Methods to Distinguish Between Polynomial and Exponential Tails

@article{Castillo2011MethodsTD,
  title={Methods to Distinguish Between Polynomial and Exponential Tails},
  author={Joan del Castillo and Jalila Daoudi and Richard A. Lockhart},
  journal={Scandinavian Journal of Statistics},
  year={2011},
  volume={41}
}
Two methods to distinguish between polynomial and exponential tails are introduced. The methods are based on the properties of the residual coefficient of variation for the exponential and non‐exponential distributions. A graphical method, called a CV‐plot, shows departures from exponentiality in the tails. The plot is applied to the daily log‐returns of exchange rates of US dollar and Japanese yen. New statistics are introduced for testing the exponentiality of tails using multiple thresholds… 
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References

SHOWING 1-10 OF 20 REFERENCES
A Simulation Analysis of the Power of Several Tests for Detecting Heavy-Tailed Distributions
Abstract This article presents estimates of the power of five tests for detecting heavy-tailed distributions with the null hypothesis of normality and alternative hypotheses of each of eleven members
On a Class of Tests of Exponentiality
The class of statistics T, = (Σα i=1, X α i /n)/ x , where α > 0 and ≠ 1, have been considered in the literature for testing exponentiality versus omnibus alternatives. These tests have a twosided
The Best Test of Exponentiality against Singly Truncated Normal Alternatives
Abstract We show that the likelihood ratio test of exponentiality against singly truncated normal alternatives is the uniformly most powerful unbiased test and can be expressed in terms of the
Testing exponentiality against generalised Pareto distribution
Test of fit for a Laplace distribution against heavier tailed alternatives
  • Y. Gel
  • Mathematics
    Comput. Stat. Data Anal.
  • 2010
THE ATKINSON INDEX, THE MORAN STATISTIC, AND TESTING EXPONENTIALITY
Constructing tests for exponentiality has been an active and fruitful research area, with numerous applications in engineering, biology and other sciences concerned with life-time data. In the
A survey of tests for exponentiality
A wide selection of tests for exponentiality is discussed and compared. Power computations, using simulations, were done for each procedure. Certain tests (e.g. Gnedenko (1969), Lin and Mudholkar
...
1
2
...