loglogistic6_gradient {drda}  R Documentation 
Evaluate at a particular set of parameters the gradient and Hessian of the 6parameter loglogistic function.
loglogistic6_gradient(x, theta)
loglogistic6_hessian(x, theta)
loglogistic6_gradient_hessian(x, theta)
x 
numeric vector at which the function is to be evaluated. 
theta 
numeric vector with the six parameters in the form

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
. When delta
is positive (negative) the
curve is monotonically increasing (decreasing).
Note: The 6parameter loglogistic function is overparameterized and nonidentifiable from data. It is available only for theoretical research.
Gradient or Hessian evaluated at the specified point.