Timeline for How to generate random points in the volume of a sphere with uniform nearest neighbour distances
Current License: CC BY-SA 3.0
11 events
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| Feb 6, 2014 at 18:28 | comment | added | Has QUIT--Anony-Mousse | It obviously isn't mathematically uniform then anymore, but has a very strong structure of having duplicates... nevertheless, for any practical purpose, it is the same data. | |
| Feb 6, 2014 at 18:26 | comment | added | Has QUIT--Anony-Mousse | I believe if you add e.g. a 5% or 10% non-uniform but also non-blunt impurity into the data - that is actually a lot - it will still look Gamma distributed. At the same time, if you duplicate every data point (think of duplicate submissions!) then the 1NN distribution will be constant 0. But it's the same data, just twice! | |
| Feb 6, 2014 at 14:10 | comment | added | Jolfaei | "...But I don't think this will be well usable for a test", I think you were trying to make a point here. | |
| Feb 6, 2014 at 14:03 | comment | added | Jolfaei | "When your sample was Nakagami distributed, than the squared distances should be Gamma distributed, right?", correct. Please see the temporary images that I added to the question. | |
| Feb 6, 2014 at 13:47 | comment | added | Has QUIT--Anony-Mousse | Can you ask a more precise question? | |
| Feb 6, 2014 at 13:22 | comment | added | Jolfaei | Can you explain more. | |
| Feb 6, 2014 at 13:08 | comment | added | Has QUIT--Anony-Mousse | When your sample was Nakagami distributed, than the squared distances should be Gamma distributed, right? Often, you will see your squared distances to be $\chi^2$ or $\Gamma$ distributed. But I don't think this will be well usable for a test. | |
| Feb 6, 2014 at 13:07 | comment | added | Has QUIT--Anony-Mousse | "Randomness" is a big too vague. You may want to look at the discrepancy of the series, goodness-of-fit tests and Hopkins statistic, for a starter. However, things that appear random to us, may be quite well ordered, see e.g. en.wikipedia.org/wiki/Low-discrepancy_sequence for "sub-random" series, that are more evenly distributed than uniform random is... | |
| Feb 6, 2014 at 10:12 | comment | added | Jolfaei | Knowing that the distribution of nearest neighbour distances is not uniform, then how can I check their randomness? | |
| Feb 6, 2014 at 10:06 | comment | added | Jolfaei | I have done a test with MATLAB. Using the method explained above I generated 10000 independent points in a sphere of radius 10. I calculated the nearest neighbour distance for all points. Using the curve fitting tool of MATLAB, I found that the best fit for the empirical distribution of nearest neighbours is Nakagami distribution. | |
| Feb 6, 2014 at 8:27 | history | answered | Has QUIT--Anony-Mousse | CC BY-SA 3.0 |