Linking the Researchers, Developing the Innovations Manuscripts submittal opens till 15th August, 2017. Please submit your papers at or

  • Volume 2016

    A Note on Some Growth Curves Arising from Box Cox Transformation
    (International Journal of Engineering Works)

    Vol. 3, Issue 6, PP. 47-51, June 2016
    Keywords: Sigmoidal function, Step function, Hausdorff distance, Box Cox transformation, Lag time

    Download PDF


    Mathematical models of growth have been developed a long period of time. Estimating the lag time in the growth process is a practically important problem. In this note we provide estimates for the one–sided Hausdorff approximation () of the shifted step–function by sigmoidal function arising from Box–Cox transformation. We present a software module (intellectual property) within the programming environment of  CAS Mathematica for analysis of growth curves. Numerical examples, illustrating our results are given, too.


    Nikolay Kyurkchiev,, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria

       Anton Iliev,, Faculty of Mathematics and Informatics, Paisii Hilendarski University of Plovdiv, 24 Tsar Assen Str., 4000 Plovdiv, Bulgaria

    Full Text


    Nikolay Kyurkchiev and Anton Iliev, "A Note on Some Growth Curves Arising from Box–Cox Transformation" International Journal of Engineering Works, Vol. 3, Issue 6, PP. 47-51, June 2016. 



    [1]     O. Garcia,  Unifying sigmoid univariate growth equations, Forest Biometry, Modelling and Information Sciences 1 (2005) 63–68

    [2]     O. Garcia,  Visualization of a general family of growth functions and probability distributions - The Growth–curve Explorer, Environmental Modelling and Software 23 (2008) 1474–1475

    [3]     G. Box, D. Cox,  An analysis of transformations, Journal of the Royal Statistical Society, B 26 (1964) 211–252

    [4]     G. Seber, C. Wild,  Nonlinear Regression, Wiley–Interscience, New York (2003)

    [5]     S. Shoffner, S. Schnell,  Estimation of the lag time in a subsequent monomer addition model for fibrill elongation, bioRxiv The preprint server for biology, (2015) 1–8,  doi:10.1101/034900

    [6]     P. Arosio, T. P. J. Knowles, S. Linse,  On the lag phase in amyloid fibril formation, Physical Chemistry Chemical Physics 17 (2015) 7606–7618,  doi:10.1039/C4CP05563B

    [7]     R. Anguelov, S. Markov, Hausdorff Continuous Interval Functions and Approximations, In: M. Nehmeier et al. (Eds), Scientific Computing, Computer Arithmetic, and Validated Numerics, 16th International Symposium, Springer, SCAN 2014, LNCS 9553 (2016) 3–13, doi:10.1007/978-3-319-31769-4

    [8]     N. Kyurkchiev, A. Andreev,  Approximation and antenna and filter synthesis: Some moduli in programming environment Mathematica, Saarbrucken, LAP LAMBERT Academic Publishing (2014), ISBN 978–3–659–53322–8.

    [9]     F. Hausdorff,  Set Theory (2 ed.) (Chelsea Publ., New York, (1962 [1957]) (Republished by AMS-Chelsea 2005), ISBN: 978–0–821–83835–8.

    [10]  B. Sendov,  Hausdorff Approximations (Kluwer, Boston, 1990), doi:10.1007/978-94-009-0673-0

    [11]  N. Kyurkchiev,  A note on the new geometric representation for the parameters in the fibril elongation process, Compt. rend. Acad. bulg. Sci. (2016) (accepted).

    [12]  N. Kyurkchiev,  On the Approximation of the step function by some cumulative distribution functions, Compt. rend. Acad. bulg. Sci. 68(12) (2015) 1475–1482.

    [13]  N. Kyurkchiev, S. Markov,  On the Hausdorff distance between the Heaviside step function and Verhulst logistic function, J. Math. Chem. 54(1) (2016) 109–119,  doi:10.1007/S10910-015-0552-0

    [14]  N. Kyurkchiev, S. Markov,  Sigmoidal functions: some computational and modelling aspects, Biomath Communications 1(2) (2014) 30–48,  doi:10.11145/j.bmc.2015.03.081

    [15]  A. Iliev, N. Kyurkchiev, S. Markov,  On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions, BIOMATH 4(2) (2015) 1510101, doi:10.11145/j.biomath.2015.10.101

    [16]  A. Iliev, N. Kyurkchiev, S. Markov,  On the Approximation of the step function by some sigmoid functions, Mathematics and Computers in Simulation (2015), doi:10.1016/j.matcom.2015.11.005

    [17]  N. Kyurkchiev, S. Markov,  On the approximation of the generalized cut function of degree  by smooth sigmoid functions, Serdica J. Computing 9(1) (2015) 101–112.

    [18]  N. Kyurkchiev, S. Markov,  Sigmoid functions: Some Approximation and Modelling Aspects, Saarbrucken, LAP LAMBERT Academic Publishing (2015), ISBN 978–3–659–76045–7.

    [19]  V. Kyurkchiev, N. Kyurkchiev,  On the Approximation of the Step function by Raised-Cosine and Laplace Cumulative Distribution Functions, European International Journal of Science and Technology 4(9) (2016) 75–84.

    [20]  N. Kyurkchiev, S. Markov, A. Iliev,  A note on the Schnute growth model, International Journal of Engineering Research and Development 12 (6) (2016) 47–54.

    [21]  N. Kyurkchiev, A. Iliev,  On some growth curve modeling: approximation theory and applications, International Journal of Trends in Research and Development 3 (3) (2016) 466–471.