Sains Malaysiana 43(9)(2014): 1433–1437

Approximate Bayesian Estimates of Weibull Parameters with Lindley’s Method

(Anggaran Pengamiran Bayesian untuk Parameter Weibull Menggunakan Kaedah Lindley’s)

CHRIS BAMBEY GUURE*¹ & NOOR AKMA IBRAHIM²

¹Department of Biostatistics, School of Public Health, University of Ghana

Legon, Accra, Ghana

²Department of Mathematics, Faculty of Science, Universiti Putra Malaysia

43400 Serdang, Selangor, Malaysia

Diserahkan: 14 Oktober 2013/Diterima: 13 Januari 2014

ABSTRACT

One of the most important lifetime distributions that is used for modelling and analysing data in clinical, life sciences and engineering is the Weibull distribution. The main objective of this paper was to determine the best estimator for the two-parameter Weibull distribution. The methods under consideration are the frequentist maximum likelihood estimator, least square regression estimator and the Bayesian estimator by using two loss functions, which are squared error and linear exponential. Lindley approximation is used to obtain the Bayes estimates. Comparisons are made through simulation study to determine the performance of these methods. Based on the results obtained from this simulation study the Bayesian approach used in estimating the Weibull parameters under linear exponential loss function is found to be superior as compared to the conventional maximum likelihood and least squared methods.

Keywords: Bayesian; least squarer; maximum Likelihood; squared error and linear exponential loss functions

ABSTRAK

Salah satu taburan jangka hayat yang sangat penting yang sering digunakan dalam pemodelan dan analisis data klinikal, sains hayat dan kejuruteraan adalah taburan Weibull. Objektif utama kertas ini adalah untuk menentukan penganggar yang paling baik bagi taburan Weibull dua-parameter. Kaedah yang dipertimbangkan adalah anggaran kebolehjadian maksimum, anggaran regresi kuasa dua terkecil dan anggaran Bayes menggunakan dua fungsi, iaitu ralat kuasa dua dan fungsi, linear eksponen. Pengamiran Lindley digunakan untuk memperoleh anggaran Bayes. Perbandingan dijalankan melalui simulasi untuk menentukan prestasi kaedah. Hasil yang diperoleh daripada kajian simulasi menunjukkan pendekatan Bayes dalam menganggar parameter Weibull dengan fungsi linear eksponen didapati lebih baik jika dibandingkan dengan kaedah konvensional kebolehjadiaan maksimum dan kaedah kuasa dua terkecil berdasarkan nilai ralat kuasa dua min.

Kata kunci: Bayesian; fungsi ralat kuasa dua dan linear eksponen; kebolehjadiaan maksimum; regresi kuasa dua terkecil

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*Pengarang untuk surat-menyurat; email: cbguure@ug.edu.gh