KARAKTERISTIK PENDUGA PARAMETER DISTRIBUSI GENERALIZED GAMMA (α, β, θ) DENGAN MENGGUNAKAN METODE GENERALIZED MOMENT

Dian Surida, 1117031014 (2015) KARAKTERISTIK PENDUGA PARAMETER DISTRIBUSI GENERALIZED GAMMA (α, β, θ) DENGAN MENGGUNAKAN METODE GENERALIZED MOMENT. Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Lampung.

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Abstrak

ABSTRAK Distribusi generalized gamma (α, β, θ) merupakan distribusi peluang kontinu dengan tiga parameter, dimana α > 0, β > 0, dan θ > 0. Parameter α dan β dikenal sebagai parameter bentuk dan parameter θ dikenal sebagai parameter skala. Jika β = 1, maka distribusi generalized gamma (α, β = 1, θ) akan membentuk distribusi gamma (α, θ). Dalam penelitian ini, akan mengkaji tentang karakteristik penduga parameter distribusi generalized gamma (α ̂, β ̂, θ ̂) dengan menggunakan metode generalized moment meliputi sifat tak bias, ragam minimum, dan konsisten serta memeriksa varian – kovarian asimtotiknya. Hasil yang diperoleh menunjukkan bahwa penduga parameter distribusi generalized gamma (α ̂, β ̂, θ ̂) merupakan penduga yang tak bias, ragam minimum, dan konsisten serta diperoleh bentuk analitik varian – kovarian asimtotik dari penduga parameter (α ̂, β ̂, θ ̂). Selain itu, disajikan pula kurva fungsi kepekatan peluang distribusi generalized gamma dengan menggunakan software R.3.1.2 untuk melihat perilaku distribusi generalized gamma. Kata kunci: Distribusi Generalized Gamma, Pendugaan Parameter, Metode Generalized Moment ABSTRACT Generalized gamma distribution (α, β, θ) is a continous probability distribution with three parameters, where as α > 0, β > 0, and θ > 0. Parameters α and β called shape parameters and parameter θ called scale parameter. If parameter β is equal to 1, then generalized gamma distribution (α, β = 1, θ) become gamma distribution (α, θ). In this research, we will examine the characteristics of unbiasness, minimum variance, and consistent also investigate the asymptotic variance – covariance. The results show that the characteristics of parameter estimators generalized gamma distribution (α ̂, β ̂, θ ̂) are unbiased, minimum variance and consistent also we are obtained the analytic of the asymptotic variance – covariance of parameter estimators (α ̂, β ̂, θ ̂). Moreover, presented by the graph of probability density function of generalized gamma distribution using software R.3.1.2 to see the behavior of generalized gamma distribution. Keywords: Generalized Gamma Distribution, Parameter Estimation, Method of Generalized Moment.

Tipe Karya Ilmiah: Skripsi
Subyek: > QA Mathematics
Program Studi: Fakultas MIPA > Prodi Matematika
Depositing User: 5134372 . Digilib
Date Deposited: 23 Feb 2015 04:21
Last Modified: 23 Feb 2015 04:21
URI: http://digilib.unila.ac.id/id/eprint/7253

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