Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District

An efficient design of flood mitigation and construction of crop growth models depend upon good understanding of the rainfall process and characteristics. Gamma distribution is usually used to model nonzero rainfall amounts. In this study, the mixed-gamma model is applied to accommodate both zero an...

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Main Authors:	Roslinazairimah, Zakaria, Nor Hafizah, Moslim
Format:	Conference or Workshop Item
Language:	English
Published:	AIP Publishing 2017
Subjects:	QA Mathematics
Online Access:	http://umpir.ump.edu.my/id/eprint/17708/ http://umpir.ump.edu.my/id/eprint/17708/ http://umpir.ump.edu.my/id/eprint/17708/1/fist-2017-roslinazairimah-modelling%20rainfall%20amount.pdf

id	ump-17708
recordtype	eprints
spelling	ump-177082018-12-20T08:12:00Z http://umpir.ump.edu.my/id/eprint/17708/ Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District Roslinazairimah, Zakaria Nor Hafizah, Moslim QA Mathematics An efficient design of flood mitigation and construction of crop growth models depend upon good understanding of the rainfall process and characteristics. Gamma distribution is usually used to model nonzero rainfall amounts. In this study, the mixed-gamma model is applied to accommodate both zero and nonzero rainfall amounts. The mixed-gamma model presented is for the independent case. The formulae of mean and variance are derived for the sum of two and three independent mixed-gamma variables, respectively. Firstly, the gamma distribution is used to model the nonzero rainfall amounts and the parameters of the distribution (shape and scale) are estimated using the maximum likelihood estimation method. Then, the mixed-gamma model is defined for both zero and nonzero rainfall amounts simultaneously. The formulae of mean and variance for the sum of two and three independent mixed-gamma variables derived are tested using the monthly rainfall amounts from rainfall stations within Kuantan district in Pahang Malaysia. Based on the Kolmogorov-Smirnov goodness of fit test, the results demonstrate that the descriptive statistics of the observed sum of rainfall amounts is not significantly different at 5% significance level from the generated sum of independent mixed-gamma variables. The methodology and formulae demonstrated can be applied to find the sum of more than three independent mixed-gamma variables. AIP Publishing 2017 Conference or Workshop Item PeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/17708/1/fist-2017-roslinazairimah-modelling%20rainfall%20amount.pdf Roslinazairimah, Zakaria and Nor Hafizah, Moslim (2017) Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District. In: AIP Conference Proceedings: The 3rd ISM International Statistical Conference 2016 (ISM-III), 9-11 August 2016 , Kuala Lumpur, Malaysia. pp. 1-8., 1842 (020001). ISBN 978-0-7354-1512-6 https://doi.org/10.1063/1.4982831
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Malaysia Pahang
building	UMP Institutional Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Roslinazairimah, Zakaria Nor Hafizah, Moslim Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District
description	An efficient design of flood mitigation and construction of crop growth models depend upon good understanding of the rainfall process and characteristics. Gamma distribution is usually used to model nonzero rainfall amounts. In this study, the mixed-gamma model is applied to accommodate both zero and nonzero rainfall amounts. The mixed-gamma model presented is for the independent case. The formulae of mean and variance are derived for the sum of two and three independent mixed-gamma variables, respectively. Firstly, the gamma distribution is used to model the nonzero rainfall amounts and the parameters of the distribution (shape and scale) are estimated using the maximum likelihood estimation method. Then, the mixed-gamma model is defined for both zero and nonzero rainfall amounts simultaneously. The formulae of mean and variance for the sum of two and three independent mixed-gamma variables derived are tested using the monthly rainfall amounts from rainfall stations within Kuantan district in Pahang Malaysia. Based on the Kolmogorov-Smirnov goodness of fit test, the results demonstrate that the descriptive statistics of the observed sum of rainfall amounts is not significantly different at 5% significance level from the generated sum of independent mixed-gamma variables. The methodology and formulae demonstrated can be applied to find the sum of more than three independent mixed-gamma variables.
format	Conference or Workshop Item
author	Roslinazairimah, Zakaria Nor Hafizah, Moslim
author_facet	Roslinazairimah, Zakaria Nor Hafizah, Moslim
author_sort	Roslinazairimah, Zakaria
title	Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District
title_short	Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District
title_full	Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District
title_fullStr	Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District
title_full_unstemmed	Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District
title_sort	modelling rainfall amounts using mixed-gamma model for kuantan district
publisher	AIP Publishing
publishDate	2017
url	http://umpir.ump.edu.my/id/eprint/17708/ http://umpir.ump.edu.my/id/eprint/17708/ http://umpir.ump.edu.my/id/eprint/17708/1/fist-2017-roslinazairimah-modelling%20rainfall%20amount.pdf
first_indexed	2023-09-18T22:24:37Z
last_indexed	2023-09-18T22:24:37Z
_version_	1777415882887135232

Modelling Rainfall Amounts using Mixed-Gamma Model for Kuantan District

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