Test for Regularly Varying Tail Against Rapidly/Slowly Varying Tail

  • Deepesh BhatiEmail author
  • Sudheesh K. Kattumannil
Research article


We introduce a new non-parametric test for testing the tail behaviour of a random variable using a characterization based on ratio of extreme order statistics. The asymptotic null distribution of the proposed test statistic is obtained. A Monte Carlo simulation study is carried out to compute the empirical size and power under different alternatives. Finally, we implement the proposed test using two real data sets.


Pareto distribution Ratio of order statistics Regularly varying tailed distribution Tail of a distribution 



The authors would like to thank the anonymous referee(s) and Editor-in-Chief for their suggestions and comments, which lead to improvement of the presentation.


There is no funding from any source for writing this article.

Compliance with ethical standards

Conflict of Interest

There is no conflict of interest among the author while publishing this article.


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Copyright information

© The Indian Society for Probability and Statistics (ISPS) 2019

Authors and Affiliations

  1. 1.Department of StatisticsCentral University of RajasthanAjmerIndia
  2. 2.Indian Statistical InstituteChennaiIndia

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