1. UKM Learning and Research Repository
2. PHD Thesis / Tesis PHD
3. Faculty of Science and Technology / Fakulti Sains dan Teknologi

Title:	Statistical inference for pareto distribution under some variation of ranked set sampling
Authors:	Aissa Omar Aissa (P48949)
Supervisor:	Kamarulzaman Ibrahim, Prof. Dr.
Keywords:	Sampling Universiti Kebangsaan Malaysia -- Dissertations Ranking and selection (Statistics) Dissertations, Academic -- Malaysia
Issue Date:	21-Jul-2014
Description:	Ranked set sampling (RSS) is recognized as a useful sampling scheme for improving the precision of the parameter estimates and increasing the efficiency of estimation.This type of scheme is appropriate when the variable of interest is expensive or time consuming to be quantified, but easy and cheap to be ranked. In this study, the estimation of the parameters of the Pareto distribution of the first type is studied for the data that are gathered under simple random sampling (SRS), RSS and several modifications of RSS. The modifications of RSS that are considered include extreme ranked set sampling (ERSS) and selective order ranked set sampling (SORSS). Several traditional estimators such as moment estimator (MOME), maximum likelihood estimator (MLE), uniformly minimum variance unbiased estimator (UMVUE) and Ad hoc estimator are considered for estimation of the Pareto parameters in the cases when only the scale parameter is known and when both the shape and scale parameters are unknown. These estimators are compared in terms of their biases and mean square errors. It is found that the estimators based on RSS, ERSS and SORSS are more efficient than those estimators based on SRS. The asymptotic confidence intervals for the Pareto parameters are also constructed and compared in terms of expected lengths and coverage probabilities. When the expected lengths and coverage probabilities for the confidence intervals of the Pareto parameters determined based on the different sampling methods are compared, the expected lengths and coverage probabilities are found to be more precise under RSS as opposed to SRS. In addition, since Pareto distribution is quite versatile in many areas of research such as reliability studies, estimation of the reliability parameter θ= P(X >Y )when X and Y are mutually independent Pareto random variables are studied under SRS, RSS, ERSS and SORSS. It is found that the estimators of θ based on RSS and some of its modifications are more efficient than their counterparts under SRS. The asymptotic confidence intervals for the reliability parameter θ are constructed as well and compared in terms of expected lengths and coverage probabilities. These confidence intervals are found to be more precise under RSS and some of its modifications as opposed to SRS.,Pensampelan set terpangkat (PST) diiktiraf sebagai satu skema pensampelan yang berguna untuk meningkatkan ketepatan anggaran parameter dan meningkatkan kecekapan dalam penganggaran. Skema ini sesuai apabila pemboleh ubah itu mahal atau memerlukan masa yang lama untuk disukat, tetapi mudah dan murah untuk dipangkatkan. Dalam kajian ini, anggaran parameter untuk taburan Pareto jenis pertama diselidiki untuk data yang dikumpulkan di bawah pensampelan rawak mudah (PRM), PST dan beberapa pengubahsuaian PST. Pengubahsuaian PST yang dipertimbangkan termasuklah pensampelan set terpangkat ekstrim (PSTE) dan statistik tertib pensampelan set terpangkat (STPST). Beberapa penganggar tradisional seperti penganggar momen (PM), penganggar kebolehjadian maksimum (PKM), penganggar seragam saksama varians minimum (PSSVM) dan penganggar Ad hoc dipertimbangkan untuk menganggar parameter Pareto dalam kes-kes apabila hanya parameter skala diketahui dan apabila kedua-dua parameter bentuk dan skala tidak diketahui. Penganggar ini dibandingkan dari segi kepincangan dan min kuasa dua ralat. Kajian ini mendapati bahawa penganggar yang berdasarkan PST, PSTE dan STPST adalah lebih cekap daripada penganggar yang berdasarkan PRM. Selang keyakinan asimptot bagi parameter Pareto juga dibina dan dibanding dari segi jangkaan panjang dan kebarangkalian liputan. Apabila nilai jangkaan panjang dan kebarangkalian liputan bagi selang keyakinan untuk parameter Pareto yang ditentukan berdasarkan kaedah pensampelan yang berlainan dibanding, didapati bahawa jangkaan panjang dan kebarangkalian liputan adalah lebih tepat dibawah PST berbanding dengan PRM. Disamping itu, disebabkan penggunaan taburan Pareto yang agak meluas dalam banyak bidang penyelidikan seperti kajian kebolehpercayaan, parameter kebolehpercayaan θ= P(X >Y ) bila X dan Y adalah pemboleh ubah Pareto yang saling bersandar dikaji dibawah PRM, PST, PSTE dan STPST. Kajian ini mendapati bahawa penganggar berdasarkan PST dan beberapa pengubahsuaian PST lebih cekap daripada rakan-rakan mereka dibawah PRM. Selang keyakinan asimptot untuk parameter kebolehpercayaan θ juga dibina dan dibanding dari segi jangkaan panjang dan kebarangkalian liputan. Selang keyakinan ini didapati lebih tepat dibawah PST dan beberapa pengubahsuaiannya apabila dibanding dengan PRM.,Ph.D.
Pages:	212
Call Number:	QA278.75.I855 2014 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.