Statistical Distance

A Statistical Distance is a measure of distance between two statistical objects .

• Example(s)
  • Total Variation Distance
  • Kullback-Leibler Divergence.
  • Hellinger Distance.
  • Jensen-Shannon Divergence.
  • Levy-Prokhorov metric.
  • Bhattacharyya Distance.
  • Wasserstein metric.
  • Energy Distance
• Counter-Example(s)
  • Signal-to-noise Ratio
  • Mahalanobis Distance.
  • Distance Correlation
• See: Probabilistic Metric Space, F-divergence.

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References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Statistical_distance 2016-08-13
  • In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.

A distance between populations can be interpreted as measuring the distance between two probability distributions and hence they are essentially measures of distances between probability measures. Where statistical distance measures relate to the differences between random variables, these may have statistical dependence, and hence these distances are not directly related to measures of distances between probability measures. Again, a measure of distance between random variables may relate to the extent of dependence between them, rather than to their individual values.

Statistical distance measures are mostly not metrics and they need not be symmetric. Some types of distance measures are referred to as (statistical) divergences.

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