SIFAT-SIFAT DAN KEJADIAN KHUSUS DISTRIBUSI GAMMA
Abstract
The gamma distribution is one of special continuous random variable distribution with scale parameter and shape parameter where is positive real numbers. On some conditions the gamma distribution astablishes other continuous distributions which are then called special cases of the gamma distribution. Therefore, this study was conducted to determine the properties of gamma distribution and the characteristics of the special cases of gamma distribution by analyzed the theories from literatures. The properties of gamma distribution include expectation value, variance, moment generating function, characteristic function, and estimation of gamma distribution parameters with the moment method to earn the special cases of the gamma distribution are Erlang, exponential, chi-square, and beta distributions.
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References
A. Lutfi, Pendugaan Parameter Distribusi Erlang Menggunakan Metode Probability Weigthed Moment, Method of Momen, dan Maximum Likelihood Estimator, S.Si [Skripsi]. Bandar Lampung, Lampung : Universitas Lampung, 2017. [Online]. Tersedia : Digital Library Universitas Lampung.
A. S. Nasution, Estimasi Parameter dan Pengujian Hipotesis Pada Model Regresi Gamma (Studi Kasus: Pemodelan Pencemaran Air Sungai di Surabaya), M.si [Tesis]. Padangsidipuan, Sumatera Utara : Universitas Graha Nusantara Padangsidipuan, 2018. [Online]. Tersedia : Universitas Graha Nu [1]santara Padangsidipuan – Jurnal Paidagogeo.
F. Ridiani. “Pendugaan Parameter Distribusi Beta dengan Metode Momen dan Metode Maksimum Likelihhod,†Jurnal Matematika UNAND, vol. 3, no. 2, pp. 23 – 28, 2014.
James Bonnar, “The Gamma Functionâ€, Treasure Trove of Mathematics, 2017, [Online]. Tersedia: Semantic Scholar.
J.M. Borwein and R. M. Corless,â€Gamma and Factorial in the Monthly,†arXiv, 15 Maret 2017, [Online]. Tersedia: https://arxiv.Org/abs /1703.05349 [Diakses: 20 Agustus 2020].
R. Kurniasih dan G. Pramesti. “Distribusi Erlang dan Penerapannya,†Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya, pp . 223 – 236, 15 Mei, 2013.
R. S. Taringan, Kajian Parameter Berdistribusi Gamma dengan Moments Method dan Maximum Likelihood Estimator, S.Si [Skripsi]. Medan, Sumatera Utara : Universitas Sumatera Utara, 2015. [Online]. Tersedia : Repository USU.
R. V. Hoog, J. W. McKean, and A. T. Craig, Introduction to Mathematical Statistics, 7th Edition, Boston, Pearson Education, Inc., 2013.
R. Yendra dan E. T. Noviadi, “ Perbandingan Estimasi Parameter Pada Distribusi Eksponensial Dengan Menggunakan Metode Maksimum Likelihhod dan Metode Bayesian,†Jurnal Sains Matematika dan Statistik, vol. 1, no. 2, pp. 62 – 72, Juli 2015.
Sugito dan M. A. Mukid. “Distribusi Poisson dan Distribusi Eksponensial dalam Proses Stokastik,†Media Statistika, vol. 4, no. 2, pp. 113 – 120. Desember 2011.
U. Hasanah, P. Yanuar, dan D. Devianto, “Pendugaan Parameter Pada Distribusi Gamma Dengan Metode Bayes,†Jurnal Matematika UNAND, vol. 7, no. 4, pp. 81 – 86, Desember 2018.
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