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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Hellinger Distance between 2 vectors of data points using cumsum in R

I have numerous vectors of data points and I want to compute the hellinger distance between the probability distributions of every 2 vectors. I am using this version of the Hellinger distance equation:...
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Sample Hellinger Distance is Negative

The Hellinger distance between a true density $f$ and an estimate $\hat f$ is defined as $$H(f,\hat f) = \sqrt{1 - \int \sqrt{\frac{\hat f(x)}{f(x)}}f(x)\ \mathrm dx}.$$ I estimate the Hellinger ...
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72 views

Is Hellinger transformation suitable for repeated (in time) site-species abundance data?

I have fish survey data from four different years and several locations, where I would like to study the difference in abundance and biomass between sites and check whether time dependence influences ...
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1answer
99 views

Hellinger distance for two shifted log-normal distributions

If I am not mistaken, Hellinger distance between P and Q is generally given by: $$ H^2(P, Q) = \frac12 \int \left( \sqrt{dP} - \sqrt{dQ} \right)^2 .$$ If P and Q, however, are two differently ...
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1k views

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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71 views

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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65 views

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 $Q$. ...
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1answer
1k views

Distance between discrete histograms

I am on the search for a universal distance metric for comparison of two histograms. Consider the two figures below. Each of the figures contains a desired distribution (blue line) and a measured ...
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1k views

Is there an unbiased estimator of the Hellinger distance between two distributions?

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 ...