Function to find horizontal asymptotes of a rational function.
asymptote(
data = NULL,
x = NULL,
y = NULL,
d1 = 1,
d2 = 1,
threshold = 0.95,
proportional = TRUE
)An output object from boot_overlap or boot_area.
Numeric vectors of independent (x) and dependent (y) variables. These parameters will be ignored if data is supplied.
Maximal degrees of numerator (d1) and denominator (d2) of a rational function.
Threshold value for considering an asymptote. Once the y value reaches the threshold, it is considered that an asymptote is reached.
If TRUE (default), a threshold is calculated as estimated asymptote * threshold. If FALSE, the value specified in threshold is used in the analysis.
A list containing a data frame (rational function fit associated with x values), an estimated horizontal asymptote, and the minimum sample size if an asymptote is reached.
This function fits a rational function to the input data.
When an output object from boot_overlap or boot_area is supplied,
a rational function is fit to the means of the bootstrap results (e.g. mean overlap probability) as a function of x (e.g. sample size).
It then estimates horizontal asymptotes and identifies the sample size when an asymptote is considered.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007). Numerical Recipes: The Art of Numerical Computing. Third Edition, Cambridge University Press, New York.
Shimada et al., (in prep)