Evaluate at a particular set of parameters the gradient and Hessian of the 2-parameter log-logistic function.
loglogistic2_gradient(x, theta, delta)loglogistic2_hessian(x, theta, delta)
loglogistic2_gradient_hessian(x, theta, delta)
Gradient or Hessian evaluated at the specified point.
numeric vector at which the function is to be evaluated.
numeric vector with the two parameters in the form
c(eta, phi).
value of delta parameter (either 1 or -1).
The 2-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), eta > 0, and
phi > 0. Only eta and phi are free to vary (therefore the name), while
c(alpha, delta) are constrained to be either c(0, 1) (monotonically
increasing curve) or c(1, -1) (monotonically decreasing curve).