| loglogistic6_fn {drda} | R Documentation |
6-parameter log-logistic function
Description
Evaluate at a particular set of parameters the 6-parameter log-logistic function.
Usage
loglogistic6_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 log-logistic function f(x; theta) is defined here as
g(x; theta) = (x^eta / (xi * x^eta + nu * phi^eta))^(1 / nu)
f(x; theta) = alpha + delta g(x; theta)
where x >= 0, theta = c(alpha, delta, eta, phi, nu, xi), eta > 0,
phi > 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 = 0.
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 log-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
log-logistic function.