Statistical Properties of Alternative Parameterizations of the von Bertalanffy Growth Curve

1986 ◽  
Vol 43 (4) ◽  
pp. 742-747 ◽  
Author(s):  
D. A. Ratkowsky
Keyword(s):  
Linear Model ◽  
Growth Curve ◽  
Asymptotic Properties ◽  
Statistical Properties ◽  
Data Sets ◽  
Von Bertalanffy ◽  
Marine Animals ◽  
Nonlinear Regression Models ◽  
Linear Behavior ◽  
Biological Interpretation

The von Bertalanffy growth curve is often used in fisheries research to describe the relationship between the weight or length of a fish and its age. The equation is also encountered in various other branches of science and applied science in a variety of different parameterizations and names; for example, it is also known as the asymptotic regression equation or the three-parameter exponential equation. Since these equations are all nonlinear regression models, the properties of the least squares estimators of the parameters of these models may be very different from their large-sample properties, where the estimators are unbiased, have the minimum attainable variance, and are normally distributed, the conditions that pertain in a linear model. Different parameterizations will have estimators which approximate the asymptotic properties to varying degrees of closeness. My study of eight parameterizations shows that one of them, a generalization which allows unequal age increments of a parameterization proposed by Schnute and Fournier, is far superior to any of the other models, which include the most commonly used parameterization, in that it exhibits close-to-linear behavior. Two of the three parameters in this model represent the expected mean lengths corresponding to the youngest and oldest ages, respectively, in the sample, and thus have a ready biological interpretation. I discuss why it is important to have a close-to-linear model when one wishes to make comparisons between two or more data sets. Methodology is briefly described for carrying out such comparisons, and some further remarks are made about why biologists should be concerned about the statistical properties of the models that they use. Although most data sets I used for illustration are obtained from marine animals, the conclusions are general and apply to all disciplines which make use of the von Bertalanffy model in whichever guise or form it appears.

Estimation of von Bertalanffy Growth Curve Parameters Using both Length Increment and Age–Length Data

1983 ◽  
Vol 40 (9) ◽  
pp. 1405-1411 ◽  
Author(s):  
G. P. Kirkwood
Keyword(s):  
Growth Curve ◽  
Full Range ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Ratio Test ◽  
Von Bertalanffy ◽  
Predictive Regression ◽  
Length Increment ◽  
Southern Bluefin Tuna ◽  
Length Data

Many fish species cannot be aged directly over their full range of lengths. Therefore, to estimate a growth curve, one often uses length increment data from a mark–recapture experiment, supplemented by whatever age–length data are available. I describe a new method for maximum likelihood estimation of the three von Bertalanffy growth curve parameters, using the length increment and age–length data jointly. Also, I describe a likelihood ratio test for determining whether the same growth curve fits both data sets adequately. The von Bertalanffy growth curve can be taken as a predictive regression with either length or age as the dependent variable. Here, age is taken as the dependent variable, as would be appropriate for estimation of age from length, but only minor modifications are necessary for the more common alternative predictive regression of length on age. As an illustration, the techniques are applied to data for southern bluefin tuna, Thunnus maccoyii.

scholarly journals PARAMETERIZATIONS OF THE VON BERTALANFFY MODEL FOR DESCRIPTION OF GROWTH CURVES

2020 ◽  
Vol 38 (3) ◽  
pp. 369
Author(s):  
Felipe Augusto FERNANDES ◽  
Édipo Menezes SILVA ◽  
Kelly Pereira LIMA ◽  
Sérgio Alberto JANE ◽  
Tales Jesus FERNANDES ◽  
...  
Keyword(s):  
Regression Models ◽  
Growth Curves ◽  
Von Bertalanffy ◽  
Growth Data ◽  
Nonlinear Regression Models ◽  
Von Bertalanffy Model ◽  
Estimated Parameters ◽  
Biological Interpretation ◽  
Curvature Measurements ◽  
Nonlinearity Measures

The growth curves of animals, in general, have an “S” shape, also known as sigmoidal curves. This type of   curve is well fitted by nonlinear regression models, including von Bertalanffy’s model, which has been widely  applied in several areas, being presented in literature through different parameterizations, which in practice, can complicate its understanding, affect nonlinearity measures and inferences about parameters. To quantify  the nonlinearity present in a Bates and Watts model, a geometric concept of curvature has been used. The aim of this work was to analytically develop three parameterizations of the von Bertalanffy’s nonlinear model  referring to its nonlinearity, implications for inferences and to establish relationships between parameters in the different ways of expressing the models. These parameterizations were adjusted to the growth data of sheep. For each parameterization, the intrinsic and parametric curvature measurements described by Bates and Watts were calculated. The parameterization choice affects nonlinearity measures, consequently, influences the reliability and inferences about estimated parameters. The forms most used in literature showed the greatest deviations from linearity, showing the importance of analyzing these measures in any growth curve study. Parameterization should be used in which the b estimate represents the abscissa of the inflection point, as it presents minor linearity deviations and direct biological interpretation for all parameters.

scholarly journals The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 474
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Hazem Al-Mofleh ◽  
Ahmed M. Gemeay ◽  
Ahmed Z. Afify ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Exponential Model ◽  
Statistical Properties ◽  
Engineering Science ◽  
Data Sets ◽  
Engineering Sciences ◽  
General Statistical ◽  
Anderson Darling

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

The New Statistics with R

2021 ◽  
Author(s):  
Andy Hector
Keyword(s):  
Linear Model ◽  
Evolutionary Biology ◽  
Environmental Science ◽  
Research Training ◽  
Model Analysis ◽  
Scientific Data ◽  
Information Criteria ◽  
Reproducible Research ◽  
Data Sets ◽  
R Programming

Statistics is a fundamental component of the scientific toolbox, but learning the basics of this area of mathematics is one of the most challenging parts of a research training. This book gives an up-to-date introduction to the classical techniques and modern extensions of linear-model analysis—one of the most useful approaches in the analysis of scientific data in the life and environmental sciences. The book emphasizes an estimation-based approach that takes account of recent criticisms of overuse of probability values and introduces the alternative approach using information criteria. The book is based on the use of the open-source R programming language for statistics and graphics, which is rapidly becoming the lingua franca in many areas of science. This second edition adds new chapters, including one discussing some of the complexities of linear-model analysis and another introducing reproducible research documents using the R Markdown package. Statistics is introduced through worked analyses performed in R using interesting data sets from ecology, evolutionary biology, and environmental science. The data sets and R scripts are available as supporting material.

Biotic and Abiotic Controls on the Phanerozoic History of Marine Animal Biodiversity

2021 ◽  
Vol 52 (1) ◽  
Author(s):  
Andrew M. Bush ◽  
Jonathan L. Payne
Keyword(s):  
Biotic Interactions ◽  
Annual Review ◽  
Publication Date ◽  
Data Sets ◽  
Marine Animal ◽  
Marine Animals ◽  
Marine Habitat ◽  
Positive Feedbacks ◽  
Abiotic Controls ◽  
Time Changes

During the past 541 million years, marine animals underwent three intervals of diversification (early Cambrian, Ordovician, Cretaceous–Cenozoic) separated by nondirectional fluctuation, suggesting diversity-dependent dynamics with the equilibrium diversity shifting through time. Changes in factors such as shallow-marine habitat area and climate appear to have modulated the nondirectional fluctuations. Directional increases in diversity are best explained by evolutionary innovations in marine animals and primary producers coupled with stepwise increases in the availability of food and oxygen. Increasing intensity of biotic interactions such as predation and disturbance may have led to positive feedbacks on diversification as ecosystems became more complex. Important areas for further research include improving the geographic coverage and temporal resolution of paleontological data sets, as well as deepening our understanding of Earth system evolution and the physiological and ecological traits that modulated organismal responses to environmental change. Expected final online publication date for the Annual Review of Ecology, Evolution, and Systematics, Volume 52 is November 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A Formulation of the von Bertalanffy Growth Curve when the Growth Rate is Roughly Constant

1969 ◽  
Vol 26 (11) ◽  
pp. 3069-3072 ◽  
Author(s):  
William Knight
Keyword(s):  
Growth Rate ◽  
Growth Curve ◽  
Von Bertalanffy ◽  
Alternate Form ◽  
Usual Form

The author contends that the parameters of any growth curve should be a direct description of the graphical appearance of the data. For growth that is even approximately linear this is not true of the von Bertalanffy curve in its usual form (von Bertalanffy, Human Biol. 10: 181–213, 1938). On the above grounds, an alternate form of the von Bertalanffy curve for use in such instances is proposed.

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

scholarly journals A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay K Singh ◽  
Umesh Singh
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Statistical Properties ◽  
New Right ◽  
Data Sets ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

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