loglogistic2_gradient_2 {drda}  R Documentation 
2parameter loglogistic function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the 2parameter loglogistic function.
Usage
loglogistic2_gradient_2(x, theta, delta)
loglogistic2_hessian_2(x, theta, delta)
loglogistic2_gradient_hessian_2(x, theta, delta)
Arguments
x 
numeric vector at which the function is to be evaluated. 
theta 
numeric vector with the two parameters in the form

delta 
value of delta parameter (either 1 or 1). 
Details
The 2parameter loglogistic 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)
, eta > 0
, and
phi > 0
. Only eta
and phi
are free to vary (therefore the name), while
c(alpha, delta)
are constrained to be either c(0, 1)
(monotonically
increasing curve) or c(1, 1)
(monotonically decreasing curve).
This set of functions use a different parameterization from
link[drda]{loglogistic2_gradient}
. To avoid the nonnegative
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.