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ITS » Undergraduate Theses » Matematika
Posted by ida at 12/08/2008 16:43:24  •  14784 Views


KAJIAN ESTIMASI PARAMETER DARI DISTRIBUSI GAMMA DENGAN METODE ESTIMASI BAYESIAN

ESTIMATION ANALYSIS OF GAMMA DISTRIBUTION PARAMETERS BY BAYESIAN ESTIMATION METHOD

Author :
Setianti, Rosvira Enggar 




ABSTRAK

Distribusi Gamma merupakan salah satu dari beberapa distribusi kontinu. Distribusi tersebut memiliki parameter yang harus diestimasi yaitu α dan β. Estimasi parameter dilakukan dengan metode Estimasi Bayesian melalui pendekatan Non Informatif Prior. Dengan menggunakan teorema Bayes, kepercayaan awal yang diambil dari bermacam-macam kemungkinan mengikuti asumsi sesuai informasi awal yang dinyatakan dengan distribusi prior untuk parameter yang diinginkan, kemudian distribusi prior dikombinasikan dengan informasi sampel yang dinyatakan dengan fungsi likelihood untuk mendapatkan distribusi posterior. Dari kajian tersebut diperoleh fungsi likelihood pada distribusi gamma adalah ()()[]ΠΣ==−−⎪⎪⎭⎪⎪⎬⎫⎪⎪⎩⎪⎪⎨⎧−Γ=niniiinxxxl111exp,ββαβααα dimana fungsi likelihood merupakan bagian yang penting dalam mengestimasi dengan metode Estimasi Bayesian. Setelah memperoleh bentuk fungsi likelihoodnya maka akan dikombinasikan dengan distribusi Prior yaitu Non Informatif Prior. Sehingga diperoleh estimator dari βadalah ()1ˆ1−=Σ=αβnxnii, sedangkan untuk parameterαdidapatkan dengan cara pendekatan numerik yaitu dengan bantuan program WinBUGS 1.4 sehingga dengan melihat nilai dari standart deviasi yang paling minimum diperoleh 7.0=αuntuk 30=ndan 5.0=αuntuk . 80=n


ABSTRACT

One of continous distributions is gamma distribution. This distribution has parameter that must be estimated, they are α and β. Parameter estimation used bayesian estimation method by non informatif prior approximation. By using bayes theorem, first trust that taken from various possibility follows assumtion based on first information, namely prior distribution for wanted parameter, and then prior distribution is combined with sample information known as likelihood funtion to get posterior distribution. Likelihood funtion for gamma distribution is ()()[]ΠΣ==−−⎪⎪⎭⎪⎪⎬⎫⎪⎪⎩⎪⎪⎨⎧−Γ=niniiinxxxl111exp,ββαβααα Where likelihood function is important part in bayesian estimation method. After get likelihood function, it can be combined with prior distribution, namely non informatif prior. estimator of β is ()1ˆ1−=Σ=αβnxnii and estimator of α is gotten with numeric approximation through WinBUGS 1.4 then with looking the smallest standart deviation value is gotten 7.0=α for and 30=n5.0=α for 80=n.

KeywordsDistribusi Gamma, Non Informatif Prior, Estimasi Bayesian, Gibbs Sampling .
 
Subject:  Statistik matematis
Contributor
  1. Dra. Farida Agustini W, MS
Date Create: 12/08/2008
Type: Text
Format: pdf
Language: Indonesian
Identifier: ITS-Undergraduate-3100007029920
Collection ID: 3100007029920
Call Number: RSMa 519.542 Set k


Source
Undergraduate Theses, DEPARTMENT OF MATHEMATICS RSMa 519.542 Set k

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Copyright @2007 by ITS Library. This publication is protected by copyright and permission should be obtained from the ITS Library prior to any prohibited reproduction, storage in a retrievel system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to ITS Library


Publication URL :
http://digilib.its.ac.id/kajian-estimasi-parameterdari-distribusi-gammadengan-metode-estimasi-bayesian-1956.html




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. , Bayesian , Distribusi , Distribusi Gamma , Estimasi , Estimasi Bayesian , Gamma , Gibbs , Gibbs Sampling . , Informatif , Non , Non Informatif Prior , Prior , Sampling




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