How to Measure the Distance Between Two Distributions?

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SUMMARY

The discussion focuses on measuring the distance between two statistical distributions. The difference between mean values is insufficient as a distance metric since distinct distributions can share the same mean. A recommended method is the Kolmogorov-Smirnov distance, which quantifies the maximum difference between the cumulative distribution functions (CDFs) of the two distributions. Understanding the properties of the distributions involved is crucial for accurate measurement.

PREREQUISITES
  • Understanding of cumulative distribution functions (CDFs)
  • Familiarity with the Kolmogorov-Smirnov test
  • Knowledge of statistical distributions and their properties
  • Basic concepts of metric spaces in statistics
NEXT STEPS
  • Research the Kolmogorov-Smirnov distance and its applications
  • Learn about other distance metrics such as Jensen-Shannon divergence
  • Explore the properties of different statistical distributions
  • Study how to compute and interpret cumulative distribution functions
USEFUL FOR

Statisticians, data scientists, and researchers analyzing the similarity between distributions or conducting hypothesis testing.

danik_ejik
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Hello,
I've some two distributions,
how can I find the distance between those two distributions?

is the difference between the mean values would be the distance ?
 
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danik_ejik said:
Hello,
I've some two distributions,
how can I find the distance between those two distributions?

is the difference between the mean values would be the distance ?

Hey there.

I'm not exactly sure what you mean by distance.

If you are talking about expectation of variance for example you need to specify things like what distribution your RV's are, if they have any dependence on each other and so on.

Like I said, try to be clearer in stating what you are trying to find out.
 
danik_ejik said:
Hello,
I've some two distributions,
how can I find the distance between those two distributions?

is the difference between the mean values would be the distance ?

Usually a "distance" measure would be defined to satisfy the axioms of a metric - which the difference of means doesn't, because distinct distributions can have the same mean.

One popular distance measure is the Kolmogorov-Smirnov distance which is effectively the maximum difference between the CDFs of the distributions.
 

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