| Title | Procjena parametara Weibullove distribucije |
| Author | Ana 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. |
| Keywords | Weibull distribution standard Weibull distribution density function distribution function parameter estimation methods of parameter estimation. |
| Parallel title (English) | Parameter Estimation for Weibull Distribution |
| Committee Members | Nenad Šuvak (committee chairperson)
Mirta Benšić (committee member)
Dragana Jankov Maširević (committee member)
|
| Granter | Josip Juraj Strossmayer University of Osijek
Department of Mathematics |
| Lower level organizational units | Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group |
| Place | Osijek |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
|
| Study programme type | university |
| Study level | graduate |
| Study programme | Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics |
| Study specialization | Financial and Statistical Mathematics |
| Academic title abbreviation | mag.math. |
| Genre | master's thesis |
| Language | Croatian |
| Defense date | 2016-10-28 |
| 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 type | text |
| Access condition | Open access |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:126:919735 |
