| logistic6_gradient {drda} | R Documentation |
6-parameter logistic function gradient and Hessian
Description
Evaluate at a particular set of parameters the gradient and Hessian of the 6-parameter logistic function.
Usage
logistic6_gradient(x, theta)
logistic6_hessian(x, theta)
logistic6_gradient_hessian(x, theta)
Arguments
x |
numeric vector at which the function is to be evaluated. |
theta |
numeric vector with the six parameters in the form
|
Details
The 6-parameter logistic function f(x; theta) is defined here as
g(x; theta) = 1 / (xi + nu * exp(-eta * (x - phi)))^(1 / nu)
f(x; theta) = alpha + delta g(x; theta)
where theta = c(alpha, delta, eta, phi, nu, xi), eta > 0, nu > 0, and
xi > 0. When delta is positive (negative) the curve is monotonically
increasing (decreasing).
Note: The 6-parameter logistic function is over-parameterized and non-identifiable from data. It is available only for theoretical research.
Value
Gradient or Hessian evaluated at the specified point.