## THERMAL SCIENCE

International Scientific Journal

### SOME IMPORTANT DETAILS ON RICHARD GROWTH MODEL

**ABSTRACT**

The distribution of the data is very important in all of the parametric methods used in the applied statistics. More clearly, if the experimental data fit well to the theoretical distribution, the results will be more efficient in parametric methods. The adaptability of experimental data to a theoretical distribution depends on the flexibility of the theoretical distribution used. If the flexibility of the theoretical distribution is sufficient, it can be used easily for experimental data. Most of the theoretical distributions have shape and location parameters. However, these two parameters are not always sufficient for the distribution to adapt to the experimental data. Therefore, theoretical distributions with high flexibility in parametric methods are needed. Obtaining the new theoretical distributions that provide this feature is important for the literature. In this study, a new probability distribution has been obtained via Richard link function which has been high flexibility. In the introduction, important information is given related to growth models and Richard growth curve. Later, some details about the Richard distribution and wrapped distribution have been given.

**KEYWORDS**

PAPER SUBMITTED: 2019-01-08

PAPER REVISED: 2019-06-19

PAPER ACCEPTED: 2019-07-25

PUBLISHED ONLINE: 2019-09-15

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Supplement 6**, PAGES [S1901 - S1908]

- Gregorczyk A., Richards Plant Growth Model. J. Agronomy and Crop Science, 181 (1998), pp. 243-247.
- Bertalanffy, Von L., Untersuchungen über die Gesetzlichkeit des Wachstums. I. Allgemeine Grundlagen der Theorie mathematische und physiologische Gesetzlichkeiten des Wachstums bei Wassertieren. Arch. Entwicklungsmech, 131 (1934), pp. 613-652.
- Richard F. J., A Flexible Growth Function for Emprical Use. J. Exp. Bot., 10 (1959), pp. 290-300.
- Gurcan M., Oner Y., On The Existence Problem in Logistic Regression Models By Alternative Form. Adv.& Appl. in Stat., (2001), pp. 165-174.
- Gurcan M. and Colak C., The Polynomial Approach in Growth Curves. Turkiye Klinikleri Bioistatistik Dergisi, 1, 2 (2009), pp. 54-62.
- Gurcan M., Colak C. and Orman M. N., Bernstein Polynomial Approach Against to Some Frequently Used Growth Curve Models on Animal Data. Pak. J. Statist, 26 (2010), pp. 509-516.
- Gurcan M. and Colak C. Generalization of Korovkin Type Approximation by Appropriate Random Variables & Moments and an Application in Medicine. Pak. J. Statist., 27 (2011), pp. 283-297.
- Tachev G., Voronovskaja's Theorem Revisited. Journal of Mathematical Analysis and Applications, 343 (2008), pp. 399-404.
- Gonska H., Tachev G., A Quantitative Variant of Voronovskaja's Theorem. Results in Mathematics, 53 (2009), pp. 287-294.
- Albert A., Anderson J. A., On the Existence of Maximum Likelihood Estimates in Logistic Regression Models. Biometrica, 71 (1984), 1, 1-10.
- Delgado J. and Pena J.M., A Linear Complexity Algorithm for the Bernstein Basis. IEEE Int. Conf. on Geometric Modeling and Graphics (GMAG), 3 (2003), pp. 162-167.
- Oner Y., Gurcan M. and Halisdemir N. On Continuous Deformation of Richards Family. International Journal of Pure and Applied Mathematics, (2005), pp. 375-377.
- Tachev G., Approximation of Bounded Continuous Functions by Linear Combinations of Phillips Operators. Demonstratio Mathematica, 4 (2014).
- Horowitz J. L., Mammen E., Nonparametric Estimation of an Additive Model with a Link Function. The Annals of Statistics, 32 (2004), pp. 2412-2443.
- Tachev G., The Distance between Bezier Curve and its Control Polygon. Jubilee Collection of Papers Dedicated to the 60th Anniversary of Prof. Mihail M. Konstantinov, (2013).
- Tachev G., On the second moment of rational Bernstein functions. Journal of Computational Analysis and Applications, 12 (2010), pp. 471-479.
- Tachev G., Voronovskaja Theorem for Schoenberg operatör. Mathematical Inequalities and Applications (MIA), 15 (2012), pp. 49-59.
- Tachev G., New Estimates in Voronovskaja's theorem. Numerical Algorithms, 59 (2012), pp. 119-129.