Saddlepoint Approximation for Data in Simplices: A Review with New Applications
| Autor: | Riccardo Gatto |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
spacing-frequencies
multivariate hypergeometric distribution Dirichlet distribution Notation 01 natural sciences 010104 statistics & probability symbols.namesake 510 Mathematics Statistics::Methodology Applied mathematics 0101 mathematics bootstrap Mathematics Simplex circular data multinomial distribution urn model spacings 010102 general mathematics likelihood ratio test Hypergeometric distribution symbols Sample space multivariate Polya distribution Dirichlet-multinomial distribution Multinomial distribution entropy Random variable 360 Social problems & social services |
| Zdroj: | Gatto, Riccardo (2019). Saddlepoint approximation for data in simplices: a review with new applications. Stats, 2(1), pp. 121-147. MPDI 10.3390/stats2010010 Stats Volume 2 Issue 1 Pages 10-147 |
| ISSN: | 2571-905X |
| DOI: | 10.3390/stats2010010 |
| Popis: | This article provides a review of the saddlepoint approximation for a M-statistic of a sample of nonnegative random variables with fixed sum. The sample vector follows the multinomial, the multivariate hypergeometric, the multivariate Polya or the Dirichlet distributions. The main objective is to provide a complete presentation in terms of a single and unambiguous notation of the common mathematical framework of these four situations: the simplex sample space and the underlying general urn model. Some important applications are reviewed and special attention is given to recent applications to models of circular data. Some novel applications are developed and studied numerically. |
| Databáze: | OpenAIRE |
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