U ovom radu pročavaju se matematički modeli za modeliranje prosječne proizvodnje jaja. Najprije se radi o samim ciljevima proizvodnje jaja, čimbenicima koji utječu na broj jaja koji koka nese te svrsi modeliranja proizvodnje jaja. Zatim se usmjerava na opis Woodovog modela, Compartmental modela i njihovih modifikacija te Adams-Bell modela, njihovu primjenu na primjeru i usporedbu kvalitete modela. Nadalje, prelazi se na karakterizaciju krivulje proizvodnje jaja koristeći višefazni pristup. Opisuju se deifinicije te modeli i njihovi parametri vezani za ovu hipotezu. U zadnjem dijelu rada se obraduju podaci ustupljeni od strane tvrtke Žito d.o.o. nad kojima se vrši statistička analiza i modeliranje pomoću četiri modela: Woodov model, modifikacija Woodovog modela, Compartmental model i modifikacija Compartmental modela. Svaki model u svojoj definiciji uključuje određeni broj parametara koje je potrebno procijeniti. Procjena je radena pomoću Levenberg-Marquardt algoritma. Usporedba modela je radena pomoću grafičkih prikaza, ali i pomoću mjera kvalitete modela kao što su prilagođeni \(\mathbb{R}^{2}\) te Akaike i Bayesov informacijski kriterij. Usporedba temeljena na prilagođenom \(\mathbb{R}^{2}\) , AIC-u i BIC-u je medu ova četiri modela pokazala da je Compartmental model najbolje prilagoden podacima. Medutim, podaci modelirani Compartmental modelom su pokazali velika odstupanja od stvarnih podataka pri kraju procesa proizvodnje, dok se Woodov model pokazao najboljim u tom području.

This thesis studies the mathematical models for modeling the average egg production. First it is about the main goals of egg production, factors that influence the number of eggs produced by a chicken and the purpose of mathematical models for egg production. After that, the study passes to the description of Wood’s model, Compartmental model, their modifications and Adams-Bell model, their application on an example and the goodness of fit of these models. Further on, the thesis passes to characterization of the egg production curve using a multiphasic approach. The definitions connected to this hypotesis are described, along with models used in it and their parameters. The last part of this thesis deals with the data from company Žito d.o.o. which are statistically analysed and four models are used to fit the data: Wood’s model, modified Wood’s model, Compartmental model and modified Compartmental model. Each model in his definition has several parameters and they need to be estimated. The Levenberg-Marquardt algorithm is used to estimate the parameters in each model. The goodness of fit of each model was measured using graphical analysis of the fitted curves and measures for the quality of models such as adjusted \(\mathbb{R}^{2}\), Akaike’s and Bayesian Information criterion. The comparison on the basis of adjusted \(\mathbb{R}^{2}\),AIC and BIC among the four models showed that the Compartmental model had the best fit. Howewer, fitted data using the Compartmental model showed large deviations from the real data at the end of the egg production process, and Wood’s model was the best in that area.