Estimating the Parameters of the Exponential-Geometric distribution based on progressively type-II censored data

  • Authors

    • Aisha Fayomi King Abdulaziz University
    • Hamdah Al-Shammari
    2018-04-05
    https://doi.org/10.14419/ijasp.v6i1.10450
  • EM algorithm, Exponential-Geometric distribution, Maximum Likelihood Estimator, Progressive type-II Censoring

  • Abstract

    This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.

  • References

    1. [1] K. Adamidis, S. Loukas, A lifetime distribution with decreasing failure rate, Statistics & Probability Letters, 39 (1998) 35-42.

      [2] F. Louzada, M. Roman, V.G. Cancho, The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart, Computational Statistics & Data Analysis, 55 (2011) 2516-2524.

      [3] N. Balakrishnan, R. Aggarwala, Progressive censoring: theory, methods, and applications, Springer Science & Business Media, Place Published, 2000.

      [4] N. Balakrishnan, N. Kannan, C.-T. Lin, H.K.T. Ng, Point and interval estimation for Gaussian distribution, based on progressively Type-II censored samples, IEEE Transactions on Reliability, 52 (2003) 90-95.

      [5] S. CHANG, T.-R. TSAI, Point and interval estimations for the Gompertz distribution under progressive type-II censoring, Metron, 61 (2003) 403-418.

      [6] N. Balakrishnan, J.-A. Kim, Point and interval estimation for bivariate normal distribution based on progressively Type-II censored data, Communications in Statistics—Theory and Methods, 34 (2005) 1297-1347.

      [7] A. Asgharzadeh, Point and interval estimation for a generalized logistic distribution under progressive type II censoring, Communications in Statistics—Theory and Methods, 35 (2006) 1685-1702.

      [8] B. Pradhan, Point and interval estimation for the lifetime distribution of a k-unit parallel system based on progressively type-II censored data, Economic Quality Control, 22 (2007) 175-186.

      [9] H. Ng, P. Chan, N. Balakrishnan, Estimation of parameters from progressively censored data using EM algorithm, Computational Statistics & Data Analysis, 39 (2002) 371-386.

      [10] B.M. Al-Zahrani, M.S. Gindwan, Estimating the parameter of the Lindley distribution under progressive type-II censored data, Electronic Journal of Applied Statistical Analysis, 8 (2015) 100-111.

      [11] G. McLachlan, T. Krishnan, The EM algorithm and extensions, John Wiley & Sons, Place Published, 2007.

      [12] O. Cappé, Online EM algorithm for hidden Markov models, Journal of Computational and Graphical Statistics, 20 (2011) 728-749.

      [13] V. Melnykov, I. Melnykov, Initializing the EM algorithm in Gaussian mixture models with an unknown number of components, Computational Statistics & Data Analysis, 56 (2012) 1381-1395.

      [14] L. Kang, R. Carter, K. Darcy, J. Kauderer, S.-Y. Liao, A fast Monte Carlo EM algorithm for estimation in latent class model analysis with an application to assess diagnostic accuracy for cervical neoplasia in women with AGC, Journal of applied statistics, 40 (2013) 2699.

      [15] C. Xu, P.D. Baines, J.-L. Wang, Standard error estimation using the EM algorithm for the joint modeling of survival and longitudinal data, Biostatistics, 15 (2014) 731-744.

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  • Received date: 2018-03-22

    Accepted date: 2018-03-24

    Published date: 2018-04-05