loglogistic6_gradient_2 {drda}  R Documentation 
6parameter loglogistic function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the 6parameter loglogistic function.
Usage
loglogistic6_gradient_2(x, theta)
loglogistic6_hessian_2(x, theta)
loglogistic6_gradient_hessian_2(x, theta)
Arguments
x 
numeric vector at which the function is to be evaluated. 
theta 
numeric vector with the six parameters in the form

Details
The 6parameter loglogistic function f(x; theta)
is defined here as
g(x; theta) = (x^eta / (xi * 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, xi)
, eta > 0
,
phi > 0
, nu > 0
, and xi > 0
.
This set of functions use a different parameterization from
link[drda]{loglogistic6_gradient}
. To avoid the nonnegative
constraints of parameters, the gradient and Hessian computed here are for
the function with eta2 = log(eta)
, phi2 = log(phi)
, nu2 = log(nu)
, and
xi2 = log(xi)
.
Note that argument theta
is on the original scale and not on the log scale.
Note: The 6parameter loglogistic function is overparameterized and nonidentifiable from data. It is available only for theoretical research.
Value
Gradient or Hessian of the alternative parameterization evaluated at the specified point.