A Generalized Logistic Function and its Applications

• Autorzy: Grzegorz Rządkowski , Lidia Sobczak
• Języki publikacji: EN

Abstrakty

EN

In the present article, we deal with a generalization of the logistic function. Starting from the Riccati differential equation with constant coefficients, we find its analytical form and describe basic properties. Then we use the generalized logistic function for modeling some economic phenomena. (original abstract)

Słowa kluczowe

EN

S-Curve; Logistic models; Time-series

PL

Krzywa S; Modele logistyczne; Szeregi czasowe

• Czasopismo: Foundations of Management
• Rocznik: 2020
• Tom: 12
• Numer: nr 1
• Strony: 85--92

Twórcy

autor

Grzegorz Rządkowski

• Warsaw University of Technology, Poland

autor

Lidia Sobczak

• Warsaw University of Technology, Poland

Bibliografia

• Franssens, G.R., 2007. Functions with Derivatives Given by Polynomials in the Function Itself or a Related Function. Analysis Mathematica, 33, pp.17-36. DOI: https://doi.org/ 10.1007/s10474-007-0102-5.
• Graham, R.L., Knuth D.E.,Patashnik O., 1994. Concrete Mathematics: A Foundation for Computer Science, Reading, Addison - Wesley.
• Harrison, J., 2011. Interview with Paul Nunes and Tim Breene, Authors of Jumping the S-curve. Strategic Direction, 9, pp.32-34.
• Johnson, W., 2012. Throw Your Life a Curve. Harvard Business Review, <https://hbr.org/2012/ 09/throw-your-life-a-curve> [access 31.05.2019]
• Junseok, H., Youngsang, Ch., Nguyen, V.L., 2009. Investigation of Factors Affecting the Diffusion of Mobile Telephone Services: An Empirical Analysis for Vietnam. Telecommunications Policy, 33, pp.534-543.
• Kucharavy, D., De Guio, R., 2011, Application of Logistic Growth Curve. Procedia Engineering, 9, pp.559-572.
• Kucharavy, D., De Guio, R., 2015, Application of Logistic Growth Curve. Procedia Engineering, 131, pp.280-290.
• Meade, N., Islam, T., 2006. Modelling and Forecasting the Diffusion of Innovation - A 25-year Review. International Journal of Forecasting, 22, pp.519-545.
• Michalakelis, C., Sphicopoulos, T., 2012. A Population Dependent Diffusion Model with a Stochastic Extension. International Journal of Forecasting, 28, pp.587-606.
• Modis, T., 2007. From my perspective. Strengths and weaknesses of S-curves. Technological Forecasting & Social Change, 74, pp.866-872.
• Nazarko, J., red., 2018. Prognozowanie w zarządzaniu przedsiębiorstwem (Forecasting in Business Management), Cz. IV (Vol. 4), Prognozowanie na podstawie modeli trendu (Forecasting Based on Trend Models). Białystok: Oficyna Wydawnicza Politechniki.
• Qian, L., Soopramanien, D., 2014. Using Diffusion Models to Forecast Market Size in Emerging Markets with Applications to the Chinese Car Market. Journal of Business Research, 67, pp.1226-1232.
• Rządkowski, G., 2006. Eulerian Numbers and Riccati's Differential Equation. In: T.E., Simos, 2006. Proceedings of ICNAAM 2006, Wiley-VCH Verlag, pp.291-294.
• Rządkowski, G., 2008. Derivatives and Eulerian Numbers. American Mathematical Monthly, 115, pp.458-460.
• Rządkowski, G., Głażewska, I., Sawińska, K., 2014. Logistic Function as a Tool of Planning. Foundations of Management, Vol. 6, No. 1, pp.57-70, DOI: 10.1515/fman-2015-0004.
• Słupiński, M., Kucharavy, D., 2011. Wykorzystanie krzywej wzrostu logistycznego (Krzywa S) do przygotowania analizy foresight w projekcie "Quality of life" (The use of the logistic growth curve (S curve) to prepare a foresight analysis in the project "Quality of life") <http://qualityoflife .ue.wroc.pl/projekt/p/Wyniki_projektu/Krzywa_ S/Krzywa-S.pdf> [access 31.05.2019]
• Wu, F.S., Chu, W.L., 2010. Diffusion Models of Mobile Telephony. Journal of Business Research, 63, pp.497-501.
• Yamakawa, P., Rees, G.H., Salas, J.M., Alva, N., 2013. The Diffusion of Mobile Telephones: An Empirical Analysis for Peru. Telecommunications Policy, 37, pp.594-606

Identyfikatory

DOI

10.2478/fman-2020-0007