Lepage test

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In statistics, the Lepage test is an exact distribution-free test (

Wilcoxon rank-sum test for location and the standardized Ansari–Bradley test for scale. The Lepage test was first introduced by Yves Lepage in 1971 in a paper in Biometrika.[1] A large number of Lepage-type tests exists in statistical literature for simultaneously testing location and scale shifts in case-control studies. The details may be found in the book: Nonparametric statistical tests: A computational approach.[2] Wolfgang Kössler[3] in 2006 also introduced various Lepage type tests using some alternative score functions optimal for various distributions. Amitava Mukherjee and Marco Marozzi introduced a class of percentile modified versions of the Lepage test.[4] An alternative to the Lepage-type tests is known as the Cucconi test proposed by Odoardo Cucconi in 1968.[5]

Conducting the Lepage test with R

Practitioners can apply the Lepage test using the pLepage function of the contributory package NSM3,[6] built under R software. Andreas Schulz and Markus Neuhäuser also provided detailed R code for computation of test statistic and p-value of the Lepage test[7] for the users.

Application in statistical process monitoring

In recent years, the Lepage statistic is a widely used statistical process for monitoring and quality control. In 2012, Amitava Mukherjee and Subhabrata Chakraborti introduced a distribution-free Shewhart-type Phase-II monitoring scheme[8] (control chart) for simultaneously monitoring of location and scale parameter of a process using a test sample of fixed size, when a reference sample of sufficiently large size is available from an in-control population. Later in 2015, the same statisticians along with Shovan Chowdhury, proposed a distribution-free CUSUM-type Phase-II monitoring scheme[9] based on the Lepage statistic. In 2017, Mukherjee further designed an EWMA-type distribution-free Phase-II monitoring scheme[10] for joint monitoring of location and scale. In the same year, Mukherjee, with Marco Marozzi, known for promoting the Cucconi test, came together to design the Circular-Grid Lepage chart – a new type of joint monitoring scheme.[11]

Multisample version of the Lepage test

In 2005, František Rublìk introduced the multisample version of the original two-sample Lepage test.[12]

See also

References

  1. JSTOR 2334333
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  2. ISBN 9781439867037
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  3. OCLC 243600853
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  4. ISSN 1435-926X
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  5. JSTOR 23241361
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  6. ^ Schneider, Grant; Chicken, Eric; Becvarik, Rachel (2018-05-16), NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken – Nonparametric Statistical Methods, Third Edition, retrieved 2019-09-17
  7. ^ Schulz, Andreas. "R Programme for Lepage Test" (PDF).
  8. ISSN 0748-8017
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  9. ISSN 0748-8017
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  10. ISSN 0268-3768
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  11. ISSN 0748-8017
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  12. ISSN 0023-5954
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