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Open AccessArticle

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

by Ashis SenGupta 1,2,3 and Moumita Roy 4,*
1
Applied Statistics Unit, Indian Statistical Institute, Kolkata 700108, India
2
Department of Population Health Sciences, MCG, Augusta University, Augusta, GA 30912, USA
3
Department of Statistics, Middle East Technical University, 06800 Ankara, Turkey
4
Department of Statistics, Midnapore College(Autonomous), Midnapore 721101, India
*
Author to whom correspondence should be addressed.
J. Risk Financial Manag. 2019, 12(4), 171; https://doi.org/10.3390/jrfm12040171
Received: 15 October 2019 / Revised: 14 November 2019 / Accepted: 18 November 2019 / Published: 23 November 2019
(This article belongs to the Special Issue Financial Statistics and Data Analytics)
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 α lies between 1 and 2. A similar approach can be adopted when α (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. View Full-Text
Keywords: Index parameter; estimation; wrapped stable; Hill estimator; characteristic function-based estimator; asymptotic; efficiency Index parameter; estimation; wrapped stable; Hill estimator; characteristic function-based estimator; asymptotic; efficiency
MDPI and ACS Style

SenGupta, A.; Roy, M. An Universal, Simple, Circular Statistics-Based Estimator of α for Symmetric Stable Family. J. Risk Financial Manag. 2019, 12, 171.

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