Evaluate at a particular set of parameters the gradient and Hessian of the 6-parameter logistic function.
logistic6_gradient(x, theta)logistic6_hessian(x, theta)
logistic6_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 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).
Note: The 6-parameter logistic function is over-parameterized and non-identifiable from data. It is available only for theoretical research.