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Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions

Received: 30 November 2013     Published: 28 February 2014
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Abstract

The paper deals with estimating shift point which occurs in any sequences of independent observations x1, x2, …, xm, xm+1, …, xn of poisson and geometric distributions. This shift point occurs in the sequence when xm i. e. m life data are observed. With known shift point 'm', the Bayes estimator on befor and after shift process means θ1 and θ2 are derived for symmetric and assymetric loss functions. The sensitivity analysis of Bayes estimators are carried out by simulation and numerical comparisons with R-programming. The results show the effectiveness of shift in sequences of both poisson and geometric distributions.

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 1)
DOI 10.11648/j.ajtas.20140301.14
Page(s) 25-30
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Bayes Estimator, Exponential Family, Squared Error Loss Function, LinexLoss Function, General Entropy Loss Function, Precautionary Loss Function, Shift Point, Poisson and Geometric Distributions

References
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Cite This Article
  • APA Style

    P. Nasiri, N. Jafari, A. Jafari. (2014). Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions. American Journal of Theoretical and Applied Statistics, 3(1), 25-30. https://doi.org/10.11648/j.ajtas.20140301.14

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    ACS Style

    P. Nasiri; N. Jafari; A. Jafari. Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions. Am. J. Theor. Appl. Stat. 2014, 3(1), 25-30. doi: 10.11648/j.ajtas.20140301.14

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    AMA Style

    P. Nasiri, N. Jafari, A. Jafari. Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions. Am J Theor Appl Stat. 2014;3(1):25-30. doi: 10.11648/j.ajtas.20140301.14

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  • @article{10.11648/j.ajtas.20140301.14,
      author = {P. Nasiri and N. Jafari and A. Jafari},
      title = {Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {3},
      number = {1},
      pages = {25-30},
      doi = {10.11648/j.ajtas.20140301.14},
      url = {https://doi.org/10.11648/j.ajtas.20140301.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140301.14},
      abstract = {The paper deals with estimating shift point which occurs in any sequences of independent observations x1, x2, …, xm, xm+1, …, xn of poisson and geometric distributions. This shift point occurs in the sequence when xm i. e. m life data are observed. With known shift point 'm', the Bayes estimator on befor and after shift process means θ1 and θ2 are derived for symmetric and assymetric loss functions. The sensitivity analysis of Bayes estimators are carried out by simulation and numerical comparisons with R-programming. The results show the effectiveness of shift in sequences of both poisson and geometric distributions.},
     year = {2014}
    }
    

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    T1  - Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions
    AU  - P. Nasiri
    AU  - N. Jafari
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    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ajtas.20140301.14
    AB  - The paper deals with estimating shift point which occurs in any sequences of independent observations x1, x2, …, xm, xm+1, …, xn of poisson and geometric distributions. This shift point occurs in the sequence when xm i. e. m life data are observed. With known shift point 'm', the Bayes estimator on befor and after shift process means θ1 and θ2 are derived for symmetric and assymetric loss functions. The sensitivity analysis of Bayes estimators are carried out by simulation and numerical comparisons with R-programming. The results show the effectiveness of shift in sequences of both poisson and geometric distributions.
    VL  - 3
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Author Information
  • Department of Statistics, Payam Noor university, I. R. of IRAN

  • Department of Statistics, Payam Noor university, I. R. of IRAN

  • Department of Statistics, Payam Noor university, I. R. of IRAN

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