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

P. Nasiri; N. Jafari; A. Jafari

doi:doi:10.11648/j.ajtas.20140301.14

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

P. Nasiri, N. Jafari, A. Jafari

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 1)

Received: 30 November 2013 Accepted: 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), 2024. 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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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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TY  - JOUR
T1  - Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions
AU  - P. Nasiri
AU  - N. Jafari
AU  - A. Jafari
Y1  - 2014/02/28
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N1  - https://doi.org/10.11648/j.ajtas.20140301.14
DO  - 10.11648/j.ajtas.20140301.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 25
EP  - 30
PB  - Science Publishing Group
SN  - 2326-9006
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
IS  - 1
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Author Information

P. Nasiri

Department of Statistics, Payam Noor university, I. R. of IRAN
N. Jafari

Department of Statistics, Payam Noor university, I. R. of IRAN
A. Jafari

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions
AU  - P. Nasiri
AU  - N. Jafari
AU  - A. Jafari
Y1  - 2014/02/28
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140301.14
DO  - 10.11648/j.ajtas.20140301.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 25
EP  - 30
PB  - Science Publishing Group
SN  - 2326-9006
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
IS  - 1
ER  -

Copy | Download