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Mixture representations for symmetric generalized Linnik laws

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  • Pakes, Anthony G.

Abstract

This paper offers a simple proof based on random variable representations for a mixture representation of symmetric Linnik laws previously derived by purely analytic means. The new approach can be set in a much more general context which embraces the symmetric and the positive generalized Linnik laws.

Suggested Citation

  • Pakes, Anthony G., 1998. "Mixture representations for symmetric generalized Linnik laws," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 213-221, March.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:3:p:213-221
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    References listed on IDEAS

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    1. Devroye, Luc, 1990. "A note on linnik's distribution," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 305-306, April.
    2. Kotz, Samuel & Ostrovskii, I. V., 1996. "A mixture representation of the Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 61-64, January.
    3. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
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    Cited by:

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    2. Lekshmi, V. Seetha & Jose, K.K., 2006. "Autoregressive processes with Pakes and geometric Pakes generalized Linnik marginals," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 318-326, February.
    3. Halvarsson, Daniel, 2013. "On the Estimation of Skewed Geometric Stable Distributions," Ratio Working Papers 216, The Ratio Institute.
    4. Yury Khokhlov & Victor Korolev & Alexander Zeifman, 2020. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems," Mathematics, MDPI, vol. 8(5), pages 1-29, May.
    5. Dexter Cahoy, 2012. "An estimation procedure for the Linnik distribution," Statistical Papers, Springer, vol. 53(3), pages 617-628, August.
    6. Ashis SenGupta & Moumita Roy, 2023. "Circular-Statistics-Based Estimators and Tests for the Index Parameter α of Distributions for High-Volatility Financial Markets," JRFM, MDPI, vol. 16(9), pages 1-14, September.

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