loggompertz_gradient {drda}

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(x, theta)

loggompertz_hessian(x, theta)

loggompertz_gradient_hessian(x, theta)

Arguments

x

numeric vector at which the function is to be evaluated.

theta

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

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.

Value

Gradient or Hessian evaluated at the specified point.