| loglogistic4_gradient_2 {drda} | R Documentation |
4-parameter log-logistic function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the 4-parameter log-logistic function.
Usage
loglogistic4_gradient_2(x, theta)
loglogistic4_hessian_2(x, theta)
loglogistic4_gradient_hessian_2(x, theta)
Arguments
x |
numeric vector at which the function is to be evaluated. |
theta |
numeric vector with the four parameters in the form
|
Details
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.
Value
Gradient or Hessian of the alternative parameterization evaluated at the specified point.