IJE TRANSACTIONS C: Aspects Vol. 27, No. 6 (June 2014) 921-932   

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MS. Fallahnezhad, B.Rasti and MH. Abooie
( Received: May 20, 2013 – Accepted in Revised Form: November 07, 2013 )

Abstract    A Bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential distributions. In This paper, we try to estimate change point which occurs in any sequence of independent exponential observations. The Bayes estimators are derived for change point, the rate of exponential distribution before shift and the rate of exponential distribution after shift. Likelihood, Prior, Posterior and Marginal distribution of the change point is derived. Also maximum likelihood estimation method is used for determining change point. The sensitivity analysis of Bayes estimators are performed by simulation. Also we suggested a new approach to achieve more precise results by determining correct choice for parameters of prior distribution and compared new approach with existing methods. The result of simulation shows good performance of proposed approach in comparison with existing methods


Keywords    Bayesian estimation, change point, exponential distribution, maximum likelihood estimation


چکیده    در این تحقیق، تحلیل بیزی برای تخمین نقطه تغییر در دنباله ای ازمتغیرهای تصادفی با توزیع نمایی استفاده شده است. در این مقاله سعی داریم که نقطه تغییر در مشاهدات مستقل نمایی را تخمین بزنیم. برآوردگرهای بیز را برای نقطه تغییر، پارامتر توزیع نمایی قبل و بعد از تغییر بدست آورده ایم. توابع درستنمایی، پیشین، پسین و توزیع حاشیه ای نقطه تغییر نیز ارائه شده است. همچنین روش تخمین درستنمایی برای تعیین نقطه تغییر ارائه شده است. تحلیل حساسیت برآوردگرهای بیز را نیز با شبیه سازی انجام داده ایم. در این مقاله یک روش جدید برای یافتن نتایج دقیقتر با تعیین انتخاب صحیح پارامترهای توزیع پیشین ارائه کرده ایم و این روش جدید را با سایر روش های موجود مقایسه می کنیم. نتایج شبیه سازی عملکرد خوب روش پیشنهادی را در مقایسسه با سایر روش ها تایید می کند.



1.        Loschi, R.H., Cruz, F.R., Takahashi, R.H., Iglesias, P.L., Arellano-Valle, R.B. and MacGregor Smith, J., "A note on bayesian identification of change points in data sequences", Computers & Operations Research,  Vol. 35, No. 1, (2008), 156-170.

2.        Pandya, M. and Pandya, H., "Bayes estimation of change point in discrete maxwell distribution", International Journal of Quality, Statistics, and Reliability,  Vol. 2011, (2011).

3.        Hinkley, D., "Inference about the shift-point in a sequence of random variables", Biometrika Vol. 57, No. 1, (1970), 1-17.

4.        Lee, C.-B., "Bayesian analysis of a change-point in exponential families with applications", Computational Statistics & Data Analysis,  Vol. 27, No. 2, (1998), 195-208.

5.        Perreault, L., Bernier, J., Bobée, B. and Parent, E., "Bayesian change-point analysis in hydrometeorological time series. Part 1. The normal model revisited", Journal of Hydrology,  Vol. 235, No. 3, (2000), 221-241.

6.        Cheon, S. and Kim, J., "Multiple change-point detection of multivariate mean vectors with the bayesian approach", Computational Statistics & Data Analysis,  Vol. 54, No. 2, (2010), 406-415.

7.        Hinkley, D. and Hinkley, E., "Inference about the chance-point in a sequence of binomial variables", Biometrika,  Vol. 57, No. 3, ((1970), 477-488

8.        Worsley, K.J., "Confidence regions and tests for a change-point in a sequence of exponential family random variables", Biometrika,  Vol. 73, No. 1, (1986), 91-104.

9.        Ghorbanzadeh, D. and Lounes, R., "Bayesian analysis for detecting a change in exponential family", Applied Mathematics and Computation,  Vol. 124, No. 1, (2001), 1-15.

10.     Johnson, T.D., Elashoff, R.M. and Harkema, S.J., "A bayesian changepoint analysis of electromyographic data: Detecting muscle activation patterns and associated applications", Biostatistics,  Vol. 4, No. 1, (2003), 143-164.

11.     D’Angelo, M.F., Palhares, R.M., Takahashi, R.H., Loschi, R.H., Baccarini, L.M. and Caminhas, W.M., "Incipient fault detection in induction machine stator-winding using a fuzzy-bayesian change point detection approach", Applied Soft Computing,  Vol. 11, No. 1, (2011), 179-192.

12.     Sertkaya Karasoy, D. and Kadilar, C., "A new bayes estimate of the change point in the hazard function", Computational Statistics & Data Analysis,  Vol. 51, No. 6, (2007), 2993-3001.

13.     Srivastava, U., "Bayesian estimation of shift point in poisson model under asymmetric loss functions", Pakistan Journal of Statistics & Operation Research,  Vol. 8, No. 1, (2012).

14.     Prakash, G., "Bayes estimation in the inverse rayleigh model", Electronic Journal of Applied Statistical Analysis,  Vol. 6, No. 1, (2013).

15.     Tourneret, J.-Y., Doisy, M. and Lavielle, M., "Bayesian off-line detection of multiple change-points corrupted by multiplicative noise: Application to sar image edge detection", Signal Processing,  Vol. 83, No. 9, (2003), 1871-1887.

16.     Keramatpour, M., Niaki, S., Khedmati, M. and Soleymanian, M., "Monitoring and change point estimation of ar (1) autocorrelated polynomial profiles", International Journal of Engineering,  Vol. 26, No. 9, (2013).

17.     Khedmati, M. and Niaki, S.T.A., "Identifying the change time of multivariate binomial processes for step changes and drifts", Journal of Industrial Engineering International,  Vol. 9, No. 3, (2013), 11-20.

18.     Ghazanfari, M., Noghondarian, K. and Alaedini, A., "A novel clustering approach for estimating the time of step changes in shewhart control charts", International Journal of Industrial Engineering & Production Research,  Vol. 19, No. 4, (2008), 39-46.

19.     Fallahnezhad, M. and Fakhrzad, M., "Determining an economically optimal (n, c) design via using loss functions", International Journal of Engineering,  Vol. 25, No. 3, (2012), 197-201.

20.     Fallahnezhad, M., Niaki, S. and Zad, M.V., "A new acceptance sampling design using bayesian modeling and backwards induction", International Journal of Engineering-Transactions C: Aspects,  Vol. 25, No. 1, (2012), 45-53.

21.     Chun, Y.H. and Sumichrast, R.T., "Bayesian inspection model with the negative binomial prior in the presence of inspection errors", European Journal of Operational Research,  Vol. 182, No. 3, (2007), 1188-1202.

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