Evaluate at a particular set of parameters the gradient and Hessian of the 5-parameter logistic function.
logistic5_gradient_2(x, theta)logistic5_hessian_2(x, theta)
logistic5_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 five parameters in the form
c(alpha, delta, eta, phi, nu).
The 5-parameter logistic function f(x; theta) is defined here as
g(x; theta) = 1 / (1 + nu * exp(-eta * (x - phi)))^(1 / nu)
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi, nu), eta > 0, and nu > 0. When
delta is positive (negative) the curve is monotonically increasing
(decreasing).
This set of functions use a different parameterization from
link[drda]{logistic5_gradient}. To avoid the non-negative
constraints of parameters, the gradient and Hessian computed here are for
the function with eta2 = log(eta) and nu2 = log(nu).
Note that argument theta is on the original scale and not on the log scale.