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Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros

The gamma distribution is commonly used to model environmental data. However, rainfall data often contain zero observations, which violates the assumption that all observations must be positive in a gamma distribution, and so a gamma model with excess zeros treated as a binary random variable is req...

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Autores principales: Khooriphan, Wansiri, Niwitpong, Sa-Aat, Niwitpong, Suparat
Formato: Online Artículo Texto
Lenguaje:English
Publicado: PeerJ Inc. 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9484466/
https://www.ncbi.nlm.nih.gov/pubmed/36132216
http://dx.doi.org/10.7717/peerj.14023
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author Khooriphan, Wansiri
Niwitpong, Sa-Aat
Niwitpong, Suparat
author_facet Khooriphan, Wansiri
Niwitpong, Sa-Aat
Niwitpong, Suparat
author_sort Khooriphan, Wansiri
collection PubMed
description The gamma distribution is commonly used to model environmental data. However, rainfall data often contain zero observations, which violates the assumption that all observations must be positive in a gamma distribution, and so a gamma model with excess zeros treated as a binary random variable is required. Rainfall dispersion is important and interesting, the confidence intervals for the variance of a gamma distribution with excess zeros help to examine rainfall intensity, which may be high or low risk. Herein, we propose confidence intervals for the variance of a gamma distribution with excess zeros by using fiducial quantities and parametric bootstrapping, as well as Bayesian credible intervals and highest posterior density intervals based on the Jeffreys’, uniform, or normal-gamma-beta prior. The performances of the proposed confidence interval were evaluated by establishing their coverage probabilities and average lengths via Monte Carlo simulations. The fiducial quantity confidence interval performed the best for a small probability of the sample containing zero observations (δ) whereas the Bayesian credible interval based on the normal-gamma-beta prior performed the best for large δ. Rainfall data from the Kiew Lom Dam in Lampang province, Thailand, are used to illustrate the efficacies of the proposed methods in practice.
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spelling pubmed-94844662022-09-20 Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros Khooriphan, Wansiri Niwitpong, Sa-Aat Niwitpong, Suparat PeerJ Statistics The gamma distribution is commonly used to model environmental data. However, rainfall data often contain zero observations, which violates the assumption that all observations must be positive in a gamma distribution, and so a gamma model with excess zeros treated as a binary random variable is required. Rainfall dispersion is important and interesting, the confidence intervals for the variance of a gamma distribution with excess zeros help to examine rainfall intensity, which may be high or low risk. Herein, we propose confidence intervals for the variance of a gamma distribution with excess zeros by using fiducial quantities and parametric bootstrapping, as well as Bayesian credible intervals and highest posterior density intervals based on the Jeffreys’, uniform, or normal-gamma-beta prior. The performances of the proposed confidence interval were evaluated by establishing their coverage probabilities and average lengths via Monte Carlo simulations. The fiducial quantity confidence interval performed the best for a small probability of the sample containing zero observations (δ) whereas the Bayesian credible interval based on the normal-gamma-beta prior performed the best for large δ. Rainfall data from the Kiew Lom Dam in Lampang province, Thailand, are used to illustrate the efficacies of the proposed methods in practice. PeerJ Inc. 2022-09-16 /pmc/articles/PMC9484466/ /pubmed/36132216 http://dx.doi.org/10.7717/peerj.14023 Text en ©2022 Khooriphan et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ) and either DOI or URL of the article must be cited.
spellingShingle Statistics
Khooriphan, Wansiri
Niwitpong, Sa-Aat
Niwitpong, Suparat
Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros
title Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros
title_full Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros
title_fullStr Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros
title_full_unstemmed Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros
title_short Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros
title_sort bayesian estimation of rainfall dispersion in thailand using gamma distribution with excess zeros
topic Statistics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9484466/
https://www.ncbi.nlm.nih.gov/pubmed/36132216
http://dx.doi.org/10.7717/peerj.14023
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