IDEAS home Printed from https://ideas.repec.org/a/wsi/ijitmx/v16y2019i07ns0219877019500500.html
   My bibliography  Save this article

Using Weibull Distribution for Modeling Bimodal Diffusion Curves: A Naive Framework to Study Product Life Cycle

Author

Listed:
  • Adarsh Anand

    (Department of Operational Research, University of Delhi, Delhi-110007, India)

  • Richie Aggarwal

    (Department of Operational Research, University of Delhi, Delhi-110007, India)

  • Ompal Singh

    (Department of Operational Research, University of Delhi, Delhi-110007, India)

Abstract

With the purpose of understanding differing shapes of sales curve (unimodal and bimodal) this paper discusses a naive way for viewing the diffusion process for consumer durables. In this paper, a step functional model involving two-step Weibull distribution with four unknown parameters is characterized wherein the shape of the density function of the models depends upon the shape and scale parameter of Weibull distribution. Empirical analysis on real life sales datasets indicates that the Weibull step function model is more flexible and fits better than the other models.

Suggested Citation

  • Adarsh Anand & Richie Aggarwal & Ompal Singh, 2019. "Using Weibull Distribution for Modeling Bimodal Diffusion Curves: A Naive Framework to Study Product Life Cycle," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-17, November.
    • Handle: RePEc:wsi:ijitmx:v:16:y:2019:i:07:n:s0219877019500500
    DOI: 10.1142/S0219877019500500
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219877019500500
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219877019500500?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. Chia-Liang Hung & Jerome Chih-Lung Chou, 2014. "Examining The Cultural Moderation On The Acceptance Of Mobile Commerce," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-19.
    2. John A. Norton & Frank M. Bass, 1987. "A Diffusion Theory Model of Adoption and Substitution for Successive Generations of High-Technology Products," Management Science, INFORMS, vol. 33(9), pages 1069-1086, September.
    3. Adarsh Anand & Ompal Singh & Richie Aggarwal & Deepti Aggrawal, 2016. "Diffusion Modeling Based on Customer's Review and Product Satisfaction," International Journal of Technology Diffusion (IJTD), IGI Global, vol. 7(1), pages 20-31, January.
    4. Deepti Aggrawal & Ompal Singh & Adarsh Anand & Mohini Agarwal, 2014. "Optimal Introduction Timing Policy for a Successive Generational Product," International Journal of Technology Diffusion (IJTD), IGI Global, vol. 5(1), pages 1-16, January.
    5. Christopher J. Easingwood & Vijay Mahajan & Eitan Muller, 1983. "A Nonuniform Influence Innovation Diffusion Model of New Product Acceptance," Marketing Science, INFORMS, vol. 2(3), pages 273-295.
    6. William E. Cox & Jr., 1967. "Product Life Cycles as Marketing Models," The Journal of Business, University of Chicago Press, vol. 40, pages 375-375.
    7. Vijay Mahajan & Robert A. Peterson, 1978. "Innovation Diffusion in a Dynamic Potential Adopter Population," Management Science, INFORMS, vol. 24(15), pages 1589-1597, November.
    8. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    9. Christophe Van den Bulte & Yogesh V. Joshi, 2007. "New Product Diffusion with Influentials and Imitators," Marketing Science, INFORMS, vol. 26(3), pages 400-421, 05-06.
    10. Amnon Frenkel & Shlomo Maital & Eran Leck & Emil Israel, 2015. "Demand-Driven Innovation: An Integrative Systems-Based Review of the Literature," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 1-31.
    11. Christophe Van den Bulte & Gary L. Lilien, 1997. "Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models," Marketing Science, INFORMS, vol. 16(4), pages 338-353.
    12. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    13. Rink, David R. & Swan, John E., 1979. "Product life cycle research: A literature review," Journal of Business Research, Elsevier, vol. 7(3), pages 219-242, September.
    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. Peres, Renana & Muller, Eitan & Mahajan, Vijay, 2010. "Innovation diffusion and new product growth models: A critical review and research directions," International Journal of Research in Marketing, Elsevier, vol. 27(2), pages 91-106.
    2. Velickovic, Stevan & Radojicic, Valentina & Bakmaz, Bojan, 2016. "The effect of service rollout on demand forecasting: The application of modified Bass model to the step growing markets," Technological Forecasting and Social Change, Elsevier, vol. 107(C), pages 130-140.
    3. Yair Orbach & Gila Fruchter, 2014. "Predicting product life cycle patterns," Marketing Letters, Springer, vol. 25(1), pages 37-52, March.
    4. Singhal, Shakshi & Anand, Adarsh & Singh, Ompal, 2020. "Studying dynamic market size-based adoption modeling & product diffusion under stochastic environment," Technological Forecasting and Social Change, Elsevier, vol. 161(C).
    5. Abedi, Vahideh Sadat, 2019. "Compartmental diffusion modeling: Describing customer heterogeneity & communication network to support decisions for new product introductions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    6. Franses, Philip Hans, 2021. "Modeling box office revenues of motion picturesâś°," Technological Forecasting and Social Change, Elsevier, vol. 169(C).
    7. Benson Tsz Kin Leung, 2022. "Innovation Diffusion among Case-based Decision-makers," Papers 2203.05785, arXiv.org, revised Jan 2023.
    8. Chumnumpan, Pattarin & Shi, Xiaohui, 2019. "Understanding new products’ market performance using Google Trends," Australasian marketing journal, Elsevier, vol. 27(2), pages 91-103.
    9. Olivier Toubia & Jacob Goldenberg & Rosanna Garcia, 2014. "Improving Penetration Forecasts Using Social Interactions Data," Management Science, INFORMS, vol. 60(12), pages 3049-3066, December.
    10. Shi, Xiaohui & Li, Feng & Bigdeli, Ali Ziaee, 2016. "An examination of NPD models in the context of business models," Journal of Business Research, Elsevier, vol. 69(7), pages 2541-2550.
    11. Yoon Seong Kim & Eun Jin Han & So Young Sohn, 2017. "Demand Forecasting for Heavy-Duty Diesel Engines Considering Emission Regulations," Sustainability, MDPI, vol. 9(2), pages 1-16, January.
    12. Giovanni Modanese, 2023. "The Network Bass Model with Behavioral Compartments," Stats, MDPI, vol. 6(2), pages 1-13, March.
    13. Sanjeev Dewan & Dale Ganley & Kenneth L. Kraemer, 2010. "Complementarities in the Diffusion of Personal Computers and the Internet: Implications for the Global Digital Divide," Information Systems Research, INFORMS, vol. 21(4), pages 925-940, December.
    14. Jun, Duk B. & Kim, Seon K. & Park, Yoon S. & Park, Myoung H. & Wilson, Amy R., 2002. "Forecasting telecommunication service subscribers in substitutive and competitive environments," International Journal of Forecasting, Elsevier, vol. 18(4), pages 561-581.
    15. Krishnan, Trichy V. & Feng, Shanfei & Jain, Dipak C., 2023. "Peak sales time prediction in new product sales: Can a product manager rely on it?," Journal of Business Research, Elsevier, vol. 165(C).
    16. Guo, Xuezhen, 2014. "A novel Bass-type model for product life cycle quantification using aggregate market data," International Journal of Production Economics, Elsevier, vol. 158(C), pages 208-216.
    17. Barnes, Belinda & Southwell, Darren & Bruce, Sarah & Woodhams, Felicity, 2014. "Additionality, common practice and incentive schemes for the uptake of innovations," Technological Forecasting and Social Change, Elsevier, vol. 89(C), pages 43-61.
    18. Saurabh Panwar & P. K. Kapur & Ompal Singh, 2019. "Modeling Technological Substitution by Incorporating Dynamic Adoption Rate," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-24, February.
    19. Saurabh Panwar & P. K. Kapur & Ompal Singh, 2021. "Technology diffusion model with change in adoption rate and repeat purchases: a case of consumer balking," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(1), pages 29-36, February.
    20. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.

    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:wsi:ijitmx:v:16:y:2019:i:07:n:s0219877019500500. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijitm/ijitm.shtml .

    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.