# Methods for Testing the Rainfall Dispersion Data Fitted to a Gamma Distribution of Songkhla, Thailand

## Keywords:

Measure of dispersion, Power of the test, Skewed distribution, Test statistics, Type I error rate## Abstract

Floods are ordinary natural disasters in Songkhla, Thailand that occur almost every year due to heavy rainfall during the rainy season. The organizations related to agriculture and water resource planning can solve or reduce the flood problem in Songkhla by testing the monthly rainfall dispersion for flood monitoring. We can use the coefficient of variation (CV) to measure the dispersion of rainfall amount in different areas because the rainfall amount varies greatly depending on the region and season. The objective of this study is to propose two methods for testing the CV for a gamma distribution. The methods based on Score-type and Wald-type confidence intervals were applied for testing the monthly rainfall dispersion which these data were well-fitted with a gamma distribution. Using Monte Carlo simulations, the type I error rate and power of the test for two test statistics were estimated under several shape parameter values in a gamma distribution. The simulation results indicated that the test statistic based on Wald-type confidence interval performed better than its competitor in terms of the attained nominal significance level (0.05). The mean of the absolute differences between the empirical type I error rates and 0.05 for those based on Score-type and Wald-type confidence intervals was 0.0480 and 0.0067, respectively. Therefore, the test statistic based on Wald-type confidence interval is recommended for analysis in similar scenarios. Both test statistics were utilized to test the rainfall dispersion data from Sa Dao Meteorological Station in Songkhla. The study concluded that the population CV of the Songkhla’s rainfall was not significantly different from the hypothesized setting of 0.90.

### Downloads

## References

Thangjai W, Niwitpong SA, Niwitpong S. Confidence intervals for the common coefficient of variation of rainfall in Thailand. Peer J 2020; 8:e10004.

Rapid Assessment for Resilient Recovery and Reconstruction Planning. Thai flood 2011. Bangkok: The World Bank; 2012.

Loc HH, Emadzadeh A, Park E, Nontikansak P, Deo RC. The Great 2011 Thailand flood disaster revisited: Could it have been mitigated by different dam operations based on better weather forecasts?. Environ Res. 2023; 216: 114493.

Hanson S, Nicholls R, Ranger N, Hallegatte S, Corfee-Morlot J, Herweijer C, Chateau J. A global ranking of port cities with high exposure to climate extremes. Clim Change 2011; 104: 89–111.

Tanim AH, Goharian E. Developing a hybrid modeling and multivariate analysis framework for storm surge and runoff interactions in urban coastal flooding. J Hydrol 2021; 595: 125670.

Shen Y, Morsy MM, Huxley C, Tahvildari N, Goodall JL. Flood risk assessment and increased resilience for coastal urban watersheds under the combined impact of storm tide and heavy rainfall. J Hydrol 2019; 579: 124159.

Dawson RJ, Speight L, Hall JW, Djordjevic S, Savic D, Leandro J. Attribution of flood risk in urban areas. J Hydroinformatics 2008; 10(4): 275-88.

Archetti R, Bolognesi A, Casadio A, Maglionico M. Development of flood probability charts for urban drainage network in coastal areas through a simplified joint assessment approach. Hydrol Earth Syst Sci 2011; 15(10): 3115-22.

Xu K, Ma C, Lian J, Bin L. Joint probability analysis of extreme precipitation and storm tide in a coastal city under changing environment. PLoS ONE 2014; 9(10): 0109341.

Wahl T, Jain S, Bender J, Meyers SD, Luther ME. Increasing risk of compound flooding from storm surge and rainfall for major US cities. Nat Clim Change 2015; 5(12): 1093-7.

Thairesidents. Songkhla flood, 62 schools closed [Internet]. [cited 2023 Mar 1]. Available from: https://thairesidents.com/local/songkhla-flood-62-schools-closed.

Weather Spark. Climate and average weather year round in Songkhla Thailand [Internet]. [cited 2023 Mar 1]. Available from: https://weatherspark.com/y/113364/Average-Weather-in-Songkhla-Thailand-Year-Round.

Albatineh AN, Boubakari I, Kibra BMG. New confidence interval estimator of the signal-to-noise ratio based on asymptotic sampling distribution. Commun Stat-Theory Methods 2017; 46(2): 574-90.

Nairy KS, Rao KA. Tests of coefficients of variation of normal population. Commun Stat-Simul Comput 2003; 32(3): 641-646.

Faber DS, Korn H. Applicability of the coefficient of variation method for analyzing synaptic plasticity. Biophys J 1991; 60(5): 1288-94.

Calif R, Soubdhan T. On the use of the coefficient of variation to measure spatial and temporal correlation of global solar radiation. Renew Energ 2016; 88: 192-9.

Reed GF, Lynn F, Meade BD. Use of coefficient of variation in assessing variability of quantitative assays. Clin Diagn Lab Immunol 2002; 9(6): 1235-1239.

Bedeian AG, Mossholder KW. On the use of the coefficient of variation as a measure of diversity. Organ Res Methods 2000; 3(3): 285-97.

Kang CW, Lee MS, Seong YJ, Hawkins DM. A control chart for the coefficient of variation. J Qual Technol 2007; 39(2): 151-8.

Castagliola P, Celano G, Psarakis S. Monitoring the coefficient of variation using EWMA charts. J Qual Technol 2011; 43(3): 249-65.

Frederick SH, Kut CS. The effect of machine breakdowns and interstage storage on the performance of production line systems. Int J Prod Res 1991; 29: 2043-55.

Döring TF, Reckling M. Detecting global trends of cereal yield stability by adjusting the coefficient of variation. Eur J Agron 2018; 99: 30-6.

Bakowskia A, Radziszewskia L, Žmindak M. Analysis of the coefficient of variation for injection pressure in a compression ignition engine. Procedia Eng 2017; 177: 297-302.

Abu-Dayyeh WA, Al-Rawi ZR, Alodat MT, Comparison of several confidence intervals for normal distribution with known coefficient of variation. Stat e Appl 2009; 12(2): 75-85.

Alodat MT, Omari DA. Estimating the normal population with known coefficient of variation using the optimal ranked set sampling scheme. Stat e Appl 2012; 10(1): 33-42.

Addisu S, Selassie YG, Fissha G, Gedif B. Time series trend analysis of temperature and rainfall in lake Tana Sub-basin, Ethiopia. Environ Syst Res 2015; 4(1): 1-12.

Wang H-J, Merz R, Yang S, Tarasova L, Basso S. Emergence of heavy tails in streamflow distributions: The role of spatial rainfall variability. Adv Water Resour 2023; 171: 104359,

McKay AT. Distribution of the coefficient of variation and the extended t distribution. J R Stat Soc 1932; 95(4): 695-98.

Vangel MG. Confidence intervals for a normal coefficient of variation. Am Stat 1996; 50(1): 21-6.

Panichkitkosolkul W. Improved confidence intervals for a coefficient of variation of a normal distribution. Thail Stat 2009; 7(2): 193-99.

Albatineh AN, Kibria BMG, Wilcox ML, Zogheib B. Confidence interval estimation for the population coefficient of variation using ranked set sampling. J Appl Stat 2014; 41(4): 733-51.

Sangnawakij P, Niwitpong SA, Niwitpong S. Confidence intervals for the ratio of coefficients of variation of the gamma distributions. In: Huynh VN, Inuiguchi M, Demoeux T, editors. Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2015. Lecture Notes in Computer Science. Cham: Springer International Publishing; 2015. p. 193-203.

Panichkitkosolkul W, Testing the ratio of the coefficients of variation for the inverse gamma distributions with an application to rainfall dispersion in Thailand. NIDA Development Journal 2022; 62(2): 80-103.

Yosboonruang N, Niwitpong SA, Niwitpong S. Measuring the dispersion of rainfall using Bayesian confidence intervals for coefficient of variation of delta-lognormal distribution: a study from Thailand. PeerJ 2019; 7: e7344.

Yosboonruang N, Niwitpong SA, Niwitpong S. Simultaneous confidence intervals for all pairwise differences between the coefficients of variation of rainfall series in Thailand. PeerJ 2021; 9: e11651,

Yosboonruang N, Niwitpong SA, Niwitpong S. Bayesian computation for the common coefficient of variation of delta-lognormal distributions with application to common rainfall dispersion in Thailand. PeerJ 2022; 10: e12858.

Casella G, Berger RL. Statistical Inference. Pacific Grove: Thomson Learning; 2002.

Rao CR. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Math Proc Camb 1948; 44(1): 50-7.

Rao CR. Score test: Historical review and recent developments. In: Advances in ranking and selection, Multiple Comparisons, and Reliability, Birkhäuser, Boston, 2005.

Gaffke N, Steyer R, von Davier AA. On the asymptotic null-distribution of the Wald statistic at singular parameter points. Stat Decis 1999; 17(4): 339-58.

Ihaka R, Gentleman R. R: A language for data analysis and graphics. J Comput Graph Stat 1996; 5(3): 299-314.

Banik S, Kibria BMG. Estimating the population coefficient of variation by confidence intervals. Commun Stat Simul 2011; 40(8): 1236-61.

McKenzie JD. Minitab student release 14: Statistical software for education. Boston: Pearson Addison-Wesley; 2004.

Ines AVM, Hansen JW. Bias correction of daily GCM rainfall for crop simulation studies. Agric For Meteorol 2006; 138(1-4): 44-53.

Block PJ, Souza Filho FA, Sun L, Kwon HH. A streamflow forecasting framework using multiple climate and hydrological models. J Am Water Resour Assoc 2009; 45(4): 828-43.

Piani C, Haerter JO, Coppola E. Statistical bias correction for daily precipitation in regional climate models over Europe. Theoretical and Applied Climatology 2010; 99(1): 187-92.

Sangnawakij P, Niwitpong S. Interval estimation for the common coefficient of variation of Gamma distributions. Thail Stat 2020; 18(3): 340-53.

Kaewprasert T, Niwitpong SA, Niwitpong S. Confidence interval for coefficient of variation of inverse gamma distributions. In: Huynh VN, Entani T, Jeenanunta C, Inuiguchi M, Yenradee P. Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2020. Lecture Notes in Artificial Intelligence: Integrated Uncertainty in Knowledge Modelling and Decision Making. Cham: Springer International Publishing; 2020. p. 407-18.

Coe R, Stern RD. Fitting models to daily rainfall data. J Appl Meteorol 1982; 21(7), 1024–1031.

## Downloads

## Published

## How to Cite

*Science & Technology Asia*,

*28*(3), 44–58. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/249110

## Issue

## Section

## License

Copyright (c) 2023 Science & Technology Asia

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.