loggompertz_gradient_2 {drda}R Documentation

Log-Gompertz function gradient and Hessian


Evaluate at a particular set of parameters the gradient and Hessian of the log-Gompertz function.


loggompertz_gradient_2(x, theta)

loggompertz_hessian_2(x, theta)

loggompertz_gradient_hessian_2(x, theta)



numeric vector at which the function is to be evaluated.


numeric vector with the four parameters in the form c(alpha, delta, eta, phi).


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.


Gradient or Hessian of the alternative parameterization evaluated at the specified point.

[Package drda version 2.0.3 Index]