Model selection among growth curve models that have the same number of parameters

References

• Aggrey, S. (2002). Comparison of three nonlinear and spline regression models for describing chicken growth curves. Poultry Science, 81, 1782–17. doi:10.1093/ps/81.12.1782
   PubMed Web of Science ®Google Scholar
• Bagchi, K. (1998). A model –Based study of CASE adoption and diffusion, in advanced computer system design (261–280). In K. B. Georege, W. Zobrist, & K. Trivedi eds. chap. 13. Amsterdam: Gordon and Breach Science Publishers.
   Google Scholar
• Bass, F. M. (1969). A new product growth for model consumer durables. Management Science, 15, 215–227. doi:10.1287/mnsc.15.5.215
   Web of Science ®Google Scholar
• Bemmaor, A. C. (1992). Modeling the diffusion of new durable goods: Word-of-month effect versus consumer heterogeneity. In G. L. L. G. Laurent & B. Pras Eds., Research traditions in marketing. (Vol. 5, 201–223). chap. 6, Springer. Dordrecht: International Series in Quantiative Marketing.
   Google Scholar
• Chu, W. L., Wu, F. S., Kao, K. S., & Yen, D. C. (2009). Diffusion of mobile telephony: An empirical study in Taiwan. Telecommunications Policy, 33, 506–520. doi:10.1016/j.telpol.2009.07.003
   Web of Science ®Google Scholar
• Çinlar, E. (1975). Introduction to stochastic process. Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Franses, P. H. (1994a). Fitting a Gompertz curve. Journal of the Operational Reasearch Society, 45, 109–113. doi:10.1057/jors.1994.11
   Web of Science ®Google Scholar
• Franses, P. H. (1994b). A method to select between Gompertz and logistic trend curves. Technological Forecasting & Social Change, 46, 45–49. doi:10.1016/0040-1625(94)90016-7
   Web of Science ®Google Scholar
• Gregg, J., Hossel, C., & Richardson, J. (1964). Mathematical trend curves, an aid to forecasting. In Monograph No.1, Mathematical trend curves: An aid to forecasting (Vol. 1). Edinburgh: Oliver & Boyd.
   Google Scholar
• Gupta, R., & Jain, K. (2012). Diffusion of mobile telephony in India: An empirical study. Technological Forecasting & Social Change, 79, 709–715. doi:10.1016/j.techfore.2011.08.003
   Web of Science ®Google Scholar
• Guseo, R., & Guidolin, M. (2009). Modelling a dynamic market potential: A class of automata networks for diffusion of innovations. Technological Forecating & Social Change, 76, 806–820. doi:10.1016/j.techfore.2008.10.005
   Web of Science ®Google Scholar
• Hirota, R. (1979). Nonlinear partial difference equations. V. nonlinear equations reducible to linear equations. Journal of the Physical Society of Japan, 46, 312–319. doi:10.1143/JPSJ.46.312
   Web of Science ®Google Scholar
• Hirota, R. (2000). Lecture on discrete equations. Saiensu-sha. in Japanese.
   Google Scholar
• Hirota, R., & Takahashi, D. (2003). Discrete and ultradiscrete systems. Kyoritsu Shuppan. in Japanese.
   Google Scholar
• Knízetová, H., Hyánek, J., Kníze, B., & Roubícek, J. (1991). Analysis of growth curve of fowl. I. chickens. British Poultry Science, 32, 1027–1038. doi:10.1080/00071669108417424
   PubMed Web of Science ®Google Scholar
• Kucharavy, D., & Guio, R. D. (2015). Application of logistic growth curve. Procedia Engineering, 131, 280–290. doi:10.1016/j.proeng.2015.12.390
   Google Scholar
• Lechman, E. (2015). ICT diffusion in developing countries: Towards a new concept of technological takeoff. Switzerland: Springer International Publishing.
   Google Scholar
• Li, T. Y., & Yorke, J. A. (1975). Period three implies chaos. The American Mathematical Monthly, 82, 985–992. doi:10.1080/00029890.1975.11994008
   Web of Science ®Google Scholar
• Mar-Molinero, C. (1980). Tractors in Spain: A logistic analysis. Journal of the Operatinal Resaerch Society, 31, 141–152. doi:10.1057/jors.1980.24
   Web of Science ®Google Scholar
• Martino, J. P. (2003). A review of selected recent advances in technological forecasting. Technological Forecasting & Social Change, 70, 719–733. doi:10.1016/S0040-1625(02)00375-X
   Web of Science ®Google Scholar
• Meade, N. (1984). The use of growth curves in forecasting market developemnt – a review and appraisal. Journal of Forecasting, 3, 429–451. doi:10.1002/for.3980030406
   Web of Science ®Google Scholar
• Meade, N., & Islam, T. (1995). Forecasting with growth curves: An empirical, Internatinal. Journal of Forecasting, 11, 119–215.
   Web of Science ®Google Scholar
• Mitsuhashi, T. (1981). Software quality assurance: Approach to statistical control. JUSE. in Japanese.
   Google Scholar
• Morisita, M. (1965). The fitting of the logistic equation to the rate of increase of population density. Researches on Population Ecology, 7, 52–55. doi:10.1007/BF02518815
   Google Scholar
• Narinc, D., Karaman, E., Firat, M. Z., & Aksoy, T. (2010). Comparison of non-linear growth models to describe the growth in Japanese quail. Journal of Animal and Veterinary Advances, 9, 1961–1966. doi:10.3923/javaa.2010.1961.1966
   Web of Science ®Google Scholar
• Nguimkeu, P. (2014). A simple selection test between the Gompertz and logistic growth models. Technological Forecasting & Social Changes, 88, 98–105. doi:10.1016/j.techfore.2014.06.017
   Web of Science ®Google Scholar
• Roush, W., & Branton, S. (2005). A comparison of fitting growth models with a genetic algorithm and nonlinear regression. Poultry Science, 84, 494–502. doi:10.1093/ps/84.3.494
   PubMed Web of Science ®Google Scholar
• Satoh, D. (2000). A discrete Gompertz equation and a software reliability growth model. IEICE Transactions, E83-D. 1508–1513.
   Google Scholar
• Satoh, D. (2001). A discrete Bass model and its parameter estimation. Journal of the Operations Research Society of Japan, 44, 1–18. doi:10.15807/jorsj.44.1
   Google Scholar
• Satoh, D. (2019). Properties of Gompertz data revealed with non-Gompertz integrable difference equation. Cogent Mathematics & Statistics (to Appear), 6, 1. doi:10.1080/25742558.2019.1596552
   Web of Science ®Google Scholar
• Satoh, D., & Matsumura, R. (2019). Monotonic decrease of upper limit estimated using Gompertz model with data described using logistic model, Japan. Journal of Industrial and Applied Mathematics, 36, 79–96. doi:10.1007/s13160-018-0333-9
   Web of Science ®Google Scholar
• Satoh, D., & Uchida, M. (2010). Computer worm model describing infection via e-mail. Bulletin of the Japan Society for Industrial and Applied Mathematics, 20, 50–53. in Japanese.
   Google Scholar
• Satoh, D., & Yamada, S. (2001). Discrete equations and software reliability growth models, Proceedings of 12th International Symposium on software Reliability Engineering (pp. 176–184). Hong Kong.
   Google Scholar
• Satoh, D., & Yamada, S. (2002). Parameter estimation of discrete logistic curve models for software reliability assessment, Japan. Journal of Industrial and Applied Mathematics, 19, 39–53. doi:10.1007/BF03167447
   Web of Science ®Google Scholar
• Skellam, J. G. (1951). Random dispersal in theoretical populations. Biometrika, 38(1/2 ), 196–218.
   PubMed Web of Science ®Google Scholar
• The World Bank. (2018). Mobile cellular subscriptions per 100 people. Retrieved from http://databank.worldbank.org/data/country/USA/556d8fa6/Population_countries
   Google Scholar
• Ushiki, S. (1982). Central difference scheme and chaos. Physica D. Nonlinear Phenomena, 4, 407–424. doi:10.1016/0167-2789(82)90044-6
   Google Scholar
• Vieira, S., & Hoffmann, R. (1977). Comparison of the logistic and the Gompertz growth functions considering additive and multiplicative error terms. Applied Statistics, 26, 143–148. doi:10.2307/2347021
   Google Scholar
• Yamada, S. (2014). Software reliability modeling fundamentals and applications. Japan: Springer.
   Google Scholar
• Yamada, S., Inoue, S., & Satoh, D. (2002). Statistical data analysis modeling based on difference equations for software reliability assessment. Transactions of the Japan Society for Industrial and Applied Mathematics, 12, 155–168. in Japanese.
   Google Scholar
• Yamada, S., & Tamura, Y. (2016). OSS reliability measurement and assessment. Switzerland: Springer International Publishing.
   Google Scholar
• Yamakawa, P., Rees, G. H., Salas, J. M., & Alva, N. (2013). The diffusion of mobile telephones: An empirical analysis for Peru. Telecommunications Policy, 37, 594–606. doi:10.1016/j.telpol.2012.12.010
   Web of Science ®Google Scholar
• Young, P., & Ord, J. (1989). Model selection and estimation for technology growth curves. International Journal of Forecasting, 5, 501–513. doi:10.1016/0169-2070(89)90005-8
   Web of Science ®Google Scholar