The Application of Modeling Gamma-Pareto Distributed Data Using GLM Gamma in Estimation of Monthly Rainfall with TRMM Data

Herlina Hanum, Aji Hamim Wigena, Anik Djuraidah, I Wayan Mangku

Abstract


As a recently developed distribution, the application of Gamma-Pareto is limited to single variable modeling.  A specific transformation of Gamma-Pareto (G-P) yields gamma distribution. Therefore, it is possible to use analysis based on gamma distribution (e.g. GLM) for modeling G-P distributed data.  In this paper we study the application of modeling G-P distributed data using GLM gamma for monthly rainfall which observed in Sukadana Station.  The modeling aims to analyze whether Tropical Rainfall Measuring Mission (TRMM) satellite data is a good estimator for unobserved station’s data.  The transformed of station’s data were considered as response variable in GLM gamma.  The explanatory variable is TRMM data in 9 grids around the station. There are two kinds of modeling i.e. model for whole data and extreme data. The results show that for both data the station’s data are G-P distributed and the transformed data are gamma distributed.  TRMM rainfall data at each grid around the station can be used to estimate the observed data of monthly rainfall. The best model for both data contains dummy variables which correspond to inter quantile data.  The coefficients of dummy variables in the best model may substitute the grouping or the correction in the previous studies.


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References


A. Alzaatreh, F. Famoye, and C. Lee, “Gamma-Pareto Distribution and Its Applications,” J. Mod. Appl. Stat. Methods, vol. 11, no. 1, p. Article 7, 2012.

H. Hanum, A. H. Wigena, A. Djuraidah, and I. W. Mangku, “Modeling extreme rainfall with Gamma-Pareto distribution,” Appl. Math. Sci., vol. 9, no. 121, pp. 6029–6039, 2015.

R. Balaji, “GLM with a Gamma-distributed Dependent Variable,” 2013. [Online]. Available: http://civil.colorado.edu/~balajir/CVEN6833/lectures/GammaGLM-01.pdf.

H. Hanum, A. H. Wigena, A. Djuraidah, and I. W. Mangku, “Modeling Gamma-Pareto distributed data using GLM Gamma,” Glob. J. Pure Appl. Math., vol. 12, no. 4, pp. 3569–3575, 2016.

TRMM, “Tropical Rainfall Measuring Mission,” 2015. [Online]. Available: http://trmm.prnm.nasa.gov.

M. Mamenun, H. Pawitan, and A. Sophaheluwakan, “Validasi dan koreksi data satelit TRMM pada tiga pola curah hujan di Indonesia,” J. Meteorol. dan Geofis., vol. 15, no. 1, pp. 13–23, 2014.

A. D. Warawati, “Prakiraan curah hujan Station Sukadana dengan teknik downscaling berdasarkan data Satelit TRMM,” Institut Pertanian Bogor, 2013.

H. Hassani and E. Silva, “A Kolmogorov-Smirnov Based Test for Comparing the Predictive Accuracy of Two Sets of Forecasts,” Econometrics, vol. 3, pp. 590–609, 2015.

K. P. Burnham and D. R. Anderson, “Multimodel Inference: Understanding AIC and BIC in Model Selection,” Sociol. Methods Res., vol. 33, no. 2, pp. 261–304, 2004.

J. J. M. Moreno, A. P. Pol, A. S. Abad, and B. C. Blasco, “Using the R-MAPE index as a resistant measure of forecast accuracy.,” Psicothema, vol. 25, no. 4, pp. 500–506, 2013.

T. Chai and R. R. Draxler, “Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature,” Geosci. Model Dev., vol. 7, pp. 1247–1250, 2014.




DOI: http://dx.doi.org/10.22135/sje.2017.2.2.40-45

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