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Parameter Estimation for Weibull Distribution
Ana Bulić (2016)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group
Cite this document

Bulić, A. (2016). Procjena parametara Weibullove distribucije (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:919735

Bulić, Ana. "Procjena parametara Weibullove distribucije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:919735

Bulić, Ana. "Procjena parametara Weibullove distribucije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:919735

Bulić, A. (2016). 'Procjena parametara Weibullove distribucije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 13 October 2019, https://urn.nsk.hr/urn:nbn:hr:126:919735

Bulić A. Procjena parametara Weibullove distribucije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2019 October 13] Available at: https://urn.nsk.hr/urn:nbn:hr:126:919735

A. Bulić, "Procjena parametara Weibullove distribucije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:919735

Metadata
TitleProcjena parametara Weibullove distribucije
Title (english)Parameter Estimation for Weibull Distribution
AuthorAna Bulić
MentorMirta Benšić (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberMirta Benšić (član povjerenstva)
Committee memberDragana Jankov Maširević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Probability and Mathematical Statistics Research Group)
Osijek
Defense date and country2016-10-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Weibullova distribucija se najčešće koristi u teoriji pouzdanosti te u teoriji životnog vijeka kao matematički model za opisivanje slučajnog vijeka trajanja nekog elementa a isto tako i u farmakologiji, biologiji, elektrotehnici, itd. U ovom diplomskom radu glavni cilj nam je procjena parametara Weibullove distribucije. Kako bi što bolje pristupili tom problemu prvo smo nešto više rekli o samoj Weibullovoj distribuciji i njezinoj primjeni. Weibullova distribucija za različite vrijednosti parametara c,α i ξ0 poprima različite oblike i možemo je dovesti u vezu s nekim drugim distribucijama (npr. dvoparametarska eksponencijalna kada je c = 1, dvoparametarska Rayleigh-ova kada je c = 2, itd.). Problem procjene parametara promatrali smo kroz 5 metoda: metode momenata, modificirane metode momenata, metode maksimalne vjerodostojnosti, modificirane metode maksimalne vjerodostojnosti te metode kvantila odnosno najmanje udaljenosti kvantila. Na samom kraju rada smo kroz simulacije uspoređivali asimptotska svojstva procjenitelja. Metodom momenata, metodom maksimalne vjerodostojnosti i metodom minimalne udaljenosti kvantila smo u programskom paketu R procijenili parametre dvoparametarske Weibullove distribucije.
Abstract (english)
Weibbull’s distribution is frequently used in theory of reliability and in theory of life expectancy as a mathematical model as well as in pharmacology, biology, electrical engineering etc. The main aim of this degree essay is the estimate parameters of Weibull distribution. In order to analyse this problem it is important to point out general facts about this distribution and it’s use. Weibull’s distribution for different values of the parameters c takes different forms and can be related to some other distributions (for example two- parameter exponential when c = 1, two-parameter Rayleigh’s when c = 2, etc.). The problem of the parameters and their estimation was analysed in five methods: moment estimation, modified moment estimation, maximum likelihood estimation, modified maximum likelihood estimation and method of quantile respectively minimum quantile distance estimation. Eventually we have compared asymptotic characteristics of estimators through simulation. With these three methods- method of moments, maximum likelihood estimation and method of minimum quantile distance we have estimated the parameters of two - parameter Weibull’s distribution in program package R.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:919735
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2016-11-04 06:52:01