loglogistic2_gradient_2 {drda}R Documentation

2-parameter log-logistic function gradient and Hessian


Evaluate at a particular set of parameters the gradient and Hessian of the 2-parameter log-logistic function.


loglogistic2_gradient_2(x, theta, delta)

loglogistic2_hessian_2(x, theta, delta)

loglogistic2_gradient_hessian_2(x, theta, delta)



numeric vector at which the function is to be evaluated.


numeric vector with the two parameters in the form c(eta, phi).


value of delta parameter (either 1 or -1).


The 2-parameter log-logistic function ⁠f(x; theta)⁠ is defined here as

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

where x >= 0, theta = c(alpha, delta, eta, phi), eta > 0, and phi > 0. Only eta and phi are free to vary (therefore the name), while c(alpha, delta) are constrained to be either c(0, 1) (monotonically increasing curve) or c(1, -1) (monotonically decreasing curve).

This set of functions use a different parameterization from link[drda]{loglogistic2_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]