ANALISIS SURVIVAL UNTUK PARAMETER SKALA DARI DISTRIBUSI WEIBULL MENGGUNAKAN MLE DAN METODE BAYESIAN

  • Ferra Yanuar Prodi Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Andalas
  • Sisca Wulandari Prodi Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Andalas
  • Izzati Rahmi HG Prodi Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Andalas
DOI: https://doi.org/10.30598/barekengvol15iss1pp147-156
Keywords: Distribusi Weibull, Analysis Survival, Maximum Likelihood Estimation, Bayesian, Absolute bias, Mean square error

Abstract

Modeling of survival data is necessary and important to do. Survival data is generally assumed to have a Weibull distribution. Bayesian approach has been implemented to estimate the parameter in such this survival analysis. This study purposes to compare the performance of the Maximum Likelihood and Bayesian using Invers Gamma as prior conjugate for estimating the survival function of scale parameter of Weibull distribution. The comparisons are made through simulation study. The best performance of both estimators is chosen based on the lowest value of absolute bias and the mean square error. Two different size samples are generated to illustrate the life time data which are used in this study. This study results that maximum likelihood is the best estimator compared to Bayes with Invers Gamma distribution as conjugate prior.

Downloads

Download data is not yet available.

References

C. B. Guure and N. A. Ibrahim, “Bayesian Analysis of the Survival Function and Failure Rate of Weibull Distribution with Censored Data,†Mathematical Problems in Engineering, vol. 2012, pp. 1–18, 2012, doi: 10.1155/2012/329489.

D. Lukitasari, A. Setiawan, and L. R. Sasangko, “Bayesian Survival Analysis Untuk Mengestimasi Parameter Model Weibull-Regression Pada Kasus Ketahanan Hidup Pasien Penderita Jantung Koroner,†dC, vol. 4, no. 1, p. 26, Feb. 2015, doi: 10.35799/dc.4.1.2015.7531.

S. Dey, “Bayesian Estimation and Prediction on Inverse Rayleigh Distribution,†Malaysian Journal of Mathematical Sciences, vol. 6, no. 1, pp. 113–124, 2012.

T. G. Ieren and P. E. Oguntunde, “A Comparison between Maximum Likelihood and Bayesian Estimation Methods for a Shape Parameter of the Weibull-Exponential Distribution,†AJPAS, pp. 1–12, May 2018, doi: 10.9734/ajpas/2018/v1i124504.

I. T. Hazhiah, S. Sugito, and R. Rahmawati, “Estimasi Parameter Distribusi Weibull Dua Parameter Menggunakan Metode Bayes,†Medstat, vol. 5, no. 1, pp. 27–35, Jun. 2012, doi: 10.14710/medstat.5.1.27-35.

Ahmed, “Comparison of the Bayesian and Maximum Likelihood Estimation for Weibull Distribution,†Journal of Mathematics and Statistics, vol. 6, no. 2, pp. 100–104, Apr. 2010, doi: 10.3844/jmssp.2010.100.104.

D. Kundu and H. Howlader, “Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data,†Computational Statistics & Data Analysis, vol. 54, no. 6, pp. 1547–1558, Jun. 2010, doi: 10.1016/j.csda.2010.01.003.

I. Iskandar and Y. S. Gondokaryono, “Competing risk models in reliability systems, a weibull distribution model with bayesian analysis approach,†IOP Conf. Ser.: Mater. Sci. Eng., vol. 114, p. 012064, Feb. 2016, doi: 10.1088/1757-899X/114/1/012064.

S. A. Thamrin, “Penaksiran Parameter Distribusi Weibull dengan Metode Bayesian Survival dan Maksimum Likelihood,†Jurnal Keteknikan dan Sains, vol. 1, no. 2, pp. 22–27, 2018.

F. Yanuar, H. Yozza, and R. V. Rescha, “Comparison of Two Priors in Bayesian Estimation for Parameter of Weibull Distribution,†sci. technol. indones., vol. 4, no. 3, p. 82, Jul. 2019, doi: 10.26554/sti.2019.4.3.82-87.

E. Avcı, “Bayesian survival analysis: comparison of survival probability of hormone receptor status for breast cancer data,†IJDATS, vol. 9, no. 1, p. 63, 2017, doi: 10.1504/IJDATS.2017.10003994.

H. Rinne, The Weibull distribution: a handbook. Boca Raton: CRC Press, 2009.

H. M. Badjana, B. Renard, J. Helmschrot, K. S. Edjamé, A. Afouda, and K. Wala, “Bayesian trend analysis in annual rainfall total, duration and maximum in the Kara River basin (West Africa),†Journal of Hydrology: Regional Studies, vol. 13, pp. 255–273, Oct. 2017, doi: 10.1016/j.ejrh.2017.08.009.

A. A. Al-Shomrani, A. I. Shawky, O. H. Arif, and M. Aslam, “Log-logistic distribution for survival data analysis using MCMC,†SpringerPlus, vol. 5, no. 1, p. 1774, Dec. 2016, doi: 10.1186/s40064-016-3476-7.

F. Yanuar, “The Use of Uniformative and Informative Prior Distribution in Bayesian SEM,†Global Journal of Pure and Applied Mathematics, vol. 11, no. 5, pp. 3259–64, 2015.

W. M. Bolstad and J. M. Curran, Introduction to Bayesian Statistics, Third Edition. John Wiley & Sons, Inc., 2017.

Published
2021-03-01
How to Cite
[1]
F. Yanuar, S. Wulandari, and I. Rahmi HG, “ANALISIS SURVIVAL UNTUK PARAMETER SKALA DARI DISTRIBUSI WEIBULL MENGGUNAKAN MLE DAN METODE BAYESIAN”, BAREKENG: J. Math. & App., vol. 15, no. 1, pp. 147-156, Mar. 2021.
Issue
Vol 15 No 1 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Section
Articles

Authors who publish with this Journal agree to the following terms:

  1. Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
  2. Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
  3. Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.