loglogistic5_gradient_2 {drda}R Documentation

5-parameter log-logistic function gradient and Hessian


Evaluate at a particular set of parameters the gradient and Hessian of the 5-parameter log-logistic function.


loglogistic5_gradient_2(x, theta)

loglogistic5_hessian_2(x, theta)

loglogistic5_gradient_hessian_2(x, theta)



numeric vector at which the function is to be evaluated.


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


The 5-parameter log-logistic function ⁠f(x; theta)⁠ is defined here as

⁠g(x; theta) = (x^eta / (x^eta + nu * phi^eta))^(1 / nu)⁠ ⁠f(x; theta) = alpha + delta g(x; theta)⁠

where x >= 0, theta = c(alpha, delta, eta, phi, nu), eta > 0, phi > 0, and nu > 0.

This set of functions use a different parameterization from link[drda]{loglogistic5_gradient}. To avoid the non-negative constraints of parameters, the gradient and Hessian computed here are for the function with eta2 = log(eta), phi2 = log(phi), and nu2 = log(nu).

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]