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https://issues.apache.org/jira/browse/MATH-984?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13672859#comment-13672859
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Radoslav Tsvetkov commented on MATH-984:
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To generate a Exception on attempt to calculate St.Dev. from single observation
is correct. It’s just that the _Exception Text_ generated by getKernel() is not
clearly pointing the cause. An average user should dig and search to get to to
the "real" cause. But as getKernel() should deliver the "kernel" and not
proliferate his chosen internal method restrictions outside, better would be
_for single observation_ to deliver uniformly distributed value. (and perhaps
warning).
generate() within EmpiricalDistribution could be "fixed" easily if it uses
truncated Gaussian on the end bins.
*So would propose 2 changes:*
1. Add generate(double min, double max) function Where *min* and *max* should
indicate the hard limits of generation. They should be checked if the conform
to input data. It means *min* should not be greater than the minimal
empirically observed value, and *max* should be no less then the biggest value
of the input for the EmpiricalDistribution. Then the new generate function
should use truncated Gaussian on the edges.
2. Change getKernel() to deliver uniformly distributed value on single
observation. (and perhaps warning)
The first change does not touch old code. So, it's a practically no risk and we
retain 100% code compatibility.
The second change is also low risk and is compatible with old code.
As a result we have smooth and correct generation and positively fixed inverse
CDF.
> Incorrect (bugged) generating function getNextValue() in
> .random.EmpiricalDistribution
> --------------------------------------------------------------------------------------
>
> Key: MATH-984
> URL: https://issues.apache.org/jira/browse/MATH-984
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.2, 3.1.1
> Environment: all
> Reporter: Radoslav Tsvetkov
>
> The generating function getNextValue() in
> org.apache.commons.math3.random.EmpiricalDistribution
> will generate wrong values for all Distributions that are single tailed or
> limited. For example Data which are resembling Exponential or Lognormal
> distributions.
> The problem could be easily seen in code and tested.
> In last version code
> ...
> 490 return getKernel(stats).sample();
> ...
> it samples from Gaussian distribution to "smooth" in_the_bin. Obviously
> Gaussian Distribution is not limited and sometimes it does generates numbers
> outside the bin. In the case when it is the last bin it will generate wrong
> numbers.
> For example for empirical non-negative data it will generate negative rubbish.
> Additionally the proposed algorithm boldly returns only the mean value of
> the bin in case of one value! This last makes the generating function
> unusable for heavy tailed distributions with small number of values. (for
> example computer network traffic)
> On the last place usage of Gaussian soothing in the bin will change greatly
> some empirical distribution properties.
> The proposed method should be reworked to be applicable for real data which
> have often limited ranges. (either non-negative or both sides limited)
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