master's thesis
Parameter Estimation for Weibull Distribution

Ana Bulić (2016)
Sveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Zavod za teorijsku matematiku
Katedra za teoriju vjerojatnosti i matematičku statistiku
Metadata
TitleProcjena parametara Weibullove distribucije
AuthorAna Bulić
Mentor(s)Mirta Benšić (thesis advisor)
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.
KeywordsWeibull distribution standard Weibull distribution density function distribution function parameter estimation methods of parameter estimation.
Parallel title (English)Parameter Estimation for Weibull Distribution
Committee MembersNenad Šuvak (committee chairperson)
Mirta Benšić (committee member)
Dragana Jankov Maširević (committee member)
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za teorijsku matematiku
Katedra za teoriju vjerojatnosti i matematičku statistiku
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Study programme typeuniversity
Study levelgraduate
Study programmeMathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Study specializationFinancial and Statistical Mathematics
Academic title abbreviationmag.math.
Genremaster's thesis
Language Croatian
Defense date2016-10-28
Parallel 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.
Parallel keywords (Croatian)Weibullova distribucija standardna Weibullova distribucija funkcija gustoće funkcija distribucije procjena parametara metode za procjenu parametara
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:919735
CommitterMirna Šušak Lukačević