The exact extreme value distribution – applied study

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    Extreme value theory is used to develop models for describing the distribution of extreme events. Exact extreme value or compound distri-bution which is based on the theory of the maximum of random variables of random numbers is one of the most important models that are applicable in various situations, for instance of interest, it uses partial duration series (PDF) data to analyze extreme hydrological. As part of our earlier study, the parameters of this model were estimated by two methods, maximum likelihood (ML) and Bayesian- based on non-informative and informative priors. Moreover, a comparative study using simulated data showed that the Bayesian based on informative prior is the best estimation method. In this paper, a real data set taken from records of the largest daily rainfall data of Jeddah city in Saudi Arabia is used to fit the model when the parameters are estimated by Bayesian method. A comparative applied study indicates that the exact extreme value model under Bayesian estimates (BE) of its parameters provides appropriate fit for this data set and it is more applicable than the same model when the parameters are estimated by ML method and other three classical extreme value models.

  • Keywords

    : Bayesian Estimation; Compound Distribution; Exact Extreme Value Distribution; Extreme Rainfall Events; Maximum Likelihood Estimation.

  • References

      [1] Todorovic, P.” Onsome problems involving random number of random variables”, The Annals of Mathematical Statistics, Vo.41, No.3, (1970), pp: 1059-1063.

      [2] Todorovic, P.and Zelenhasic,E. ”A stochastic model for flood analysis”,Water Resources Research, Vo .6, No.6, (1970), pp:1641-1648.

      [3] Afif, W. M. M. The Compound and Extreme Value Distributions. M.Sc. Thesis, King Abdul-Aziz University,Jeddah,(2011).

      [4] Qutb, N., Fayomi, A., and Al-Beladi, O.”Estimation of the parameters of the exact extreme value distribution”,International Organization of Scientific Research- Journal of Mathematics, Vo .13, No.2, (2017), pp: 1-9.

      [5] Kotb, N. S. A. Estimation of the Parameters of Compound Distribution. Ph. D. Thesis, Department of Statistics, Faculty of Commerce, Al-Azhar University, (2002).

      [6] Robert, C. P. and Casella, G., Monte Carlo Statistical Methods, Springer- Verlag, (2004).

      [7] Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E.”Equation of state calculations by fast computing machines”,The Journal of Chemical Physics, Vo.21, No.6, (1953), pp: 1087–1092.

      [8] Hastings, W. K.”Monte Carlo sampling methods using Markov chains and their applications”,Biometrika, Vo.57, No.1, (1970), pp:97–109.

      [9] Geman, S. and Geman, D”Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images”,IEEE Transaction on Pattern Analysis and Machine Intelligence, Vo.6,No.6, (1984),pp: 721–741.

      [10] Chib, S. and Greenberg, E.”Understanding the metropolis-hasting's algorithm”,The American Statistician , Vo.49, No.4, (1995), pp:327–335.

      [11] Gamerman, D. and Lopes, H. F.,Markov Chain Monte Carlo Stochastic Simulation for Bayesian Inference,Chapman and Hall,(2006).




Article ID: 7834
DOI: 10.14419/ijasp.v5i2.7834

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.