Generalisasi Algoritma Thinning Process pada Proses Poisson Majemuk dengan Komponen Proses Poisson Nonhomogen dan Distribusi Gamma

Syarif Abdullah (1), Sidik Susilo (2), Miftahul Huda (3), Nina Valentika (4), Sri Istiyarti Uswatun Chasanah (5), Agusyarif Rezka Nuha (6), Aswata Wisnuadji (7), Fajri Ikhsan (8), Yazid Rukmayadi (9)
(1) Universitas Sultan Ageng Tirtayasa, Banten, Indonesia,
(2) Universitas Sultan Ageng Tirtayasa, Indonesia,
(3) Universitas Bina Bangsa, Indonesia,
(4) Universitas Pamulang, Indonesia,
(5) UIN Sunan Kalijaga Yogyakarta, Indonesia,
(6) Universitas Negeri Gorontalo, Indonesia,
(7) Universitas Sultan Ageng Tirtayasa, Indonesia,
(8) Universitas Sultan Ageng Tirtayasa, Indonesia,
(9) Universitas Sultan Ageng Tirtayasa, Indonesia
https://doi.org/10.30651/must.v5i2.6485

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Vol. 5 No. 2 (2020): DECEMBER
Keywords:
    distribusi gamma, generalisasi algoritma, penduga parameter, proses Poisson majemuk, proses Poisson nonhomogen.
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Abstract

Proses Poisson majemuk (compound Poissonprocess (CPP)) adalah salah satu pengembangan dari teori stokastik yang digunakan untuk memodelkan fenomena nyata. Proses ini memiliki minimal dua komponen utama, yaitu komponen pada proses Poisson-nya berupa fungsi intensitas konstan atau fungsi tertentu dan komponen besaran akibat berupa distribusi tertentu. Penelitian ini bertujuan untuk membuat model CPP yang memiliki komponen fungsi intensitas nonhomogen pada proses Poisson-nya (non-homogeneous Poisson process (NHPP)) dan komponen besaran akibat yang berdistribusi gamma (gamma distribution (GD)). Selanjutnya dibuat penduga parameter (parameter estimation) dan algoritma untuk membangkitkan CPP yang memiliki komponen fungsi intensitas NHPP dan komponen akibat GD. Metode yang digunakan dalam menentukan penduga parameter yaitu metode moment. Sedangkan pembuatan algoritma pada penelitian ini menggunakan metode acceptance and rejections berupa generalisasi teknik thinning process. Hasil penelitian telah didapatkan rumusan penduga-penduga untuk fungsi nilai harapan dan varian pada CPP dengan komponen NHPP dan komponen GD. Penelitian ini didapatkan pula generalisasi algoritma thinning process pada CPP-NHPP-GD tipe 1 dan 2. Algoritma tipe 1 merupakan hasil modifikasi dan generalisasi algoritma dari model CPP-HPP dengan mengubah komponen pada proses Poisson-nya menjadi bentuk NHPP dan komponen pada bagian besaran akibat berupa distribusi gamma. Algoritma tipe 2 merupaan hasil modifikasi dari tipe 1 dengan melakukan breakdown interval menjadi subinterval.

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References

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Authors

Syarif Abdullah
Universitas Sultan Ageng Tirtayasa, Banten
abdullahsyarifayis@untirta.ac.id (Primary Contact)
Sidik Susilo
Universitas Sultan Ageng Tirtayasa
Miftahul Huda
Universitas Bina Bangsa
Nina Valentika
Universitas Pamulang
Sri Istiyarti Uswatun Chasanah
UIN Sunan Kalijaga Yogyakarta
Agusyarif Rezka Nuha
Universitas Negeri Gorontalo
Aswata Wisnuadji
Universitas Sultan Ageng Tirtayasa
Fajri Ikhsan
Universitas Sultan Ageng Tirtayasa
Yazid Rukmayadi
Universitas Sultan Ageng Tirtayasa
Author Biographies

Syarif Abdullah, Universitas Sultan Ageng Tirtayasa, Banten

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http://sinta.ristekbrin.go.id/authors/detail?id=6693983&view=overview

SCOPUS ID: 

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Sidik Susilo, Universitas Sultan Ageng Tirtayasa

Teknik Mesin Fakultas Teknik Universitas Sultan Ageng Tirtayasa

Miftahul Huda, Universitas Bina Bangsa

Jurusan Statistik Universitas Bina Bangsa

Nina Valentika, Universitas Pamulang

JUrusan Matematika Universitas Pamulang

Sri Istiyarti Uswatun Chasanah, UIN Sunan Kalijaga Yogyakarta

Jurusan Matematika UIN Sunan Kalijaga Yogyakarta

Agusyarif Rezka Nuha, Universitas Negeri Gorontalo

Jurusan Matematika Universitas Negeri Gorontalo

Aswata Wisnuadji, Universitas Sultan Ageng Tirtayasa

Teknik Mesin Fakultas Teknik Universitas Sultan Ageng Tirtayasa

Fajri Ikhsan, Universitas Sultan Ageng Tirtayasa

Teknik Metalurgi Universitas Sultan Ageng Tirtayasa

Yazid Rukmayadi, Universitas Sultan Ageng Tirtayasa

Teknik Mesin Fakultas Teknik Universitas Sultan Ageng Tirtayasa
Abdullah, S., Susilo, S., Huda, M., Valentika, N., Chasanah, S. I. U., Nuha, A. R., … Rukmayadi, Y. (2020). Generalisasi Algoritma Thinning Process pada Proses Poisson Majemuk dengan Komponen Proses Poisson Nonhomogen dan Distribusi Gamma. MUST: Journal of Mathematics Education, Science and Technology, 5(2), 221–239. https://doi.org/10.30651/must.v5i2.6485
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