Evaluate at a particular set of parameters the 6-parameter logistic function.
logistic6_fn(x, theta)Numeric vector of the same length of x with the values of the
logistic function.
numeric vector at which the function is to be evaluated.
numeric vector with the six parameters in the form
c(alpha, delta, eta, phi, nu, xi).
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.