IDEAS home Printed from https://ideas.repec.org/a/eee/intfor/v37y2021i3p1192-1211.html
   My bibliography  Save this article

Discrete Gompertz equation and model selection between Gompertz and logistic models

Author

Listed:
  • Satoh, Daisuke

Abstract

A discrete Gompertz model and model selection between the Gompertz and logistic models are proposed. The proposed method utilizes the difference between the regression equations for the proposed and the discrete logistic models. The difference is whether the log of both sides is taken or not. The proposed discrete model has higher goodness-of-fit for actual data than the non-homogeneous Poisson process Gompertz model that is commonly used in software reliability engineering. The proposed model selection method is simpler than an existing method based on the mean relative squared error, because the proposed method requires only the correlation coefficients between variables on regression equations for both discrete Gompertz and logistic models. It yields absolutely correct selection when pseudo-data are on exact solutions of the Gompertz and logistic models. Also, it yields correct results earlier than the existing model selection for actual data.

Suggested Citation

  • Satoh, Daisuke, 2021. "Discrete Gompertz equation and model selection between Gompertz and logistic models," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1192-1211.
    • Handle: RePEc:eee:intfor:v:37:y:2021:i:3:p:1192-1211
    DOI: 10.1016/j.ijforecast.2021.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0169207021000054
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijforecast.2021.01.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    2. Nguimkeu, Pierre, 2014. "A simple selection test between the Gompertz and Logistic growth models," Technological Forecasting and Social Change, Elsevier, vol. 88(C), pages 98-105.
    3. Meade, Nigel & Islam, Towhidul, 1995. "Forecasting with growth curves: An empirical comparison," International Journal of Forecasting, Elsevier, vol. 11(2), pages 199-215, June.
    4. Young, Peg & Ord, J. Keith, 1989. "Model selection and estimation for technological growth curves," International Journal of Forecasting, Elsevier, vol. 5(4), pages 501-513.
    5. Chu, Wen-Lin & Wu, Feng-Shang & Kao, Kai-Sheng & Yen, David C., 2009. "Diffusion of mobile telephony: An empirical study in Taiwan," Telecommunications Policy, Elsevier, vol. 33(9), pages 506-520, October.
    6. S. Vieira & R. Hoffmann, 1977. "Comparison of the Logistic and the Gompertz Growth Functions Considering Additive and Multiplicative Error Terms," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(2), pages 143-148, June.
    7. Shigeru Yamada & Yoshinobu Tamura, 2016. "OSS Reliability Measurement and Assessment," Springer Series in Reliability Engineering, Springer, edition 1, number 978-3-319-31818-9, February.
    8. Yamakawa, Peter & Rees, Gareth H. & Manuel Salas, José & Alva, Nikolai, 2013. "The diffusion of mobile telephones: An empirical analysis for Peru," Telecommunications Policy, Elsevier, vol. 37(6), pages 594-606.
    9. Satoh, Daisuke & Uchida, Masato, 2021. "Riccati equation as topology-based model of computer worms and discrete SIR model with constant infectious period," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    10. Gupta, Ruchita & Jain, Karuna, 2012. "Diffusion of mobile telephony in India: An empirical study," Technological Forecasting and Social Change, Elsevier, vol. 79(4), pages 709-715.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jha, Ashutosh & Saha, Debashis, 2020. "“Forecasting and analysing the characteristics of 3G and 4G mobile broadband diffusion in India: A comparative evaluation of Bass, Norton-Bass, Gompertz, and logistic growth models”," Technological Forecasting and Social Change, Elsevier, vol. 152(C).
    2. Thakur Dhakal & Dae-Eun Lim, 2020. "Understanding ICT adoption in SAARC member countries," Letters in Spatial and Resource Sciences, Springer, vol. 13(1), pages 67-80, April.
    3. Tseng, Fang-Mei & Wang, Shenq-Yuan & Hsieh, Chih-Hung & Guo, Aifang, 2014. "An integrated model for analyzing the development of the 4G telecommunications market in Taiwan," Telecommunications Policy, Elsevier, vol. 38(1), pages 14-31.
    4. Avila, Luz Angelica Pirir & Lee, Deok-Joo & Kim, Taegu, 2018. "Diffusion and competitive relationship of mobile telephone service in Guatemala: An empirical analysis," Telecommunications Policy, Elsevier, vol. 42(2), pages 116-126.
    5. Ashutosh Jha & Debashis Saha, 2022. "Mobile Broadband for Inclusive Connectivity: What Deters the High-Capacity Deployment of 4G-LTE Innovation in India?," Information Systems Frontiers, Springer, vol. 24(4), pages 1305-1329, August.
    6. Bacha, Radia & Gasmi, Farid, 2022. "The broadband diffusion process and its determinants in Algeria: A simultaneous estimation," TSE Working Papers 22-1309, Toulouse School of Economics (TSE).
    7. Lee, Chul-Yong & Huh, Sung-Yoon, 2017. "Forecasting the diffusion of renewable electricity considering the impact of policy and oil prices: The case of South Korea," Applied Energy, Elsevier, vol. 197(C), pages 29-39.
    8. Xiaoxia Fu & Ping Zhang & Juzhi Zhang, 2017. "Forecasting and Analyzing Internet Users of China with Lotka–Volterra Model," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-18, February.
    9. Baburin, Vyacheslav & Zemtsov, Stepan, 2014. "Diffussion of ICT-products and "five Russias"," MPRA Paper 68926, University Library of Munich, Germany, revised 10 May 2014.
    10. Wu, Feng-Shang & Chu, Wen-Lin, 2010. "Diffusion models of mobile telephony," Journal of Business Research, Elsevier, vol. 63(5), pages 497-501, May.
    11. Islam, Towhidul & Fiebig, Denzil G. & Meade, Nigel, 2002. "Modelling multinational telecommunications demand with limited data," International Journal of Forecasting, Elsevier, vol. 18(4), pages 605-624.
    12. Ashish Sood & Gareth M. James & Gerard J. Tellis & Ji Zhu, 2012. "Predicting the Path of Technological Innovation: SAW vs. Moore, Bass, Gompertz, and Kryder," Marketing Science, INFORMS, vol. 31(6), pages 964-979, November.
    13. Nigel Meade & Towhidul Islam, 1998. "Technological Forecasting---Model Selection, Model Stability, and Combining Models," Management Science, INFORMS, vol. 44(8), pages 1115-1130, August.
    14. Al-Alawi, Baha M. & Bradley, Thomas H., 2013. "Review of hybrid, plug-in hybrid, and electric vehicle market modeling Studies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 21(C), pages 190-203.
    15. Sang-Gun Lee & Eui-bang Lee & Chang-Gyu Yang, 2014. "Strategies for ICT product diffusion: the case of the Korean mobile communications market," Service Business, Springer;Pan-Pacific Business Association, vol. 8(1), pages 65-81, March.
    16. Snellman, Jussi & Vesala, Jukka, 1999. "Forecasting the elecronification of payments with learning curves : The case of Finland," Research Discussion Papers 8/1999, Bank of Finland.
    17. Jongsu Lee & Minkyu Lee, 2009. "Analysis on the growth of telecommunication services: a global comparison of diffusion patterns," Applied Economics, Taylor & Francis Journals, vol. 41(24), pages 3143-3150.
    18. Chang, Byeong-Yun & Li, Xu & Kim, Yun Bae, 2014. "Performance comparison of two diffusion models in a saturated mobile phone market," Technological Forecasting and Social Change, Elsevier, vol. 86(C), pages 41-48.
    19. Eryarsoy, Enes & Delen, Dursun & Davazdahemami, Behrooz & Topuz, Kazim, 2021. "A novel diffusion-based model for estimating cases, and fatalities in epidemics: The case of COVID-19," Journal of Business Research, Elsevier, vol. 124(C), pages 163-178.
    20. Dewenter, Ralf & Kruse, Jörn, 2011. "Calling party pays or receiving party pays? The diffusion of mobile telephony with endogenous regulation," Information Economics and Policy, Elsevier, vol. 23(1), pages 107-117, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:intfor:v:37:y:2021:i:3:p:1192-1211. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijforecast .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.