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January 2023

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ENH: Feature Request - Non-parametric test based on Chebyshev's Inequality #17690
by Arnab Paul Choudhury Jan. 1, 2023

Jan. 1, 2023

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

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