Krawtchouk polynomial approximation for binomial convo-lutions
- Authors
- Ha, H.-T.
- Issue Date
- 2017
- Publisher
- Kyungpook National University
- Keywords
- Distribution approximation; Krawtchouk polynomials; Saddlepoint approximation; Sum of Independent nonidentical Binomial Distributions
- Citation
- Kyungpook Mathematical Journal, v.57, no.3, pp.493 - 502
- Journal Title
- Kyungpook Mathematical Journal
- Volume
- 57
- Number
- 3
- Start Page
- 493
- End Page
- 502
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/6627
- DOI
- 10.5666/KMJ.2017.57.3.493
- ISSN
- 1225-6951
- Abstract
- We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program. © Kyungpook Mathematical Journal.
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