| gompertz_gradient_2 {drda} | R Documentation |
Gompertz function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the Gompertz function.
Usage
gompertz_gradient_2(x, theta)
gompertz_hessian_2(x, theta)
gompertz_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 Gompertz function f(x; theta) is defined here as
g(x; theta) = exp(-exp(-eta * (x - phi)))
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi) and eta > 0. When delta is
positive (negative) the curve is monotonically increasing (decreasing).
This set of functions use a different parameterization from
link[drda]{gompertz_gradient}. To avoid the non-negative
constraints of parameters, the gradient and Hessian computed here are for
the function with eta2 = log(eta).
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.