Bayesian and E-Bayesian estimation for the Kumaraswamy distribution based on type-ii censoring

  • Authors

    • Hesham Reyad Lecture in EL Qassim University
    • Soha Othman Ahmed
    2016-03-05
    https://doi.org/10.14419/ijams.v4i1.5750
  • Censored Sampling, E-Bayes Estimates, Kumaraswamy Distribution, Type-II Censored, Loss Functions, Monte Carlo Simulation.
  • Abstract

    This paper introduces the Bayesian and E-Bayesian estimation for the shape parameter of the Kumaraswamy distribution based on type-II censored schemes. These estimators are derived under symmetric loss function [squared error loss (SELF))] and three asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF) and Quadratic loss function (QLF)]. Monte Carlo simulation is performed to compare the E-Bayesian estimators with the associated Bayesian estimators in terms of Mean Square Error (MSE).

  • References

    1. [1] P. Kumaraswamy, Sinepower probability density function, Journal of Hydrology, 31(1976) 181-184. http://dx.doi.org/10.1016/0022-1694(76)90029-9.

      [2] P. Kumaraswamy, Extended sinepower probability density function, Journal of Hydrology, 37(1978) 81-89. http://dx.doi.org/10.1016/0022-1694(78)90097-5.

      [3] P. Kumaraswamy, A generalized probability density functions for double-bounded random processes, Journal of Hydrology, 46(1980) 79-88. http://dx.doi.org/10.1016/0022-1694(80)90036-0.

      [4] K. Ponnambalam, A. Seifi, J. Viach, Probabilistic design of system with general distributions of parameters, International Journal of Circuit Theory Applications, 29(2001) 527-536. http://dx.doi.org/10.1002/cta.173.

      [5] S. Nadarajah, on the distribution of Kumaraswamy, Journal of Hydrology, 384(2008) 586-569. http://dx.doi.org/10.1016/j.jhydrol.2007.09.008.

      [6] M. C. Jones, Kumaraswamy distribution: A beta-type distribution with some tractability advantages, Statistical Methodology, 6, 1(2009):70-81. http://dx.doi.org/10.1016/j.stamet.2008.04.001.

      [7] T. N. Sindhu, N. Feroze, M. Aslam, Bayesian Analysis of the Kumaraswamy Distribution under Failure Censoring Sampling Scheme, International Journal of Advanced Science and Technology, 51(2013): 39-58.

      [8] M. M. Eldin, N. Khalil, M. Amein, Estimation of parameters of the Kumaraswamy distribution based on general progressive type II censoring, American Journal of Theoretical and Applied Statistics, 3,6 (2014):217-222. http://dx.doi.org/10.11648/j.ajtas.20140306.17.

      [9] M. Han, Expected Bayesian Method for Forecast of Security Investment, Journal of Operations Research and Management Science 14, 5 (2005) 89-102.

      [10] M. Han, E-Bayesian Method to Estimate Failure Rate, The Sixth International Symposium on Operations Research and Its Applications (ISOR06) Xinjiang (2006)299-311.

      [11] Q. Yin, H. Liu, Bayesian estimation of geometric distribution parameter under scaled squared error loss function, Conference on Environmental Science and Information Application Technology (2010)650-653.

      [12] J. Wei, B. Song, W. Yan, Z. Mao, Reliability Estimations of Burr-XII Distribution under Entropy Loss Function, IEEE (2011) 244-247. http://dx.doi.org/10.1109/icrms.2011.5979276.

      [13] Z. F. Jaheen, H. M. and Okasha, E-Bayesian Estimation for the Burr type XII model based on type-2 censoring. Applied Mathematical Modelling 35 (2011) 4730 - 4737. http://dx.doi.org/10.1016/j.apm.2011.03.055.

      [14] G. Cai, W. Xu, W. Zhang, P. Wang, Application of E-Bayes method in stock forecast, Fourth International Conference on Information and Computing (2011)504-506. http://dx.doi.org/10.1109/icic.2011.40.

      [15] H. M. and Okasha, E-Bayesian estimation of system reliability with Weibull distribution of components based on type-2 censoring, Journal of Advanced Research in Scientific Computing 4,4 (2012)34-45.

      [16] R. Azimi, F, Yaghamei, B. Fasihi, E-Bayesian estimation based on generalized half Logistic progressive type-II censored data, International Journal of Advanced Mathematical Science 1, 2 (2013) 56-63.

      [17] N. Javadkani, P. Azhdari, R. Azimi, On Bayesian estimation from two parameter Bathtub-shaped lifetime distribution based on progressive first-failure-censored sampling, International Journal of Scientific World 2, 1 (2014).31-41. http://dx.doi.org/10.14419/ijsw.v2i1.2513

      [18] H. M. Okasha, E-Bayesian Estimation for the Lomax distribution based on type-II censored data, Journal of the Egyptian Mathematical Society 22, 3 (2014) 489-495. http://dx.doi.org/10.1016/j.joems.2013.12.009.

      [19] H. M. Reyad, S. O. Ahmed, E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme, International Journal of Advanced Mathematical Sciences 3, 2 (2015) 108-120. http://dx.doi.org/10.14419/ijams.v3i2.5093.

      [20] A. Zellner, Bayesian estimation and Prediction using Asymmetric loss Function. Journal of American Statistical Association 81 (1986) 446-451. http://dx.doi.org/10.1080/01621459.1986.10478289.

      [21] M. h. Degroot, Optimal Statistical Decision, McGraw-Hill Inc. (1970).

      [22] M. K. Bhuiyan, M. K. Roy, M. F. Iman, Minimax estimation of the parameter of Rayleigh distribution,(2007) 207-212.

      [23] M. Han, The structure of hierarchical prior distribution and its applications, Chinese Operations Research and Management Science 6, 3 (1997) 31-40.

      [24] M. Han, E- Bayesian estimation and hierarchical Bayesian estimation of failure rate. Applied Mathematical Modelling 33 (2009) 1915-1922. http://dx.doi.org/10.1016/j.apm.2008.03.019.

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  • How to Cite

    Reyad, H., & Ahmed, S. O. (2016). Bayesian and E-Bayesian estimation for the Kumaraswamy distribution based on type-ii censoring. International Journal of Advanced Mathematical Sciences, 4(1), 10-17. https://doi.org/10.14419/ijams.v4i1.5750