Estimates of parameters for stochastic logistic growth laws through the maximum likelihood and the L1 distance procedures
| Author | Affiliation | |
|---|---|---|
LT |
| Date |
|---|
2005 |
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.