| logistic5_fn {drda} | R Documentation |
5-parameter logistic function
Description
Evaluate at a particular set of parameters the 5-parameter logistic function.
Usage
logistic5_fn(x, theta)
Arguments
x |
numeric vector at which the logistic function is to be evaluated. |
theta |
numeric vector with the five parameters in the form
|
Details
The 5-parameter logistic function f(x; theta) is defined here as
g(x; theta) = 1 / (1 + nu * exp(-eta * (x - phi)))^(1 / nu)
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi, nu), eta > 0, and nu > 0.
When delta is positive (negative) the curve is monotonically increasing
(decreasing). When x -> -Inf the value of the function is alpha while the
value of the function for x -> Inf is alpha + delta .
Parameter alpha is the value of the function when x -> -Inf.
Parameter delta is the (signed) height of the curve.
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.
Value
Numeric vector of the same length of x with the values of the
logistic function.