@misc{eprints7253,
           month = {Pebruari},
           title = {
KARAKTERISTIK PENDUGA PARAMETER DISTRIBUSI GENERALIZED GAMMA ({\ensuremath{\alpha}}, {\ensuremath{\beta}}, {\ensuremath{\theta}}) DENGAN MENGGUNAKAN 
METODE GENERALIZED MOMENT
},
          author = {1117031014 Dian Surida},
         address = {Universitas Lampung},
       publisher = {Fakultas Matematika dan Ilmu Pengetahuan Alam},
            year = {2015},
             url = {http://digilib.unila.ac.id/7253/},
        abstract = {ABSTRAK

Distribusi generalized gamma ({\ensuremath{\alpha}}, {\ensuremath{\beta}}, {\ensuremath{\theta}}) merupakan distribusi peluang kontinu dengan tiga parameter, dimana {\ensuremath{\alpha}} {\ensuremath{>}} 0, {\ensuremath{\beta}} {\ensuremath{>}} 0, dan {\ensuremath{\theta}} {\ensuremath{>}} 0. Parameter {\ensuremath{\alpha}} dan {\ensuremath{\beta}} dikenal sebagai parameter bentuk dan parameter {\ensuremath{\theta}} dikenal sebagai parameter skala. Jika   {\ensuremath{\beta}} = 1, maka distribusi generalized gamma ({\ensuremath{\alpha}}, {\ensuremath{\beta}} = 1, {\ensuremath{\theta}}) akan membentuk distribusi gamma ({\ensuremath{\alpha}}, {\ensuremath{\theta}}). Dalam penelitian ini, akan mengkaji tentang karakteristik penduga parameter distribusi generalized gamma ({\ensuremath{\alpha}} ?, {\ensuremath{\beta}} ?, {\ensuremath{\theta}} ?) 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 ({\ensuremath{\alpha}} ?, {\ensuremath{\beta}} ?, {\ensuremath{\theta}} ?) merupakan penduga yang tak bias, ragam minimum, dan konsisten serta diperoleh bentuk analitik varian ? kovarian asimtotik dari penduga parameter ({\ensuremath{\alpha}} ?, {\ensuremath{\beta}} ?, {\ensuremath{\theta}} ?). 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 ({\ensuremath{\alpha}}, {\ensuremath{\beta}}, {\ensuremath{\theta}}) is a continous probability distribution with three parameters, where as {\ensuremath{\alpha}} {\ensuremath{>}} 0, {\ensuremath{\beta}} {\ensuremath{>}} 0, and {\ensuremath{\theta}} {\ensuremath{>}} 0. Parameters {\ensuremath{\alpha}} and {\ensuremath{\beta}} called shape parameters and parameter {\ensuremath{\theta}} called scale parameter. If parameter {\ensuremath{\beta}} is equal to 1, then generalized gamma distribution ({\ensuremath{\alpha}}, {\ensuremath{\beta}} = 1, {\ensuremath{\theta}}) become gamma distribution ({\ensuremath{\alpha}}, {\ensuremath{\theta}}). 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 ({\ensuremath{\alpha}} ?, {\ensuremath{\beta}} ?, {\ensuremath{\theta}} ?) are unbiased, minimum variance and consistent also we  are obtained the analytic of the asymptotic variance ? covariance of parameter estimators ({\ensuremath{\alpha}} ?, {\ensuremath{\beta}} ?, {\ensuremath{\theta}} ?). 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.



}
}