| loglogistic5_gradient_2 {drda} | R Documentation |
5-parameter log-logistic function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the 5-parameter log-logistic function.
Usage
loglogistic5_gradient_2(x, theta)
loglogistic5_hessian_2(x, theta)
loglogistic5_gradient_hessian_2(x, theta)
Arguments
x |
numeric vector at which the function is to be evaluated. |
theta |
numeric vector with the five parameters in the form
|
Details
The 5-parameter log-logistic function f(x; theta) is defined here as
g(x; theta) = (x^eta / (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), eta > 0,
phi > 0, and nu > 0.
This set of functions use a different parameterization from
link[drda]{loglogistic5_gradient}. To avoid the non-negative
constraints of parameters, the gradient and Hessian computed here are for
the function with eta2 = log(eta), phi2 = log(phi), and nu2 = log(nu).
Note that argument theta is on the original scale and not on the log scale.
Value
Gradient or Hessian of the alternative parameterization evaluated at the specified point.