On the Estimation of the Shape Parameter of a Symmetric Distribution

22 Pages Posted: 24 Feb 2020

See all articles by Jennifer Chan

Jennifer Chan

The University of Sydney

Boris Choy

University of Sydney Business School

Stephen Walker

affiliation not provided to SSRN

Date Written: January 1, 2018

Abstract

The shape parameter of a symmetric probability distribution is often more difficult to estimate accurately than the location and scale parameters. In this paper, we suggest an intuitive but innovative matching quantile estimation method for this parameter. The proposed shape parameter estimate is obtained by setting its value to a level such that the central 1-1/n portion of the distribution will just cover all n observations, while the location and scale parameters are estimated using existing methods such as maximum likelihood (ML). This hybrid estimator is proved to be consistent and is illustrated by two distributions, namely Student-t and Exponential Power. Simulation studies show that the hybrid method provides reasonably accurate estimates. In the presence of extreme observations, this method provides thicker tails than the full ML method and protect inference on the location and scale parameters. This feature offered by the hybrid method is also demonstrated in the empirical study using two real data sets.

Keywords: Student-t; Exponential Power; Matching quantile; Tails; Consistency

JEL Classification: C81

Suggested Citation

Chan, Jennifer and Choy, S. T. Boris and Walker, Stephen, On the Estimation of the Shape Parameter of a Symmetric Distribution (January 1, 2018). Available at SSRN: https://ssrn.com/abstract=3526544 or http://dx.doi.org/10.2139/ssrn.3526544

Jennifer Chan (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NC NSW 2006
Australia
61293514873 (Phone)
2218 (Fax)

HOME PAGE: http://https://www.maths.usyd.edu.au/u/jchan/index.html

S. T. Boris Choy

University of Sydney Business School ( email )

Cnr. of Codrington and Rose Streets
Sydney, NSW 2006
Australia

Stephen Walker

affiliation not provided to SSRN

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