ENH: Feature Request - Non-parametric test based on Chebyshev's Inequality #17690

Hi,
Whenever I need to perform a non-parametric test using Chebyshev's
Inequality, I have to write the equation myself. It would be good to have
it as a part of Scipy. A function which takes in a distribution(array), a
scalar value to be used for the test, the type of
test(one-tailed/two-tailed), and significance level and returns whether the
scalar value is within or outside the level selected.

To give a little context, Chebyshev's inequality can also be used to define
Confidence intervals which can be used to perform significance/hypothesis
tests much like student's t-test. However, it is much more conservative
than the student's t-test as Chebyshev's inequality doesn't assume the
distribution to be normal. The inequality can be found in the attachment.

A few papers where this inequality is used are mentioned below,

   - https://doi.org/10.1109/ICSPCC.2013.6663961, Credibility test for
   blind processing results of sinusoid using Chebyshev's Inequality
   - https://doi.org/10.1002/for.3980080207, An examination of the accuracy
   of judgemental confidence intervals in time series forecasting
   - https://doi.org/10.1111/j.1467-9876.2004.00428.x, Chebyshev's
   inequality for nonparametric testing with small N and α in microarray
   research
   - https://doi.org/10.23919/FRUCT48808.2020.9087459, Stream Data
   Preprocessing: Outlier Detection Based on the Chebyshev Inequality with
   Applications

There are many more papers where you can find this inequality being used
especially when the distribution is not normal or if one wants to take a
conservative approach to define the confidence intervals.

if anyone thinks this will be a useful feature, do let me know I can raise
a pull request.

Cheers

_______________________________________________
SciPy-Dev mailing list -- [email protected]
To unsubscribe send an email to [email protected]
https://mail.python.org/mailman3/lists/scipy-dev.python.org/
Member address: [email protected]