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Advanced Techniques in Computing Sciences and Software Engineering pp 1–5Cite as

Bridging Calculus and Statistics: Null - Hypotheses Underlain by Functional Equations

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Abstract

Statistical interpretation of Cauchy functional equation f(x+y)=f(x)+f(y) and related functional equations is suggested as a tool for generating hypotheses regarding the rate of growth: linear, polynomial, or exponential, respectively. Suggested approach is based on analysis of internal dynamics of the phenomenon, rather than on finding best-fitting regression curve. As a teaching tool, it presents an example of investigation of abstract objects based on their properties and demonstrates opportunities for exploration of the real world based on combining mathematical theory with statistical techniques. Testing Malthusian theory of population growth is considered as an example.

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Authors and Affiliations

  1. Hostos Community College of The City University of New York, New York, USA

    Alexander Vaninsky

Authors
  1. Alexander Vaninsky
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Correspondence to Alexander Vaninsky .

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Editors and Affiliations

  1. School of Engineering, University of Bridgeport, University Avenue 221, Bridgeport, 06604, U.S.A.

    Khaled Elleithy

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Vaninsky, A. (2010). Bridging Calculus and Statistics: Null - Hypotheses Underlain by Functional Equations. In: Elleithy, K. (eds) Advanced Techniques in Computing Sciences and Software Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3660-5_1

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  • DOI: https://doi.org/10.1007/978-90-481-3660-5_1

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-3659-9

  • Online ISBN: 978-90-481-3660-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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