Open Access Open Access  Restricted Access Subscription or Fee Access

Intercomparison of Parameter Estimation Methods of EVI Distribution for Rainfall Frequency Analysis

N VIVEKANANDAN

Abstract


For planning, design and management of civil and hydraulic structures, estimation of extreme rainfall for a given return period is considered as one of the important parameters. This can be achieved through Extreme Value Analysis (EVA) by fitting of Extreme Value Type-I (EVI) distribution to the observed data. In this paper, a comparative study on determination of parameters of EVI distribution by eight different methods such as graphical method, method of moments, maximum likelihood method, method of least squares, L-moments, probability weighted moments, principle of maximum entropy and order statistics approach for EVA of rainfall is carried out. The adequacy on fitting of EVI distribution adopted for EVA of rainfall is evaluated by applying Goodness-of-Fit tests viz., Anderson-Darling and Kolmogorov-Smirnov and diagnostic test viz., correlation coefficient, model efficiency, mean absolute error and root mean squared error. The paper presents the methodology adopted in EVA of rainfall with illustrative example and the results obtained thereof.


Keywords


Anderson-Darling, Correlation Coefficient, Extreme Value Type-I, Mean Absolute Error, Kolmogorov-Smirnov, Model Efficiency, Rainfall, Root Mean Squared Error

Full Text:

PDF

References


International Atomic Energy Agency (IAEA). Meteorological events in site evaluation for nuclear power plants – IAEA Safety Guide No. Ns-G-3.4. International Atomic Energy Agency, Vienna, 2003.

Manik, Datta SK. A comparative study of estimation of extreme value. Journal of River Behaviour & Control. 1998; 25 (1): 41-47.

Arora K, Singh VP. 1987, On statistical intercomparison of EVI estimators by Monte Carlo simulation. Advances in Water Resources. 1987; 10(2): 87-107.

Phien HN. A review of methods of parameter estimation for the extreme value type–1 distribution. Journal of Hydraulics. 1987: 90(3-4): 251-268.

Ranyal JA, Salas JD. Estimation procedures for the type-1 extreme value distribution. Journal of Hydrology. 1986; 87(3-4); 315-336.

Prabhu J, George T, Vijayakumar B, and Ravi PM. 2016, Extreme value statistical analysis of meteorological parameters observed at Kudankulam site during 2004–2014. Radiation Protection Environment. 2016; 39(2):107-112.

Celik AN. On the distributional parameters used in assessment of the suitability of wind speed probability density functions. Energy Conversion and Management. 2004; 45(11-12): 1735-1747.

Phien HN. Sampling properties of the maximum entropy estimators for the extreme-value type-1 distribution. Journal of Hydrology. 1986; 86(3-4): 391–398.

Hosking JRM. L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of Royal Statistics Society, Series B. 1990; 52: 105-124.

Shannon EC. 1948, A mathematical theory of communication, Bell Labs Technical Journal, 1948; 27(3): 379-423.

Jaynes ET. On the rationale of maximum-entropy methods. Proceedings of IEEE. 1982; 70(9): 939–952.

Singh V. Entropy-Based Parameter Estimation in Hydrology; Kluwer Academic Publishers: Boston, M.A, USA, 1998.

Atomic Energy Regulatory Board (AERB). Extreme values of meteorological parameters – AERB Safety Guide No. NF/SG/S-3, 2008.

Gumbel EJ. Statistic of Extremes. Columbia University Press, New York, 1995.

Rasel M, Hossain SM. Development of rainfall intensity duration frequency equations and curves for seven divisions in Bangladesh. International Journal of Scientific and Engineering Research. 2015; 6(5): 96-101.

May W. Variability and extremes of daily rainfall during the Indian summer monsoon in the period 1901-1989. Global and Planetary Change. 2004; 44(1-2): 83-105.

Surwade KB, Ramesh C, Kshirsagar, MM, and Govindan S. Assessment of peak maximum rainfall for estimation of peak flood for ungauged Lakya catchment – A case study. Hydrology Journal. Indian Association of Hydrologists. 2009; 32(1-2): 1-16.

Vivekanandan N. A comparative study on Gumbel and LP3 probability distributions for estimation of extreme rainfall. International Journal of Water Resources Engineering. 2020; 6(1): 21-33.

Sonuga JO. Principle of maximum entropy in hydrologic frequency analysis. Journal of Hydrology. 1972; 17(3):177–191.

Vivekanandan N, Mathew FT and Roy SK. 2012, Modelling of wind speed data using probabilistic approach. Journal of Power and River Valley Development. 2012; 62(3-4): 42-45.

Lieblein J. Note on simplified estimates for Type I extreme value distribution - NBSIR 75-647. National Bureau of Standards, U.S. Department of Commerce, Washington D.C., 1974.

Aydin D. Estimation of the lower and upper quantiles of Gumbel distribution: An application to wind speed data. Applied Ecology and Environmental Research. 2018; 16(1): 1-15.

Zhang J. Powerful goodness-of-fit tests based on the likelihood ratio. Journal of Royal Statistical Society. 2002; 64(2): 281-294.

Chen J and Adams BJ. Integration of artificial neural networks with conceptual models in rainfall-runoff modelling. Journal of Hydrology. 2006; 318(1-4): 232-249.

Charles Annis PE. Goodness-of-Fit tests for statistical distributions. 2009.


Refbacks

  • There are currently no refbacks.