Rainfall Frequency Analysis Using Order Statistics Approach of Extreme Value Distributions

International Journal of Civil Engineering
© 2014 by SSRG - IJCE Journal
Volume 1 Issue 4
Year of Publication : 2014
Authors : N Vivekanandan
How to Cite?

N Vivekanandan, "Rainfall Frequency Analysis Using Order Statistics Approach of Extreme Value Distributions," SSRG International Journal of Civil Engineering, vol. 1,  no. 4, pp. 6-12, 2014. Crossref, https://doi.org/10.14445/23488352/IJCE-V1I4P102


Estimation of rainfall for a desired return period is of utmost importance for planning, design and management of the hydraulic structures in the project site. This can be achieved by fitting of probability distributions to the series of annual 1-day maximum rainfall. This paper illustrates the use of extreme value distributions for estimation of rainfall for Fatehabad, Hansi, Hissar and Tohana stations. Order Statistics Approach is used for determination of parameters of the extreme value distributions. Goodness-of-Fit tests such as Anderson-Darling and Kolmogorov-Smirnov are applied for checking the adequacy of fitting of the distributions to the recorded data. A diagnostic test of D-index is used for the selection of a suitable probability distribution for rainfall estimation. Based on GoF and diagnostic tests results, the study shows the Gumbel distribution is better suited for rainfall estimation for the stations under study.


Frechet, Gumbel, KolmogorovSmirnov, D-index, Order Statistics, Return period


[1] 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.
[2] S.R. Bhakar, A.K. Bansal, N. Chhajed and R.C. Purohit, Frequency analysis of consecutive days maximum rainfall at Banswara, Rajasthan, India, ARPN journal of Engineering and Applied Sciences, 1(1), 2006, 64-67.
[3] Atomic Energy Regulatory Board (AERB) (2008), Extreme values of meteorological parameters (Guide No. NF/SG/ S-3).
[4] L.S. Esteves, Consequences to flood management of using different probability distributions to estimate extreme rainfall, Environmental Management, 115(1), 2013, 98- 105.
[5] F. Uboldi, A.N. Sulis, C. Lussana, M. Cislaghi and M. Russo, A spatial bootstrap technique for parameter estimation of rainfall annual maxima distribution,
Hydrology and Earth System Sciences Discussions, 10(10), 2013, 11755–11794.
[6] B.A. Olumide, M. Saidu and A. Oluwasesan, Evaluation of best fit probability distribution models for the prediction of rainfall and runoff volume (Case Study Tagwai Dam, Minna-Nigeria), Engineering and Technology, 3 (2), 2013, 94-98.
[7] N. Mujere, Flood frequency analysis using the Gumbel distribution, Computer Science and Engineering, 3(7), 2011, 2774-2778.
[8] A.H. Ang and W.H. Tang, Probability concepts in engineering planning and design, Vol. 2, John Wiley & Sons, 1984.
[9] J. Zhang, Powerful goodness-of-fit tests based on the likelihood ratio, Royal Statistical Society, 64(2), 2002, 281-294.
[10] United States Water Resources Council (USWRC) (1981), Guidelines for determining flood flow frequency, Bulletin No.17B, 15-19.