Theoretical and Applied Climatology

, Volume 104, Issue 1–2, pp 111–122 | Cite as

Statistical analysis of annual maximum rainfall in North-East India: an application of LH-moments

  • Surobhi Deka
  • Munindra Borah
  • Sarat Chandra Kakaty
Original Paper


An attempt has been made to determine the best fitting distribution to describe the annual series of maximum daily rainfall data for the period 1966 to 2007 of nine distantly located stations in North East India. The LH-moments of order zero (L) to order four (L4) are used to estimate the parameters of three extreme value distributions viz. generalized extreme value distribution (GEV), generalized logistic distribution (GLD), and generalized Pareto distribution (GPD). The performances of the distributions are assessed by evaluating the relative bias (RBIAS) and relative root mean square error (RRMSE) of quantile estimates through Monte Carlo simulations. Then, the boxplot is used to show the location of the median and the associated dispersion of the data. Finally, it can be revealed from the results of boxplots that zero level of LH-moments of the generalized Pareto distribution would be appropriate to the majority of the stations for describing the annual maximum rainfall series in North East India.


  1. Aronica G, Cannarozzo M, Noto L (2002) Investigating the changes in extreme rainfall series recorded in an urbanised area. Water Sci Technol 45:49–54Google Scholar
  2. Baloutsos G, Koutsoyiannis D (2000) Analysis of a long record of annual maximum rainfall in Athens, Greece, and design rainfall inferences. Nat Hazards 22:31–51Google Scholar
  3. Coles S (2007) An introduction to statistical modeling of extreme values. Springer series in statistics, LondonGoogle Scholar
  4. Greenwood JA, Landwehr JM, Matalas NC, Wallis JR (1979) Probability weighted moments: definition and relation to parameters of distribution expressible in inverse form. Water Resour Res 15:1049–1054CrossRefGoogle Scholar
  5. Hosking JRM, Wallis JR, Wood EF (1985) Estimation of the generalized extreme value distribution by the method of probability weighted moments. Technometrics 23:251–261CrossRefGoogle Scholar
  6. Hosking JRM (1986) The theory of probability weighted moments, RC12210, 3–16. IBM Research Division, T.J. Watson Research Center, Yorktown HeightsGoogle Scholar
  7. Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B Methodol 52:105–124Google Scholar
  8. Hosking JRM, Wallis JR (1997) Regional frequency analysis: an approach based on L-moments. University Press, CambridgeCrossRefGoogle Scholar
  9. Koutsoyiannis D (2004) Statistics of extremes and estimation of extreme rainfall, 2, empirical investigation of long rainfall records. Hydrol Sci J 49:591–610Google Scholar
  10. Kysely J, Picek J (2007) Probability estimates of heavy precipitation events in a flood-prone central-European region with enhanced influence of Mediterranean cyclones. Adv Geosci 12:43–50CrossRefGoogle Scholar
  11. Meshgi A, Khalili D (2009a) Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. I. A re-visit to regional homogeneity. Stoch Environ Res Risk Assess 23:119–135CrossRefGoogle Scholar
  12. Meshgi A, Khalili D (2009b) Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. II. Development of LH-moments parameters for the generalized Pareto and generalized logistic distributions. Stoch Environ Res Risk Assess 23:137–152CrossRefGoogle Scholar
  13. Nadarajah S, Withers CS (2001) Evidence of trend in return levels for daily rainfall in New Zealand. J Hydrol 39:155–166Google Scholar
  14. Nadarajah S (2005) Extremes of daily rainfall in West Central Florida. Clim Change 69:325–342CrossRefGoogle Scholar
  15. Rakhecha PR, Soman MK (1994) Trends in the annual extreme rainfall events of 1 to 3 days duration over India. Theor Appl Climatol 48:227–237CrossRefGoogle Scholar
  16. Sillitto GP (1951) Interrelations between certain linear systematic statistics of samples from any continuous population. Biometrika 38:377–382Google Scholar
  17. Tukey JW (1977) Expolratory data analysis. Addision-Wesley, ReadingGoogle Scholar
  18. Wang QJ (1997) LH-moments for statistical analysis of extreme events. Water Resourse Res 33:2841–2848CrossRefGoogle Scholar
  19. Zalina MD, Desa MN, Nguyen VTV, Hashim MK (2002) Selecting a probability distribution for extreme rainfall series in Malaysia. Water Sci Technol 45:63–68Google Scholar
  20. Zin WZW, Jemain AA, Ibrahim K (2008) The best fitting distribution of annual maximum rainfall in Peninsular Malaysia based on method of L-moment and LQ-moment. Theor Appl Climatol 96:337–344CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Surobhi Deka
    • 1
  • Munindra Borah
    • 1
  • Sarat Chandra Kakaty
    • 2
  1. 1.Department of Mathematical SciencesTezpur UniversityNapaamIndia
  2. 2.Department of StatisticsDibrugarh UniversityDibrugarhIndia

Personalised recommendations