Questions tagged [hellinger]

The Hellinger distance measures a distance between two distributions that are absolutely continuous wrt the same dominating measure. It is bounded by one.

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An unbiased estimator for distance between two observed categorical distributions?

I have two empirical categorical distributions: P and q with |P| >> |q|. P is the full description of my population, so I treat it as the reference baseline distribution. q, however, is a much ...
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Should I use Hellinger transformed species (abundance) data for NMDS if this is what I used for RDA ordination?

I am conducting both constrained and unconstrained analyses on the same species abundance data. For the constrained ordination, I ran the RDA (redundancy analysis) on log x+1 and hellinger transformed ...
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Is this Hellinger Distance expression correct?

Further to my previous post on the Hellinger Distance, there was one comment raised about there being different expressions of the Hellinger Distance. This has intrigued me. In the Encyclopedia of ...
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Is Hellinger transformation suitable to access species abundance - environmental variable relationships?

While working with a multivariate dataset, I noticed that Hellinger transformation reveals relationships with the dataset I did not see otherwise. The fact that a transformation affects species ...
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Hellinger distance to find outliers. How to go from data to probability distribution?

One can find outliers in a data set if you fit that data in a probability distribution and see how well the data fits in the model (Normal data instances occur in high probability regions of a ...
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Lower bound for difference of probabilities of a same event under two different distributions

Say $P$ and $Q$ are two probabilities distributions on $[n]$. I can upper bound the difference of the probability of an event $A$ under $P$ and $Q$ by the total variation distance between $P$ and $Q$. ...
In a setting where one observes $X_1,\ldots,X_n$ distributed from a distribution with density $f$, I wonder if there is an unbiased estimator (based on the $X_i$'s) of the Hellinger distance to ...