Extreme rainfalls often occur everywhere just in a moment, very difficult to be anticipated and produce very detrimental impact to the environment and human society. Floods and landslides are influenced by high variability of extreme rainfalls, especially in the watershed area for floods and the hills as well as mountains for landslides, such as in Malang Residence, East Java, Indonesia as a case study in this study. The prediction tools for determining location and time of the next extreme rainfalls event will occur are required. The behavior of extreme rainfalls measured on one or several stations rain gauge could be approximated by Generalized Pareto (GP) Distribution. The prediction tools must be able to identify and characterize parameters of the GP Distribution such as shape and scale parameters over the entire area. Shape parameter of GP distribution has associated with characteristics of extreme rainfalls distributions. To identify characteristics of shape parameter on each station and their similarity, an algorithm to make a partition of shape parameters into several spatial clusters and investigate the type of distribution was proposed. In order to determine threshold value, mean residual life plot and stability of modified scale and shape parameters at a range of thresholds were used, Maximum Likelihood method was utilized to estimate parameter value and k-means method combined by Silhouette values to make the cluster of extreme rainfalls distribution. By using rainfalls data on twenty eight different stations rain gauge, the results showed that the proposed algorithm well performed and extreme rainfalls were heterogeneous with three type of GP distribution. In general, shape parameter values were negative and positive except on nine stations which were close to zero and were well partitioned by six clusters.

Original languageEnglish
Pages (from-to)357-366
Number of pages10
JournalJournal of Mathematics and Statistics
Issue number4
Publication statusPublished - 2013


  • Extreme rainfalls
  • Generalized pareto distribution
  • Shape parameter
  • Silhouette value
  • k-Means algorithm


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