Estimasi Parameter Distribusi Weibull Menggunakan Metode Maksimum Likelihood

Isnaini Hafizhah Aziz; Zahedi Zahedi; Sutarman Sutarman; Muhammad Romi Syahputra

doi:10.61132/arjuna.v3i1.1531

Authors

Isnaini Hafizhah Aziz Universitas Sumatera Utara
Zahedi Zahedi Universitas Sumatera Utara
Sutarman Sutarman Universitas Sumatera Utara
Muhammad Romi Syahputra Universitas Sumatera Utara

DOI:

https://doi.org/10.61132/arjuna.v3i1.1531

Keywords:

Weibull distribution, Maximum likelihood method, Parameter estimation, Newton-Raphson

Abstract

In various types of statistical analysis, the Weibull distribution is an important continuous probability distribution. One crucial aspect of studying this distribution is estimating its parameters. The maximum likelihood method is the approach used for the two-parameter Weibull distribution. This method aims to determine the parameter values by maximizing the likelihood function based on the available data. The advantages of the maximum likelihood method lie in its properties, such as consistency, efficiency, and asymptotic normality. Since the form of the likelihood function in the Weibull distribution is quite complex and cannot be solved analytically, numerical solutions are required. One approach used is the Newton-Raphson method, which serves to approximate the parameter values or find the optimal solution.

Downloads

Download data is not yet available.

References

Bain, L.J. and Engelhardt, M. (1992) Introduction Probability and Mathimatical Statistics. California: Wadsworth Publishing Company.

Harinaldi (2005) Prinsip-Prinsip Statistika untuk Teknik dan Sains. Jakarta: Erlangga

Hassan, M.I. (2002) Pokok-Pokok Materi Statistika 2 (Statistika Deskriptif). Jakarta: Bumi Putera.

Hidayati, T., Aedi, W.G. and Masitoh, L.F. (2022) METODE NUMERIK.

Latib, I. and Doaly, C.O. (2018) ‘Usulan Penjadwalan Penggatian dan Pemeriksaan Komponen Kritis Mesin Feeder dan Fanblower (Studi Kasus di PT. Petnesia Resindo)’, Jurnal Teknik Industri, 8(2).

Matematika, Jurnal et al. (no date) ESTIMASI PARAMETER DARI DISTRIBUSI WEIBULL BERDASARKAN SAMPEL TERSENSOR TIPE II DAN TIPE I. Available at: http://ojs.uho.ac.id/index.php/JMKS.

Nketiah, E.A. (2021) ‘Parameter estimation of the Weibull Distribution; Comparison of the Least-Squares Method and the Maximum Likelihood estimation’, International Journal of Advanced Engineering Research and Science, 8(9), pp. 210–224. Available at: https://doi.org/10.22161/ijaers.89.21.

Nuryadi et al. (2017) DASAR-DASAR STATISTIK PENELITIAN. Edited by Nuryadi et al. Yogyakarta: SIBUKU MEDIA. Available at: www.sibuku.com.

Otaya, L.G. (2016) Distribusi Probabilitas Weibull Dan Aplikasinya (Pada Persoalan Keandalan (Reliability) Dan Analisis Rawatan (Mantainability).

Purba, S.A. (2020) ESTIMASI PARAMETER DATA BERDISTRIBUSI NORMAL MENGGUNAKAN MAKSIMUM LIKELIHOOD BERDASARKAN NEWTON RAPHSON ESTIMATION OF NORMAL DISTRIBUTED DATA PARAMETERS USING THE MAXIMUM LIKELIHOOD BASED ON NEWTON RAPHSON, J. Sains.

Yanuar, F., Wulandari, S. and Rahmi HG, I. (2021) ‘ANALISIS SURVIVAL UNTUK PARAMETER SKALA DARI DISTRIBUSI WEIBULL MENGGUNAKAN MLE DAN METODE BAYESIAN’, BAREKENG: Jurnal Ilmu Matematika dan Terapan, 15(1), pp. 147–156. Available at: https://doi.org/10.30598/barekengvol15iss1pp147-156.

Yendra, R. et al. (2015) Perbandingan Estimasi Parameter Pada Distribusi Eksponensial Dengan Menggunakan Metode Maksimum Likelihood Dan Metode Bayesian, Jurnal Sains Matematika dan Statistika.