An Universal, Simple, Circular Statistics-Based Estimator of alpha for Symmetric Stable Family

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2019-12-01

Author

SenGupta, Ashis
Roy, Moumita

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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

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Citation Formats

A. SenGupta and M. Roy, “An Universal, Simple, Circular Statistics-Based Estimator of alpha for Symmetric Stable Family,” JOURNAL OF RISK AND FINANCIAL MANAGEMENT, pp. 0–0, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64513.