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Some Improvements in Numerical Evaluation of Symmetric Stable Density and its Derivatives

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  • Muneya Matsui

    (Graduate School of Economics, University of Tokyo)

  • Akimichi Takemura

    (Graduate School of Information Science and Technology, University of Tokyo)

Abstract

We propose improvements in numerical evaluation of symmetric stable density and its partial derivatives with respect to the parameters. They are useful for more reliable evaluation of maximum likelihood estimator and its standard error. Numerical values of the Fisher information matrix of symmetric stable distributions are also given. Our improvements consist of modification of the method of Nolan (1997) for the boundary cases, i.e., in the tail and mode of the densities and in the neighborhood of the Cauchy and the normal distributions.

Suggested Citation

  • Muneya Matsui & Akimichi Takemura, 2004. "Some Improvements in Numerical Evaluation of Symmetric Stable Density and its Derivatives," CIRJE F-Series CIRJE-F-292, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2004cf292
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2004/2004cf292.pdf
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    References listed on IDEAS

    as
    1. Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-285, July-Sept.
    2. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
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    Cited by:

    1. Davood Farbod & Karen V. Gasparian, 2012. "On the confidence intervals of parametric functions for Distributions Generated by Symmetric Stable Laws," Statistica, Department of Statistics, University of Bologna, vol. 72(4), pages 405-413.
    2. Tibor K. Pogány & Saralees Nadarajah, 2015. "Remarks on the Stable S α (β,γ,μ) Distribution," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 515-524, June.

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