Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
Fitting of Statistical Distribution in Assessing Rainfall Patterns Across Various Zones of Assam, India
Ajuste de la distribución estadística para evaluar los patrones de precipitaciones en diversas zonas de Assam, India
DOI:
https://doi.org/10.15446/esrj.v29n3.119576Keywords:
AIC, BIC, K-S test, Maximum Likelihood Estimation, Precipitation (en)AIC, BIC, prueba K-S, precipitación máxima proyectada, precipitation (es)
Downloads
The maximum and minimum projected rainfall for a specific time of the year, taking into account a particular level of probabilities, makes up the probable rainfall, which is a great meteorological parameter of information. The purpose of this study is to assess the performance of probability distributions using various goodness-of-fit tests in order to develop a standard for selecting them in various zones of Assam based on monthly rainfall data from 1985-2022. Ten different distributions such as Gumbel, Weibull, Gamma, Logistic, Exponential, log-Normal, Pearson-0, Pearson-I, Pearson-III and Pearson-V distributions have been considered in the study. The maximum likelihood estimation approach was used to estimate the parameters associated with these distributions. The best fitted probability distribution is determined using a variety of goodness of fit techniques, including the Bayesian information criteria (BIC), Akaike information criterion (AIC), and Kolmogorov-Smirnov (K-S) test. Although not one distribution fits the rainfall data perfectly for every month, the Pearson-I distribution typically fits the data better than the other distributions most of the time, according to the goodness of fit tools. The data has been collected from the National Data Centre (NDC), India Meteorological Department (IMD), Pune.
La precipitación máxima y mínima proyectada para una época específica del año, con un nivel particular de probabilidades, constituye la precipitación probable, que es un gran parámetro meteorológico de información. El propósito de este estudio es evaluar el rendimiento de las distribuciones de probabilidad utilizando varias pruebas de bondad de ajuste con el fin de desarrollar un estándar para luego aplicarlo en varias zonas de Assam con base en datos mensuales de precipitación de 1985 a 2022. En el estudio se han considerado diez distribuciones diferentes como Gumbel, Weibull, Gamma, Logística, Exponencial, log-Normal, Pearson-0, Pearson-I, Pearson-III y Pearson-V. El enfoque de estimación de máxima verosimilitud se utilizó para estimar los parámetros asociados con estas distribuciones. La distribución de probabilidad mejor ajustada se determina utilizando una variedad de técnicas de bondad de ajuste, incluyendo los criterios de información bayesianos (BIC), el criterio de información de Akaike (AIC) y la prueba de Kolmogorov-Smirnov (K-S). Aunque ninguna distribución se ajusta perfectamente a los datos de precipitación para todos los meses, la distribución Pearson-I suele ajustarse mejor a los datos que las demás distribuciones la mayor parte del tiempo, según las herramientas de bondad de ajuste. Los datos se recopilaron del Centro Nacional de Datos (NDC) del Departamento Meteorológico de la India (IMD) en Pune.
References
Akaike, H. (1969), Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics, 21, 243-247.
Abreu, C. M., De Souza, A, Lyra, B. G., De Oliveira-Junior, J. F., Pobocikova, I., De Almeida, T. L., De Souza Fraga, M., Aristone, F., & Cecilio, R. A. (2023). Assessment and characterization of the monthly probabilities of rainfall in Midwest Brazil using different goodness-of-fit tests as probability density functions selection criteria. Theoretical and Applied Climatology, 151, 491-513. https://doi.org/10.1007/s00704-022-04286-z
ASTEC (2011). Assam’s strategy and action plan on climate change—Recommendations—First draft—ASTEC (2011). India Water Portal Hindi. https://https://www.indiawaterportal.org/articles/assams-strategy-and-action-plan-climate-change-recommendations-first-draft-astec-2011
Amin, M., Rizwan, M., & Alazba, P. (2016). A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan. Open Life Sciences, 11, 432-440. https://doi.org/10.1515/biol-2016-0057
Bobee, B., & Ashkar, F. (1991). The Gamma Family and Derived Distributions Applied in Hydrology. Water Resources Publication, Littleton, Colorado.
Bobee, B. B., & Robitaille, R. (1977). The use of the Pearson type 3 and log Pearson type 3 distributions revisited. Water Resources Research, 13(2), 427-443. https://doi.org/10.1029/WR013i002p00427
Bhavyashree, S., & Bhattacharyya, B. (2018). Fitting Probability Distributions for Rainfall
Analysis of Karnataka, India. International Journal of Current Microbiology and Applied Sciences, 7(03), 1498-1506. https://doi.org/10.20546/ijcmas.2018.703.178
Chandran, S., Selvan, P., Namitha, M. R., Mishra, P., & Kumar, V. (2023). Probability analysis and rainfall forecasting using ARIMA model. MAUSAM Journal, 74(4), 1081-1092. https://doi.org/10.54302/mausam.v74i4.805
Deka, S., Borah, M., & Kakaty, S. C. (2009). Distributions of Annual Maximum Rainfall Series of North-East India. European Water, 3–14.
Douka, M., & Karacostas, T. (2018). Statistical analyses of extreme rainfall events in Thessaloniki, Greece. Atmospheric Research, 208, 60-77. https://doi.org/10.1016/j.atmosres.2017.08.025
Feng, S., & Nadarajah, S., & Hu, Q. (2007). Modeling Annual Extreme Precipitation in China Using the Generalized Extreme Value Distribution. Journal of the Meteorological Society of Japan, 85, 599–613.
Ferguson, T. S. (1964). A Characterization of the Exponential Distribution. The Annals of Mathematical Statistics, 35(3), 199–1207
Gaddum, J. H. (1945). Lognormal Distributions. Nature, 156(3964), 463-466. https://doi.org/10.1038/156463a0
Griffis, V. W., & Stedinger, J. R. (2007). Log-Pearson Type 3 Distribution and Its Application in Flood Frequency Analysis. I: Distribution Characteristics. Journal of Hydrologic Engineering, 12(5), 482–491. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:5(482)
Ghosh, S., Roy, K. M., & Biswas, C. S. (2016). Determination of the Best fit Probability Distribution for Monthly Rainfall Data in Bangladesh. American Journal of Mathematics and Statistics, 6(4), 170-174. DOI: 10.5923/j.ajms.20160604.05
Gupta, S. C., & Kapoor, V. K. (1997). Fundamentals of Mathematical Statistics. Sultan Chand and Sons, New Delhi: 11.23-12.2
Gumbel, E. J. (1941). The return period of flood flows. The Annals of mathematical Statistics, 12, 163-190.
Haseeb, F., Ali, S., Ahmed, N., Alarifi, N., & Youssef, Y. M. (2025). Comprehensive Probabilistic Analysis and Practical Implications of Rainfall Distribution in Pakistan. Atmosphere, 16(2), 122. https://doi.org/10.3390/atmos16020122
Johnson, N. L., Kotz. S., & Balakrishnan, N. (1995). Continuous Univariate Distributions. Wiley, New York, 2nd. Edition.
Karami, H., Ghazvinian, H., & Dadrasajirlou, Y. (2023). Application of statistical and geostatistical approaches in temporal and spatial estimations of rainfall. Journal of Water and Climate Change, 14(5), 1696-1722. https://doi.org/10.2166/wcc.2023.
Kottegoda, N. T. (1987). Fitting Johnson SB curve by the method of maximum likelihood to annual maximum daily rainfalls. Water Resources Research, 23(4), 728–732
Koutrouvelis, I. A., & Canavos, G. C. (1999). Estimation in the Pearson type 3 distribution. Water Resources Research, 35(9), 2693–2704.
Kumar, V., Khan, S., & Jahangeer, J. (2017). Statistical distribution of rainfall in Uttarakhand, India. Applied Water Science, 7, 4765-4777. https://doi.org/10.1007/s13201-017-0586-5
Kurniawan, V. (2019). Distribution fitting on rainfall data in Jakarta. First International Conference of Construction, Infrastructure, and Materials, 650. DOI: 10.1088/1757-899X/650/1/012060
Mamoon, A. A. & Rahman, A. (2017). Selection of the best fit probability distribution in rainfall frequency analysis for Qatar. Natural Hazards, 86, 281-296. https://doi.org/10.1007/s11069-016-2687-0
Mandal, S., & Choudhury, B. (2015). Estimation and prediction of maximum daily rainfall at Sagar Island using best fit probability models. Theoretical and Applied Climatology, 121, 87-97. https://doi.org/10.1007/s00704-014-1212-1
Millington, N., Das, S., & Simonovic, S. (2011). The Comparison of GEV, Log-Pearson Type 3 and Gumbel Distributions in the Upper Thames River Watershed under Global Climate Models (Water Resource Report no. 077). Department of Civil and Environmental Engineering, The University of Western Ontario.
Moccia, B., Mineo, C., Ridolfi, E., Russo, F., & Napolitano, F. (2021). Probability distributions of daily rainfall extremes in Lazio and Sicily, Italy, and design rainfall inferences. Journal of Hydrology: Regional Studies, 33, 100771. https://doi.org/10.1016/j.ejrh.2020.100771
Mohamed, J., & Adam, B. M. (2022). Modeling of magnitude and frequency of extreme rainfall in Somalia. Modelling Earth Systems and Environment, 8, 4277-4294. https://doi.org/10.1007/s40808-022-01363-0
Olofintoye, O., Sule, B., & Salami, A. (2009). Best-fit Probability Distribution model for peak daily rainfall of selected Cities in Nigeria. New York Science Journal, 2, 1–12.
Ozonur, D., Pobocikova, I., & Souza, A. (2021). Statistical analysis of monthly rainfall in Central West Brazil using probability distributions. Modeling Earth Systems and Environment, 7, 1979-1989. https://doi.org/10.1007/s40808-020-00954-z
Pearson, K. (1895). Continuous to the mathematical theory of evolution, II: Skew variation in homogeneous materials. Philosophical Transactions of the Royal Society, London, 186, 343-414.
Phien, H. N., & Jivajirajah, T. (1984). Applications of the log Pearson type-3 distribution in hydrology. Journal of Hydrology, 73(3), 359–372.
Sarker, R. P., Biswas, B. C., & Khambete, N. N. (1982). Probability analysis of short period rainfall in dry farming tract in India. MAUSAM Journal, 33(3), 269-284.
Schellander, H., Lieb, A., & Hell, T. (2019). Error Structure of Metastatistical and Generalized Extreme Value Distributions for Modeling Extreme Rainfall in Austria. Earth and Space Science, 6(9), 1616-1632. https://doi.org/10.1029/2019EA000557
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464
Sharma MA, & Singh JB (2010). Use of Probability Distribution in Rainfall Analysis. New York Science Journal, 3(9)
Shaharudin, S. M., Ahmad, N., Mohamed, N. S., & Mahdin, H. (2020). Fitting statistical
Distribution of extreme rainfall data for the purpose of simulation. Indonesian Journal of Electrical Engineering and Computer Science, 18(3), 1367-1374. http://doi.org/10.11591/ijeecs.v18.i3.pp1367-1374
Swift, L. W., & Schreuder, H. T. (1981). Fitting Daily Precipitation Amounts Using the SB Distribution. Monthly Weather Review, 109(12), 2535–2540.
Thom, H. C. S. (1958). A note on the Gamma distribution. Monthly Weather Review, 86(4), 117–122.
Weibull, W. (1939). A Statistical Theory of the strength of Materials. Ingeniors Ventenskaps Akademiens Handlingar, Royal Swedish Institute for Engineering Research, Stockholm Sweden, 151
How to Cite
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
License
Copyright (c) 2025 Earth Sciences Research Journal
This work is licensed under a Creative Commons Attribution 4.0 International License.
Earth Sciences Research Journal holds a Creative Commons Attribution license.
You are free to:
Share — copy and redistribute the material in any medium or format
Adapt — remix, transform, and build upon the material for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.
The Earth Sciences Research Journal is the copyright holder for these license attributes.
