Distribution approximation and modelling via orthogonal polynomial sequences
- Authors
- Provost, Serge B.; Ha, Hyung-Tae
- Issue Date
- 2016
- Publisher
- TAYLOR & FRANCIS LTD
- Keywords
- approximate distributions; moment-matching techniques; orthogonal polynomials; percentiles; test statistics; data modelling; density estimation
- Citation
- STATISTICS, v.50, no.2, pp.454 - 470
- Journal Title
- STATISTICS
- Volume
- 50
- Number
- 2
- Start Page
- 454
- End Page
- 470
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/9726
- DOI
- 10.1080/02331888.2015.1053809
- ISSN
- 0233-1888
- Abstract
- A general methodology is developed for approximating the distribution of a random variable on the basis of its exact moments. More specifically, a probability density function is approximated by the product of a suitable weight function and a linear combination of its associated orthogonal polynomials. A technique for generating a sequence of orthogonal polynomials from a given weight function is provided and the coefficients of the linear combination are explicitly expressed in terms of the moments of the target distribution. On applying this approach to several test statistics, we observed that the resulting percentiles are consistently in excellent agreement with the tabulated values. As well, it is explained that the same moment-matching technique can be utilized to produce density estimates on the basis of the sample moments obtained from a given set of observations. An example involving a well-known data set illustrates the density estimation methodology advocated herein.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - 사회과학대학 > 응용통계학과 > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.