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Yıl 2019, Cilt: 68 Sayı: 2, 1664 - 1674, 01.08.2019
https://doi.org/10.31801/cfsuasmas.455276

Öz

Kaynakça

  • Weibull, W. A Statistical Distribution Function of Wide Applicability, Journal of Applied Mechanics, 18, 293-297,1951.
  • Soland, R. M. Bayesian Analysis Of The Weibull Process With Unknown Scale and Shape Parameters, IEEE Transactions On Reliability, Vol. R- 18 No. 4, 1969, November.
  • Kundu, D. Bayesian Inference And Life Testing Plan For The Weibull Distribution in Presence Of Progressive Censoring, Technometrics, 50:2, 144-154, 2008.
  • Papadopoulos, A.S. and Tsokos, C.P. Bayesian analysis of the Weibull failure model with unknown scale and shape parameters, Statistica, XXXVI, No. 4, 1976.
  • Kundu,D. Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring, Technometrics, 50 (2) pp. 114-154, 2008.
  • Banerjee, A. and Kundu, D. Inference Based on Type-II Hybrid Censored Data From a Weibull Distribution, IEEE Trans. Reliab., Vol. 57. No. 2, pp. 369-378, 2008.
  • Lindley, D. Approximate Bayes Methods, University College London, 1980.

A simulation study of the Bayes estimator for parameters in Weibull distribution

Yıl 2019, Cilt: 68 Sayı: 2, 1664 - 1674, 01.08.2019
https://doi.org/10.31801/cfsuasmas.455276

Öz

The Weibull
distribution is one of the most popular distributions in analyzing the lifetime
data. In this study, we consider the Bayes
estimators of the scale and shape parameters of  Weibull distribution under the assumptions of
gamma priors and squared error loss function. While computing the Bayes
estimates for a Weibull distribution, the continuous conjugate joint prior
distribution of the shape and scale parameters does not exist and the closed form
expressions of the Bayes estimators cannot be obtained.



In this study first we
will consider the Bayesian inference of the scale parameter under the
assumption that the shape parameter is known. We will assume that the scale
parameter has a gamma prior. Under these assumptions Bayes estimate can be
obtained in explicit form. When both the parameters are unknown, the Bayes
estimates cannot be obtained in closed form. In this case, we will assume that
the scale parameter has the gamma prior, and the shape parameter also has the gamma
prior and they are independently distributed. We will use the Lindley
approximation to obtain the approximate Bayes estimators.



Under these
assumptions, we will compute approximate Bayes estimators and compare with the
maximum likelihood estimators by Monte Carlo simulations. 

Kaynakça

  • Weibull, W. A Statistical Distribution Function of Wide Applicability, Journal of Applied Mechanics, 18, 293-297,1951.
  • Soland, R. M. Bayesian Analysis Of The Weibull Process With Unknown Scale and Shape Parameters, IEEE Transactions On Reliability, Vol. R- 18 No. 4, 1969, November.
  • Kundu, D. Bayesian Inference And Life Testing Plan For The Weibull Distribution in Presence Of Progressive Censoring, Technometrics, 50:2, 144-154, 2008.
  • Papadopoulos, A.S. and Tsokos, C.P. Bayesian analysis of the Weibull failure model with unknown scale and shape parameters, Statistica, XXXVI, No. 4, 1976.
  • Kundu,D. Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring, Technometrics, 50 (2) pp. 114-154, 2008.
  • Banerjee, A. and Kundu, D. Inference Based on Type-II Hybrid Censored Data From a Weibull Distribution, IEEE Trans. Reliab., Vol. 57. No. 2, pp. 369-378, 2008.
  • Lindley, D. Approximate Bayes Methods, University College London, 1980.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Esin Köksal Babacan 0000-0002-9649-5276

Samet Kaya 0000-0002-6937-8138

Yayımlanma Tarihi 1 Ağustos 2019
Gönderilme Tarihi 27 Ağustos 2018
Kabul Tarihi 4 Ekim 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 2

Kaynak Göster

APA Köksal Babacan, E., & Kaya, S. (2019). A simulation study of the Bayes estimator for parameters in Weibull distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1664-1674. https://doi.org/10.31801/cfsuasmas.455276
AMA Köksal Babacan E, Kaya S. A simulation study of the Bayes estimator for parameters in Weibull distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2019;68(2):1664-1674. doi:10.31801/cfsuasmas.455276
Chicago Köksal Babacan, Esin, ve Samet Kaya. “A Simulation Study of the Bayes Estimator for Parameters in Weibull Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 2 (Ağustos 2019): 1664-74. https://doi.org/10.31801/cfsuasmas.455276.
EndNote Köksal Babacan E, Kaya S (01 Ağustos 2019) A simulation study of the Bayes estimator for parameters in Weibull distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1664–1674.
IEEE E. Köksal Babacan ve S. Kaya, “A simulation study of the Bayes estimator for parameters in Weibull distribution”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 2, ss. 1664–1674, 2019, doi: 10.31801/cfsuasmas.455276.
ISNAD Köksal Babacan, Esin - Kaya, Samet. “A Simulation Study of the Bayes Estimator for Parameters in Weibull Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (Ağustos 2019), 1664-1674. https://doi.org/10.31801/cfsuasmas.455276.
JAMA Köksal Babacan E, Kaya S. A simulation study of the Bayes estimator for parameters in Weibull distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1664–1674.
MLA Köksal Babacan, Esin ve Samet Kaya. “A Simulation Study of the Bayes Estimator for Parameters in Weibull Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 2, 2019, ss. 1664-7, doi:10.31801/cfsuasmas.455276.
Vancouver Köksal Babacan E, Kaya S. A simulation study of the Bayes estimator for parameters in Weibull distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1664-7.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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