loggompertz_gradient_2 {drda} | R Documentation |
Log-Gompertz function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the log-Gompertz function.
Usage
loggompertz_gradient_2(x, theta)
loggompertz_hessian_2(x, theta)
loggompertz_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 log-Gompertz function f(x; theta)
is defined here as
f(x; theta) = alpha + delta exp(-(phi / x)^eta)
where x >= 0
, theta = c(alpha, delta, eta, phi)
, eta > 0
, and
phi > 0
. By convention we set
f(0; theta) = lim_{x -> 0} f(x; theta) = alpha
.
This set of functions use a different parameterization from
link[drda]{loggompertz_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.