Growth-curve Explorer
CAN'T RUN THE APPLET, NO JAVA SUPPORT.
Click or drag on the parameters area.
This is a translation into JavaScript by CheerpJ of the Java applet described in
García, O. (2008) "Visualization of a general family of growth functions and probability distributions — The Growth-curve Explorer". Environmental Modelling & Software 23(12), 1474-1475 (DOI).
Java applets are not longer natively supported in modern browsers, but another alternative is to run the original applet with the CheerpJ Chrome browser plugin. There is also an R Shiny implementation here.
Model
A family of growth curves with two shape parameters (a and b),
that includes most of the known univariate growth models as special cases.
It also describes probability distributions with an explicit form for
the cumulative, useful in computer simulation, including the Burr Type
III and Type XII, among others.
The growth curve equation is y = B-1[B-1(t,
b), a], where B is the negative Box-Cox
transformation B(x, c) = (1 - xc)
/ c if c ≠ 0, B(x,
0) = -ln x. Or B-1(x, c)
= (1 - c x)1/c if c ≠ 0,
B-1(x, 0) = e-x.
In general, t and y are subject to affine
transformations, with additional location and scale parameters.
Negative scale parameters reverse the t- and y-axis,
and are specified here by ticking the Reverse checkbox (both axes,
reversing only one would give decreasing curves). For details see García, - xc)
37
/ c if c ≠ 0, B(x,
38
0) = -ln x. Or B-1(x, c)
39
= (1 - c x)1/c if c ≠ 0,
40
B-1(x, 0) = e-x.
41
In general, t and y are subject to affine
42
transformations, with additional location and scale parameters. - xc)
37
/ c if c ≠ 0, B(x,
38
0) = -ln x. Or B-1(x, c)
39
= (1 - c x)1/c if c ≠ 0,
40
B-1(x, 0) = e-x.
41
In general, t and y are subject to affine
42
transformations, with additional location and scale parameters.
43
Negative scale parameters reverse the t- and y-axis,
44
and are specified here by ticking the Reverse checkbox (both axes,
45
reversing only one would give decreasing curves). For details see García,
43
Negative scale parameters reverse the t- and y-axis,
44
and are specified here by ticking the Reverse checkbox (both axes,
45
reversing only one would give decreasing curves). For details see García,
O. (2005) "Unifying sigmoid univariate growth equations", Forest Biometry,
Modelling and Information Sciences 1, 63-68 (generalized logistic.In the forestry literature
the function is often referred to as "Chapman-Richards", although Chapman's
1961 application of it to fish growth follows a well-known 1957
fisheries monograph by Beverton and Holt. In fisheries, the von Bertalanffy model often refers to the monomolecular a = 1, b = 0 (for growth in length, instead of weight). This is also called Mitscherlich, although that author used a more general model where 1/a is an integer.
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