Bayes approach to study shape parameter of Frechet distribution

  • Authors

    • Wajiha Nasir Riphah International University Islamabad
    • Muhammad Aslam Riphah International University Islamabad
    2015-06-02
    https://doi.org/10.14419/ijbas.v4i3.4644
  • Informative Prior, Bayes Estimates, Posterior Risks, Loss Functions, Elicitation, Monte Carlo simulation.

  • Abstract

    In this paper, Frechet distribution under Bayesian paradigm is studied. Posterior distributions are derived by using Gumbel Type-II and Levy prior. Quadrature numerical integration technique is utilized to solve posterior distribution. Bayes estimators and their risks have been obtained by using four loss functions. Prior predictive distributions are derived for elicitation of hyperparameters. The performance of Bayes estimators are compared by using Monte Carlo simulation study.

  • References

    1. [1] Francois M Longin, "The asymptotic distribution of extreme stock market returns.", Journal of business,(1996), pp.383-408.

      [2] Diwinder Kaur Arora, Er Avadhesh Kumar Maurya, and Ram Asrey Gautam., " Exact modelling and analytical study of annual maximum rainfall with Gumbel and Frechet distributions using parameter estimation techniques..", World of Sciences Journal,Vol.2,(2013), pp.11-26.

      [3] Mohamed Mubarak., "Parameter estimation based on the frechet progressive type ii censored data with binomial removals", International Journal of Quality, Statistics, and Reliability, (2012)

      [4] Alexander McFarlane Mood, Introduction to the theory of statistics, (1950)

      [5] Kamran Abbas and Yincai Tang., "Estimation of parameters for frechet distribution based on type-ii censored samples", Caspian Journal of Applied Sciences Research,Vol(2), (2013)

      [6] Kamran Abbas and Yincai Tang., "Comparison of estimation methods for frechet distribution with known shape", Caspian Journal of Applied Sciences Research,Vol(1), (2012)

      [7] Muhammad Aslam.,An application of prior predictive distribution to elicit the prior density, Journal of Statistical Theory and Applications, Vol(1), (2003) 70-83.

      [8] Sindhu Tabassum Naz, Muhammad Aslam, Navid Feroze, On estimation of the frechet distribution with known shape under di_erent sample schemes., International Journal of Intelligent Technologies and Applied Statistics, Vol(7), (2004), 353-358

      [9] VM Tummala and Prakash T Sathe., Minimum expected loss estimators of reliability and parameters of certain lifetime distributions, Reliability, IEEE Transactions on, (1978),Vol(27),283-285

      [10] Jan Gerhard Norstrom, The use of precautionary loss functions in risk analysis, Reliability, IEEE Transactions on, (1996),Vol(3),400-403

  • Downloads

  • How to Cite

    Nasir, W., & Aslam, M. (2015). Bayes approach to study shape parameter of Frechet distribution. International Journal of Basic and Applied Sciences, 4(3), 246-254. https://doi.org/10.14419/ijbas.v4i3.4644

    Received date: 2015-04-18

    Accepted date: 2015-05-18

    Published date: 2015-06-02