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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Abstract
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.
| Item Type: | Other |
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| Subjects: | Q Science (General) > QA Mathematics |
| Divisions: | 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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