Evaluate at a particular set of parameters the gradient and Hessian of the 6-parameter log-logistic function.
loglogistic6_gradient(x, theta)loglogistic6_hessian(x, theta)
loglogistic6_gradient_hessian(x, theta)
Gradient or Hessian evaluated at the specified point.
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 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).
Note: The 6-parameter log-logistic function is over-parameterized and non-identifiable from data. It is available only for theoretical research.