| logistic6_fn {drda} | R Documentation |
6-parameter logistic function
Description
Evaluate at a particular set of parameters the 6-parameter logistic function.
Usage
logistic6_fn(x, theta)
Arguments
x |
numeric vector at which the function is to be evaluated. |
theta |
numeric vector with the six parameters in the form
|
Details
The 6-parameter logistic function f(x; theta) is defined here as
g(x; theta) = 1 / (xi + nu * exp(-eta * (x - phi)))^(1 / nu)
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi, nu, xi), eta > 0, nu > 0, and
xi > 0. When delta is positive (negative) the curve is monotonically
increasing (decreasing).
Parameter alpha is the value of the function when x -> -Inf.
Parameter delta affects the value of the function when x -> Inf.
Parameter eta represents the steepness (growth rate) of the curve.
Parameter phi is related to the mid-value of the function.
Parameter nu affects near which asymptote maximum growth occurs.
Parameter xi affects the value of the function when x -> Inf.
Note: The 6-parameter logistic function is over-parameterized and non-identifiable from data. It is available only for theoretical research.
Value
Numeric vector of the same length of x with the values of the
logistic function.