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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. Saralees Nadarajah & Mahdi Teimouri, 2012. "On the Characteristic Function for Asymmetric Exponential Power Distributions," Econometric Reviews, Taylor & Francis Journals, vol. 31(4), pages 475-481.
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    7. Asquith, William H., 2007. "L-moments and TL-moments of the generalized lambda distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4484-4496, May.
    8. 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.
    9. 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.
    10. 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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    Cited by:

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