International Journal of Mathematics Trends and Technology
Volume 68 | Issue 6 | Year 2022 | Article Id. IJMTT-V68I6P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I6P508
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 06 Apr 2022 | 23 May 2022 | 07 Jun 2022 | 24 Jun 2022 |
Modeling rainfall is very important to be developed in managing natural resources to deal with the impacts of climate change. We modelled the daily rainfall for data recorded in Pekanbaru City from 1999 to 2008. the main goal of this study is to find the best fitting distribution to the daily rainfalls by using the maximum likelihood approach. for this purpose, Gamma distribution and some Extended Gamma Distribution will be used and tested to determine the best model to describe daily rainfall in Pekanbaru City. the extended gamma distribution meaning some mixture two and three gamma distribution, namely rani, shanker and sujatha distribution. the maximum likelihood method will be used to get the estimated parameter value from the distribution used in this study. the distributions will be selected based on graphical inspection probability density function (pdf), numerical criteria Akaike’s information criterion (AIC) and Bayesian Information Criterion (BIC). in most the cases, graphical inspection gave the same result but their AIC and BIC result differed. the best fit result was chosen as the distribution with the lowest values of AIC and BIC. in general, the Gamma distribution has been selected as the best model
[1] R. Syafruddin, A. M. Soleh, and A. H. Wigena, Clusterwise Regression Model Development with Gamma Distribution. Icsa. 1. 2019
[2] A. M. Bagirov, A. Mahmood, and A. Barton, Prediction of Monthly Rainfall in Victoria, Australia: Clusterwise Linear Regression. J Atmosres. (2017) 20-29.
[3] H. Spath. Algorithm 39: Clusterwise Linear Regression. Computing. 22 (1979) 367-373.
[4] M. Wedel, and W. S Desarbo. A Mixture Likelihod Approach for Generalized Linear Models. Journal of Classification. 12 (1995) 21- 55
[5] A. M. Bagirov, J. Ugon and H. Mirzayeva, An Algorithm for Clusterwise Linear Regression Based on Smoothing Techniques. Optimization Letters. 9(1) (2015) 375-390.
[6] A. M. Bagirov, J. Ugon and H. Mirzayeva, Nonsmooth Nonconvex Optimization Approach to Clusterwise Linear Regression Problems. Eropan Journal of Operational Research. 229(1) (2013) 132-142.
[7] A. K. Yadav, Rainfall-Runoff Modelling Using Artificial Neural Networks (Anns) Model. Int.J.Curr.Microbiol.App.Sci. 9(3) (2020) 127-135.
[8] R. L. Linsley, Rainfall-Runoff Models An Overview in Rainfall-Runoff Relationship. in: Proceedings of the International Symposium on Rainfallrunoff Modelling, May, 18-21 (1982) 3-22.
[9] M. B. Mcpherson, Some Notes on the Rational Method of Storm Drain Design. Tech. Memo. No. 6 Asce, Water Resources Research Program, Harvard University, Cambridge, Ma. (1969).
[10] D. R. Maidment, Handbook of Hydrology. 1st Edn. New York: Mcgraw Hill Publication. (1993).
[11] W. H. Green, and G. A. Ampt, Studies on Soil Physics. the Flow of Air and Water Through Soils. Journal of Agriculture Science. 4 (1911) 1-24.
[12] J. E. Nash, Determination of Runoff From Rainfall. Institute of Civil Engineering. 10 (1958) 163-184.
[13] P. S. Kumbhare, and R. A. Rastogi, Determination of Surface Runoff from Himalayan Watershed using Two Parameter Conceptual Model. in: 21st Annual Convocation of Indian Society of Agricultural Engineering, Indian Agriculture Research Institute, New Delhi. 1984
[14] V. Kumar, and R. A. Rastogi, Determination of Direct Runoff from a Small Agricultural Watershed. J of Agric. Engg. Isae. 26(3) (1989) 223-228.
[15] B. Lahcene, A New Extended-Gamma Family of Distributions: Properties and Applications. Journal of Applied Mathematics and Computation , 5(1) (2021) 9-17.
[16] S. K. Agarwal, and S. L. Kalla, A Generalized Gamma Distribution and Its Application in Reliability. Commun. Statist. Theory Meth., 25(1) (1996) 201-210.
[17] E. W. Stacy, and G. A. Mihram, Parameter Estimation for A Generalized Gamma Distribution. Technimetrics, 7(3) (1965), 349-358.
[18] E. W. Stacy, A Generalization of the Gamma Distribution. Annals of Mathematical Statistics, (33) (1962) 1187-1192.
[19] G. M. Cordeiro, F. Castellares, L. C. Montenegro, and M. De Castro, the Beta Generalized Gamma Distribution. Statistics (Berlin), (46) (2012): 1-13.
[20] S. Suksaengrakcharoen and W. Bodhisuwan. A New Family of Generalized Gamma Distribution and Its Application. Journal of Mathematics and Statistics, 10(2) (2014) 211-220.
[21] L. Bachioua, on Extended and Reliability General Mixture Gamma Distribution Model. A Dissertation Submitted to the College of Science, University of Baghdad in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Ph.D.) of Science in Mathematics, University of Baghdad, Iraq. 2004
[22] L. Bachioua, and A. M. Mohammed, on a Five and Six Parameter Generalization of the Gamma Function. Journal Theoretical Mathematics & Applications. 7(1) (2017) 1-14.
[23] L. Bachioua, Extended Generalized Gamma Function and Same Its Applications. International Archive of Applied Sciences and Technology, 4(3) (2013) 16-30.
[24] J. Piantadosi, J. Boland, and P. Howlett, Generating Synthetic Rainfall on Various Timescales—Daily, Monthly and Yearly. Environ Modeling & Assessment, 14 (2009) 431–438
[25] D. A. Woolhiser, and J. Roldan, Stochastic Daily Precipitation Models 2. A Comparison of Distribution of Amounts. Water Resour. Research. 18(5) (1982) 1461-1468
[26] D. S. Wilks, Interannual Variability and Extreme Value Characteristics of Several Stochastics Daily Models. Agricultural and Forest Meteorology. 93(3) (1999) 153-169
[27] B. Kedem, L. S. Chiu, and Z. Karni. An Analysis of the Threshold Method for Measuring Area-Average Rainfall. Journal of Applied Meteorolgy, 29(1) (1990) 3-20
[28] R. Shanker, and F. Hagos, On Modeling of Lifetimes Data using Exponential and Lindley Distributions, Biometrics & Biostatistics International Journal. 2(5) (2015) 1-9
[29] R. Shanker, Sujatha Distribution and Its Applications. Statistics in Transition-New Series. 17(3) (2016) 1-20
[30] R. Shanker, Rani Distribution and Its Application. Biometrics & Biostatistics International Journal. 6(1) (2017) 256-265. Doi: 10.15406/Bbij.2017.06.0015
Muhammad Rajab, Rado Yendra, Muhammad Marizal, Ari Pani Desvina, Rahmadeni, "Modelling Daily Rainfall Amount in Pekanbaru City using Gamma and Some Extended Gamma Distribution," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 6, pp. 80-86, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P508
PDF 
Abstract 
Keywords 
References 
Citation