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ITS » Master Theses » Statistika - S2
Posted by yeni at 27/12/2006 11:46:50  •  12065 Views


STATISTIK UJI EMPIRICAL LIKELIHOOD RATIO PARAMETER POPULASI DALAM MODEL NONPARAMETRIK

Created by :
SULIYANTO 



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Description:

Salah satu permasalahan penting dalam statistika adalah inferensi statistika. Jika diberikan sampel random Xi, X2, ... , Xn dari fungsi distribusi F(x) yang diketahui, maka dapat dilakukan inferensi statistik untuk menguji hipotesis parameter populasinya dan membuat interval konfidensi bagi parameter populasinya dengan menggunanakan salah satu alat uji statistik rasio likelihood . Inferensi statistik semacam ini dikatakan inferensi parametrik. Tetapi bagaimana jika fungsi distribusinya tidak diketahui, dalam hal ini kita tidak mungkin melakukan inferensi parametrik melainkan dengan inferensi nonparametrik (Qin, 1993) . Salah satu bentuk inferensi nonparametrik yang dibahas dalam penelitian ini berkaitan dengan sampel random dari dua populasi yang mempunyai fungsi distribusi kontinu tetapi tidak diketahui. Diasumsikan sampel random si = {xi , X2 ,..., xm } diambil dari populasi pertama yang mempunyai fungsi distribusi kontinu F(x) tidak diketahui dan sampel random kedua S2 = {yi,y2,--, yn } diambil dari populasi kedua yang mempunyai fungsi distribusi terboboti G(y) yang tidak diketahui, yaitu G(y) = — \a>(x) dF(x) , co(x) > 0 , y > 0 , w = \o)(x) dF(x) < o>, dimana co(x) adalah fungsi pembobot. n Tujuan dari penelitian ini adalah mencari statistik uji Empirical Likelihood Ratio (ELR), mencari distribusi asimtotik dari statistik uji ELR untuk menguji hipotesis : Ho : 0 = 0o versus Hi :: 0 * 0o , dimana 0 = EF(X), dan menerapkan statistik uji ELR pada data ultrafdtration in vivo untuk mendapatkan interval konfidensi dari rata-rata nilai Ultrafiltration rate (UFR) dalam ml/hr yang dihasilkan oleh dialyzer-dialyzer pada Center 1 akibat pemberian Transmembran pressure (TMP) antara 155 mmHg sampai 471 mmHg dengan menggunakan tingkat signifikan a = 5 % . Dari hasil penelitian didapat statistik uji ELRyaitu R(0) = 2 {l(w)-l(w,9)} dengan menggunakan metode pengali lagrange. Distribusi asimtotik dari statistik uji ELR adalah R(90J —^—*xf\) untuk N —> oo. Hasil uji hipotesis menunjukkan bahwa rata-rata nilai UFR yang dihasilkan oleh dialyzer-dialyzer pada Center 1 akibat pemberian TMP antara 155 mmHg sampai 471 mmHg berada dalam interval 903 ml/hr sampai 1068 ml / hr dengan tingkat signifikan a = 5 %.


Alt. Description

One of important matter in the statistical is statistic inference. If we let random sample Xi, X2, ..., Xn for distnbution function F(x) that it had known, then can be done a statistic inference to examine of the population parameter hypotesis and to create confidence interval for the population parameter with using one of test instrument that is statistical likelihood ratio. Statistic inference like as this can say as parametric inference. But, how if the distrtbution function didn't know, in this case we impossible to do the parametric inference except with nonparametric inference (Qin, 1993). One of model from nonparametric inference that had studied in this research connected with random sample from two populations had distribution function of continuous but didn't know. Assumsed that random sample Si = {xi, x2, ..., xm} taken from first population which had have distribution function of continuous F(x) didn't know and second random sample s2 = {yi, y2, ... , yn} taken from weighted distribution function V 00 G(y) didn't too, that is G(y) = — \co(x)dF(x), co(x) >0,y>0 , w= \(o(x) dF(x), 0 0 where a>(x) is weighted function. Goal of this research is to look for Empirical Likelihood Ratio (ELR) statistic test, to look for asymptotic distribution of ELR statistic test to examine of hypotesis Ho : 0 = 0o versus Hi : 0 * 0o, where 0 = EF(X), and to apply ELR statistic test for ultrafiltration in vivo data to take confidence interval from rate of Ultrafiltration rate (UFR) value in ml/hr that resulted by dialyzers in Center 1 as consequence of Transmembran pressure (TMP) giving between 155 mmHg up to 471 mmHg with to use level of significant a = 5%. For research result has gotten ELR statistic test, that is R(0) = 2{l(w) l(w,6 )} with using lagrange multiplier method. Asymptotic distribution of ELR statistic test, that is R(0O ) —^—> x2(i) f°r N —> QO. Test result of hypotesis shown that rates UFR value that resulted by dialyzers in Center 1 as consequence TMP giving between 155 mmHG up to 471 lie on interval 903 ml/hr up to 1068 ml/hr with level of significant a = 5%.

Contributor:
  1. Dr. Drs. I Nyoman Budiantara, MS.
    Bambang Widjanarko Otok, S.Si, M.Si
Date Create:27/12/2006
Type:Text
Format:pdf; 62 pages
Language:Indonesian
Identifier:ITS-Master-3100003018397
Collection ID:3100003017678
Call Number:519.54 Sul s


Source :
Theses Statistica RT 519.54 Sul s, 2002

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ITS Community

Rights :
Copyright @2002 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/statistik-uji-empirical-likelihood-ratio-parameter-populasi-dalam-model-nonparametrik-316.html




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