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Communities & Collections
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An Universal, Simple, Circular Statistics-Based Estimator of alpha for Symmetric Stable Family
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Date
2019-12-01
Author
SenGupta, Ashis
Roy, Moumita
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter alpha lies between 1 and 2. A similar approach can be adopted when alpha (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions.
Subject Keywords
Index parameter
,
Efficiency
,
Asymptotic
,
Characteristic function-based estimator
,
Hill estimator
,
Wrapped stable
,
Estimation
URI
https://hdl.handle.net/11511/64513
Journal
JOURNAL OF RISK AND FINANCIAL MANAGEMENT
DOI
https://doi.org/10.3390/jrfm12040171
Collections
Department of Statistics, Article