Improved inference for the generalized Pareto distribution under linear, power and exponential normalization

Osama Mohareb Khaled; Haroon Mohamed Barakat; Nourhan Khalil Rakha

Kybernetika (2022)

  • Volume: 58, Issue: 6, page 883-902
  • ISSN: 0023-5954

Abstract

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We discuss three estimation methods: the method of moments, probability weighted moments, and L-moments for the scale parameter and the extreme value index in the generalized Pareto distribution under linear normalization. Moreover, we adapt these methods to use for the generalized Pareto distribution under power and exponential normalizations. A simulation study is conducted to compare the three methods on the three models and determine which is the best, which turned out to be the probability weighted moments. A new computational technique for improving fitting quality is proposed and tested on two real-world data sets using the probability weighted moments. We looked back at various maximal data sets that had previously been addressed in the literature and for which the generalized extreme value distribution under linear normalization had failed to adequately explain them. We use the suggested procedure to find good fits.

How to cite

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Mohareb Khaled, Osama, Mohamed Barakat, Haroon, and Khalil Rakha, Nourhan. "Improved inference for the generalized Pareto distribution under linear, power and exponential normalization." Kybernetika 58.6 (2022): 883-902. <http://eudml.org/doc/299545>.

@article{MoharebKhaled2022,
abstract = {We discuss three estimation methods: the method of moments, probability weighted moments, and L-moments for the scale parameter and the extreme value index in the generalized Pareto distribution under linear normalization. Moreover, we adapt these methods to use for the generalized Pareto distribution under power and exponential normalizations. A simulation study is conducted to compare the three methods on the three models and determine which is the best, which turned out to be the probability weighted moments. A new computational technique for improving fitting quality is proposed and tested on two real-world data sets using the probability weighted moments. We looked back at various maximal data sets that had previously been addressed in the literature and for which the generalized extreme value distribution under linear normalization had failed to adequately explain them. We use the suggested procedure to find good fits.},
author = {Mohareb Khaled, Osama, Mohamed Barakat, Haroon, Khalil Rakha, Nourhan},
journal = {Kybernetika},
keywords = {generalized Pareto distribution; generalized extreme value distribution; method of moments; probability weighted moments; L-moments; linear-power-exponential normalization},
language = {eng},
number = {6},
pages = {883-902},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Improved inference for the generalized Pareto distribution under linear, power and exponential normalization},
url = {http://eudml.org/doc/299545},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Mohareb Khaled, Osama
AU - Mohamed Barakat, Haroon
AU - Khalil Rakha, Nourhan
TI - Improved inference for the generalized Pareto distribution under linear, power and exponential normalization
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 6
SP - 883
EP - 902
AB - We discuss three estimation methods: the method of moments, probability weighted moments, and L-moments for the scale parameter and the extreme value index in the generalized Pareto distribution under linear normalization. Moreover, we adapt these methods to use for the generalized Pareto distribution under power and exponential normalizations. A simulation study is conducted to compare the three methods on the three models and determine which is the best, which turned out to be the probability weighted moments. A new computational technique for improving fitting quality is proposed and tested on two real-world data sets using the probability weighted moments. We looked back at various maximal data sets that had previously been addressed in the literature and for which the generalized extreme value distribution under linear normalization had failed to adequately explain them. We use the suggested procedure to find good fits.
LA - eng
KW - generalized Pareto distribution; generalized extreme value distribution; method of moments; probability weighted moments; L-moments; linear-power-exponential normalization
UR - http://eudml.org/doc/299545
ER -

References

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  1. Balkema, A. A., Haan, L. de, 10.1214/aop/1176996548, Ann. Prob. 2 (1974), 5, 792-804. MR0359049DOI10.1214/aop/1176996548
  2. Barakat, H. M., Nigm, E. H., Zaid, E. O. Abo, , Bull. Belg. Math. Soc. Simon Stevin 26 (2019), 743-758. MR4053851DOI
  3. Barakat, H. M., Nigm, E. M-, Alaswed, H. A., , App. Math. Modell. 45 (2017), 813-822. MR3654695DOI
  4. Barakat, H. M., Nigm, E. M., El-Adll, M. E., , Stat. Pap. 51 (2010), 1, 149-164. Zbl1247.60030MR2556592DOI
  5. Barakat, H. M., Nigm, E. M., Khaled, O. M., , App. Math. Modell. 37 (2013), 10162-10169. MR3125527DOI
  6. Barakat, H. M., Nigm, E. M., Khaled, O. M., Statistical modeling of extremes under linear and power normalizations with applications to air pollutions., Kuwait J. Sci. 41 (2014), 1, 1-19. MR3125527
  7. Barakat, H. M., Nigm, E. M., Khaled, O. M., , Kybernetika 51 (2015), 923-932. MR3453678DOI
  8. Barakat, H. M., Khaled, O. M., Rakha, N. Khalil, , Symmetry 12 (2020), 11, 1876. DOI
  9. Barakat, H. M., Nigm, E. M., Khaled, O. M., Alaswed, H. A., The counterparts of Hill estimators under power normalization., Special Issue J. App. Stat. Sci. (JASS) 22 (2016), 1-2, 87-98. MR3616870
  10. Barakat, H. M., Omar, A. R., Khaled, O. M., , Stat. Probab. Lett. 130 (2017), 25-31. MR3692214DOI
  11. Barakat, H. M., Nigm, E. M., Khaled, O. M., Alaswed, H. A., , AStA Adv. Stat. Anal. 102 (2018), 3, 431-454. MR3829556DOI
  12. Barakat, H. M., Nigm, E. M., Khaled, O. M., Khan, F. M., 10.1080/03610918.2013.805051, Comm. Statis.-Sim. Comp. 44 (2015), 1477-1491. MR3290573DOI10.1080/03610918.2013.805051
  13. BuHamra, S., Al-Kandari, N., Al-Harbi, M., Parametric and nonparametric bootstrap: An analysis of indoor air data from Kuwait., Kuwait J. Sci. 45 (2018), 2, 22-29. 
  14. Castillo, E., Hadi, A. S., Balakrishnan, N., Sarabia, J. M., Extreme Value and Related Models with Applications in Engineering and Science., Wiley, New-Jersey 2004. MR2191401
  15. Coles, S., An Introduction to Statistical Modeling of Extreme Values., Springer, London 2001. MR1932132
  16. Christoph, G., Falk, M., , Stat. Prob. Lett. 28 (1996), 279-284. MR1407002DOI
  17. Davison, A. C., Smith, R. L., Models for exceedances over high threshold., J. Roy. Stat. Soc. Ser. B. 52 (1990), 393-442. MR1086795
  18. Bermudez, P. de Zea, Kotz, S., , J. Stat. Plan. Inf. 140 (2010), 1353-1373. MR2592216DOI
  19. Gnedenko, B. V., 10.2307/1968974, Ann. Math. 44 (1943), 423-453. MR0008655DOI10.2307/1968974
  20. Greenwood, J. A., Landwehr, J. M., Matalas, N. C., Wallis, J. R., , Water Resour. Res. 15 (1979), 5, 1049-1054. DOI
  21. Hosking, J. R. M., L-moments: analysis and estimation of distributions using linear combinations of order statistics., J. Roy. Stat. Soc. B52 (1990), 105-124. MR1049304
  22. Landwehr, J. M., Matalas, N. C., Wallis, J. R., , Water Resour. Res. 15 (1979), 1055-1064. DOI
  23. Nasri-Roudsari, D., , Comm. Statis.- Theory Meth. 28 (1999), 6, 1379-1389. MR1705779DOI
  24. Pancheva, E., Limit theorems for extreme order statistics under nonlinear normalization., In: Stability Problems for Stochastic Models, Lecture Notes in Math., Springer, Berlin 1155 (1984), 284-309. MR0825331
  25. Pickands, J., Statistical inference using extreme order statistics., Ann. Stat. 3 (1975), 119-131. MR0423667
  26. Ravi, S., Mavitha, T. S., New limit distributions for extreme under a nonlinear normalization., ProbStat Forum 9 (2016), 1-20. 

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