Manuscript Number : IJSRCE19337
Intercomparison of Estimators of Gumbel Distribution using Goodness-of-Fit Tests for Estimation of Extreme Rainfall
Authors(4) :-R. S. Bharadwaj , (Mrs.) A. D. Thube, N. Vivekanandan, C. Srishailam
Estimation of extreme rainfall for a given return period is of utmost importance for planning, design and management of hydraulic structures and riverfront development projects. This can be achieved through Extreme Value Analysis (EVA) that involves fitting of Gumbel probability distribution to the series of Annual 1-day Maximum Rainfall (AMR). Standard parameter estimation procedures such as Method of Moments (MoM), Maximum Likelihood Method (MLM) and Probability Weighted Moments (PWM) are applied for determination of parameters of the Gumbel distribution. This paper presents a study on comparison of MoM, MLM and PWM estimators of Gumbel distribution adopted in EVA of rainfall for Kalyan, Thane and Ulhasnagar sites of Ulhas river basin. Goodness-of-Fit tests viz., Anderson–Darling, Kolmogorov–Smirnov and Mean Absolute Percentage Error are used for checking the adequacy of fitting of three methods of Gumbel probability distribution to the AMR data. Based on the GoF tests results, the MLM is identified as better-suited method amongst three methods applied for determination of parameters of Gumbel distribution for estimation of extreme rainfall at Kalyan, Thane and Ulhasnagar sites
R. S. Bharadwaj
M.Tech. Scholar, Department of Civil Engineering, College of Engineering, Pune, Maharashtra, India
(Mrs.) A. D. Thube
Associate Professor, Department of Civil Engineering, College of Engineering, Pune , Maharashtra, India
Scientist-B, Central Water and Power Research Station, Pune, Maharashtra, India
Scientist-C, Central Water and Power Research Station, Pune, Maharashtra, India
Anderson–Darling test, Extreme Value Analysis, Gumbel distribution, Kolmogorov Smirnov test, Mean Absolute Percentage Error, Probability Weighted Moments, Rainfall
- V.N. Sharda and P.K. Das. 2005. Modelling weekly rainfall data for crop planning in a sub-humid climate of India. Agricultural Water Management, 76(2), 120–138.
- M. C. Casas., R. Rodriguez, M. Prohom, A. Gazquez and A. Redano. 2011. Estimation of the probable maximum precipitation in Barcelona (Spain). Journal of Climatology, 31(9), 1322–1327.
- S. Deka and M. Borah. 2009. Distribution of annual maximum rainfall series of North East India. European Water Publications, 27, 3-14.
- M.A. Sharma and J.B. Singh. 2010. Use of probability distribution in rainfall analysis. New York Science Journal, 3(9), 40-49.
- N. Mujere. 2011. Flood frequency analysis using the Gumbel distribution. Journal of Computer Science and Engineering, 3(7), 2774-2778.
- L.S. Esteves. 2013. Consequences to ?ood management of using different probability distributions to estimate extreme rainfall. Journal of Environmental Management, 115(1), 98–105.
- N. Vivekanandan. 2014. Modelling annual rainfall of Krishna and Godavari river basins using Extreme Value Type-1 distribution. i-manger Journal of Structural Engineering, 3(1), 7-12.
- M.M. Rasel and S.M. Hossain. 2015. Development of rainfall intensity duration frequency equations and curves for seven divisions in Bangladesh. International Journal of Scientific and Engineering Research, 6(5), 96-101.
- S. Mohammed and H. Azhar. 2017. Estimation of design flood at Kol dam using hydrometeorological approach. International Journal of Environmental Sciences & Natural Resources, 4(1), 1-6.
- K. Arora and V.P. Singh. 1987. On statistical intercomparison of EVI estimators by Monte Carlo simulation. Advances in Water Resources, 10(2), 87-107.
- J.M. Landwehr, N.C. Matalas and J.R. Wallis. 1979. Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Water Resources Research, 15(5), 1055–1064
- J.A. Ranyal and J.D. Salas. 1986. Estimation procedures for the type-1 extreme value distribution. Journal of Hydrology, 87(3&4), 315–336.
- H.N. Phien. 1987. A review of methods of parameter estimation for the extreme value type–1 distribution. Journal of Hydraulics, 90(3&4), 251-268.
- B.L.P. Swami, K. Seetaramulu and K.K. Chaudhry. 1986. A critical review of the methods for correcting the sampling errors in the extreme wind speeds. Journal of Structural Engineering, 12(4), 143–148.
- J. Zhang. 2002. Powerful goodness-of-?t tests based on the likelihood ratio. Journal of the Royal Statistical Society, 64(2), 281–294.
- E.J. Gumbel. 1960. Statistics of extremes (2nd edition). New York: Columbia University Press.
- D. Manik and S.K. Datta. 1998. A comparative study of estimation of extreme value. Journal of River Behaviour & Control, 25(1), 41–47.
- Annis Charles P.E. 2009. Goodness-of-Fit tests for statistical distributions.
Published in : Volume 3 | Issue 3 | May-June 2019
Date of Publication : 2019-06-30
License: This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 38-46
Manuscript Number : IJSRCE19337
Publisher : Technoscience Academy
URL : http://ijsrce.com/IJSRCE19337