On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

• Autorzy: Darija Marković , Dragan Jukić
• Języki publikacji: EN

Abstrakty

EN

The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the ls norm (1 ≤ s < ∞). One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Several illustrative numerical examples are given to support the theoretical work.

Słowa kluczowe

EN

Bass model; least squares estimate; existence problem; data fitting

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2013
• Tom: 23
• Numer: 1
• Strony: 145-155

Daty

wydano

2013

otrzymano

2012-02-07

poprawiono

2012-08-06

Twórcy

autor

Darija Marković

• Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31 000 Osijek, Croatia,

autor

Dragan Jukić

• Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31 000 Osijek, Croatia,

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Identyfikatory

DOI

10.2478/amcs-2013-0012