,0.7339,0.7383,0.7446,0.7523,0.7530,0.7578,
0.7598,0.7645,0.7657,0.7675,0.7683,0.7706,0.7755,0.7758,0.7764,0.7773,
0.7778,0.7812,0.7822,0.7841,0.7851,0.7880,0.7890,0.7898,0.7906,0.7992,
0.8023,0.8072,0.8180,0.8217,0.8246,0.8259,0.8266,0.8278,0.8296,0.8305,
0.8312,0.8385,0.8386,0.8401,0.8443,0.8550,0.8577,0.8622,0.8627,0.8663,
0.8746,0.8772,0.8790,0.8813,0.8827,0.8841,0.8858,0.8876,0.8886,0.8997,
0.9031,0.9033,0.9059,0.9062,0.9079,0.9082,0.9146,0.9171,0.9191,0.9280,
0.9336,0.9338,0.9350,0.9393,0.9397,0.9400,0.9430,0.9547,0.9564,0.9578,
0.9606,0.9635,0.9712,0.9777,0.9806,0.9840,0.9872,0.9893,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.166013
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.