A generalization of the Gompertz diffusion model: Statistical inference and application
- Autores: R. Gutiérrez, Ahmed Nafidi, Ramón Gutiérrez Sánchez
- Localización: Ninth international conference Zaragoza-Pau on applied mathematics and statistics: Jaca (Spain). September 19-21, 2005 / coord. por Monique Madaune-Tort, 2006, ISBN 84-7733-871-X, págs. 273-280
- Idioma: inglés
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Resumen
The aim of this work is to study a non-homogenous extension of the Gompertz diffusion process (cf. [1], [8]), based on the fact that only the deceleration factor in the drift is a time-dependent function (this version can be considered as a Gompertz diffusion with exogenous factors). A particular case of this model has been considered (cf. [4]) in the study of the first passage time problem in the non-homogeneous diffusion process.
The proposed extended non-homogeneous model is studied by the methodology based on Kolmogorov equations, whereas in [1, 8], the homogeneous process is studied by a methodology using Ito¿s equations. Firstly, we obtain the probability density function (p.d.f.) of the process and its trend functions (non conditional and conditional). Then, the statistical inference in the model is achieved, estimating the parameters by the maximum likelihood method using discrete sampling, and obtaining the distributions of the resulting estimators and the confidence intervals of the parameters. Finally, the proposed model is applied to real data for electricity consumption in Morocco
