Roslinazairimah, Zakaria and Nor Hafizah, Moslim (2015) Independent Mixedgamma Variables for Modelling Rainfall. In: 6th NAUN European Conference on Applied Mathematics and Informatics (AMATHI 2015), 1012 January 2015 , Spain. pp. 239244..

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Abstract
Understanding the rainfall process and characteristics are crucial to the efficient design of flood mitigation and construction of crop growth models. Modelling rainfall is not limited to fit the historical data to a suitable distribution but the model should be able to generate synthetic rainfall data. In this study, we derive sets of formulae of mean and variance for the sum of two and three independent mixedgamma variables, respectively. Firstly, the positive data is fitted to gamma model marginally and the shape and scale parameters are estimated using the maximum likelihood estimation method. Then, the mixedgamma model is defined to include zero and positive data. The formulae of mean and variance for the sum of two and three independent mixedgamma variables are derived and tested using the daily rainfall totals from Pooraka station in South Australia for the period of 19011990. The results demonstrate that the values of generated mean and using formula are close to the observed mean. However, the values of the variance are sometimes overestimated or underestimated of the observed values. The observed variance is lower possibly due to correlation between the experimental data, that have not been included in the mixedgamma models. The Kolmogorov–Smirnov and Anderson–Darling goodness of fit tests are used to assess the fit between the observed sum and the generated sum of independent mixedgamma variables. In both cases, the observed sum is not significantly different from the generated sum of independent mixedgamma model at 5% significance level. This methodology and formulae derived can be applied to find the sum of more than three independent mixedgamma variables and the general form of the formulae can be derived.
Item Type:  Conference or Workshop Item (Lecture) 

Additional Information:  ISBN: 9781618042811 
Uncontrolled Keywords:  Gamma variable; Mixedgamma variables; Rainfall model, Independent variables; Synthetic data 
Subjects:  G Geography. Anthropology. Recreation > GB Physical geography 
Faculty/Division:  Faculty of Industrial Sciences And Technology 
Depositing User:  Mrs. Neng Sury Sulaiman 
Date Deposited:  03 Feb 2015 02:28 
Last Modified:  28 Jun 2018 08:25 
URI:  http://umpir.ump.edu.my/id/eprint/8293 
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