On the Estimation of Skewed Geometric Stable Distributions
The increasing interest in the application of geometric stable distributions has lead to a need for appropriate estimators. Building on recent procedures for estimating the Linnik distribution, this paper develops two estimators for the geometric stable distribution. Closed form expressions are provided for the signed and unsigned fractional moments of the distribution. The estimators are then derived using the methods of fractional lower order moments and that of logarithmic moments. Their performance is tested on simulated data, where the lower order estimators, in particular, are found to give efficient results over most of the parameter space.
|Date of creation:||21 Aug 2013|
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- V. Lekshmi & K. Jose, 2004. "An autoregressive process with geometric α-laplace marginals," Statistical Papers, Springer, vol. 45(3), pages 337-350, July.
- Pakes, Anthony G., 1998. "Mixture representations for symmetric generalized Linnik laws," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 213-221, March.
- repec:nys:sunysb:93-02 is not listed on IDEAS
- Kotz, Samuel & Ostrovskii, I. V., 1996. "A mixture representation of the Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 61-64, January.
- Dexter Cahoy, 2012. "An estimation procedure for the Linnik distribution," Statistical Papers, Springer, vol. 53(3), pages 617-628, August.
- Devroye, Luc, 1990. "A note on linnik's distribution," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 305-306, April.
- Anderson, Dale N., 1992. "A multivariate Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 333-336, July.
- Kozubowski, Tomasz J. & Rachev, Svetlozar T., 1994. "The theory of geometric stable distributions and its use in modeling financial data," European Journal of Operational Research, Elsevier, vol. 74(2), pages 310-324, April.
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