Please use this identifier to cite or link to this item:https://hdl.handle.net/20.500.12259/78227
Type of publication: Straipsnis kituose recenzuojamuose leidiniuose / Article in other peer-reviewed editions (S5)
Field of Science: Matematika / Mathematics (N001)
Author(s): Rupšys, Petras
Title: Estimates of parameters for stochastic logistic growth laws through the maximum likelihood and the L1 distance procedures
Other Title: Stochastinių logistinių augimo modelių parametrų įvertinimas maksimalaus tikėtinumo ir L1 normos metodais
Is part of: Lietuvos statistikos darbai. , T. 42 (2005)
Extent: p. 49-60
Date: 2005
Keywords: Lygtis, stochastinė diferencialinė;Parametras;Įvertinimas;Funkcija, maksimalaus tikėtinumo;L1 norma;Aukštis;Ląstelės, vėžinės;Equation, stochastic differential;Maximum likelihood;L1 norm;Parameter;Estimate;Height;Tumour
Abstract: Darbe vienos populiacijos augimui modeliuoti suformuoti šeši stochastiniai logistiniai augimo modeliai (eksponentinis, Verhulst, Gompertz, Mitscherlich, Bertalanffy, Rikards). Modeliai apibrėžiami paprastąja stochastine diferencialine lygtimi, priklausančia nuo keleto parametrų. Parametrų įvertinimams gauti naudojami maksimalaus tikėtumo ir L1 normos metodai. Darbe pateikiama maksimalaus tikėtinumo funkcija visiems šešiems stochastiniams augimo modeliams. Analizuojant parametrų įvertinimus L1 normos metodu, penkiems stochastiniams modeliams gaunami stacionarinių tankio funkcijų pavidalai.Darbe aptariami du pavyzdžiai: medžių aukštis medyne ir vėžinių ląstelių skaičius pelių smegenyse. Skaičiavimus realizuojame MAPLE aplinkoje
Stochastic logistic type growth models of a single species population have been considered. Six alternative stochastic logistic growth models, the exponential, the Verhulst, the Gompertz, the Mitcherlich, the Bertalanffy, the Richards were used for modeling of the growth process. The objective was working out a procedure on the estimation of parameters for all these stochastic logistic growth models. To estimate parameters the maximum likelihood procedure with the local linearization method was applied. As the second alternative approven for the estimate of parameters the L1 distance procedure was proposed. As an illustrative experience, the actual data to model the height of an individual tree and the EAT in a mouse were used. Numerical experiments use Monte Carlo approach. Numerical approximations of trajectories for the stochastic logistic growth laws were simulated by the Milshtein method. In addition, to test the performance of models: the Akaike's Information Criterion, the L1 norm and the efficiency (R2) were used.The results have been implemented in the symbolic computational language MAPLE
Internet: https://hdl.handle.net/20.500.12259/78227
Affiliation(s): Vytauto Didžiojo universitetas
Žemės ūkio akademija
Appears in Collections:Universiteto mokslo publikacijos / University Research Publications

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