Evaluate at a particular set of parameters the gradient and Hessian of the 4-parameter log-logistic function.
loglogistic4_gradient_2(x, theta)loglogistic4_hessian_2(x, theta)
loglogistic4_gradient_hessian_2(x, theta)
Gradient or Hessian of the alternative parameterization evaluated at the specified point.
numeric vector at which the function is to be evaluated.
numeric vector with the four parameters in the form
c(alpha, delta, eta, phi).
The 4-parameter log-logistic function f(x; theta) is defined here as
g(x; theta) = x^eta / (x^eta + phi^eta)
f(x; theta) = alpha + delta g(x; theta)
where x >= 0, theta = c(alpha, delta, eta, phi, nu), eta > 0, and
phi > 0.
This set of functions use a different parameterization from
link[drda]{loglogistic4_gradient}. To avoid the non-negative
constraints of parameters, the gradient and Hessian computed here are for
the function with eta2 = log(eta) and phi2 = log(phi).
Note that argument theta is on the original scale and not on the log scale.