UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

Approximating stable densities with Padé approximants and asymptotic series

Thumbnail Image

Files

Liang_Jiaxi.pdf (628.67 KB)

Date

2011-04-29T17:25:43Z

Authors

Liang, Jiaxi

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

In this thesis, we are interested in using the Padé approximants and asymptotic series to approximate the density functions of the stable distributions. The paper specifically discusses the selection of the optimal degree and central point of Padé approximants as well as how to connect the Padé approximants and asymptotic series as a piecewise function. Based on such approximation, a computational algorithm is developed to estimate the maximum likelihood estimator with confidence interval of the parameters, using quasi-Newton method. Simulations are conducted to evaluate the performance of this algorithm, and comparisons are made to Nolan's integral method to show that the method introduced in the thesis is fast and reliable in approximation and estimation.

Description

Keywords

Stable distribution, Padé approximants

LC Keywords

Citation

URI

http://hdl.handle.net/10012/5886

Collections

Theses
Statistics and Actuarial Science