On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve
By:
Open Access
|Mar 2013References
- Atieg, A. and Watson, G.A. (2004). Use of lpnorms in fitting curves and surfaces to data, The ANZIAM Journal 45(E): C187-C200.
- Bailey, N.T.J. (1975). The Mathematical Theory of InfectiousDiseases and Its Applications, Griffin, London.
- Bailey, N.T.J. (1957). The Mathematical Theory of Epidemics, Griffin, London.
- Bass, F.M. (1969). A new product growth model for consumer durables, Management Science 15(5): 215-227.
- Bates, D.M. andWatts, D.G. (1988). Nonlinear Regression Analysisand Its Applications, Wiley, New York, NY.
- Björck, Å. (1996). Numerical Methods for Least Squares Problems, SIAM, Philadelphia, PA.
- Demidenko, E.Z. (2008). Criteria for unconstrained global optimization, Journal of Optimization Theory and Applications136(3): 375-395.
- Demidenko, E.Z. (2006). Criteria for global minimum of sum of squares in nonlinear regression, Computational Statistics& Data Analysis 51(3): 1739-1753.
- Demidenko, E.Z. (1996). On the existence of the least squares estimate in nonlinear growth curve models of exponential type, Communications in Statistics-Theory and Methods25(1): 159-182.
- Dennis, J.E. and Schnabel, R.B. (1996). Numerical Methodsfor Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia, PA.
- Gill, P.E., Murray, W. and Wright, M.H. (1981). Practical Optimization, Academic Press, London.
- Gonin, R. and Money, A.H. (1989). Nonlinear Lp-Norm Estimation, Marcel Dekker, New York, NY.
- Hadeler, K.P., Jukić, D. and Sabo, K. (2007). Least squares problems for Michaelis Menten kinetics, MathematicalMethods in the Applied Sciences 30(11): 1231-1241.
- Jukić, D. (2011). Total least squares fitting Bass diffusion model, Mathematical and Computer Modelling 53(9-10): 1756-1770.
- Jukić, D. (2013) On nonlinear weighted least squares estimation of Bass diffusion model, Applied Mathematics and Computation, (accepted).
- Jukić, D. and Marković, D. (2010). On nonlinear weighted errors-in-variables parameter estimation problem in the three-parameter Weibull model, Applied Mathematics andComputation 215(10): 3599-3609.
- Jukić, D. (2009). On the existence of the best discrete approximation in lpnorm by reciprocals of real polynomials, Journal of Approximation Theory 156(2): 212-222.
- Jukić, D., Benšić, M. and Scitovski, R. (2008). On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution, ComputationalStatistics & Data Analysis 52(9): 4502-4511.
- Jukić, D., Kralik, G. and Scitovski, R. (2004). Least squares fitting Gompertz curve, Journal of Computational and AppliedMathematics 169(2): 359-375.
- Mahajan, V. Muller, E. and Wind, Y. (Eds.). (2000). New-Product Diffusion Models, Kluwer Academic Publishers, London.
- Mahajan, V., Mason, C.H. and Srinivasan, V. (1986). An evaluation of estimation procedures for new product diffusion models, in V. Mahajan and Y. Wind (Eds.), InnovationDiffusion Models of New Product Acceptance, Ballinger Publishing Company, Cambridge, pp. 203-232.
- Mahajan, V. and Sharma, S. (1986). A simple algebraic estimation procedure for innovation diffusion models of new product acceptance, Technological Forecasting andSocial Change 30(4): 331-346.
- Marković, D. and Jukić, D. (2010). On nonlinear weighted total least squares parameter estimation problem for the three-parameter Weibull density, Applied MathematicalModelling 34(7): 1839-1848.
- Marković, D., Jukić, D. and Benšić, M. (2009). Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start, Journalof Computational and Applied Mathematics 228(1): 304-312.
- Rogers, E.M. (1962). Diffusion of Innovations, The Free Press, New York, NY.
- Ross, G.J.S. (1990). Nonlinear Estimation, Springer, New York, NY.
- Schmittlein, D. and Mahajan, V. (1982). Maximum likelihood estimation for an innovation diffusion model of new product acceptance, Marketing Science 1(1): 57-78.
- Scitovski, R. and Meler, M. (2002). Solving parameter estimation problem in new product diffusion models, AppliedMathematics and Computation 127(1): 45-63.
- Seber, G.A.F. and Wild, C.J. (1989). Nonlinear Regression, Wiley, New York, NY.
- Srinivasan, V. and Mason, C.H. (1986). Nonlinear least squares estimation of new product diffusion models, MarketingScience 5(2): 169-178.
Language: English
Page range: 145 - 155
Published on: Mar 26, 2013
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Related subjects:
© 2013 Darija Marković, Dragan Jukić, published by University of Zielona Góra
This work is licensed under the Creative Commons License.