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Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R

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  • Asquith, William H.

Abstract

The implementation characteristics of two method of L-moments (MLM) algorithms for parameter estimation of the 4-parameter Asymmetric Exponential Power (AEP4) distribution are studied using the R environment for statistical computing. The objective is to validate the algorithms for general application of the AEP4 using R. An algorithm was introduced in the original study of the L-moments for the AEP4. A second or alternative algorithm is shown to have a larger L-moment-parameter domain than the original. The alternative algorithm is shown to provide reliable parameter production and recovery of L-moments from fitted parameters. A proposal is made for AEP4 implementation in conjunction with the 4-parameter Kappa distribution to create a mixed-distribution framework encompassing the joint L-skew and L-kurtosis domains. The example application provides a demonstration of pertinent algorithms with L-moment statistics and two 4-parameter distributions (AEP4 and the Generalized Lambda) for MLM fitting to a modestly asymmetric and heavy-tailed dataset using R.

Suggested Citation

  • Asquith, William H., 2014. "Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 955-970.
  • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:955-970
    DOI: 10.1016/j.csda.2012.12.013
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    References listed on IDEAS

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    1. Zhu, Dongming & Zinde-Walsh, Victoria, 2009. "Properties and estimation of asymmetric exponential power distribution," Journal of Econometrics, Elsevier, vol. 148(1), pages 86-99, January.
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    5. Serfling, Robert & Xiao, Peng, 2007. "A contribution to multivariate L-moments: L-comoment matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1765-1781, October.
    6. Delicado, P. & Goria, M.N., 2008. "A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1661-1673, January.
    7. Sean Holly & Ivan Petrella & Emiliano Santoro, 2013. "Aggregate fluctuations and the cross-sectional dynamics of firm growth," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(2), pages 459-479, February.
    8. Karvanen, Juha & Nuutinen, Arto, 2008. "Characterizing the generalized lambda distribution by L-moments," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1971-1983, January.
    9. Karvanen, Juha, 2006. "Estimation of quantile mixtures via L-moments and trimmed L-moments," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 947-959, November.
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    1. repec:taf:japsta:v:45:y:2018:i:2:p:187-209 is not listed on IDEAS

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