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All Journal Jurnal Riset Rumpun Matematika dan Ilmu Pengetahuan Alam (JURRIMIPA)
Meili Yanti
Universitas Sumatera Utara
Mathematics

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Penaksiran Parameter Pada Distribusi Erlang Berdasarkan Metode Maksimum Likelihood Dengan Menggunakan Algoritma Newton Raphson Dan Fisher Scoring Meili Yanti; Open Darnius
Jurnal Riset Rumpun Matematika dan Ilmu Pengetahuan Alam (JURRIMIPA) Vol. 2 No. 1 (2023): April : Jurnal Riset Rumpun Matematika dan Ilmu Pengetahuan Alam
Publisher : Pusat riset dan Inovasi Nasional

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55606/jurrimipa.v2i1.720

Abstract

The Erlang distribution is a special case of the Gamma distribution with the k shape parameter and the λ rate parameter. In this study, the parameter estimation of the Erlang distribution was carried out using the Maximum Likelihood method. In maximizing the function, an implicit and non-linear form is obtained, then it is solved using the Newton Raphson algorithm. Apart from Newton Raphon, the estimation of parameters was also carried out using the Fisher Scoring algorithm. The Fisher Scoring algorithm is similar to the Newton Raphson algorithm, the difference is that Fisher Scoring uses an matrix information. The result of parameter estimation in Erlang distribution using Newton Raphson algorithm which is applied to outgoing telephone call data that generated by Matlab R2010a software cannot be done simultaneously. Therefore, the parameter assessment is carried out on the k parameter first, then followed by the λ parameter estimation and the parameter and = 0.6886812 are obtained. Meanwhile, the parameter estimation using the Fisher Scoring algorithm produces an equation that is not different from the Newton Raphson algorithm
Co-Authors Open Darnius